Semiclassical approximation to time-dependent Hartree--Fock theory
International Nuclear Information System (INIS)
Dworzecka, M.; Poggioli, R.
1976-01-01
Working within a time-dependent Hartree-Fock framework, one develops a semiclassical approximation appropriate for large systems. It is demonstrated that the standard semiclassical approach, the Thomas-Fermi approximation, is inconsistent with Hartree-Fock theory when the basic two-body interaction is short-ranged (as in nuclear systems, for example). However, by introducing a simple extension of the Thomas-Fermi approximation, one overcomes this problem. One also discusses the infinite nuclear matter problem and point out that time-dependent Hartree-Fock theory yields collective modes of the zero sound variety instead of ordinary hydrodynamic (first) sound. One thus emphasizes that one should be extremely circumspect when attempting to cast the equations of motion of time-dependent Hartree-Fock theory into a hydrodynamic-like form
Time-dependent--S-matrix Hartree-Fock theory of complex reactions
International Nuclear Information System (INIS)
Griffin, J.J.; Lichtner, P.C.; Dworzecka, M.
1980-01-01
Some limitations of the conventional time-dependent Hartree-Fock method for describing complex reactions are noted, and one particular ubiquitous defect is discussed in detail: the post-breakup spurious cross channel correlations which arise whenever several asymptotic reaction channels must be simultaneously described by a single determinant. A reformulated time-dependent--S-matrix Hartree-Fock theory is proposed, which obviates this difficulty. Axiomatic requirements minimal to assure that the time-dependent--S-matrix Hartree-Fock theory represents an unambiguous and physically interpretable asymptotic reaction theory are utilized to prescribe conditions upon the definition of acceptable asymptotic channels. That definition, in turn, defines the physical range of the time-dependent--S-matrix Hartree-Fock theory to encompass the collisions of mathematically well-defined ''time-dependent Hartree-Fock droplets.'' The physical properties of these objects then circumscribe the content of the Hartree-Fock single determinantal description. If their periodic vibrations occur for continuous ranges of energy then the resulting ''classical'' time-dependent Hartree-Fock droplets are seen to be intrinsically dissipative, and the single determinantal description of their collisions reduces to a ''trajectory'' theory which can describe the masses and relative motions of the fragments but can provide no information about specific asymptotic excited states beyond their constants of motion, or the average properties of the limit, if it exists, of their equilibrization process. If, on the other hand, the periodic vibrations of the time-dependent Hartree-Fock droplets are discrete in energy, then the time-dependent--S-matrix Hartree-Fock theory can describe asymptotically the time-average properties of the whole spectrum of such periodic vibrations
An adiabatic time-dependent Hartree-Fock theory of collective motion in finite systems
International Nuclear Information System (INIS)
Baranger, M.; Veneroni, M.
1977-11-01
It is shown how to derive the parameters of a phenomenological collective model from a microscopic theory. The microscopic theory is Hartree-Fock, and one starts from the time-dependent Hartree-Fock equation. To this, the adiabatic approximation is added, and the energy in powers of an adiabatic parameter is expanded, which results in a collective kinetic energy quadratic in the velocities, with coefficients depending on the coordinates, as in the phenomenological models. The adiabatic equations of motion are derived in different ways and their analogy with classical mechanics is stressed. The role of the adiabatic hypothesis and its range of validity, are analyzed in detail. It assumes slow motion, but not small amplitude, and is therefore suitable for large-amplitude collective motion. The RPA is obtained as the limiting case where the amplitude is also small. The translational mass is correctly given and the moment of inertia under rotation is that of Thouless and Valatin
The time dependent Hartree-Fock-theory for collective nuclear motions
International Nuclear Information System (INIS)
Goeke, K.
1976-11-01
The time-dependent Hartree-Fock theory (TDHF) approximately solves the Schroedinger equation by a variational method in the space of the time-dependent Slater determinants. As the TDHF wave function, similar to the exact solution has the property of being determined completely for all times by the nucleon-nucleon interaction and by assuming initial conditions. TDHF is expected to describe collective motion of nuclei with large amplitudes, too. The subject of this paper is to formulate the TDHF theory and its adiabatic limiting case (ATDHF) suited for setting up a collective Schroedinger equation, to investigate the relations with other theories, and to show the applicability for solving practical problems. (orig./WL) [de
Multiconfiguration hartree-fock theory for pseudorelativistic systems: The time-dependent case
Hajaiej, Hichem
2014-03-01
In [Setting and analysis of the multi-configuration time-dependent Hartree-Fock equations, Arch. Ration. Mech. Anal. 198 (2010) 273-330] the third author has studied in collaboration with Bardos, Catto and Mauser the nonrelativistic multiconfiguration time-dependent Hartree-Fock system of equations arising in the modeling of molecular dynamics. In this paper, we extend the previous work to the case of pseudorelativistic atoms. We show the existence and the uniqueness of global-in-time solution to the underlying system under technical assumptions on the energy of the initial data and the charge of the nucleus. Moreover, we prove that the result can be extended to the case of neutron stars when the number of electrons is less than a critical number N cr. © 2014 World Scientific Publishing Company.
Beyond time-dependent Hartree-Fock: The collision terms in a mean-field theory
International Nuclear Information System (INIS)
Pauli, H.C.
1983-01-01
Generalised, time-dependent Hartree-Fock equations are shown to solve a well-defined part of the Hamiltonian problem. The complementary residual interaction is treated approximately, rather than by ensemble averages, and gives rise to the appearance of collision terms. The final set of equations is self-consistent. For colliding heavy ions the collision terms lead to a diffusion of the collective variables, which possibly can improve the agreement between mean-field calculations and experiment. (author)
van Meer, R; Gritsenko, O V; Baerends, E J
2017-01-28
Straightforward interpretation of excitations is possible if they can be described as simple single orbital-to-orbital (or double, etc.) transitions. In linear response time-dependent density functional theory (LR-TDDFT), the (ground state) Kohn-Sham orbitals prove to be such an orbital basis. In contrast, in a basis of natural orbitals (NOs) or Hartree-Fock orbitals, excitations often employ many orbitals and are accordingly hard to characterize. We demonstrate that it is possible in these cases to transform to natural excitation orbitals (NEOs) which resemble very closely the KS orbitals and afford the same simple description of excitations. The desired transformation has been obtained by diagonalization of a submatrix in the equations of linear response time-dependent 1-particle reduced density matrix functional theory (LR-TDDMFT) for the NO transformation, and that of a submatrix in the linear response time-dependent Hartree-Fock (LR-TDHF) equations for the transformation of HF orbitals. The corresponding submatrix is already diagonal in the KS basis in the LR-TDDFT equations. While the orbital shapes of the NEOs afford the characterization of the excitations as (mostly) simple orbital-to-orbital transitions, the orbital energies provide a fair estimate of excitation energies.
International Nuclear Information System (INIS)
Simenel, Cedric
2010-01-01
A particle-number projection technique is used to calculate transfer probabilities in the 16 O+ 208 Pb reaction below the fusion barrier. The time evolution of the many-body wave function is obtained with the time-dependent Hartree-Fock (TDHF) mean-field theory. The agreement with experimental data for the sum of the proton-transfer channels is good, considering that TDHF has no parameter adjusted on the reaction mechanism. Some perspectives for extensions beyond TDHF to include cluster transfers are discussed.
Time-dependent projected Hartree-Fock.
Tsuchimochi, Takashi; Van Voorhis, Troy
2015-03-28
Projected Hartree-Fock (PHF) has recently emerged as an alternative approach to describing degenerate systems where static correlation is abundant, when the spin-symmetry is projected. Here, we derive a set of linearized time-dependent equations for PHF in order to be able to access excited states. The close connection of such linear-response time-dependent PHF (TDPHF) to the stability condition of a PHF wave function is discussed. Expanding this analysis also makes it possible to give analytical expressions for the projected coupling terms of Hamiltonian and overlaps between excited Slater determinants. TDPHF with spin-projection (TDSUHF) and its Tamm-Dancoff approximation are benchmarked for several electronically degenerate molecules including the dissociating H2, F2 and O3 at equilibrium, and the distorted ethylene. It is shown that they give consistently better descriptions of excited states than does time-dependent HF (TDHF). Furthermore, we demonstrate that they offer not only singly but also doubly excited states, which naturally arise upon spin-projection. We also address the thermodynamic limit of TDSUHF, using non-interacting He gas. While TDPHF singly excited states tend to converge to those of HF with the size of the system due to the lack of size-extensivity of PHF, doubly excited states remain reasonable even at the thermodynamic limit. We find that the overall performance of our method is systematically better than the regular TDHF in many cases at the same computational scaling.
Time Dependent Hartree Fock Equation: Gateway to Nonequilibrium Plasmas
International Nuclear Information System (INIS)
Dufty, James W.
2007-01-01
This is the Final Technical Report for DE-FG02-2ER54677 award 'Time Dependent Hartree Fock Equation - Gateway to Nonequilibrium Plasmas'. Research has focused on the nonequilibrium dynamics of electrons in the presence of ions, both via basic quantum theory and via semi-classical molecular dynamics (MD) simulation. In addition, fundamental notions of dissipative dynamics have been explored for models of grains and dust, and for scalar fields (temperature) in turbulent edge plasmas. The specific topics addressed were Quantum Kinetic Theory for Metallic Clusters, Semi-classical MD Simulation of Plasmas , and Effects of Dissipative Dynamics.
Peng, Daoling; Li, Shaopeng; Peng, Liang; Gu, Feng Long; Yang, Weitao
2017-09-12
The time-dependent coupled perturbed Hartree-Fock/density-functional-theory (TDHF/TDDFT) approach has been reformulated based on nonorthogonal localized molecular orbitals (NOLMOs). Based on the NOLMO Fock equation, we have derived the corresponding NOLMO-TDHF/TDDFT equations up to the third order, and the formula for the frequency-dependent (hyper)polarizabilities has been given. Our approach has been applied to calculate both static and dynamic (hyper)polarizabilities of molecules varying from small molecules to large molecules. The NOLMO-TDHF/TDDFT approach can reproduce the reference canonical molecular orbital (CMO) results for all of our testing calculations. With the help of ongoing development of optimized local virtual molecular orbitals, the NOLMO-TDHF/TDDFT approach would be a very efficient method for large system calculations and tp achieve linear scaling.
Time dependent Hartree-Fock treatment of elastic scattering of electrons by H and He/+/.
Jamieson, M. J.
1972-01-01
Time dependent Hartree-Fock theory, in its coupled and uncoupled forms, is used to calculate the elastic singlet p-wave phase shifts for the scattering of electrons by H and He/+/. On comparison with the best available results it is concluded that the coupled scheme, which contains correlation to at least first order, is superior. Levinson's theorem is confirmed.
An introduction to the adiabatic time-dependent Hartree-Fock method
International Nuclear Information System (INIS)
Giannoni, M.J.
1984-05-01
The aim of the adiabatic time-dependent Hartree-Fock method is to investigate the microscopic foundations of the phenomenological collective models. We briefly review the general formulation, which consists in deriving a Bohr-like Hamiltonian from a mean field theory, and discuss the limiting case where only a few collective variables participate to the motion. Some applications to soft nuclei and heavy ion collisions are presented
Yanai, Takeshi; Fann, George I; Beylkin, Gregory; Harrison, Robert J
2015-12-21
A fully numerical method for the time-dependent Hartree-Fock and density functional theory (TD-HF/DFT) with the Tamm-Dancoff (TD) approximation is presented in a multiresolution analysis (MRA) approach. From a reformulation with effective use of the density matrix operator, we obtain a general form of the HF/DFT linear response equation in the first quantization formalism. It can be readily rewritten as an integral equation with the bound-state Helmholtz (BSH) kernel for the Green's function. The MRA implementation of the resultant equation permits excited state calculations without virtual orbitals. The integral equation is efficiently and adaptively solved using a numerical multiresolution solver with multiwavelet bases. Our implementation of the TD-HF/DFT methods is applied for calculating the excitation energies of H2, Be, N2, H2O, and C2H4 molecules. The numerical errors of the calculated excitation energies converge in proportion to the residuals of the equation in the molecular orbitals and response functions. The energies of the excited states at a variety of length scales ranging from short-range valence excitations to long-range Rydberg-type ones are consistently accurate. It is shown that the multiresolution calculations yield the correct exponential asymptotic tails for the response functions, whereas those computed with Gaussian basis functions are too diffuse or decay too rapidly. We introduce a simple asymptotic correction to the local spin-density approximation (LSDA) so that in the TDDFT calculations, the excited states are correctly bound.
Existence of minimizers in restricted Hartree-Fock theory
Directory of Open Access Journals (Sweden)
Fabian Hantsch
2014-02-01
Full Text Available In this note we establish the existence of ground states for atoms within several restricted Hartree-Fock theories. It is shown, for example, that there exists a ground state for closed shell atoms with N electrons and nuclear charge $Z \\geq N-1$. This has to be compared with the general Hartree-Fock theory where the existence of a minimizer is known for $Z >N-1$ only.
International Nuclear Information System (INIS)
Griffin, J.J.; Lichtner, P.C.; Dworzecka, M.; Kan, K.K.
1979-01-01
It is suggested that the TDHF method be viewed, not as an approximation to but as a model of the exact Schroedinger system; that is, as a gedanken many-body experiment whose analysis with digital computers provides data worthy in itself of theoretical study. From such a viewpoint attention is focused on the structural analogies of the TDHF system with the exact theory rather than upon its quantitative equivalence, and the TDHF many-body system is studied as a challenge of its own which, although much simpler than the realistic problem, may still offer complexity enough to educate theorists in the present state of knowledge. In this spirit, the TDHF description of continuum reactions can be restructured from an initial-value problem into a form analogous to the S-matrix version of the Schroedinger theory. The resulting TD-S-HF theory involves only self-consistent single determinantal solutions of the TDHF equations and invokes time averaging to obtain a consistent interpretation of the TDHF analogs of quantities which are constant in the exact theory, such as the S-matrix and the asymptotic reaction channel characteristics. Periodic solutions then play the role of stationary eigenstates in the construction of suitable asymptotic reaction channels. If these periodic channel states occur only at discrete energies, then the resulting channels are mutually orthogonal (on the time average) and the theory exhibits a structure fully analogous to the exact theory. In certain special cases where the periodic solutions are known to occur as an energy continuum, the requirement that the periodicity of the channel solutions be gauge invariant provides a natural requantization condition which (suggestively) turns out to be identical with the Bohr-Sommerfeld quantization rule. 11 references
Holomorphic Hartree-Fock Theory and Configuration Interaction.
Hiscock, Hamish G; Thom, Alex J W
2014-11-11
We investigate the Hartree-Fock solutions to H2 in a minimal basis. We note the properties of the solutions and their disappearance with geometry and propose a new method, called Holomorphic Hartree-Fock theory, where we modify the self-consistent field (SCF) equations to avoid disappearance of the solutions. We use these solutions as a basis for a nonorthogonal configuration interaction to produce a smooth binding curve over a complete range of geometries.
Time-dependent Hartree-Fock studies of the dynamical fusion threshold
Directory of Open Access Journals (Sweden)
Nakatsukasa Takashi
2012-12-01
Full Text Available A microscopic description of dynamical fusion threshold in heavy ion collisions is performed in the framework of time-dependent Hartree-Fock (TDHF theory using Skyrme energy density functional (EDF. TDHF fusion threshold is in a better agreement with experimental fusion barrier. We find that the onset of extra push lies at the effective fissility 33, which is consistent with the prediction of Swiateckis macroscopic model. The extra push energy in our TDHF simulation is systematically smaller than the prediction in macroscopic model. The important dynamical effects and the way to fit the parameter might be responsible for the different results.
Optimal control of interacting particles: a multi-configuration time-dependent Hartree-Fock approach
International Nuclear Information System (INIS)
Mundt, Michael; Tannor, David J
2009-01-01
We combine optimal control theory with the multi-configuration time-dependent Hartree-Fock method to control the dynamics of interacting particles. We use the resulting scheme to optimize state-to-state transitions in a one-dimensional (1D) model of helium and to entangle the external degrees-of-freedom of two rubidium atoms in a 1D optical lattice. Comparisons with optimization results based on the exact solution of the Schroedinger equation show that the scheme can be used to optimize even involved processes in systems consisting of interacting particles in a reliable and efficient way.
Alguire, Ethan C; Ou, Qi; Subotnik, Joseph E
2015-06-18
A pseudo-wavefunction description of time-dependent Hartree-Fock (TDHF) states is proposed and used to develop an analytic expression for derivative couplings between TDHF excited states based on the Hellmann-Feynman theorem. The resulting expression includes Pulay terms associated with using an atom-centered basis as well as a correction to ensure translational invariance. We demonstrate that our formalism recovers the well-known Chernyak-Mukamel expression near a crossing and in the limit of a complete basis, and thus our approach is consistent with time-dependent response theory. In a companion paper (DOI 10.1021/jp5057682 ), we investigate these derivative couplings near conical intersections and show that they behave correctly.
Hartree-Fock Theory in Nuclear Physics.
1986-02-01
AD-R167 4" HWTREE-FOCK THEORY IN NUCLEAR PHYSICS(U) NISCONSIN III UNIV-NAOISON MATHENATICS RESEARCH CENTER D GOYNY ET AL. FEB 86 NRC-TSR-2914 DRR29...methods to compute the ground state of nucleii is quite recent (see for example the review papers by H. Bethe [7], J. W. Negele [411, [42], P. Quentin... computational advantage being obvious). If one is interested in the ground state of a nucleus, the resulting problem by HF method is roughly speaking a
Functionals Hartree-Fock equations in the Schrodinger representation of quantum field theory
International Nuclear Information System (INIS)
Gamboa, J.
1989-08-01
Hartree-Fock equations for a scalar field theory in the Schrodinger representation are derived. It is shown that renormalization of the total energy in the functional Schrodinger equation is enterely contained in the eigenvalues of the Hartree-Fock hamiltonian. (A.C.A.S.) [pt
Rabilloud, Franck
2014-10-14
Absorption spectra of Ag20 and Ag55(q) (q = +1, -3) nanoclusters are investigated in the framework of the time-dependent density functional theory in order to analyse the role of the d electrons in plasmon-like band of silver clusters. The description of the plasmon-like band from calculations using density functionals containing an amount of Hartree-Fock exchange at long range, namely, hybrid and range-separated hybrid (RSH) density functionals, is in good agreement with the classical interpretation of the plasmon-like structure as a collective excitation of valence s-electrons. In contrast, using local or semi-local exchange functionals (generalized gradient approximations (GGAs) or meta-GGAs) leads to a strong overestimation of the role of d electrons in the plasmon-like band. The semi-local asymptotically corrected model potentials also describe the plasmon as mainly associated to d electrons, though calculated spectra are in fairly good agreement with those calculated using the RSH scheme. Our analysis shows that a portion of non-local exchange modifies the description of the plasmon-like band.
Abuzaid, N. (Nuha)
2016-01-01
Abstract Hartree-Fock theory, a computational method to solve electronic structure of molecules, is reviewed in this thesis. The emphasis is on spotlighting the physical reasoning behind the assumptions of the Hartree-Fock theory. Also, three post-Hartree-Fock electron correlation methods are introduced, configuration interaction, coupled cluster, and Møller-Plesset theory.
Derivation of an adiabatic time-dependent Hartree-Fock formalism from a variational principle
International Nuclear Information System (INIS)
Brink, D.M.; Giannoni, M.J.; Veneroni, M.
1975-10-01
A derivation of the adiabatic time-dependent Hartree-Fock formalism is given, which is based on a variational principle analogous to Hamilton's principle in classical mechanics. The method leads to a Hamiltonian for collective motion which separates into a potential and a kinetic energy and gives mass and potential parameters in terms of the nucleon-nucleon interaction. The adiabatic approximation assumes slow motion but not small amplitudes and can therefore describe anharmonic effects. The RPA is a limiting case where both amplitudes and velocities are small. The variational approach provides a consistent way of extracting coordinated and momenta from the density matrix and of obtaining equations of motion when particular trial forms for this density matrix are chosen. One such choice leads to Thouless-Valatin formula. An other choice leads to irrotational hydrodynamics [fr
On particle emission in the time-dependent Hartree-Fock approximation
International Nuclear Information System (INIS)
Maedler, P.
1984-01-01
Investigations of fast particle emission in the time-dependent Hartree-Fock mean-field approximation (TDHF) have been performed for one-dimensional slab collisions. For a fixed target mass number and incident velocity the total yields of PEP exhibit pronounced srtructures as a function of the pro ectile mass number, which strongly correcate with the binding energy of the last nucleon in the projectnle. This is in explicit disagreement with experiment. The conclusion has been drawn that the Fermi-jet mechanism cannot be responsible for most of the fast particles observed in experiment, even if quantum diffraction is taken into account (as in TDHF). After PEP emission large amplitude density oscillations, which are the only possible modes in the slab geometry, are found to be damped by further particle emission
Energy Technology Data Exchange (ETDEWEB)
Ripka, G. [Commissariat a l' Energie Atomique, 91 - Saclay (France). Centre d' Etudes Nucleaires
1968-09-01
Most of the content of this thesis is published in english in Advances In Nuclear Physics, Vol. 1 (Editors: Baranger and Vogt - Plenum Press). The Hartree- Fock equations are derived. The expansions of the orbits and the possible symmetries of the Hartree-Fock field are discussed. Wavefunctions of even-even N = Z nuclei are given for 12 {<=} A {<=} 40. The role of the monopole, quadrupole and exchange components of the force are discussed. The multiplicity of the solutions and the effect of the spin-orbit interaction are discussed. Exact angular momentum projection is used to generate rotational bands. The validity of the adiabatic rotational model in light nuclei is discussed. Hartree-Fock calculations are extended to include major-shell mixing in order to obtain quadrupole deformations without the use of effective charge. The incompressibility, of nuclei is discussed and the compatibility between the Hartree-Fock solutions, the Mottelson model of quadrupole deformations and the SU3 states of J.P. Elliott and M. Moshinsky is established. (author) [French] La theorie de Hartree-Fock est appliquee au calcul des fonctions d'onde des noyaux legers deformes. Les equations de Hartree-Fock, les symetries permises et le choix du developpement des orbites sont discutes. Les fonctions d'onde des noyaux pair-pairs N = Z (12 {<=} A {<=} 40) sont tabulees. Les contributions des composantes monopolaires et quadrupolaires ainsi que des termes d'echange de la force nucleon-nucleon sont discutees. La methode de projection de moment cinetique est utilisee pour engendrer les bandes de rotation. La validite du modele rotationnel adiabatique est discutee. Les calculs de Hartree-Fock qui tiennent compte du melange de plusieurs couches majeures dans chaque orbite sont appliques au calcul des deformations quadrupolaires sans l'utilisation de charge effective. L'incompressibilite des noyaux et la compatibilite des fonctions d'onde de Hartree- Fock avec les
Amour, Laurent; Khodja, Mohamed; Nourrigat, Jean
2011-01-01
We study the Wick symbol of a solution of the time dependent Hartree Fock equation, under weaker hypotheses than those needed for the Weyl symbol in the first paper with thesame title. With similar, we prove some kind of Ehrenfest theorem for observables that are not pseudo-differential operators.
Lötstedt, Erik; Kato, Tsuyoshi; Yamanouchi, Kaoru
2016-04-21
An approximate implementation of the multiconfiguration time-dependent Hartree-Fock method is proposed, in which the matrix of configuration-interaction coefficients is decomposed into a product of matrices of smaller dimension. The applicability of this method in which all the configurations are kept in the expansion of the wave function, while the configuration-interaction coefficients are approximately calculated, is discussed by showing the results on three model systems: a one-dimensional model of a beryllium atom, a one-dimensional model of a carbon atom, and a one-dimensional model of a chain of four hydrogen atoms. The time-dependent electronic dynamics induced by a few-cycle, long-wavelength laser pulse is found to be well described at a lower computational cost compared to the standard multiconfiguration time-dependent Hartree-Fock treatment. Drawbacks of the method are also discussed.
Energy Technology Data Exchange (ETDEWEB)
Lötstedt, Erik, E-mail: lotstedt@chem.s.u-tokyo.ac.jp; Kato, Tsuyoshi; Yamanouchi, Kaoru [Department of Chemistry, School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033 (Japan)
2016-04-21
An approximate implementation of the multiconfiguration time-dependent Hartree-Fock method is proposed, in which the matrix of configuration-interaction coefficients is decomposed into a product of matrices of smaller dimension. The applicability of this method in which all the configurations are kept in the expansion of the wave function, while the configuration-interaction coefficients are approximately calculated, is discussed by showing the results on three model systems: a one-dimensional model of a beryllium atom, a one-dimensional model of a carbon atom, and a one-dimensional model of a chain of four hydrogen atoms. The time-dependent electronic dynamics induced by a few-cycle, long-wavelength laser pulse is found to be well described at a lower computational cost compared to the standard multiconfiguration time-dependent Hartree-Fock treatment. Drawbacks of the method are also discussed.
Excess Charge for Pseudo-relativistic Atoms in Hartree-Fock Theory
DEFF Research Database (Denmark)
Dall'Acqua, Anna; Solovej, Jan Philip
2010-01-01
We prove within the Hartree-Fock theory of pseudo-relativistic atoms that the maximal negative ionization charge and the ionization energy of an atom remain bounded independently of the nuclear charge $Z$ and the fine structure constant $\\alpha$ as long as $Z\\alpha$ is bounded.......We prove within the Hartree-Fock theory of pseudo-relativistic atoms that the maximal negative ionization charge and the ionization energy of an atom remain bounded independently of the nuclear charge $Z$ and the fine structure constant $\\alpha$ as long as $Z\\alpha$ is bounded....
Time-dependent Hartree-Fock calculation of the escape width of the giant monopole resonance in 16O
International Nuclear Information System (INIS)
Pacheco, J.M.; Maglione, E.; Broglia, R.A.
1988-01-01
The damping of the giant monopole resonance in 16 O is calculated within the framework of the time-dependent Hartree-Fock approximation. The strength function contains two peaks, centered at around 25 and 33 MeV, with escape widths of ∼11 and ∼2 MeV, associated with the 1p(0p) -1 and 1s(0s) -1 configurations, respectively
Rivero, Pablo; Jiménez-Hoyos, Carlos A; Scuseria, Gustavo E
2013-10-24
We study strong correlation effects in a series of fused benzene rings (acenes) of varying length and width using our recently developed projected Hartree-Fock (PHF) method. These molecules, commonly known as polycyclic aromatic hydrocarbons or nanographenes, are very challenging for electronic structure theory because of their strong multireference character. This challenge is here met by PHF at moderate computational cost optimizing a spin eigenfunction obtained by projection of an unrestricted Hartree-Fock (UHF) trial determinant. The resulting method, known as SUHF, predicts that polyradical behavior and orbital entanglement are enhanced with molecular size, especially in systems whose structural motifs are dominated by zigzag edges, like oligoacenes.
Stationary perturbation theory for atoms with two open shells in the Hartree-Fock approximation
International Nuclear Information System (INIS)
Malykhanov, Yu.B.; Eremkin, I.N.
2007-01-01
In the framework of the Hartree-Fock method, equations of a stationary 'bound' perturbation theory are obtained which are applicable to multielectronic systems with two open shells of different symmetry types (Huzinaga method) in the orbital representation. Corrections to the Hartree-Fock orbitals are determined in the form of expansions in terms of unperturbed orbitals, which are calculated in the LCAO approximation in the basis of atomic orbitals of the Slater type. The static polar inability of a number of atoms with two open shells is calculated using an optimized basis set of atomic orbitals. (authors)
Spatial and Spin Symmetry Breaking in Semidefinite-Programming-Based Hartree-Fock Theory.
Nascimento, Daniel R; DePrince, A Eugene
2018-04-16
The Hartree-Fock problem was recently recast as a semidefinite optimization over the space of rank-constrained two-body reduced-density matrices (RDMs) [ Phys. Rev. A 2014 , 89 , 010502(R) ]. This formulation of the problem transfers the nonconvexity of the Hartree-Fock energy functional to the rank constraint on the two-body RDM. We consider an equivalent optimization over the space of positive semidefinite one-electron RDMs (1-RDMs) that retains the nonconvexity of the Hartree-Fock energy expression. The optimized 1-RDM satisfies ensemble N-representability conditions, and ensemble spin-state conditions may be imposed as well. The spin-state conditions place additional linear and nonlinear constraints on the 1-RDM. We apply this RDM-based approach to several molecular systems and explore its spatial (point group) and spin ( Ŝ 2 and Ŝ 3 ) symmetry breaking properties. When imposing Ŝ 2 and Ŝ 3 symmetry but relaxing point group symmetry, the procedure often locates spatial-symmetry-broken solutions that are difficult to identify using standard algorithms. For example, the RDM-based approach yields a smooth, spatial-symmetry-broken potential energy curve for the well-known Be-H 2 insertion pathway. We also demonstrate numerically that, upon relaxation of Ŝ 2 and Ŝ 3 symmetry constraints, the RDM-based approach is equivalent to real-valued generalized Hartree-Fock theory.
DEFF Research Database (Denmark)
Kjærgaard, Thomas; Jørgensen, Poul; Thorvaldsen, Andreas
2009-01-01
-orbital density-matrix based formulation of response theory and use London atomic orbitals to parametrize the magnetic field dependence. It yields a computational procedure which is both gauge-origin independent and suitable for linear-scaling at the level of time-dependent Hartree-Fock and density functional...
Miranda, R P; Fisher, A J; Stella, L; Horsfield, A P
2011-06-28
The solution of the time-dependent Schrödinger equation for systems of interacting electrons is generally a prohibitive task, for which approximate methods are necessary. Popular approaches, such as the time-dependent Hartree-Fock (TDHF) approximation and time-dependent density functional theory (TDDFT), are essentially single-configurational schemes. TDHF is by construction incapable of fully accounting for the excited character of the electronic states involved in many physical processes of interest; TDDFT, although exact in principle, is limited by the currently available exchange-correlation functionals. On the other hand, multiconfigurational methods, such as the multiconfigurational time-dependent Hartree-Fock (MCTDHF) approach, provide an accurate description of the excited states and can be systematically improved. However, the computational cost becomes prohibitive as the number of degrees of freedom increases, and thus, at present, the MCTDHF method is only practical for few-electron systems. In this work, we propose an alternative approach which effectively establishes a compromise between efficiency and accuracy, by retaining the smallest possible number of configurations that catches the essential features of the electronic wavefunction. Based on a time-dependent variational principle, we derive the MCTDHF working equation for a multiconfigurational expansion with fixed coefficients and specialise to the case of general open-shell states, which are relevant for many physical processes of interest.
Fractional Electron Loss in Approximate DFT and Hartree-Fock Theory.
Peach, Michael J G; Teale, Andrew M; Helgaker, Trygve; Tozer, David J
2015-11-10
Plots of electronic energy vs electron number, determined using approximate density functional theory (DFT) and Hartree-Fock theory, are typically piecewise convex and piecewise concave, respectively. The curves also commonly exhibit a minimum and maximum, respectively, in the neutral → anion segment, which lead to positive DFT anion HOMO energies and positive Hartree-Fock neutral LUMO energies. These minima/maxima are a consequence of using basis sets that are local to the system, preventing fractional electron loss. Ground-state curves are presented that illustrate the idealized behavior that would occur if the basis set were to be modified to enable fractional electron loss without changing the description in the vicinity of the system. The key feature is that the energy cannot increase when the electron number increases, so the slope cannot be anywhere positive, meaning frontier orbital energies cannot be positive. For the convex (DFT) case, the idealized curve is flat beyond a critical electron number such that any additional fraction of an electron added to the system is unbound. The anion HOMO energy is zero. For the concave (Hartree-Fock) case, the idealized curve is flat up to some critical electron number, beyond which it curves down to the anion energy. A minimum fraction of an electron is required before any binding occurs, but beyond that, the full fraction abruptly binds. The neutral LUMO energy is zero. Approximate DFT and Hartree-Fock results are presented for the F → F(-) segment, and results approaching the idealized behavior are recovered for highly diffuse basis sets. It is noted that if a DFT calculation using a highly diffuse basis set yields a negative LUMO energy then a fraction of an electron must bind and the electron affinity must be positive, irrespective of whether an electron binds experimentally. This is illustrated by calculations on Ne → Ne(-).
Second-Order Moller-Plesset Perturbation Theory for Molecular Dirac-Hartree-Fock Wave Functions
Dyall, Kenneth G.; Arnold, James O. (Technical Monitor)
1994-01-01
Moller-Plesset perturbation theory is developed to second order for a selection of Kramers restricted Dirac-Hartree-Fock closed and open-shell reference wave functions. The open-shell wave functions considered are limited to those with no more than two electrons in open shells, but include the case of a two-configuration SCF reference. Denominator shifts are included in the style of Davidson's OPT2 method. An implementation which uses unordered integrals with labels is presented, and results are given for a few test cases.
Veeraraghavan, Srikant; Mazziotti, David A
2014-03-28
We present a density matrix approach for computing global solutions of restricted open-shell Hartree-Fock theory, based on semidefinite programming (SDP), that gives upper and lower bounds on the Hartree-Fock energy of quantum systems. While wave function approaches to Hartree-Fock theory yield an upper bound to the Hartree-Fock energy, we derive a semidefinite relaxation of Hartree-Fock theory that yields a rigorous lower bound on the Hartree-Fock energy. We also develop an upper-bound algorithm in which Hartree-Fock theory is cast as a SDP with a nonconvex constraint on the rank of the matrix variable. Equality of the upper- and lower-bound energies guarantees that the computed solution is the globally optimal solution of Hartree-Fock theory. The work extends a previously presented method for closed-shell systems [S. Veeraraghavan and D. A. Mazziotti, Phys. Rev. A 89, 010502-R (2014)]. For strongly correlated systems the SDP approach provides an alternative to the locally optimized Hartree-Fock energies and densities with a certificate of global optimality. Applications are made to the potential energy curves of C2, CN, Cr2, and NO2.
Guidez, Emilie B; Gordon, Mark S
2015-03-12
The modeling of dispersion interactions in density functional theory (DFT) is commonly performed using an energy correction that involves empirically fitted parameters for all atom pairs of the system investigated. In this study, the first-principles-derived dispersion energy from the effective fragment potential (EFP) method is implemented for the density functional theory (DFT-D(EFP)) and Hartree-Fock (HF-D(EFP)) energies. Overall, DFT-D(EFP) performs similarly to the semiempirical DFT-D corrections for the test cases investigated in this work. HF-D(EFP) tends to underestimate binding energies and overestimate intermolecular equilibrium distances, relative to coupled cluster theory, most likely due to incomplete accounting for electron correlation. Overall, this first-principles dispersion correction yields results that are in good agreement with coupled-cluster calculations at a low computational cost.
Hu, Jinniu; Toki, Hiroshi; Shen, Hong
2016-10-18
We study the properties of nuclear matter with lattice nucleon-nucleon (NN) potential in the relativistic Brueckner-Hartree-Fock (RBHF) theory. To use this potential in such a microscopic many-body theory, we firstly have to construct a one-boson-exchange potential (OBEP) based on the latest lattice NN potential. Three mesons, pion, σ meson, and ω meson, are considered. Their coupling constants and cut-off momenta are determined by fitting the on-shell behaviors and phase shifts of the lattice force, respectively. Therefore, we obtain two parameter sets of the OBEP potential (named as LOBEP1 and LOBEP2) with these two fitting ways. We calculate the properties of symmetric and pure neutron matter with LOBEP1 and LOBEP2. In non-relativistic Brueckner-Hartree-Fock case, the binding energies of symmetric nuclear matter are around -3 and -5 MeV at saturation density, while it becomes -8 and -12 MeV in relativistic framework with 1 S 0 , 3 S 1 , and 3 D 1 channels using our two parameter sets. For the pure neutron matter, the equations of state in non-relativistic and relativistic cases are very similar due to only consideration 1 S 0 channel with isospin T = 1 case.
Exact norm-conserving stochastic time-dependent Hartree-Fock
International Nuclear Information System (INIS)
Tessieri, Luca; Wilkie, Joshua; Cetinbas, Murat
2005-01-01
We derive an exact single-body decomposition of the time-dependent Schroedinger equation for N pairwise interacting fermions. Each fermion obeys a stochastic time-dependent norm-preserving wave equation. As a first test of the method, we calculate the low energy spectrum of helium. An extension of the method to bosons is outlined
Parrish, Robert M; Gonthier, Jérôme F; Corminbœuf, Clémence; Sherrill, C David
2015-08-07
We develop a simple methodology for the computation of symmetry-adapted perturbation theory (SAPT) interaction energy contributions for intramolecular noncovalent interactions. In this approach, the local occupied orbitals of the total Hartree-Fock (HF) wavefunction are used to partition the fully interacting system into three chemically identifiable units: the noncovalent fragments A and B and a covalent linker C. Once these units are identified, the noninteracting HF wavefunctions of the fragments A and B are separately optimized while embedded in the HF wavefunction of C, providing the dressed zeroth order wavefunctions for A and B in the presence of C. Standard two-body SAPT (particularly SAPT0) is then applied between the relaxed wavefunctions for A and B. This intramolecular SAPT procedure is found to be remarkably straightforward and efficient, as evidenced by example applications ranging from diols to hexaphenyl-ethane derivatives.
Fusion hindrance in heavy systems with time-dependent Hartree-Fock
Washiyama, Kouhei
2017-11-01
We analyze fusion hindrance in heavy systems, where the fusion probability around the Coulomb barrier is hindered compared with that in light and medium-mass systems. We perform simulations of central collisions around the Coulomb barrier in heavy systems with time-dependent Hartree‒Fock (TDHF) and find that the fusion hindrance is realized in TDHF simulations. We extract nucleus‒nucleus potential and energy dissipation in heavy systems by a method combining a microscopic TDHF evolution to a macroscopic collective equation of motion. We find that the extracted potentials exhibit a dynamical increase at small relative distances, while the extracted friction coefficients show rather a behavior similar to that in light and medium-mass systems. We find from our analysis that the dynamical increase in potential is a main contribution to this fusion hindrance.
On the problem of representability and the Bogolyubov-Hartree-Fock theory
Energy Technology Data Exchange (ETDEWEB)
Knoerr, Hans Konrad
2013-11-22
The general topic of this thesis is an approximation of the ground state energy for many-particle quantum systems. In particular the Bogolyubov-Hartree-Fock theory and the representability of one- and two-particle density matrices are studied. After an introductory chapter we specify some basic notation of many-body quantum mechanics in Chapter 2. In Chapter 3 we consider boson, as well as fermion systems. We first tackle the question of representability for bosons, i.e., the question which conditions a one- and a two-particle operator must satisfy to ensure that they are the one- and the two-particle density matrix of a state. For a particle number-conserving system, the representability conditions up to second order for bosons are well-known and called admissibility, P-, and G-conditions. Since, however, most physical systems consisting of bosons are not particle number-conserving, we give an alternative for such systems: Generalizing the two-particle density matrix, we observe that the representability conditions up to second order hold if and only if this generalized two-particle density matrix is positive semi-definite and the one- and the two-particle density matrices fulfill trace class and symmetry conditions. Moreover, we study the Bogolyubov-Hartree-Fock energy of boson and fermion systems. We generalize Lieb's variational principle which in its original formulation holds for purely repulsive particle interactions for fermions only. Our second main result is the following: for bosons, as well as for fermions the infimum of the energy for a variation over pure quasifree states coincides with the one for a variation over all quasifree states under the assumption that the Hamiltonian is bounded below. In the last section of Chapter 3 we specify the relation between centered quasifree states and their corresponding generalized one-particle density matrix, which finds an application in the variational process in the Bogolyubov-Hartree-Fock theory. It is
Microscopic optical model potential based on Brueckner-Hartree-Fock theory
International Nuclear Information System (INIS)
Li Lulu; Zhao Enguang; Zhou Shangui; Li Zenghua; Zuo Wei; Bonaccorso, Angela; Lonbardo, Umberto
2010-01-01
The optical model is one of the most important models in the study of nuclear reactions. In the optical model, the elastic channel is considered to be dominant and the contributions of all other absorption channels are described by introducing an imaginary potential, Koning and Delaroche obtained empirically the so-called KDR optical potentials based on a best-fitting of massive experimental data on nucleon-nucleus scattering reactions. The volume part is found to be dominant in the real component of the OMP at low energies. Using the Bruckner-Hartree-Fock theory with Bonn B potential plus self consistent three body force, the nucleon-nucleus optical potential is studied in this thesis. In the Bruckner theory, the on-shell self energy, is corresponding to the depth of the volume part of the optical model potential (OMP) for nucleon-nucleus scattering. Using Bruckner-Hartree-Fock theory, the nucleon on-shell self energy is calculated based on Hughenoltz-Van Hove (HVH) theorem. The microscopic optical potentials thus obtained agree well with the volume part of the KDR potentials. Furthermore, the isospin splitting in the volume part of the OMP is also reproduced satisfactorily. The isospin effect in the volume part of the OMP is directly related to the isospin splitting of the effective mass of the nucleon. According to our results, the isospin splitting of neutron to proton effective mass is such that the neutron effective mass increases with isospin, whereas the proton effective mass decreases. The isovector potential U n (E) - U p (E) vanishes at energy E ≈ 200 MeV and then changes sign indicating a possible inversion in the effective mass isospin spitting. We also calculated from the Bruckner theory the imaginary part of the OMP, and the microscopic calculations predict that the isospin splitting exists also in the imaginary OMP whereas the empirical KDR potentials do not show this feature. The shape of the real component of the nucleon-nucleus OMP is
A simple and efficient dispersion correction to the Hartree-Fock theory.
Yoshida, Tatsusada; Mashima, Akira; Sasahara, Katsunori; Chuman, Hiroshi
2014-02-15
One of the most challenging problems in computational chemistry and in drug discovery is the accurate prediction of the binding energy between a ligand and a protein receptor. It is well known that the binding energy calculated with the Hartree-Fock molecular orbital theory (HF) lacks the dispersion interaction energy that significantly affects the accuracy of the total binding energy of a large molecular system. We propose a simple and efficient dispersion energy correction to the HF theory (HF-Dtq). The performance of HF-Dtq was compared with those of several recently proposed dispersion corrected density functional theory methods (DFT-Ds) as to the binding energies of 68 small non-covalent complexes. The overall performance of HF-Dtq was found to be nearly equivalent to that of more sophisticated B3LYP-D3. HF-Dtq will thus be a useful and powerful method for accurately predicting the binding energy between a ligand and a protein, albeit it is a simple correction procedure based on HF. Copyright © 2014 Elsevier Ltd. All rights reserved.
Garza, Alejandro J; Jiménez-Hoyos, Carlos A; Scuseria, Gustavo E
2013-04-07
This paper explores the possibility of combining projected Hartree-Fock and density functional theories for treating static and dynamic correlations in molecular systems with mean-field computational cost. The combination of spin-projected unrestricted Hartree-Fock (SUHF) with the TPSS correlation functional (SUHF+TPSS) yields excellent results for non-metallic molecular dissociations and singlet-triplet splittings. However, SUHF+TPSS fails to provide the qualitatively correct dissociation curve for the notoriously difficult case of the chromium dimer. By tuning the TPSS correlation parameters and adding complex conjugation symmetry breaking and restoration to SUHF, the right curve shape for Cr2 can be obtained; unfortunately, such a combination is found to lead to overcorrelation in the general case.
Holomorphic Hartree-Fock Theory: The Nature of Two-Electron Problems.
Burton, Hugh G A; Gross, Mark; Thom, Alex J W
2018-02-13
We explore the existence and behavior of holomorphic restricted Hartree-Fock (h-RHF) solutions for two-electron problems. Through algebraic geometry, the exact number of solutions with n basis functions is rigorously identified as 1 / 2 (3 n - 1), proving that states must exist for all molecular geometries. A detailed study on the h-RHF states of HZ (STO-3G) then demonstrates both the conservation of holomorphic solutions as geometry or atomic charges are varied and the emergence of complex h-RHF solutions at coalescence points. Using catastrophe theory, the nature of these coalescence points is described, highlighting the influence of molecular symmetry. The h-RHF states of HHeH 2+ and HHeH (STO-3G) are then compared, illustrating the isomorphism between systems with two electrons and two electron holes. Finally, we explore the h-RHF states of ethene (STO-3G) by considering the π electrons as a two-electron problem and employ NOCI to identify a crossing of the lowest energy singlet and triplet states at the perpendicular geometry.
Density Functional Theory versus the Hartree-Fock Method: Comparative Assessment
International Nuclear Information System (INIS)
Amusia, M.Ya.; Shaginyan, V.R.; Msezane, A.Z.
2003-01-01
We compare two different approaches to investigations of many-electron systems. The first is the Hartree-Fock (HF) method and the second is the Density Functional Theory (DFT). Overview of the main features and peculiar properties of the HF method are presented. A way to realize the HF method within the Kohn-Sham (KS) approach of the DFT is discussed. We show that this is impossible without including a specific correlation energy, which is defined by the difference between the sum of the kinetic and exchange energies of a system considered within KS and HF, respectively. It is the nonlocal exchange potential entering the HF equations that generates this correlation energy. We show that the total correlation energy of a finite electron system, which has to include this correlation energy, cannot be obtained from considerations of uniform electron systems. The single-particle excitation spectrum of many-electron systems is related to the eigenvalues of the corresponding KS equations. We demonstrate that this spectrum does not coincide in general with the eigenvalues of KS or HF equations
Density Functional Theory versus the Hartree-Fock Method: Comparative Assessment
Energy Technology Data Exchange (ETDEWEB)
Amusia, M.Ya.; Shaginyan, V.R. [The Hebrew University, Jerusalem (Israel); Msezane, A.Z. [Clark Atlanta Univ., Atlanta, GA (United States). Center for Theoretical Studies of Physical Systems
2003-12-01
We compare two different approaches to investigations of many-electron systems. The first is the Hartree-Fock (HF) method and the second is the Density Functional Theory (DFT). Overview of the main features and peculiar properties of the HF method are presented. A way to realize the HF method within the Kohn-Sham (KS) approach of the DFT is discussed. We show that this is impossible without including a specific correlation energy, which is defined by the difference between the sum of the kinetic and exchange energies of a system considered within KS and HF, respectively. It is the nonlocal exchange potential entering the HF equations that generates this correlation energy. We show that the total correlation energy of a finite electron system, which has to include this correlation energy, cannot be obtained from considerations of uniform electron systems. The single-particle excitation spectrum of many-electron systems is related to the eigenvalues of the corresponding KS equations. We demonstrate that this spectrum does not coincide in general with the eigenvalues of KS or HF equations.
Liang, Wenkel; Isborn, Christine M.; Li, Xiaosong
2009-11-01
The calculation of doubly excited states is one of the major problems plaguing the modern day excited state workhorse methodology of linear response time dependent Hartree-Fock (TDHF) and density function theory (TDDFT). We have previously shown that the use of a resonantly tuned field within real-time TDHF and TDDFT is able to simultaneously excite both the α and β electrons to achieve the two-electron excited states of minimal basis H2 and HeH+ [C. M. Isborn and X. Li, J. Chem. Phys. 129, 204107 (2008)]. We now extend this method to many electron systems with the use of our Car-Parrinello density matrix search (CP-DMS) with a first-principles fictitious mass method for wave function optimization [X. Li, C. L. Moss, W. Liang, and Y. Feng, J. Chem. Phys. 130, 234115 (2009)]. Real-time TDHF/TDDFT is used during the application of the laser field perturbation, driving the electron density toward the doubly excited state. The CP-DMS method then converges the density to the nearest stationary state. We present these stationary state doubly excited state energies and properties at the HF and DFT levels for H2, HeH+, lithium hydride, ethylene, and butadiene.
Deformed Brueckner-Hartree-Fock calculations.
Ford, W. F.; Braley, R. C.; Becker, R. L.; Patterson, M. R.
1972-01-01
The renormalized Brueckner-Hartree-Fock (RBHF) theory for many-body nuclear systems has been generalized to permit calculations for intrinsic states having permanent deformation. Both Hartree-Fock and Brueckner self-consistencies are satisfied, and details of the numerical techniques are discussed. The Hamada-Johnston interaction is used in a study of deformations, binding, size, and separation energies for several nuclei. Electromagnetic transition rates, moments, and electron scattering form factors are calculated using nuclear wave functions obtained by angular momentum projection. Comparison is made to experiment as well as to predictions of ordinary and density-dependent Hartree-Fock theory.
Mateus, Margarida P. S.; Cabral, Benedito J. C.
2007-11-01
Theoretical calculations for the electron binding energies (EBEs) of several organic azides including hydrazoic acid, methyl azide, ethyl azide, 2-chloroethyl azide, 2-azidoethanol, azidoacetone, 2-azidoacetic acid, 3-azido-2-butanone, and 2-azidoethyl acetate are reported. EBEs were calculated with ab initio Green's function (GF) and density functional theory (DFT). Complete basis-set extrapolated coupled cluster calculations with single, double, and perturbative triple excitations [CCSD(T)] for the first ionization energy of azides are also reported. It is shown that EBEs from GF and DFT calculations are in better agreement with experiment than Hartree-Fock predictions.
Kehle, Christoph
2017-01-01
We will give a proof that the maximal excess charge for an atom described by a family of density-matrix-functionals, which includes Hartree-Fock and Müller theories, is bounded by a universal constant. We will use the new technique introduced by Frank et al. [preprint arXiv:1608.05625 (2016)].
International Nuclear Information System (INIS)
Brut, F.
1982-01-01
The spectroscopy of odd-A nuclei, in the 1p and 2s-1d shells, is studied in the framework of the projected Hartree-Fock method and by the generator coordinate method. The nuclear effective interactions of Cohen and Kurath, on the one hand, and of Kuo or Preedom-Wildenthal, on the other hand, are used. The binding energies, the nuclear spectra, the static moments and the electromagnetic transitions obtained by these two approaches are compared to the same quantities given by a complete diagonalization in the shell model basis. This study of light nuclei gives some possibilities to put in order the energy levels by coupled rotational bands. In the microscopic approach, thus we find all the elements of the unified model of Bohr and Mottelson. To give evidence of such a relation, the functions of the angle β, in the integrals of the projection method of Peierls and Yoccoz, for a Slater determinant, are developed in the vicinity of the bounds β = O and β = π. The microscopic coefficients are evaluated in the Hartree-Fock approximation, using the particle-hole formalism. Calculations are made for 20 Ne and 21 Ne and the resulting microscopic coefficients are compared with the corresponding terms of the unified model of Bohr and Mottelson [fr
Relativistic Hartree-Fock theory. Part I: density-dependent effective Lagrangians
Energy Technology Data Exchange (ETDEWEB)
LongWen Hui [School of Physics, Peking University, 100871 Beijing (China)]|[CNRS-IN2P3, UMR 8608, F-91406 Orsay Cedex (France)]|[Univ Paris-Sud, F-91405 Orsay (France); Giai, Nguyen Van [CNRS-IN2P3, UMR 8608, F-91406 Orsay Cedex (France)]|[Univ Paris-Sud, F-91405 Orsay (France); Meng, Jie [School of Physics, Peking University, 100871 Beijing (China)]|[Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing (China)]|[Center of Theoretical Nuclear Physics, National Laboratory of Heavy Ion Accelerator, 730000 Lanzhou (China)
2006-10-15
Effective Lagrangians suitable for a relativistic Hartree-Fock description of nuclear systems are presented. They include the 4 effective mesons {sigma}, {omega}, {rho} and {pi} with density-dependent meson-nucleon couplings. The criteria for determining the model parameters are the reproduction of the binding energies in a number of selected nuclei, and the bulk properties of nuclear matter (saturation point, compression modulus, symmetry energy). An excellent description of nuclear binding energies and radii is achieved for a range of nuclei encompassing light and heavy systems. The predictions of the present approach compare favorably with those of existing relativistic mean field models, with the advantage of incorporating the effects of pion-nucleon coupling. (authors)
Rayka, Milad; Goli, Mohammad; Shahbazian, Shant
2018-02-07
An effective set of Hartree-Fock (HF) equations are derived for electrons of muonic systems, i.e., molecules containing a positively charged muon, conceiving the muon as a quantum oscillator, which are completely equivalent to the usual two-component HF equations used to derive stationary states of the muonic molecules. In these effective equations, a non-Coulombic potential is added to the orthodox coulomb and exchange potential energy terms, which describes the interaction of the muon and the electrons effectively and is optimized during the self-consistent field cycles. While in the two-component HF equations a muon is treated as a quantum particle, in the effective HF equations it is absorbed into the effective potential and practically transformed into an effective potential field experienced by electrons. The explicit form of the effective potential depends on the nature of muon's vibrations and is derivable from the basis set used to expand the muonic spatial orbital. The resulting effective Hartree-Fock equations are implemented computationally and used successfully, as a proof of concept, in a series of muonic molecules containing all atoms from the second and third rows of the Periodic Table. To solve the algebraic version of the equations muon-specific Gaussian basis sets are designed for both muon and surrounding electrons and it is demonstrated that the optimized exponents are quite distinct from those derived for the hydrogen isotopes. The developed effective HF theory is quite general and in principle can be used for any muonic system while it is the starting point for a general effective electronic structure theory that incorporates various types of quantum correlations into the muonic systems beyond the HF equations.
International Nuclear Information System (INIS)
Villars, F.
1975-01-01
The objective of the work is to draw attention to the essential equivalence of the two apparently quite distinct ways of describing nuclear collective dyanmics, the adiabatic time-dependent Hartree-Fock method (ADTHF) on the one hand, and the Generator Coordinate (GC) method on the other hand. To demonstrate this relation, an analysis of the simplest case, in which collective motion is described by a single collective para- meter q(t) is presented. In the ATDHF approach, two self-consistency conditions are obtained; the resultant expressions for the collective potential and kinetic energies represent a special case of the more general results of Baranger and Veneroni. In the G.C. approach to the same system (with the same collective parameter q), the narrow overlap approximation must be made, as the counterpart of the adiabatic approximation in the TDHF method. In its conventional form, the G.C. method leads to a different expression for the collective kinetic energy. It is shown however, that a simple generalization of the G.C.-wave function leads to corrections determined by a variational principle. In leading order, the corrected expression for the collective kinetic energy is identical with the TDHF result In both cases, the collective inertia is determined by a self-consistent cranking formula
DEFF Research Database (Denmark)
Norman, Patrick; Schimmelpfennig, Bernd; Ruud, Kenneth
2002-01-01
A systematic investigation of a hierarchy of methods for including relativistic effects in the calculation of linear and nonlinear optical properties was carried out. The simple ECP method and the more involved spin-averaged Douglas-Kroll approximation were compared to benchmark results obtained ...... with the time-dependent Dirac-Hartree-Fock method. It was found that in many cases, the performance of the ECP method exceeds its rank....
Fias, Stijn; Stuyver, Thijs
2017-11-01
The recent source and sink potential approach by Pickup et al. [J. Chem. Phys. 143, 194105 (2015)] is extended to Hartree-Fock and density functional theory, allowing the calculation of the transmission and the visualization of ballistic currents through molecules at these levels of theory. This visualization allows the study of the transmission process in real-space, providing an important tool to better understand the conduction process.
Comparison of Smooth Hartree-Fock Pseudopotentials.
Trail, J R; Needs, R J
2014-05-13
The accuracy of two widely used scalar relativistic Hartree-Fock pseudopotentials, the Trail-Needs-Dirac-Fock (TNDF) and the Burkatzki-Filippi-Dolg (BFD) pseudopotentials, is assessed. The performance of the pseudopotentials is tested for a chemically representative set of 34 first-row molecules. All comparisons are made at the Hartree-Fock level of theory, and both sets of pseudopotentials give good results. The all-electron equilibrium geometries, molecular dissociation energies, and zero-point vibrational energies are reproduced a little more accurately by the TNDF pseudopotentials than the BFD ones.
Small, David W; Sundstrom, Eric J; Head-Gordon, Martin
2015-03-07
We introduce a necessary and sufficient condition for an arbitrary wavefunction to be collinear, i.e., its spin is quantized along some axis. It may be used to obtain a cheap and simple computational procedure to test for collinearity in electronic structure theory calculations. We adapt the procedure for Generalized Hartree Fock (GHF), and use it to study two dissociation pathways in CO2. For these dissociation processes, the GHF wave functions transform from low-spin Unrestricted Hartree Fock (UHF) type states to noncollinear GHF states and on to high-spin UHF type states, phenomena that are succinctly illustrated by the constituents of the collinearity test. This complements earlier GHF work on this molecule.
Liu, Zhi Wei; Qian, Zhuang; Xing, Ruo Yu; Niu, Jia Rui; Sun, Bao Yuan
2018-02-01
Adopting the density dependent relativistic mean-field (RMF) and relativistic Hartree-Fock (RHF) approaches, the properties of the nuclear fourth-order symmetry energy S4 are studied within the covariant density functional (CDF) theory. It is found that the fourth-order symmetry energies are suppressed in RHF at both saturation and supranuclear densities, where the extra contribution from the Fock terms is demonstrated, specifically via the isoscalar meson-nucleon coupling channels. The reservation of S4 and higher-order symmetry energies in the nuclear equation of state then affects essentially the prediction of neutron star properties, which is illustrated in quantities such as the proton fraction, the core-crust transition density, as well as the fraction of crustal moment of inertia. Since the Fock terms enhance the density dependence of the thermodynamical potential, the RHF calculations predict systematically smaller values of density, proton fraction, and pressure at the core-crust transition boundary of neutron stars than density dependent RMF ones. In addition, a linear anticorrelation between the core-crust transition density ρt and the density slope of symmetry energy L is found which is then utilized to constrain the core-crust transition density as ρt˜[0.069 ,0.098 ] fm-3 with the recent empirical information on L . The study clarifies the important role of the fourth-order symmetry energy in determining the properties of nuclear matter at extreme isospin or density conditions.
Ozaki, Taisuke; Toyoda, Masayuki
2011-06-01
An accurate finite element method is developed for atomic calculations based on density functional theory (DFT) within local density approximation (LDA) and Hartree-Fock (HF) method. The radial wave functions are expanded by cubic Hermite spline functions on a uniform mesh for x=√{r}, and all the associated integrals are analytically evaluated in conjunction with fitting procedures of the Hartree and the exchange-correlation potentials to the same cubic Hermite spline functions using a set of recurrence formulas. The total energy of atoms systematically converges from above, and the error algebraically decays as the mesh spacing decreases. When the mesh spacing d is taken to be 0.025/√{Z} bohr, the total energy for an atom of atomic number Z can be calculated within error of 10 hartree for both the LDA and HF methods. The equal applicability of the method to DFT and the HF method with a similar degree of high accuracy enables the method to be a reliable platform for development of new functionals in DFT such as hybrid functionals.
Generalized Hartree-Fock Description of Molecular Dissociation.
Jiménez-Hoyos, Carlos A; Henderson, Thomas M; Scuseria, Gustavo E
2011-09-13
An electronic structure method is said to be size-consistent if the energy of noninteracting fragments is the same when the fragments are treated in a supermolecule approach or are treated in isolation. Size consistency is often violated by Hartree-Fock when symmetries of the exact wave function are imposed on the Hartree-Fock determinant. Relaxing the requirement that the Hartree-Fock wave function be a spin eigenfunction leads to unrestricted Hartree-Fock, which is often (but not always) size-consistent. In this Perspective, we discuss the usually forgotten fact that imposing none of the exact symmetries in what is known as generalized Hartree-Fock allows Hartree-Fock to always be size-consistent and allows size extensive correlated methods such as coupled cluster theory to also be size-consistent. Furthermore, with all symmetries broken, dissociation curves connect the molecule to the fragments better than with symmetries imposed, although the curves are not smooth and show derivative discontinuities akin to unphysical phase transitions. In many cases, correlated dissociation curves based on this generalized Hartree-Fock reference are discontinuous.
Tanak, Hasan; Toy, Mehmet
2016-01-05
The molecular geometry and vibrational frequencies of 1-[N-(2-pyridyl)aminomethylidene}-2(1H)-Naphtalenone in the ground state have been calculated by using the Hartree-Fock (HF) and density functional method (B3LYP) with 6-311++G(d,p) basis set. The results of the optimized molecular structure are presented and compared with the experimental X-ray diffraction. The computed vibrational frequencies were used to determine the types of molecular motions associated with each of the experimental bands observed. In addition, calculated results are related to the linear correlation plot of computed data versus experimental geometric parameters and IR data. From the results it was concluded that the B3LYP method is superior to the HF method for the vibrational frequencies. Using the time-dependent density functional theory (TD-DFT) and Hartree-Fock (TD-HF) methods, electronic absorption spectra of the title compound have been predicted and a good agreement with the TD-DFT method and experimental ones is determined. Copyright © 2014 Elsevier B.V. All rights reserved.
An open-shell restricted Hartree-Fock perturbation theory based on symmetric spin orbitals
Lee, Timothy J.; Jayatilaka, Dylan
1993-01-01
A new open-shell perturbation theory is formulated in terms of symmetric spin orbitals. Only one set of spatial orbitals is required, thereby reducing the number of independent coefficients in the perturbed wavefunctions. For second order, the computational cost is shown to be similar to a closed-shell calculation. This formalism is therefore more efficient than the recently developed RMP, ROMP or RMP-MBPT theories. The perturbation theory described herein was designed to have a close correspondence with our recently proposed coupled-cluster theory based on symmetric spin orbitals. The first-order wavefunction contains contributions from only doubly excited determinants. Equilibrium structures and vibrational frequencies determined from second-order perturbation theory are presented for OH, NH, CH, 02, NH2 and CH2.
Cui, Yao; Bulik, Ireneusz W; Jiménez-Hoyos, Carlos A; Henderson, Thomas M; Scuseria, Gustavo E
2013-10-21
We study the spectra of the molecular orbital Hessian (stability matrix) and random-phase approximation (RPA) Hamiltonian of broken-symmetry Hartree-Fock solutions, focusing on zero eigenvalue modes. After all negative eigenvalues are removed from the Hessian by following their eigenvectors downhill, one is left with only positive and zero eigenvalues. Zero modes correspond to orbital rotations with no restoring force. These rotations determine states in the Goldstone manifold, which originates from a spontaneously broken continuous symmetry in the wave function. Zero modes can be classified as improper or proper according to their different mathematical and physical properties. Improper modes arise from symmetry breaking and their restoration always lowers the energy. Proper modes, on the other hand, correspond to degeneracies of the wave function, and their symmetry restoration does not necessarily lower the energy. We discuss how the RPA Hamiltonian distinguishes between proper and improper modes by doubling the number of zero eigenvalues associated with the latter. Proper modes in the Hessian always appear in pairs which do not double in RPA. We present several pedagogical cases exemplifying the above statements. The relevance of these results for projected Hartree-Fock methods is also addressed.
Energy Technology Data Exchange (ETDEWEB)
Small, David W.; Sundstrom, Eric J.; Head-Gordon, Martin [Department of Chemistry, University of California, Berkeley, California 94720, USA and Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720 (United States)
2015-01-14
Restricted Hartree Fock using complex-valued orbitals (cRHF) is studied. We introduce an orbital pairing theorem, with which we obtain a concise connection between cRHF and real-valued RHF, and use it to uncover the close relationship between cRHF, unrestricted Hartree Fock, and generalized valence bond perfect pairing. This enables an intuition for cRHF, contrasting with the generally unintuitive nature of complex orbitals. We also describe an efficient computer implementation of cRHF and its corresponding stability analysis. By applying cRHF to the Be + H{sub 2} insertion reaction, a Woodward-Hoffmann violating reaction, and a symmetry-driven conical intersection, we demonstrate in genuine molecular systems that cRHF is capable of removing certain potential energy surface singularities that plague real-valued RHF and related methods. This complements earlier work that showed this capability in a model system. We also describe how cRHF is the preferred RHF method for certain radicaloid systems like singlet oxygen and antiaromatic molecules. For singlet O{sub 2}, we show that standard methods fail even at the equilibrium geometry. An implication of this work is that, regardless of their individual efficacies, cRHF solutions to the HF equations are fairly commonplace.
The fractal geometry of Hartree-Fock
Theel, Friethjof; Karamatskou, Antonia; Santra, Robin
2017-12-01
The Hartree-Fock method is an important approximation for the ground-state electronic wave function of atoms and molecules so that its usage is widespread in computational chemistry and physics. The Hartree-Fock method is an iterative procedure in which the electronic wave functions of the occupied orbitals are determined. The set of functions found in one step builds the basis for the next iteration step. In this work, we interpret the Hartree-Fock method as a dynamical system since dynamical systems are iterations where iteration steps represent the time development of the system, as encountered in the theory of fractals. The focus is put on the convergence behavior of the dynamical system as a function of a suitable control parameter. In our case, a complex parameter λ controls the strength of the electron-electron interaction. An investigation of the convergence behavior depending on the parameter λ is performed for helium, neon, and argon. We observe fractal structures in the complex λ-plane, which resemble the well-known Mandelbrot set, determine their fractal dimension, and find that with increasing nuclear charge, the fragmentation increases as well.
Bučinský, Lukáš
2015-05-11
"Kramers pairs symmetry breaking" is evaluated at the 2-component (2c) Kramers unrestricted and/or general complex Hartree-Fock (GCHF) level of theory, and its analogy with "spin contamination" at the 1-component (1c) unrestricted Hartree-Fock (UHF) level of theory is emphasized. The GCHF "Kramers pairs symmetry breaking" evaluation is using the square of overlaps between the set of occupied spinorbitals with the projected set of Kramers pairs. In the same fashion, overlaps between α and β orbitals are used in the evaluation of "spin contamination" at the UHF level of theory. In this manner, UHF Š2 expectation value is made formally extended to the GCHF case. The directly evaluated GCHF expectation value of the Š2 operator is considered for completeness. It is found that the 2c GCHF Kramers pairs symmetry breaking has a very similar extent in comparison to the 1c UHF spin contamination. Thus higher excited states contributions to the 1c and 2c unrestricted wave functions of open shell systems have almost the same extent and physical consequences. Moreover, it is formally shown that a single determinant wave function in the restricted open shell Kramers case has the expectation value of K2 operator equal to the negative number of open shell electrons, while the eigenvalue of K2 for the series of simple systems (H, He, He*-triplet, Li and Li*-quartet) are found to be equal to minus the square of the number of open shell electrons. The concept of unpaired electron density is extended to the GCHF regime and compared to UHF and restricted open shell Hartree-Fock spin density. The "collinear" and "noncollinear" analogs of spin density at the GCHF level of theory are considered as well. Spin contamination and/or Kramers pairs symmetry breaking, spin populations and spin densities are considered for H2O+, Cl, HCl+, phenoxyl radical (C6H5O) as well as for Cu, Cu2+, Fe and the [OsCl5(1H-pyrazole)]- anion. The 1c and 2c unpaired electron density representation is found
Ucun, Fatih; Sağlam, Adnan; Güçlü, Vesile
2007-06-01
The molecular structures, vibrational frequencies and corresponding vibrational assignments of xanthine and its methyl derivatives (caffeine and theobromine) have been calculated using ab initio Hartree-Fock (HF) and density functional theory (B3LYP) methods with 6-31G(d, p) basis set level. The calculations were utilized to the CS symmetries of the molecules. The obtained vibrational frequencies and optimised geometric parameters (bond lengths and bond angles) were seen to be well agreement with the experimental data. The used scale factors which have been obtained the ratio of the frequency values of the strongest peaks in the calculated and experimental spectra seem to cause the gained vibrations well corresponding to the experimental ones. Theoretical infrared intensities and Raman activities are also reported.
Ramya, T; Gunasekaran, S; Ramkumaar, G R
2013-10-01
The Fourier Transform Infrared (FTIR) and FT Raman spectra of lamotrigine have been recorded in the region 4000-450 cm(-1) and 4000-50 cm(-1), respectively. The title compound is used as Antiepileptic drug. The optimized geometry, frequency, and intensities of the vibrational bands of the lamotrigine were obtained by Density Functional Theory (DFT) using B3LYP/631G** basis set and ab initio method at the restricted Hartree Fock/6-31** level. The harmonic vibrational frequencies, Natural population analysis, HOMO-LUMO energy gap, infra red intensities and Raman scattering activities, force constant were calculated by DFT and RHF methods. The quality of lamotrigine under different storage containers were analyzed using UV-Vis spectral technique. Copyright © 2013 Elsevier B.V. All rights reserved.
Yoshida, Tatsusada; Hayashi, Takahisa; Mashima, Akira; Chuman, Hiroshi
2015-10-01
One of the most challenging problems in computer-aided drug discovery is the accurate prediction of the binding energy between a ligand and a protein. For accurate estimation of net binding energy ΔEbind in the framework of the Hartree-Fock (HF) theory, it is necessary to estimate two additional energy terms; the dispersion interaction energy (Edisp) and the basis set superposition error (BSSE). We previously reported a simple and efficient dispersion correction, Edisp, to the Hartree-Fock theory (HF-Dtq). In the present study, an approximation procedure for estimating BSSE proposed by Kruse and Grimme, a geometrical counterpoise correction (gCP), was incorporated into HF-Dtq (HF-Dtq-gCP). The relative weights of the Edisp (Dtq) and BSSE (gCP) terms were determined to reproduce ΔEbind calculated with CCSD(T)/CBS or /aug-cc-pVTZ (HF-Dtq-gCP (scaled)). The performance of HF-Dtq-gCP (scaled) was compared with that of B3LYP-D3(BJ)-bCP (dispersion corrected B3LYP with the Boys and Bernadi counterpoise correction (bCP)), by taking ΔEbind (CCSD(T)-bCP) of small non-covalent complexes as 'a golden standard'. As a critical test, HF-Dtq-gCP (scaled)/6-31G(d) and B3LYP-D3(BJ)-bCP/6-31G(d) were applied to the complex model for HIV-1 protease and its potent inhibitor, KNI-10033. The present results demonstrate that HF-Dtq-gCP (scaled) is a useful and powerful remedy for accurately and promptly predicting ΔEbind between a ligand and a protein, albeit it is a simple correction procedure. Copyright © 2015 Elsevier Ltd. All rights reserved.
Energy Technology Data Exchange (ETDEWEB)
Song, Jong-Won; Hirao, Kimihiko, E-mail: hirao@riken.jp [Computational Chemistry Unit, RIKEN Advanced Institute for Computational Science, 7-1-26, Minatojima-minami-machi, Chuo-ku, Kobe, Hyogo 650-0047 (Japan)
2015-10-14
Since the advent of hybrid functional in 1993, it has become a main quantum chemical tool for the calculation of energies and properties of molecular systems. Following the introduction of long-range corrected hybrid scheme for density functional theory a decade later, the applicability of the hybrid functional has been further amplified due to the resulting increased performance on orbital energy, excitation energy, non-linear optical property, barrier height, and so on. Nevertheless, the high cost associated with the evaluation of Hartree-Fock (HF) exchange integrals remains a bottleneck for the broader and more active applications of hybrid functionals to large molecular and periodic systems. Here, we propose a very simple yet efficient method for the computation of long-range corrected hybrid scheme. It uses a modified two-Gaussian attenuating operator instead of the error function for the long-range HF exchange integral. As a result, the two-Gaussian HF operator, which mimics the shape of the error function operator, reduces computational time dramatically (e.g., about 14 times acceleration in C diamond calculation using periodic boundary condition) and enables lower scaling with system size, while maintaining the improved features of the long-range corrected density functional theory.
Fahleson, Tobias; Norman, Patrick
2017-10-14
The second-order nonlinear (or cubic) response function is derived from the Ehrenfest theorem with inclusion made of the finite lifetimes of the excited states, representing the extension of the derivation of the quadratic response function in the same framework [P. Norman et al., J. Chem. Phys. 123, 194103 (2005)]. The resulting damped response functions are physically sound and converging also in near-resonance and resonance regions of the spectrum. Being an accurate approximation for small complex frequencies (defined as the sum of an optical frequency and an imaginary damping parameter), the polynomial expansion of the complex cubic response function in terms of the said frequencies is presented and used to validate the program implementation. In terms of approximate state theory, the computationally tractable expressions of the damped cubic response function are derived and implemented at the levels of Hartree-Fock and Kohn-Sham density functional theory. Numerical examples are provided in terms of studies of the intensity-dependent refractive index of para-nitroaniline and the two-photon absorption cross section of neon. For the latter property, a numerical comparison is made against calculations of the square of two-photon matrix elements that are identified from a residue analysis of the resonance-divergent quadratic response function.
Goerigk, Lars; Collyer, Charles A; Reimers, Jeffrey R
2014-12-18
We demonstrate the importance of properly accounting for London dispersion and basis-set-superposition error (BSSE) in quantum-chemical optimizations of protein structures, factors that are often still neglected in contemporary applications. We optimize a portion of an ensemble of conformationally flexible lysozyme structures obtained from highly accurate X-ray crystallography data that serve as a reliable benchmark. We not only analyze root-mean-square deviations from the experimental Cartesian coordinates, but also, for the first time, demonstrate how London dispersion and BSSE influence crystallographic R factors. Our conclusions parallel recent recommendations for the optimization of small gas-phase peptide structures made by some of the present authors: Hartree-Fock theory extended with Grimme's recent dispersion and BSSE corrections (HF-D3-gCP) is superior to popular density functional theory (DFT) approaches. Not only are statistical errors on average lower with HF-D3-gCP, but also the convergence behavior is much better. In particular, we show that the BP86/6-31G* approach should not be relied upon as a black-box method, despite its widespread use, as its success is based on an unpredictable cancellation of errors. Using HF-D3-gCP is technically straightforward, and we therefore encourage users of quantum-chemical methods to adopt this approach in future applications.
Song, Jong-Won; Hirao, Kimihiko
2015-10-14
Since the advent of hybrid functional in 1993, it has become a main quantum chemical tool for the calculation of energies and properties of molecular systems. Following the introduction of long-range corrected hybrid scheme for density functional theory a decade later, the applicability of the hybrid functional has been further amplified due to the resulting increased performance on orbital energy, excitation energy, non-linear optical property, barrier height, and so on. Nevertheless, the high cost associated with the evaluation of Hartree-Fock (HF) exchange integrals remains a bottleneck for the broader and more active applications of hybrid functionals to large molecular and periodic systems. Here, we propose a very simple yet efficient method for the computation of long-range corrected hybrid scheme. It uses a modified two-Gaussian attenuating operator instead of the error function for the long-range HF exchange integral. As a result, the two-Gaussian HF operator, which mimics the shape of the error function operator, reduces computational time dramatically (e.g., about 14 times acceleration in C diamond calculation using periodic boundary condition) and enables lower scaling with system size, while maintaining the improved features of the long-range corrected density functional theory.
Ohmura, S.; Kato, T.; Oyamada, T.; Koseki, S.; Ohmura, H.; Kono, H.
2018-02-01
The mechanisms of anisotropic near-IR tunnel ionization and high-order harmonic generation (HHG) in a CO molecule are theoretically investigated by using the multiconfiguration time-dependent Hartree-Fock (MCTDHF) method developed for the simulation of multielectron dynamics of molecules. The multielectron dynamics obtained by numerically solving the equations of motion (EOMs) in the MCTDHF method is converted to a single orbital picture in the natural orbital representation where the first-order reduced density matrix is diagonalized. The ionization through each natural orbital is examined and the process of HHG is classified into different optical paths designated by a combinations of initial, intermediate and final natural orbitals. The EOMs for natural spin-orbitals are also derived within the framework of the MCTDHF, which maintains the first-order reduced density matrix to be a diagonal one throughout the time propagation of a many-electron wave function. The orbital dependent, time-dependent effective potentials that govern the dynamics of respective time-dependent natural orbitals are deduced from the derived EOMs, of which the temporal variation can be used to interpret the motion of the electron density associated with each natural spin-orbital. The roles of the orbital shape, multiorbital ionization, linear Stark effect and multielectron interaction in the ionization and HHG of a CO molecule are revealed by the effective potentials obtained. When the laser electric field points to the nucleus O from C, tunnel ionization from the C atom side is enhanced; a hump structure originating from multielectron interaction is then formed on the top of the field-induced distorted barrier of the HOMO effective potential. This hump formation, responsible for the directional anisotropy of tunnel ionization, restrains the influence of the linear Stark effect on the energy shifts of bound states.
Issaoui, Noureddine; Ghalla, Houcine; Muthu, S; Flakus, H T; Oujia, Brahim
2015-02-05
In this work, the molecular structure, harmonic vibrational frequencies, UV, NBO and AIM of 3-thiophenecarboxilic acid (abbreviated as 3-TCA) monomer and dimer has been investigated. The FT-IR and FT-Raman spectra were recorded. The ground-state molecular geometry and vibrational frequencies have been calculated by using the Hartree-Fock (HF) and density functional theory (DFT)/B3LYP methods and 6-311++G(d,p) as a basis set. The fundamental vibrations were assigned on the basis of the total energy distribution (TED) of the vibrational modes, calculated with VEDA program. Comparison of the observed fundamental vibrational frequencies of 3-TCA with calculated results by HF and DFT methods indicates that B3LYP is better to HF method for molecular vibrational problems. The difference between the observed and scaled wavenumber values is very small. The theoretically predicted FT-IR and FT-Raman spectra of the title compound have been constructed. A study on the Mulliken atomic charges, the electronic properties were performed by time-dependent DFT (TD-DFT) approach, frontier molecular orbitals (HOMO-LUMO), molecular electrostatic potential (MEP) and thermodynamic properties have been performed. The electric dipole moment (μ) and the first hyperpolarizability (β) values of the investigated molecule have been also computed. Copyright © 2014 Elsevier B.V. All rights reserved.
Hartree-Fock description of superdeformed states
International Nuclear Information System (INIS)
Dobaczewski, J.; Meyer, J.
1991-10-01
The discovery of superdeformation has been preceded by theoretical predictions made in Nilsson-Strutinsky calculations and a description of the phenomenon still constitutes an exciting challenge to the theory of nuclear collective motion. In particular, a determination of electromagnetic transition rates requires a knowledge of microscopic collective wave functions, which can be achieved by using the Hartree-Fock (HF) theory and the generator coordinate method (GCM). In this study we present results of our calculations concerning the properties and superdeformed states in the mercury region. Using the GCM, we diagonalize the microscopic two-body hamiltonian within the basis set of constrained HF+BCS wave functions. The GCM provides values for the energy of the ground and excited states including the shape isomer which take into account the effect of correlations in the collective degree of freedom. The GCM will also allow us to discuss the qualitative modifications of the shape isomeric stability as induced by changes in pairing correlations
Derivative discontinuity with localized Hartree-Fock potential.
Nazarov, V U; Vignale, G
2015-08-14
The localized Hartree-Fock potential has proven to be a computationally efficient alternative to the optimized effective potential, preserving the numerical accuracy of the latter and respecting the exact properties of being self-interaction free and having the correct -1/r asymptotics. In this paper we extend the localized Hartree-Fock potential to fractional particle numbers and observe that it yields derivative discontinuities in the energy as required by the exact theory. The discontinuities are numerically close to those of the computationally more demanding Hartree-Fock method. Our potential enjoys a "direct-energy" property, whereby the energy of the system is given by the sum of the single-particle eigenvalues multiplied by the corresponding occupation numbers. The discontinuities c↑ and c↓ of the spin-components of the potential at integer particle numbers N↑ and N↓ satisfy the condition c↑N↑ + c↓N↓ = 0. Thus, joining the family of effective potentials which support a derivative discontinuity, but being considerably easier to implement, the localized Hartree-Fock potential becomes a powerful tool in the broad area of applications in which the fundamental gap is an issue.
Yoshida, Tatsusada; Hayashi, Takahisa; Mashima, Akira; Sasahara, Katsunori; Chuman, Hiroshi
2016-01-15
Accurate prediction of the intermolecular interaction energy (ΔEbind) has been a challenging and serious problem. Current in silico drug screening demands efficient and accurate evaluation of ΔEbind for ligands and their target proteins. It is desirable that ΔEbind including the dispersion interaction energy (Edisp) is calculated using a post-Hartree-Fock (HF) theory, such as the high-order coupled-cluster one, with a larger basis set. However, it remains computationally too expensive to apply such a one to large molecular systems. As another problem, it is necessary to consider the contribution of the basis set superposition error (BSSE) in calculation of ΔEbind. In Bioorg. Med. Chem. Lett. 2014 and 2015, we proposed simple and efficient corrections of dispersion and BSSE for the HF theory, which is not able to express the dispersion interaction energy correctly. The current Letter, as the final one in the series, aims to verify the HF theory enhanced by the dispersion correction (HF-Dtq) in the light of reproducibility of 'accurate' intermolecular ligand-protein interaction energy values, with comprehensive comparison with the MP2 and recently proposed various DFT-D theories. Taking ΔEbind calculated with the coupled-cluster theory coupled with a complete basis set as a reference, ΔEbind of over a hundred small sized noncovalent complexes as well as real ligand-protein complexes models was systematically examined in terms of accuracy and computational cost. The comprehensive comparison in the current work showed that HF-Dtq is a practical and reliable approach for in silico drug screening and quantitative structure-activity relationships. Copyright © 2015 Elsevier Ltd. All rights reserved.
Prospects for Brueckner-Hartree-Fock calculations in the Density Matrix Expansion approach
Zhang, Yinu; Dyhdalo, Alex; Bogner, Scott; Furnstahl, Richard
2017-09-01
Recently, a microscopically based nuclear energy density functional was derived by applying the Density Matrix Expansion (DME) to the Hartree-Fock energy obtained from chiral effective field theory (χEFT) two- and three-nucleon interactions. The Hartree-Fock approach cannot contain the full many-body correlations. Brueckner-Hartree-Fock (BHF) theory gives an improved definition of the one-body potential U by replacing the interaction by a reaction matrix G. The central result of modern renormalization theory is that a general RG decoupling generates an infinite series of counterterms consistent with the input interaction. Then we can apply the DME at Hartree-Fock level with long-range χEFT interactions and zero-range contact interactions to model BHF correlations. This work was supported in part by the National Science Foundation under Grant No. PHY-1614460 and the NUCLEI SciDAC Collaboration under Department of Energy Grant DE-SC0008533.
International Nuclear Information System (INIS)
Lara-Castells, María Pilar de; Bartolomei, Massimiliano; Mitrushchenkov, Alexander O.; Stoll, Hermann
2015-01-01
The accuracy and transferability of the electronic structure approach combining dispersionless density functional theory (DFT) [K. Pernal et al., Phys. Rev. Lett. 103, 263201 (2009)] with the method of increments [H. Stoll, J. Chem. Phys. 97, 8449 (1992)], are validated for the interaction between the noble-gas Ne, Ar, Kr, and Xe atoms and coronene/graphene/graphite surfaces. This approach uses the method of increments for surface cluster models to extract intermonomer dispersion-like (2- and 3-body) correlation terms at coupled cluster singles and doubles and perturbative triples level, while periodic dispersionless density functionals calculations are performed to estimate the sum of Hartree-Fock and intramonomer correlation contributions. Dispersion energy contributions are also obtained using DFT-based symmetry-adapted perturbation theory [SAPT(DFT)]. An analysis of the structure of the X/surface (X = Ne, Ar, Kr, and Xe) interaction energies shows the excellent transferability properties of the leading intermonomer correlation contributions across the sequence of noble-gas atoms, which are also discussed using the Drude oscillator model. We further compare these results with van der Waals-(vdW)-corrected DFT-based approaches. As a test of accuracy, the energies of the low-lying nuclear bound states supported by the laterally averaged X/graphite potentials (X = 3 He, 4 He, Ne, Ar, Kr, and Xe) are calculated and compared with the best estimations from experimental measurements and an atom-bond potential model using the ab initio-assisted fine-tuning of semiempirical parameters. The bound-state energies determined differ by less than 6–7 meV (6%) from the atom-bond potential model. The crucial importance of including incremental 3-body dispersion-type terms is clearly demonstrated, showing that the SAPT(DFT) approach effectively account for these terms. With the deviations from the best experimental-based estimations smaller than 2.3 meV (1.9%), the accuracy of
de Lara-Castells, María Pilar; Bartolomei, Massimiliano; Mitrushchenkov, Alexander O; Stoll, Hermann
2015-11-21
The accuracy and transferability of the electronic structure approach combining dispersionless density functional theory (DFT) [K. Pernal et al., Phys. Rev. Lett. 103, 263201 (2009)] with the method of increments [H. Stoll, J. Chem. Phys. 97, 8449 (1992)], are validated for the interaction between the noble-gas Ne, Ar, Kr, and Xe atoms and coronene/graphene/graphite surfaces. This approach uses the method of increments for surface cluster models to extract intermonomer dispersion-like (2- and 3-body) correlation terms at coupled cluster singles and doubles and perturbative triples level, while periodic dispersionless density functionals calculations are performed to estimate the sum of Hartree-Fock and intramonomer correlation contributions. Dispersion energy contributions are also obtained using DFT-based symmetry-adapted perturbation theory [SAPT(DFT)]. An analysis of the structure of the X/surface (X = Ne, Ar, Kr, and Xe) interaction energies shows the excellent transferability properties of the leading intermonomer correlation contributions across the sequence of noble-gas atoms, which are also discussed using the Drude oscillator model. We further compare these results with van der Waals-(vdW)-corrected DFT-based approaches. As a test of accuracy, the energies of the low-lying nuclear bound states supported by the laterally averaged X/graphite potentials (X = (3)He, (4)He, Ne, Ar, Kr, and Xe) are calculated and compared with the best estimations from experimental measurements and an atom-bond potential model using the ab initio-assisted fine-tuning of semiempirical parameters. The bound-state energies determined differ by less than 6-7 meV (6%) from the atom-bond potential model. The crucial importance of including incremental 3-body dispersion-type terms is clearly demonstrated, showing that the SAPT(DFT) approach effectively account for these terms. With the deviations from the best experimental-based estimations smaller than 2.3 meV (1.9%), the accuracy of
Energy Technology Data Exchange (ETDEWEB)
Lara-Castells, María Pilar de, E-mail: Pilar.deLara.Castells@csic.es; Bartolomei, Massimiliano [Instituto de Física Fundamental (C.S.I.C.), Serrano 123, E-28006 Madrid (Spain); Mitrushchenkov, Alexander O. [Laboratoire Modélisation et Simulation Multi Echelle, Université Paris-Est, MSME UMR 8208 CNRS, 5 bd Descartes, 77454 Marne-la-Vallée (France); Stoll, Hermann [Institut für Theoretische Chemie, Universität Stuttgart, D-70550 Stuttgart (Germany)
2015-11-21
The accuracy and transferability of the electronic structure approach combining dispersionless density functional theory (DFT) [K. Pernal et al., Phys. Rev. Lett. 103, 263201 (2009)] with the method of increments [H. Stoll, J. Chem. Phys. 97, 8449 (1992)], are validated for the interaction between the noble-gas Ne, Ar, Kr, and Xe atoms and coronene/graphene/graphite surfaces. This approach uses the method of increments for surface cluster models to extract intermonomer dispersion-like (2- and 3-body) correlation terms at coupled cluster singles and doubles and perturbative triples level, while periodic dispersionless density functionals calculations are performed to estimate the sum of Hartree-Fock and intramonomer correlation contributions. Dispersion energy contributions are also obtained using DFT-based symmetry-adapted perturbation theory [SAPT(DFT)]. An analysis of the structure of the X/surface (X = Ne, Ar, Kr, and Xe) interaction energies shows the excellent transferability properties of the leading intermonomer correlation contributions across the sequence of noble-gas atoms, which are also discussed using the Drude oscillator model. We further compare these results with van der Waals-(vdW)-corrected DFT-based approaches. As a test of accuracy, the energies of the low-lying nuclear bound states supported by the laterally averaged X/graphite potentials (X = {sup 3}He, {sup 4}He, Ne, Ar, Kr, and Xe) are calculated and compared with the best estimations from experimental measurements and an atom-bond potential model using the ab initio-assisted fine-tuning of semiempirical parameters. The bound-state energies determined differ by less than 6–7 meV (6%) from the atom-bond potential model. The crucial importance of including incremental 3-body dispersion-type terms is clearly demonstrated, showing that the SAPT(DFT) approach effectively account for these terms. With the deviations from the best experimental-based estimations smaller than 2.3 meV (1.9%), the
Existence of Hartree-Fock excited states for atoms and molecules
Lewin, Mathieu
2017-10-01
For neutral and positively charged atoms and molecules, we prove the existence of infinitely many Hartree-Fock critical points below the first energy threshold (that is, the lowest energy of the same system with one electron removed). This is the equivalent, in Hartree-Fock theory, of the famous Zhislin-Sigalov theorem which states the existence of infinitely many eigenvalues below the bottom of the essential spectrum of the N-particle linear Schrödinger operator. Our result improves a theorem of Lions in 1987 who already constructed infinitely many Hartree-Fock critical points, but with much higher energy. Our main contribution is the proof that the Hartree-Fock functional satisfies the Palais-Smale property below the first energy threshold. We then use minimax methods in the N-particle space, instead of working in the one-particle space.
Qualitative breakdown of the unrestricted Hartree-Fock energy.
Mori-Sánchez, Paula; Cohen, Aron J
2014-10-28
The stretching of closed-shell molecules is a qualitative problem for restricted Hartree-Fock that is usually circumvented by the use of unrestricted Hartree-Fock (UHF). UHF is well known to break the spin symmetry at the Coulson-Fischer point, leading to a discontinuous derivative in the potential energy surface and incorrect spin density. However, this is generally not considered as a major drawback. In this work, we present a set of two electron molecules which magnify the problem of symmetry breaking and lead to drastically incorrect potential energy surfaces with UHF. These molecules also fail with unrestricted density-functional calculations where a functional such as B3LYP gives both symmetry breaking and an unphysically low energy due to the delocalization error. The implications for density functional theory are also discussed.
Hartree--Fock density matrix equation
International Nuclear Information System (INIS)
Cohen, L.; Frishberg, C.
1976-01-01
An equation for the Hartree--Fock density matrix is discussed and the possibility of solving this equation directly for the density matrix instead of solving the Hartree--Fock equation for orbitals is considered. Toward that end the density matrix is expanded in a finite basis to obtain the matrix representative equation. The closed shell case is considered. Two numerical schemes are developed and applied to a number of examples. One example is given where the standard orbital method does not converge while the method presented here does
Non-linearity of the Hartree-Fock equations. Multiple Hartree-Fock solutions.
de Andrade, Micael D; Sobrinho, Antonio M de C; Malbouisson, Luiz A C
2017-09-26
We determined multiple closed-shell Hartree-Fock-Roothaan solutions for the systems: BH, FH, LiH, and OH - , considering double and triple zeta bases. To calculate them, we used the self-consistent field method and the algebraic method. The Hartree-Fock solutions obtained were classified with respect to the kind of extreme. All these extremes generate the same configuration interaction space. Our key objective in this work is to illustrate that it is possible to obtain a wide variety of Hartree-Fock solutions for any molecular system.
Hartree-Fock description of spin systems
Energy Technology Data Exchange (ETDEWEB)
Hirsch, J.G.; Castanos, O.; Lopez P, R.; Jimenez F, O. [Instituto de Ciencias Nucleares, Universidad Nacional Autonoma de Mexico, Apartado Postal 70-543 Mexico 04510 D.F. (Mexico); Lopez M, E. [Departamento de Fisica, Facultad de Ciencias, Universidad Nacional Autonoma de Mexico, Apartado Postal 70-542 Mexico 04510 D.F. (Mexico)]. e-mail: hirsch@nucleares.unam.mx
2007-12-15
A mean-field treatment of a general spin Hamiltonian containing linear and quadratic terms is presented. The equivalence between atomic coherent states and Hartree-Fock states is explicitly demonstrated. The relevance of symmetry restoration is exhibited. Entanglement properties at the different phases are briefly discussed. (Author)
Huntington, Lee M J; Krupička, Martin; Neese, Frank; Izsák, Róbert
2017-11-07
The similarity transformed equation of motion coupled-cluster approach is extended for applications to high-spin open-shell systems, within the unrestricted Hartree-Fock (UHF) formalism. An automatic active space selection scheme has also been implemented such that calculations can be performed in a black-box fashion. It is observed that both the canonical and automatic active space selecting similarity transformed equation of motion (STEOM) approaches perform about as well as the more expensive equation of motion coupled-cluster singles doubles (EOM-CCSD) method for the calculation of the excitation energies of doublet radicals. The automatic active space selecting UHF STEOM approach can therefore be employed as a viable, lower scaling alternative to UHF EOM-CCSD for the calculation of excited states in high-spin open-shell systems.
Huntington, Lee M. J.; Krupička, Martin; Neese, Frank; Izsák, Róbert
2017-11-01
The similarity transformed equation of motion coupled-cluster approach is extended for applications to high-spin open-shell systems, within the unrestricted Hartree-Fock (UHF) formalism. An automatic active space selection scheme has also been implemented such that calculations can be performed in a black-box fashion. It is observed that both the canonical and automatic active space selecting similarity transformed equation of motion (STEOM) approaches perform about as well as the more expensive equation of motion coupled-cluster singles doubles (EOM-CCSD) method for the calculation of the excitation energies of doublet radicals. The automatic active space selecting UHF STEOM approach can therefore be employed as a viable, lower scaling alternative to UHF EOM-CCSD for the calculation of excited states in high-spin open-shell systems.
Hartree-Fock calculations of nuclear masses
Quentin, P
1976-01-01
Hartree-Fock calculations pertaining to the determination of nuclear binding energies throughout the whole chart of nuclides are reviewed. Such an approach is compared with other methods. Main techniques in use are shortly presented. Advantages and drawbacks of these calculations are also discussed with a special emphasis on the extrapolation towards nuclei far from the stability valley. Finally, a discussion of some selected results from light to superheavy nuclei, is given.
Hartree-Fock calculations of nuclear masses
International Nuclear Information System (INIS)
Quentin, P.
1976-01-01
Hartree-Fock calculations pertaining to the determination of nuclear binding energies throughout the whole chart of nuclides are reviewed. Such an approach is compared with other methods. Main techniques in use are shortly presented. Advantages and drawbacks of these calculations are also discussed with a special emphasis on the extrapolation towards nuclei far from the stability valley. Finally, a discussion of some selected results from light to superheavy nuclei, is given [fr
The any particle molecular orbital grid-based Hartree-Fock (APMO-GBHF) approach.
Posada, Edwin; Moncada, Félix; Reyes, Andrés
2018-02-28
The any particle molecular orbital grid-based Hartree-Fock approach (APMO-GBHF) is proposed as an initial step to perform multi-component post-Hartree-Fock, explicitly correlated, and density functional theory methods without basis set errors. The method has been applied to a number of electronic and multi-species molecular systems. Results of these calculations show that the APMO-GBHF total energies are comparable with those obtained at the APMO-HF complete basis set limit. In addition, results reveal a considerable improvement in the description of the nuclear cusps of electronic and non-electronic densities.
Efficient Implementation of Variation after Projection Generalized Hartree-Fock.
Lestrange, Patrick J; Williams-Young, David B; Petrone, Alessio; Jiménez-Hoyos, Carlos A; Li, Xiaosong
2018-02-13
Projected Hartree-Fock (PHF) theory can restore important symmetries to broken symmetry wave functions. Variation after projection (VAP) implementations make it possible to deliberately break and then restore a given symmetry by directly minimizing the projected energy expression. This technique can be applied to any symmetry that can be broken from relaxing constraints on single Slater determinant wave functions. For instance, generalized Hartree-Fock (GHF) wave functions are eigenfunctions of neither Ŝ z nor S 2 . By relaxing these constraints, the wave function can explore a larger variational space and can reach lower energies than more constrained HF solutions. We have implemented spin-projected GHF (SGHF), which retains many of the advantages of breaking symmetry while also being a spin eigenfunction, with some notable improvements over previous implementations. Our new algorithm involves the formation of new intermediate matrices not previously discussed in the literature. Discretization of the necessary integration over the rotation group SO(3) is also accomplished much more efficiently using Lebedev grids. A novel scheme to incrementally build rotated Fock matrices is also introduced and compared with more standard approaches.
An algebraic method for solving Hartree-Fock-Roothaan equations
International Nuclear Information System (INIS)
Malbouisson, L.; Vianna, J.D.M.
1990-01-01
A mathematical method for studying of Hartree - Fock equations in LCAO approximation is presented. The method provides Hartree - Fock - Roothaan solutions for any occupancy scheme and does not use ordering rules of the usual iterative self-consistent procedures. Equations and applications for closed-shell configuration are considered explicitly
Computational Nuclear Physics and Post Hartree-Fock Methods
Lietz, Justin G.; Novario, Samuel; Jansen, Gustav R.; Hagen, Gaute; Hjorth-Jensen, Morten
We present a computational approach to infinite nuclear matter employing Hartree-Fock theory, many-body perturbation theory and coupled cluster theory. These lectures are closely linked with those of Chaps. 9, 10 and 11 and serve as input for the correlation functions employed in Monte Carlo calculations in Chap. 9, the in-medium similarity renormalization group theory of dense fermionic systems of Chap. 10 and the Green's function approach in Chap. 11 We provide extensive code examples and benchmark calculations, allowing thereby an eventual reader to start writing her/his own codes. We start with an object-oriented serial code and end with discussions on strategies for porting the code to present and planned high-performance computing facilities.
Computational Nuclear Physics and Post Hartree-Fock Methods
Energy Technology Data Exchange (ETDEWEB)
Lietz, Justin [Michigan State University; Sam, Novario [Michigan State University; Hjorth-Jensen, M. [University of Oslo, Norway; Hagen, Gaute [ORNL; Jansen, Gustav R. [ORNL
2017-05-01
We present a computational approach to infinite nuclear matter employing Hartree-Fock theory, many-body perturbation theory and coupled cluster theory. These lectures are closely linked with those of chapters 9, 10 and 11 and serve as input for the correlation functions employed in Monte Carlo calculations in chapter 9, the in-medium similarity renormalization group theory of dense fermionic systems of chapter 10 and the Green's function approach in chapter 11. We provide extensive code examples and benchmark calculations, allowing thereby an eventual reader to start writing her/his own codes. We start with an object-oriented serial code and end with discussions on strategies for porting the code to present and planned high-performance computing facilities.
Parallel scalability of Hartree-Fock calculations.
Chow, Edmond; Liu, Xing; Smelyanskiy, Mikhail; Hammond, Jeff R
2015-03-14
Quantum chemistry is increasingly performed using large cluster computers consisting of multiple interconnected nodes. For a fixed molecular problem, the efficiency of a calculation usually decreases as more nodes are used, due to the cost of communication between the nodes. This paper empirically investigates the parallel scalability of Hartree-Fock calculations. The construction of the Fock matrix and the density matrix calculation are analyzed separately. For the former, we use a parallelization of Fock matrix construction based on a static partitioning of work followed by a work stealing phase. For the latter, we use density matrix purification from the linear scaling methods literature, but without using sparsity. When using large numbers of nodes for moderately sized problems, density matrix computations are network-bandwidth bound, making purification methods potentially faster than eigendecomposition methods.
The Hartree-Fock approximation applied to nuclear structure problems
International Nuclear Information System (INIS)
Oliveira, D.R. de.
1972-01-01
The Hartree-Fock indepedent-particle state basis is firstly constructed, whose wave functions are expressed as linear combinations of states of a Known basis. The coefficients of these combinations are reals e from themselves the Hartree-Fock density matrix is defined. The symmetries which characterize the system in study are embedded in these coefficients and in the density matrix. The formalism is applied to the Ne 20 , Si 28 and Ar 36 nuclei whose lowest Hartree-Fock energies are obtained admitting that theirs wave functions having axial symmetry. Once known the Hartree-Fock wave function, states are projected from it with well-defined total angular momentum using the Peierls and Yoccoz method. From these wave functions energy levels of the ground band are calculated as well as the electric quadrupole transition probabilities among these levels. (L.C.) [pt
DEFF Research Database (Denmark)
Miyagi, Haruhide; Madsen, Lars Bojer
2013-01-01
We present the time-dependent restricted-active-space self-consistent-field (TD-RASSCF) theory as a framework for the time-dependent many-electron problem. The theory generalizes the multiconfigurational time-dependent Hartree-Fock (MCTDHF) theory by incorporating the restricted-active-space scheme...... well known in time-independent quantum chemistry. Optimization of the orbitals as well as the expansion coefficients at each time step makes it possible to construct the wave function accurately while using only a relatively small number of electronic configurations. In numerical calculations of high...
Caffarel, Michel; Giner, Emmanuel; Scemama, Anthony; Ramírez-Solís, Alejandro
2014-12-09
We present a comparative study of the spatial distribution of the spin density of the ground state of CuCl2 using Density Functional Theory (DFT), quantum Monte Carlo (QMC), and post-Hartree-Fock wave function theory (WFT). A number of studies have shown that an accurate description of the electronic structure of the lowest-lying states of this molecule is particularly challenging due to the interplay between the strong dynamical correlation effects in the 3d shell and the delocalization of the 3d hole over the chlorine atoms. More generally, this problem is representative of the difficulties encountered when studying open-shell metal-containing molecular systems. Here, it is shown that qualitatively different results for the spin density distribution are obtained from the various quantum-mechanical approaches. At the DFT level, the spin density distribution is found to be very dependent on the functional employed. At the QMC level, Fixed-Node Diffusion Monte Carlo (FN-DMC) results are strongly dependent on the nodal structure of the trial wave function. Regarding wave function methods, most approaches not including a very high amount of dynamic correlation effects lead to a much too high localization of the spin density on the copper atom, in sharp contrast with DFT. To shed some light on these conflicting results Full CI-type (FCI) calculations using the 6-31G basis set and based on a selection process of the most important determinants, the so-called CIPSI approach (Configuration Interaction with Perturbative Selection done Iteratively) are performed. Quite remarkably, it is found that for this 63-electron molecule and a full CI space including about 10(18) determinants, the FCI limit can almost be reached. Putting all results together, a natural and coherent picture for the spin distribution is proposed.
Approximate singly excited states from a two-component Hartree-Fock reference.
Goings, Joshua J; Ding, Feizhi; Davidson, Ernest R; Li, Xiaosong
2015-10-14
For many molecules, relaxing the spin symmetry constraint on the wave function results in the lowest energy mean-field solution. The two-component Hartree-Fock (2cHF) method relaxes all spin symmetry constraints, and the wave function is no longer an eigenfunction of the total spin, spin projection, or time-reversal symmetry operators. For ground state energies, 2cHF is a superior mean-field method for describing spin-frustrated molecules. For excited states, the utility of 2cHF is uncertain. Here, we implement the 2cHF extensions of two single-reference excited state methods, the two-component configuration interaction singles and time-dependent Hartree-Fock. We compare the results to the analogous methods based off of the unrestricted Hartree-Fock approximation, as well as the full configuration interaction for three small molecules with distinct 2cHF solutions, and discuss the nature of the 2cHF excited state solutions.
Janesko, Benjamin G; Proynov, Emil
2017-02-07
Density functional approximations (DFAs) often suffer from self-repulsion and delocalization errors which are reduced by exact (Hartree-Fock-like) exchange admixture. Oyeyemi and co-workers recently showed that several DFAs with little exact exchange incorrectly predict bent alkynyl radical geometries, giving errors in ab initio composite methods using density functional theory geometries [V. B. Oyeyemi et al., J. Phys. Chem. Lett. 3, 289 (2012)]. We show that the simple Hartree-Fock-Slater and Xα DFAs, which have substantial delocalization error, predict linear alkynyl radical geometries without incorporating exact exchange. Our Rung 3.5 DFAs, and rescaled generalized gradient approximations, can give either linear σ, bent σ-π, or nearly linear π radicals, all without incorporating exact exchange. This highlights the complexity of delocalization error, the utility of accurate empirical DFA geometries for ab initio composite methods, and the insights to be gained from Rung 3.5 DFAs.
Linearized Jastrow-style fluctuations on spin-projected Hartree-Fock.
Henderson, Thomas M; Scuseria, Gustavo E
2013-12-21
The accurate and efficient description of strong electronic correlations remains an important objective in electronic structure theory. Projected Hartree-Fock theory, where symmetries of the Hamiltonian are deliberately broken and projectively restored, all with a mean-field computational scaling, shows considerable promise in this regard. However, the method is neither size extensive nor size consistent; in other words, the correlation energy per particle beyond broken-symmetry mean field vanishes in the thermodynamic limit, and the dissociation limit of a molecule is not the sum of the fragment energies. These two problems are closely related. Recently, Neuscamman [Phys. Rev. Lett. 109, 203001 (2012)] has proposed a method to cure the lack of size consistency in the context of the antisymmetrized geminal power wave function (equivalent to number-projected Hartree-Fock-Bogoliubov) by using a Jastrow-type correlator in Hilbert space. Here, we apply the basic idea in the context of projected Hartree-Fock theory, linearizing the correlator for computational simplicity but extending it to include spin fluctuations. Results are presented for the Hubbard Hamiltonian and for some simple molecular systems.
Linearized Jastrow-style fluctuations on spin-projected Hartree-Fock
International Nuclear Information System (INIS)
Henderson, Thomas M.; Scuseria, Gustavo E.
2013-01-01
The accurate and efficient description of strong electronic correlations remains an important objective in electronic structure theory. Projected Hartree-Fock theory, where symmetries of the Hamiltonian are deliberately broken and projectively restored, all with a mean-field computational scaling, shows considerable promise in this regard. However, the method is neither size extensive nor size consistent; in other words, the correlation energy per particle beyond broken-symmetry mean field vanishes in the thermodynamic limit, and the dissociation limit of a molecule is not the sum of the fragment energies. These two problems are closely related. Recently, Neuscamman [Phys. Rev. Lett. 109, 203001 (2012)] has proposed a method to cure the lack of size consistency in the context of the antisymmetrized geminal power wave function (equivalent to number-projected Hartree-Fock-Bogoliubov) by using a Jastrow-type correlator in Hilbert space. Here, we apply the basic idea in the context of projected Hartree-Fock theory, linearizing the correlator for computational simplicity but extending it to include spin fluctuations. Results are presented for the Hubbard Hamiltonian and for some simple molecular systems
Semiclassical approximations in a mean-field theory with collision terms
International Nuclear Information System (INIS)
Galetti, D.
1986-01-01
Semiclassical approximations in a mean-field theory with collision terms are discussed taking the time dependent Hartree-Fock method as framework in the obtainment of the relevant parameters.(L.C.) [pt
Hartree-Fock treatment of Fermi polarons using the Lee-Low-Pine transformation
Kain, Ben; Ling, Hong Y.
2017-09-01
We consider the Fermi polaron problem at zero temperature, where a single impurity interacts with noninteracting host fermions. We approach the problem starting with a Fröhlich-like Hamiltonian where the impurity is described with canonical position and momentum operators. We apply the Lee-Low-Pine (LLP) transformation to change the fermionic Fröhlich Hamiltonian into the fermionic LLP Hamiltonian, which describes a many-body system containing host fermions only. We adapt the self-consistent Hartree-Fock (HF) approach, first proposed by Edwards, to the fermionic LLP Hamiltonian in which a pair of host fermions with momenta k and k' interact with a potential proportional to k .k' . We apply the HF theory, which has the advantage of not restricting the number of particle-hole pairs, to repulsive Fermi polarons in one dimension. When the impurity and host fermion masses are equal our variational ansatz, where HF orbitals are expanded in terms of free-particle states, produces results in excellent agreement with McGuire's exact analytical results based on the Bethe ansatz. This work raises the prospect of using the HF ansatz and its time-dependent generalization as building blocks for developing all-coupling theories for both equilibrium and nonequilibrium Fermi polarons in higher dimensions.
Divide-and-Conquer Hartree-Fock Calculations on Proteins
He, Xiao; Merz, Kenneth M.
2010-01-01
The ability to perform ab initio electronic structure calculations that scales linearly with the system size is one of the central aims in theoretical chemistry. In this study, the implementation of the divide-and-conquer (DC) algorithm, an algorithm with the potential to aid the achievement of true linear scaling within Hartree-Fock (HF) theory is revisited. Standard HF calculations solve the Roothaan-Hall equations for the whole system; in the DC-HF approach, the diagonalization of the Fock matrix is carried out on smaller subsystems. The DC algorithm for HF calculations was validated on polyglycines, polyalanines and eleven real three-dimensional proteins of up to 608 atoms in this work. We also found that a fragment-based initial guess using molecular fractionation with conjugated caps (MFCC) method significantly reduces the number of SCF cycles and even is capable of achieving convergence for some globular proteins where the simple superposition of atomic densities (SAD) initial guess fails. PMID:20401160
Rolke, J.; Zheng, Y.; Brion, C. E.; Shi, Z.; Wolfe, Saul; Davidson, E. R.
1999-06-01
The momentum distributions of the valence orbitals of methanol have been studied by electron momentum spectroscopy (EMS) and Hartree-Fock (HF), multi-reference singles and doubles configuration interaction (MRSD-CI), localized valence bond (VB) and density functional theory (DFT) calculations. The experiment was performed using a multichannel EMS spectrometer at a total energy of 1200 eV plus the binding energy. Binding-energy spectra measured in the energy range of 6-47 eV are presented for the azimuthal angles φ=0° and φ=8°. Synthetic binding-energy spectra from Green's function and HF calculations for the azimuthal angles φ=0° and φ=8° in the 6-47 eV energy region are also compared to experiment. In the inner valence region strong splitting of the 4a' and 3a' ionization is observed due to final-state electron correlation effects. The measured momentum profiles are compared with HF calculations at the level of the target HF approximation using basis sets ranging from simple (STO-3G) to large (110-GTO and Trun-pV5Z). DFT calculations at the level of the target Kohn-Sham approximation employing the local density approximation or hybrid functional methods and the large Trun-pV5Z basis set are also compared to experiment. The effects of electron correlation and relaxation are also investigated in the outer valence region by MRSD-CI calculations of the full ion-neutral overlap amplitude using the 110-G(CI) basis set. The shapes of all momentum profiles are well predicted by higher level theory. Some small discrepancy still exists between all theoretical treatments and experiment in the low-momentum region for the HOMO 2a″ orbital. MRSD-CI or DFT (i.e. correlated) methods are needed to adequately describe the shape of the 7a' and (6a'+1a″) momentum profiles. The s-type character in the 5a' momentum profile is underestimated by HF theory and overemphasized by density functional theory (DFT). The 110-G(CI) calculation best predicts the shape for the 5a
DEFF Research Database (Denmark)
Miyagi, Haruhide; Madsen, Lars Bojer
We have developed a new theoretical framework for time-dependent many-electron problems named time-dependent restricted-active-space self-consistent field (TD-RASSCF) theory. The theory generalizes the multicongurational time-dependent Hartree-Fock (MCTDHF) theory by truncating the expansion...... at a specific excitation level. In a numerical application to laser-driven electron dynamics of the one-dimensional beryllium atom, the TD-RASSCF method performs accurately while largely reducing the computational complexity compared to the MCTDHF method....
Gomez, John A; Degroote, Matthias; Zhao, Jinmo; Qiu, Yiheng; Scuseria, Gustavo E
2017-08-23
Our overarching goal is to be able to describe both weak and strong correlation with a single, computationally affordable method without sacrificing important qualities of the wavefunction, e.g. symmetries of the Hamiltonian. We know that coupled cluster theory with low-order excitations is excellent at describing weakly-correlated systems near equilibrium, but breaks down as systems become more strongly correlated. Projected Hartree-Fock on the other hand is inherently capable of describing multireference character, but misses weak correlation. We are thus exploring how best to combine coupled cluster and projected Hartree-Fock in our search for a computationally feasible method that is applicable across a wide range of correlation strengths. In this manuscript, we adapt our earlier work on the pairing Hamiltonian to repulsive Hamiltonians, resulting in the spin polynomial similarity transformation (SpinPoST) interpolation. SpinPoST parameterizes the wavefunction in order to interpolate between the coupled cluster and spin-projected unrestricted Hartree-Fock ansätze self consistently, and is a spin-symmetry adapted model which involves only single and double excitations. We employ a unique approach of optimizing the wavefunction by minimizing the effect of connected quadruple excitations, resulting in a method which is spin-symmetry adapted and is comparable energetically to coupled cluster with singles and doubles for weak correlation and spin-projected Hartree-Fock for strong correlation.
Energy Technology Data Exchange (ETDEWEB)
Barbosa, Rugles Cesar
2002-07-01
The present thesis is divided into two parts. The first part describes the many kind of the formalisms of the Generator Coordinate Hartree-Fock method (GCHFM) and second part describes the computational aspect applied to the GCHFM formalism in its discreet form. The major aim of this work is the development of an alternative method to non-linear parameters optimization (basis set) and later uses these optimized parameters to adjust the weight function into GCHFM method. The study of the weight function when N {yields} {infinity} (or for large N), where N represents the number of mesh, is important since the GCHFM theory in its continuous form depend on understanding of such behavior. In this thesis, a detailed study is carried out about the methodologies of the self-consistent solution of the GCHFM and some methodology aspects of non-linear parameters optimization. This work shows that the Generator Coordinate Hartree-Fock method is general and it has as particular case the Hartree-Fock Roothaan method. Some possible variations or combinations around of the characteristics of the GCHFM and a comparison with conventional SCF procedure are reported in this thesis. The piecewise weight function method developed in this work shows to be very good for collective parameter optimizations of the Generator Coordinate (GC). The GCHFM calculations are necessary restrict (GCM-RHF), especially when the calculated value energies approach of its numerical values or Hartree-Fock limit. In the optimization methods of state functions for atomic electronic systems is very common the application of the gradient method and its efficacy is not contested. However, the method describes above allow us to obtain results as good as the gradient method. The basis set generated using the piecewise weight function method for Gaussian type function were used in the Restrict Hartree-Fock (RHF) calculations to obtain the total energies for some atomic electronic systems, such as neutron atoms and
International Nuclear Information System (INIS)
Barbosa, Rugles Cesar
2002-01-01
The present thesis is divided into two parts. The first part describes the many kind of the formalisms of the Generator Coordinate Hartree-Fock method (GCHFM) and second part describes the computational aspect applied to the GCHFM formalism in its discreet form. The major aim of this work is the development of an alternative method to non-linear parameters optimization (basis set) and later uses these optimized parameters to adjust the weight function into GCHFM method. The study of the weight function when N → ∞ (or for large N), where N represents the number of mesh, is important since the GCHFM theory in its continuous form depend on understanding of such behavior. In this thesis, a detailed study is carried out about the methodologies of the self-consistent solution of the GCHFM and some methodology aspects of non-linear parameters optimization. This work shows that the Generator Coordinate Hartree-Fock method is general and it has as particular case the Hartree-Fock Roothaan method. Some possible variations or combinations around of the characteristics of the GCHFM and a comparison with conventional SCF procedure are reported in this thesis. The piecewise weight function method developed in this work shows to be very good for collective parameter optimizations of the Generator Coordinate (GC). The GCHFM calculations are necessary restrict (GCM-RHF), especially when the calculated value energies approach of its numerical values or Hartree-Fock limit. In the optimization methods of state functions for atomic electronic systems is very common the application of the gradient method and its efficacy is not contested. However, the method describes above allow us to obtain results as good as the gradient method. The basis set generated using the piecewise weight function method for Gaussian type function were used in the Restrict Hartree-Fock (RHF) calculations to obtain the total energies for some atomic electronic systems, such as neutron atoms and ions in
Koopmans' theorem in the Hartree-Fock method. General formulation
Plakhutin, Boris N.
2018-03-01
This work presents a general formulation of Koopmans' theorem (KT) in the Hartree-Fock (HF) method which is applicable to molecular and atomic systems with arbitrary orbital occupancies and total electronic spin including orbitally degenerate (OD) systems. The new formulation is based on the full set of variational conditions imposed upon the HF orbitals by the variational principle for the total energy and the conditions imposed by KT on the orbitals of an ionized electronic shell [B. N. Plakhutin and E. R. Davidson, J. Chem. Phys. 140, 014102 (2014)]. Based on these conditions, a general form of the restricted open-shell HF method is developed, whose eigenvalues (orbital energies) obey KT for the whole energy spectrum. Particular attention is paid to the treatment of OD systems, for which the new method gives a number of unexpected results. For example, the present method gives four different orbital energies for the triply degenerate atomic level 2p in the second row atoms B to F. Based on both KT conditions and a parallel treatment of atoms B to F within a limited configuration interaction approach, we prove that these four orbital energies, each of which is triply degenerate, are related via KT to the energies of different spin-dependent ionization and electron attachment processes (2p)N → (2p ) N ±1. A discussion is also presented of specific limitations of the validity of KT in the HF method which arise in OD systems. The practical applicability of the theory is verified by comparing KT estimates of the ionization potentials I2s and I2p for the second row open-shell atoms Li to F with the relevant experimental data.
Exact-exchange time-dependent density-functional theory with the frequency-dependent kernel
International Nuclear Information System (INIS)
Shigeta, Yasuteru; Hirao, Kimihiko; Hirata, So
2006-01-01
The effects of the adiabatic approximation in time-dependent density-functional theory (TDDFT) on dynamic polarizabilities and van der Waals C 6 coefficients have been analyzed quantitatively. These effects are shown to be small in the off-resonance region of the perturbation frequencies by comparing the results from the exact-exchange TDDFT employing the optimized effective potentials and the corresponding frequency-dependent kernel [time-dependent optimized effective potentials (TDOEP)] and those from the frequency-independent kernel [adiabatic TDOEP (ATDOEP)]. The magnitude of the computed dynamic polarizabilities near the static limit is found to be in the order: time-dependent Hartree-Fock (TDHF)>ATDOEP>TDOEP, whereas that of C 6 is: TDHF>TDOEP>ATDOEP
Energy Technology Data Exchange (ETDEWEB)
Tretiak, Sergei [Los Alamos National Laboratory
2008-01-01
Four different numerical algorithms suitable for a linear scaling implementation of time-dependent Hartree-Fock and Kohn-Sham self-consistent field theories are examined. We compare the performance of modified Lanczos, Arooldi, Davidson, and Rayleigh quotient iterative procedures to solve the random-phase approximation (RPA) (non-Hermitian) and Tamm-Dancoff approximation (TDA) (Hermitian) eigenvalue equations in the molecular orbital-free framework. Semiempirical Hamiltonian models are used to numerically benchmark algorithms for the computation of excited states of realistic molecular systems (conjugated polymers and carbon nanotubes). Convergence behavior and stability are tested with respect to a numerical noise imposed to simulate linear scaling conditions. The results single out the most suitable procedures for linear scaling large-scale time-dependent perturbation theory calculations of electronic excitations.
Deformed Brueckner-Hartree-Fock calculation for light nuclei
Braley, R. C.; Ford, W. F.; Becker, R. L.; Patterson, M. R.
1971-01-01
For the first time the Brueckner-Hartree-Fock (BHF) method was applied to nuclei whose intrinsic structure is nonspherical. One aim was to investigate whether the energy dependent reaction matrix calculated from a realistic nucleon-nucleon interaction leads to deformations similar to, or different from, those obtained from energy independent interactions in Hartree-Fock (HF) calculations. Reaction matrix elements were calculated as a function of starting energy for the Hamada-Johnston interaction, using a Pauli operator appropriate to O-16 and a shifted oscillator spectrum for virtual excited states. Binding energies, single-particle energies, radii, and shape deformations of the intrinsic state in unrenormalized as well as renormalized BHF are discussed and compared with previous HF studies. Results are presented for C-12, O-16, and Ne-20.
Stability of the complex generalized Hartree-Fock equations.
Goings, Joshua J; Ding, Feizhi; Frisch, Michael J; Li, Xiaosong
2015-04-21
For molecules with complex and competing magnetic interactions, it is often the case that the lowest energy Hartree-Fock solution may only be obtained by removing the spin and time-reversal symmetry constraints of the exact non-relativistic Hamiltonian. To do so results in the complex generalized Hartree-Fock (GHF) method. However, with the loss of variational constraints comes the greater possibility of converging to higher energy minima. Here, we report the implementation of stability test of the complex GHF equations, along with an orbital update scheme should an instability be found. We apply the methodology to finding the local minima of several spin-frustrated hydrogen rings, as well as the non-collinear molecular magnet Cr3, illustrating the utility of the broken symmetry GHF method and some of its lesser-known nuances.
Spin contamination in unrestricted Hartree-Fock calculations.
Schug, J. C.; Phillips, D. H.
1973-01-01
Several pi-electron doublets are treated by both the unrestricted Hartree-Fock method and the restricted approximation of Longuet-Higgins and Pople. For two of the molecules, which contain oxygen heteroatoms, serious spin contamination occurs in the UHF wavefunctions, and this negates the usefulness of the single annihilation procedure that is often used for spin-density calculations. The restricted approximation provides a convenient alternative, especially because configuration interaction is easily taken into account.
How good are Hartree-Fock charge densities
International Nuclear Information System (INIS)
Campi, X.
1975-01-01
The principle characteristics of Hartree-Fock charge densities (mean square radius, surface thickness, quantum fluctuation) calculated using different effective interactions are discussed in terms of their nuclear matter properties (Fermi momentum, effective mass, incompressibility). A comparison with the experimental charge distributions is made. Differences between the charge densities of neighbouring nuclei (isotope and isotone shifts) are also considered and the main factors governing these effects are discussed [fr
The Hartree-Fock seniority method and its foundation
International Nuclear Information System (INIS)
Gomez, J.M.G.; Prieto, C.
1987-01-01
The seniority scheme is discussed in the framewok of quasi-spin formalism. It is shown that the ground-state wave function of the seniority scheme can be determined self-consistently from a set of Hartree-Fock seniority equations derived from the variational prinicple. The method takes into account the mean-field and the pairing correlations in nuclei at the same time. Angular momentum and particle number are exactly conserved. (author)
A finite-temperature Hartree-Fock code for shell-model Hamiltonians
Bertsch, G. F.; Mehlhaff, J. M
2016-01-01
The codes HFgradZ.py and HFgradT.py find axially symmetric minima of a Hartree-Fock energy functional for a Hamiltonian supplied in a shell-model basis. The functional to be minimized is the Hartree-Fock energy for zero-temperature properties or the Hartree-Fock grand potential for finite-temperature properties. Various constraints may be imposed on the minima.
Two-component hybrid time-dependent density functional theory within the Tamm-Dancoff approximation
Energy Technology Data Exchange (ETDEWEB)
Kühn, Michael [Institut für Physikalische Chemie, Karlsruher Institut für Technologie, Kaiserstraße 12, 76131 Karlsruhe (Germany); Weigend, Florian, E-mail: florian.weigend@kit.edu [Institut für Physikalische Chemie, Karlsruher Institut für Technologie, Kaiserstraße 12, 76131 Karlsruhe (Germany); Institut für Nanotechnologie, Karlsruher Institut für Technologie, Postfach 3640, 76021 Karlsruhe (Germany)
2015-01-21
We report the implementation of a two-component variant of time-dependent density functional theory (TDDFT) for hybrid functionals that accounts for spin-orbit effects within the Tamm-Dancoff approximation (TDA) for closed-shell systems. The influence of the admixture of Hartree-Fock exchange on excitation energies is investigated for several atoms and diatomic molecules by comparison to numbers for pure density functionals obtained previously [M. Kühn and F. Weigend, J. Chem. Theory Comput. 9, 5341 (2013)]. It is further related to changes upon switching to the local density approximation or using the full TDDFT formalism instead of TDA. Efficiency is demonstrated for a comparably large system, Ir(ppy){sub 3} (61 atoms, 1501 basis functions, lowest 10 excited states), which is a prototype molecule for organic light-emitting diodes, due to its “spin-forbidden” triplet-singlet transition.
CRYSCOR: a program for the post-Hartree-Fock treatment of periodic systems.
Pisani, Cesare; Schütz, Martin; Casassa, Silvia; Usvyat, Denis; Maschio, Lorenzo; Lorenz, Marco; Erba, Alessandro
2012-06-07
Cryscor is a periodic post-Hartree-Fock program based on local functions in direct space, i.e., Wannier functions and projected atomic orbitals. It uses atom centered Gaussians as basis functions. The Hartree-Fock reference, as well as symmetry information, is provided by the Crystal program. Cryscor presently features an efficient and parallel implementation of periodic local second order Møller-Plesset perturbation theory (MP2), which allows us to study 1D-, 2D- and 3D-periodic systems beyond 1000 basis functions per unit cell. Apart from the correlation energy also the MP2 density matrix, and from that the Compton profile, are available. Very recently, a new module for calculating excitonic band gaps at the uncorrelated Configuration-Interaction-Singles (CIS) level has been added. Other advancements include new extrapolation techniques for calculating surface adsorption on semi-infinite solids. In this paper the diverse features and recent advances of the present Cryscor version are illustrated by exemplary applications to various systems: the adsorption of an argon monolayer on the MgO (100) surface, the rolling energy of a boron nitride nanoscroll, the relative stability of different aluminosilicates, the inclusion energy of methane in methane-ice-clathrates, and the effect of electron correlation on charge and momentum density of α-quartz. Furthermore, we present some first tentative CIS results for excitonic band gaps of simple 3D-crystals, and their dependence on the diffuseness of the basis set.
Predicting singlet-triplet energy splittings with projected Hartree-Fock methods.
Rivero, Pablo; Jiménez-Hoyos, Carlos A; Scuseria, Gustavo E
2013-08-22
Hartree-Fock (HF) and density functional theory (DFT) methods are known for having problems in predicting singlet-triplet energy splittings when the system displays significant diradical character. Multireference methods are traditionally advocated to deal with the spin-contamination problem inherent in broken-symmetry mean-field methods. In the present work, spin-contamination is rigorously eliminated by means of a symmetry projection approach, carried out in a variation-after-projection fashion, recently implemented in our research group. We here explore the performance of a variety of projected Hartree-Fock (PHF) approaches (SUHF, KSUHF, SGHF, and KSGHF) in predicting singlet-triplet energy gaps in a broad set of diradical systems: small diatomic molecules, carbenes and silenes, and a few larger molecules (trimethylenemethane and benzyne isomers). For most of these systems, accurate experimental data is available in the literature. Additionally, we assess the quality of the geometrical parameters obtained in SUHF-based optimizations for some of the systems considered. Our results indicate that PHF methods yield high-quality multireference wave functions, providing a good description of the ground state potential surface as well as an accurate singlet-triplet splitting gap, all within a modest mean-field computational cost.
Exponential convergence and acceleration of Hartree-Fock calculations
International Nuclear Information System (INIS)
Bonaccorso, A.; Di Toro, M.; Lomnitz-Adler, J.
1979-01-01
It is shown that one can expect an exponential behaviour for the convergence of the Hartree-Fock solution during the HF iteration procedure. This property is used to extrapolate some collective degrees of freedom, in this case the shape, in order to speed up the self-consistent calculation. For axially deformed nuclei the method is applied to the quadrupole moment which corresponds to a simple scaling transformation on the single particle wave functions. Results are shown for the deformed nuclei 20 Ne and 28 Si with a Skyrme interaction. (Auth.)
Hartree-Fock-Bogoliubov approximation for finite systems
International Nuclear Information System (INIS)
Bulgac, A.
1980-08-01
The features of the spectrum of the Hartree-Fock-Bogoliubov equations are examined. Special attention is paid to the asymptotic behaviours of the single quasiparticle wave functions (s.qp.w.fs.), matter density distribution and density of the pair condensate. It is shown that, due to the coupling between hole and particle, the sufficiently deeply bound hole states acquire a width and consequently have to be treated as continuum states. The proper normalization of the s.qp.w.fs. is discussed. (author)
A Hartree-Fock program for atomic structure calculations
International Nuclear Information System (INIS)
Mitroy, J.
1999-01-01
The Hartree-Fock equations for a general open shell atom are described. The matrix equations that result when the single particle orbitals are written in terms of a linear combination of analytic basis functions are derived. Attention is paid to the complexities that occur when open shells are present. The specifics of a working FORTRAN program which is available for public use are described. The program has the flexibility to handle either Slater-type orbitals or Gaussian-type orbitals. It can be obtained over the internet at http://lacebark.ntu.edu.au/j_mitroy/research/atomic.htm Copyright (1999) CSIRO Australia
International Nuclear Information System (INIS)
Chacon-Taylor, M.R.; McCarthy, M.I.
1995-01-01
The energetics of the H 2 O/MgO(001), HCl/MgO(001), and NH 3 /MgO(001) interface were investigated using the ab initio periodic Hartree-Fock LCAO method and a classical interaction energy model. The QM calculations treated a system that was periodic in two dimensions with the adsorbate approaching a three-layer slab of MgO(001). The authors used an approximation to the classical interaction energy, where the surface is represented by its potential, electric field, and electric field derivatives at the positions of the molecule center of mass, and the molecule is described by its charge, electric dipole, electric quadrupole and polarizability. The potential, electric field and electric field gradient are obtained for the clean three-layer slab using the ab initio periodic Hartree-Fock LCAO method (CRYSTAL) and an optimized split valence basis 8-61G on Mg and 8-51G on O. The charge, electric dipole, and electric quadrupole are calculated using ab initio Hartree-Fock theory (GAUSSIAN-92) with a 6-31G* basis set while the SCF polarizability is determined analytically using the same basis set
On the relation between the Hartree-Fock and Kohn-Sham approaches
Energy Technology Data Exchange (ETDEWEB)
Amusia, M.Ya. [Racah Institute of Physics, Hebrew University, 91904 Jerusalem (Israel); A.F. Ioffe Physical-Technical Institute, 194021 St. Petersburg (Russian Federation); Msezane, A.Z. [CTSPS, Clark Atlanta University, Atlanta, GA 30314 (United States); Shaginyan, V.R. [CTSPS, Clark Atlanta University, Atlanta, GA 30314 (United States); Petersburg Nuclear Physics Institute, 188300 Gatchina (Russian Federation)]. E-mail: vrshag@thd.pnpi.spb.ru; Sokolovski, D. [Queen' s University of Belfast, Belfast BT7 1NN (United Kingdom)
2004-09-13
We show that the Hartree-Fock (HF) results cannot be reproduced within the framework of Kohn-Sham (KS) theory because the single-particle densities of finite systems obtained within the HF calculations are not v-representable, i.e., do not correspond to any ground state of a N non-interacting electron systems in a local external potential. For this reason, the KS theory, which finds a minimum on a different subset of all densities, can overestimate the ground state energy, as compared to the HF result. The discrepancy between the two approaches provides no grounds to assume that either the KS theory or the density functional theory suffers from internal contradictions.
On the relation between the Hartree-Fock and Kohn-Sham approaches
International Nuclear Information System (INIS)
Amusia, M.Ya.; Msezane, A.Z.; Shaginyan, V.R.; Sokolovski, D.
2004-01-01
We show that the Hartree-Fock (HF) results cannot be reproduced within the framework of Kohn-Sham (KS) theory because the single-particle densities of finite systems obtained within the HF calculations are not v-representable, i.e., do not correspond to any ground state of a N non-interacting electron systems in a local external potential. For this reason, the KS theory, which finds a minimum on a different subset of all densities, can overestimate the ground state energy, as compared to the HF result. The discrepancy between the two approaches provides no grounds to assume that either the KS theory or the density functional theory suffers from internal contradictions
The Gogny-Hartree-Fock-Bogoliubov nuclear-mass model
Energy Technology Data Exchange (ETDEWEB)
Goriely, S. [Universite Libre de Bruxelles, Institut d' Astronomie et d' Astrophysique, CP-226, Brussels (Belgium); Hilaire, S.; Girod, M.; Peru, S. [CEA, DAM, DIF, Arpajon (France)
2016-07-15
We present the Gogny-Hartree-Fock-Bogoliubov model which reproduces nuclear masses with an accuracy comparable with the best mass formulas. In contrast to the Skyrme-HFB nuclear-mass models, an explicit and self-consistent account of all the quadrupole correlation energies is included within the 5D collective Hamiltonian approach. The final rms deviation with respect to the 2353 measured masses is 789 keV in the 2012 atomic mass evaluation. In addition, the D1M Gogny force is shown to predict nuclear and neutron matter properties in agreement with microscopic calculations based on realistic two- and three-body forces. The D1M properties and its predictions of various observables are compared with those of D1S and D1N. (orig.)
Toroidal Superheavy Nuclei in Skyrme-Hartree-Fock Approach
International Nuclear Information System (INIS)
Staszczak, A.; Wong, Cheuk-Yin
2009-01-01
Within the self-consistent constraint Skyrme-Hartree-Fock+BCS model (SHF+BCS), we found equilibrium toroidal nuclear density distributions in the region of superheavy elements. For nuclei with a sufficient oblate deformation (Q 20 < -200 b), it becomes energetically favorable to change the genus of nuclear surface from 0 to 1, i.e., to switch the shape from a biconcave disc to a torus. The energy of the toroidal (genus=1) SHF+BCS solution relative to the compact (genus=0) ground state energy is strongly dependent both on the atomic number Z and the mass number A. We discuss the region of Z and A where the toroidal SHF+BCS total energy begins to be a global minimum
Computation of Large Molecules with the Hartree-Fock Model
Clementi, Enrico
1972-01-01
The usual way to compute Hartree-Fock type functions for molecules is by an expansion of the one-electron functions (molecular orbitals) in a linear combination of analytical functions (LCAO-MO-SCF, linear combination of atomic orbitals—Molecular Orbital—Self Consistent field). The expansion coefficients are obtained variationally. This technique requires the computation of several multicenter two-electron integrals (representing the electron-electron interaction) proportional to the fourth power of the basis set size. There are several types of basis sets; the Gaussian type introduced by S. F. Boys is used herein. Since it requires from a minimum of 10 (or 15) Gaussian-type functions to about 25 (or 30) Gaussian functions to describe a second-row atom in a molecule, the fourth power dependency of the basis set has been the de facto bottleneck of quantum chemical computations in the last decade. In this paper, the concept is introduced of a “dynamical” basis set, which allows for drastic computational simplifications while retaining full numerical accuracy. Examples are given that show that computational saving in computer time of more than a factor of one hundred is achieved and that large basis sets (up to the order of several hundred Gaussian functions per molecule) can be used routinely. It is noted that the limitation in the Hartree-Fock energy (correlation energy error) can be easily computed by use of a statistical model introduced by Wigner for solid-state systems in 1934. Thus, large molecules can now be simulated by computational techniques without reverting to semi-empirical parameterization and without requiring enormous computational time and storage. PMID:16592020
Directory of Open Access Journals (Sweden)
Thomas Gomez
2018-04-01
Full Text Available Atomic structure of N-electron atoms is often determined by solving the Hartree-Fock equations, which are a set of integro-differential equations. The integral part of the Hartree-Fock equations treats electron exchange, but the Hartree-Fock equations are not often treated as an integro-differential equation. The exchange term is often approximated as an inhomogeneous or an effective potential so that the Hartree-Fock equations become a set of ordinary differential equations (which can be solved using the usual shooting methods. Because the Hartree-Fock equations are an iterative-refinement method, the inhomogeneous term relies on the previous guess of the wavefunction. In addition, there are numerical complications associated with solving inhomogeneous differential equations. This work uses matrix methods to solve the Hartree-Fock equations as an integro-differential equation. It is well known that a derivative operator can be expressed as a matrix made of finite-difference coefficients; energy eigenvalues and eigenvectors can be obtained by using linear-algebra packages. The integral (exchange part of the Hartree-Fock equation can be approximated as a sum and written as a matrix. The Hartree-Fock equations can be solved as a matrix that is the sum of the differential and integral matrices. We compare calculations using this method against experiment and standard atomic structure calculations. This matrix method can also be used to solve for free-electron wavefunctions, thus improving how the atoms and free electrons interact. This technique is important for spectral line broadening in two ways: it improves the atomic structure calculations, and it improves the motion of the plasma electrons that collide with the atom.
Density-Based Multilevel Hartree-Fock Model.
Sæther, Sandra; Kjærgaard, Thomas; Koch, Henrik; Høyvik, Ida-Marie
2017-11-14
We introduce a density-based multilevel Hartree-Fock (HF) method where the electronic density is optimized in a given region of the molecule (the active region). Active molecular orbitals (MOs) are generated by a decomposition of a starting guess atomic orbital (AO) density, whereas the inactive MOs (which constitute the remainder of the density) are never generated or referenced. The MO formulation allows for a significant dimension reduction by transforming from the AO basis to the active MO basis. All interactions between the inactive and active regions of the molecule are retained, and an exponential parametrization of orbital rotations ensures that the active and inactive density matrices separately, and in sum, satisfy the symmetry, trace, and idempotency requirements. Thus, the orbital spaces stay orthogonal, and furthermore, the total density matrix represents a single Slater determinant. In each iteration, the (level-shifted) Newton equations in the active MO basis are solved to obtain the orbital transformation matrix. The approach is equivalent to variationally optimizing only a subset of the MOs of the total system. In this orbital space partitioning, no bonds are broken and no a priori orbital assignments are carried out. In the limit of including all orbitals in the active space, we obtain an MO density-based formulation of full HF.
Hartree-Fock symmetry breaking around conical intersections
Jake, Lena C.; Henderson, Thomas M.; Scuseria, Gustavo E.
2018-01-01
We study the behavior of Hartree-Fock (HF) solutions in the vicinity of conical intersections. These are here understood as regions of a molecular potential energy surface characterized by degenerate or nearly degenerate eigenfunctions with identical quantum numbers (point group, spin, and electron numbers). Accidental degeneracies between states with different quantum numbers are known to induce symmetry breaking in HF. The most common closed-shell restricted HF instability is related to singlet-triplet spin degeneracies that lead to collinear unrestricted HF solutions. Adding geometric frustration to the mix usually results in noncollinear generalized HF (GHF) solutions, identified by orbitals that are linear combinations of up and down spins. Near conical intersections, we observe the appearance of coplanar GHF solutions that break all symmetries, including complex conjugation and time-reversal, which do not carry good quantum numbers. We discuss several prototypical examples taken from the conical intersection literature. Additionally, we utilize a recently introduced magnetization diagnostic to characterize these solutions, as well as a solution of a Jahn-Teller active geometry of H8+2.
Auxiliary Density Matrix Methods for Hartree-Fock Exchange Calculations.
Guidon, Manuel; Hutter, Jürg; VandeVondele, Joost
2010-08-10
The calculation of Hartree-Fock exchange (HFX) is computationally demanding for large systems described with high-quality basis sets. In this work, we show that excellent performance and good accuracy can nevertheless be obtained if an auxiliary density matrix is employed for the HFX calculation. Several schemes to derive an auxiliary density matrix from a high-quality density matrix are discussed. Key to the accuracy of the auxiliary density matrix methods (ADMM) is the use of a correction based on standard generalized gradient approximations for HFX. ADMM integrates seamlessly in existing HFX codes and, in particular, can be employed in linear scaling implementations. Demonstrating the performance of the method, the effect of HFX on the structure of liquid water is investigated in detail using Born-Oppenheimer molecular dynamics simulations (300 ps) of a system of 64 molecules. Representative for large systems are calculations on a solvated protein (Rubredoxin), for which ADMM outperforms the corresponding standard HFX implementation by approximately a factor 20.
Sears, John S.; Koerzdoerfer, Thomas; Zhang, Cai-Rong; Brédas, Jean-Luc
2011-10-01
Long-range corrected hybrids represent an increasingly popular class of functionals for density functional theory (DFT) that have proven to be very successful for a wide range of chemical applications. In this Communication, we examine the performance of these functionals for time-dependent (TD)DFT descriptions of triplet excited states. Our results reveal that the triplet energies are particularly sensitive to the range-separation parameter; this sensitivity can be traced back to triplet instabilities in the ground state coming from the large effective amounts of Hartree-Fock exchange included in these functionals. As such, the use of standard long-range corrected functionals for the description of triplet states at the TDDFT level is not recommended.
Microscopic theories for collective motions of large amplitude
International Nuclear Information System (INIS)
Souza Cruz, F.F. de.
1986-01-01
The many proposals of ''Collective Paths'' that have appeared in literature, were derived through a local analysis of the Time Dependent Hartree Fock dynamics. Those proposals were compared and validity conditions obtained for Semiclassical Hamiltonians which have only quadratic terms in momenta. A careful analysis of the parametrization of Slater Determinants allowed us to exploit the geometrical features of the Time Dependent Hartree Fock Theory and construct the Paths in a covariant way. The analysis was applied to a three level model (Su(3)). (author) [pt
Zheng, Xiao; Zhou, Ting; Yang, Weitao
2013-05-07
A nonempirical scaling correction (SC) approach has been developed for improving bandgap prediction in density functional theory [X. Zheng, A. J. Cohen, P. Mori-Sánchez, X. Hu, and W. Yang, Phys. Rev. Lett. 107, 026403 (2011)]. For finite systems such as atoms and molecules, the SC approach restores the Perdew-Parr-Levy-Balduz condition [Phys. Rev. Lett. 49, 1691 (1982)] that the total electronic energy should scale linearly with number of electrons between integers. Although the original SC approach is applicable to a variety of mainstream density functional approximations, it gives zero correction to the Hartree-Fock method. This is because the relaxation of orbitals with the change in electron number is completely neglected. In this work, with an iterative scheme for the evaluation of Fukui function, the orbital relaxation effects are accounted for explicitly via a perturbative treatment. In doing so, the SC approach is extended to density functionals involving substantial amount of Hartree-Fock exchange. Our new SC approach is demonstrated to improve systematically the predicted Kohn-Sham frontier orbital energies, and alleviate significantly the mismatch between fundamental and derivative gaps.
Exploration of (super-)heavy elements using the Skyrme-Hartree-Fock model
International Nuclear Information System (INIS)
Erler, Jochen
2011-01-01
Motivated by the steadily increasing number of known nuclei and nuclear properties, theories of nuclear structure are presently a field of intense research. This work concentrates on the self-consistent description of nuclei in terms of the Skyrme-Hartree-Fock (SHF) approach. The extrapolation of nuclear shell structure to the region of super-heavy elements (SHE) using the SHF model, the dependence on different parameterization and the influence of collective correlation will be studied. The general scope of this work are large scale calculation for a global survey of properties of SHE like binding energies, separation energies and decay characteristics and lifetimes. These calculations were done in a collaboration with the theory group of the GSI in Darmstadt and have the aim to develop a database of lifetimes and reaction rates for α, β-decay and spontaneous fission in a very wide range with proton numbers 86 ≤ Z ≤ 120 and neutron numbers up to N ∼ 260 relevant for the astrophysical r-process. The results of this study for example predictions of a possible islands of very stable nuclei and information of favored decay mode for each nuclei are also applicable in the recent experimental synthesis of exotic SHE. For these calculation a framework to calculate β-decay half-lives within the SHF model has been developed and the existing axial SHF code has been extended to compute β-transition matrix elements and so to provide an estimation of half-lives. (orig.)
Exploration of (super-)heavy elements using the Skyrme-Hartree-Fock model
Energy Technology Data Exchange (ETDEWEB)
Erler, Jochen
2011-01-31
Motivated by the steadily increasing number of known nuclei and nuclear properties, theories of nuclear structure are presently a field of intense research. This work concentrates on the self-consistent description of nuclei in terms of the Skyrme-Hartree-Fock (SHF) approach. The extrapolation of nuclear shell structure to the region of super-heavy elements (SHE) using the SHF model, the dependence on different parameterization and the influence of collective correlation will be studied. The general scope of this work are large scale calculation for a global survey of properties of SHE like binding energies, separation energies and decay characteristics and lifetimes. These calculations were done in a collaboration with the theory group of the GSI in Darmstadt and have the aim to develop a database of lifetimes and reaction rates for {alpha}, {beta}-decay and spontaneous fission in a very wide range with proton numbers 86 {<=} Z {<=} 120 and neutron numbers up to N {approx} 260 relevant for the astrophysical r-process. The results of this study for example predictions of a possible islands of very stable nuclei and information of favored decay mode for each nuclei are also applicable in the recent experimental synthesis of exotic SHE. For these calculation a framework to calculate {beta}-decay half-lives within the SHF model has been developed and the existing axial SHF code has been extended to compute {beta}-transition matrix elements and so to provide an estimation of half-lives. (orig.)
Parallel and Low-Order Scaling Implementation of Hartree-Fock Exchange Using Local Density Fitting.
Köppl, Christoph; Werner, Hans-Joachim
2016-07-12
Calculations using modern linear-scaling electron-correlation methods are often much faster than the necessary reference Hartree-Fock (HF) calculations. We report a newly implemented HF program that speeds up the most time-consuming step, namely, the evaluation of the exchange contributions to the Fock matrix. Using localized orbitals and their sparsity, local density fitting (LDF), and atomic orbital domains, we demonstrate that the calculation of the exchange matrix scales asymptotically linearly with molecular size. The remaining parts of the HF calculation scale cubically but become dominant only for very large molecular sizes or with many processing cores. The method is well parallelized, and the speedup scales well with up to about 100 CPU cores on multiple compute nodes. The effect of the local approximations on the accuracy of computed HF and local second-order Møller-Plesset perturbation theory energies is systematically investigated, and default values are established for the parameters that determine the domain sizes. Using these values, calculations for molecules with hundreds of atoms in combination with triple-ζ basis sets can be carried out in less than 1 h, with just a few compute nodes. The method can also be used to speed up density functional theory calculations with hybrid functionals that contain HF exchange.
Bubble nuclei within the self-consistent Hartree-Fock mean field plus pairing approach
Phuc, L. Tan; Hung, N. Quang; Dang, N. Dinh
2018-02-01
The depletion of the nuclear density at its center, called the nuclear bubble, is studied within the Skyrme Hartree-Fock mean field consistently incorporating the superfluid pairing. The latter is obtained within the finite-temperature Bardeen-Cooper-Schrieffer theory and within the approach using the exact pairing. The numerical calculations are carried out for 22O and 34Si nuclei, whose bubble structures, caused by a very low occupancy of the 2 s1 /2 level, were previously predicted at T =0 . Among 24 Skyrme interactions under consideration, the MSk3 is the only one which reproduces the experimentally measured occupancy of the 2 s1 /2 proton level as well as the binding energy, and consequently produces the most pronounced bubble structure in 34Si. As compared to the approaches employing the same BSk14 interaction, our approach with exact pairing predicts a pairing effect which is stronger in 22O and weaker in 34Si. The increase in temperature depletes the bubble structure and completely washes it out when the temperature reaches a critical value, at which the factor measuring the depletion of the nucleon density vanishes.
Cho, Daeheum; Ko, Kyoung Chul; Ikabata, Yasuhiro; Wakayama, Kazufumi; Yoshikawa, Takeshi; Nakai, Hiromi; Lee, Jin Yong
2015-01-14
The intramolecular magnetic coupling constant (J) of diradical systems linked with five- or six-membered aromatic rings was calculated to obtain the scaling factor (experimental J/calculated J ratio) for various density functional theory (DFT) functionals. Scaling factors of group A (PBE, TPSSh, B3LYP, B97-1, X3LYP, PBE0, and BH&HLYP) and B (M06-L, M06, M06-2X, and M06-HF) were shown to decrease as the amount of Hartree-Fock exact exchange (HFx) increases, in other words, overestimation of calculated J becomes more severe as the HFx increases. We further investigated the effect of HFx fraction of DFT functional on J value, spin contamination, and spin density distributions by comparing the B3LYP analogues containing different amount of HFx. It was revealed that spin contamination and spin densities at each atom increases as the HFx increases. Above all, newly developed BLYP-5 functional, which has 5% of HFx, was found to have the scaling factor of 1.029, indicating that calculated J values are very close to that of experimental values without scaling. BLYP-5 has potential to be utilized for accurate evaluation of intramolecular magnetic coupling constant (J) of diradicals linked by five- or six-membered aromatic ring couplers.
Ground-State Charge Transfer: Lithium-Benzene and the Role of Hartree-Fock Exchange.
Borca, Carlos H; Slipchenko, Lyudmila V; Wasserman, Adam
2016-10-07
Most approximations to the exchange-correlation functional of Kohn-Sham density functional theory lead to delocalization errors that undermine the description of charge-transfer phenomena. We explore how various approximate functionals and charge-distribution schemes describe ground-state atomic-charge distributions in the lithium-benzene complex, a model system of relevance to carbon-based supercapacitors. To understand the trends, we compare Hartree-Fock (HF) and correlated post-HF calculations, confirming that the HOMO-LUMO gap is narrower in semilocal functionals but widened by hybrid functionals with large fractions of HF exchange. For semilocal functionals, natural bond orbital (NBO) and Mulliken schemes yield opposite pictures of how charge transfer occurs. In PBE, for example, when lithium and benzene are <1.5 Å apart, NBO yields a positive charge on the lithium atom, but the Mulliken scheme yields a negative charge. Furthermore, the partial charges in conjugated materials depend on the interplay between the charge-distribution scheme employed and the underlying exchange-correlation functional, being critically sensitive to the admixture of HF exchange. We analyze and explain why this happens, discuss implications, and conclude that hybrid functionals with an admixture of about one-fourth of HF exchange are particularly useful in describing charge transfer in the lithium-benzene model.
General technique for analytical derivatives of post-projected Hartree-Fock.
Tsuchimochi, Takashi; Ten-No, Seiichiro
2017-02-21
In electronic structure theory, the availability of an analytical derivative is one of the desired features for a method to be useful in practical applications, as it allows for geometry optimization as well as computation of molecular properties. With the recent advances in the development of symmetry-projected Hartree-Fock (PHF) methods, we here aim at further extensions by devising the analytic gradients of post-PHF approaches with a special focus on spin-extended (spin-projected) configuration interaction with single and double substitutions (ECISD). Just like standard single-reference methods, the mean-field PHF part does not require the corresponding coupled-perturbed equation to be solved, while the correlation energy term needs the orbital relaxation effect to be accounted for, unless the underlying molecular orbitals are variationally optimized in the presence of the correlation energy. We present a general strategy for post-PHF analytical gradients, which closely parallels that for single-reference methods, yet addressing the major difference between them. The similarity between ECISD and multi-reference CI not only in the energy but also in the optimized geometry is clearly demonstrated by the numerical examples of ozone and cyclobutadiene.
Linear-response time-dependent density-functional theory with pairing fields.
Peng, Degao; van Aggelen, Helen; Yang, Yang; Yang, Weitao
2014-05-14
Recent development in particle-particle random phase approximation (pp-RPA) broadens the perspective on ground state correlation energies [H. van Aggelen, Y. Yang, and W. Yang, Phys. Rev. A 88, 030501 (2013), Y. Yang, H. van Aggelen, S. N. Steinmann, D. Peng, and W. Yang, J. Chem. Phys. 139, 174110 (2013); D. Peng, S. N. Steinmann, H. van Aggelen, and W. Yang, J. Chem. Phys. 139, 104112 (2013)] and N ± 2 excitation energies [Y. Yang, H. van Aggelen, and W. Yang, J. Chem. Phys. 139, 224105 (2013)]. So far Hartree-Fock and approximated density-functional orbitals have been utilized to evaluate the pp-RPA equation. In this paper, to further explore the fundamentals and the potential use of pairing matrix dependent functionals, we present the linear-response time-dependent density-functional theory with pairing fields with both adiabatic and frequency-dependent kernels. This theory is related to the density-functional theory and time-dependent density-functional theory for superconductors, but is applied to normal non-superconducting systems for our purpose. Due to the lack of the proof of the one-to-one mapping between the pairing matrix and the pairing field for time-dependent systems, the linear-response theory is established based on the representability assumption of the pairing matrix. The linear response theory justifies the use of approximated density-functionals in the pp-RPA equation. This work sets the fundamentals for future density-functional development to enhance the description of ground state correlation energies and N ± 2 excitation energies.
Conrad, Justin A; Gordon, Mark S
2015-05-28
The accuracy of the Hartree-Fock method with an empirical dispersion correction, HF-D3, to model interaction energies and locate constrained minimum geometries is tested against more conventional correlation methods, such as second-order perturbation theory and coupled cluster theory, and against the sophisticated effective fragment potential model. HF-D3 was applied to substituted-benzene dimers in both sandwich and T-shaped configurations and to DNA base pair complexes in both hydrogen bonded and stacked geometries. Overall, HF-D3 is found to be a plausible and cost efficient substitute for higher levels of electronic structure theory, such as MP2, in systems with π-π interactions.
A few methods for the theory of collective motions and collisions
International Nuclear Information System (INIS)
Giraud, B.G.
1984-01-01
In this series of lectures the time-dependent Hartree-Fock theory of nuclear motions and collisions are treated for collective motion only. For the theory of collisions a representation, the boosted shell model, is proposed in which matrix elements of the T-matrix are easier to evaluate via a variational principle
Holomorphic Hartree-Fock Theory: An Inherently Multireference Approach.
Burton, Hugh G A; Thom, Alex J W
2016-01-12
We investigate the existence of holomorphic Hartree–Fock solutions using a revised SCF algorithm. We use this algorithm to study the Hartree–Fock solutions for H2 and H42+ and report the emergence of holomorphic solutions at points of symmetry breaking. Finally, we find these holomorphic solutions for H4 and use them as a basis for Non-Orthogonal Configuration Interaction at a range of rectangular geometries and show them to produce energies in good agreement with Full Configuration Interaction.
On the behaviour of the Hartree-Fock energy at short internuclear distances
DEFF Research Database (Denmark)
Gilka, Natalie; Solovej, Jan Philip; Taylor, Peter R.
2011-01-01
There are well-established mathematical relationships for the energy of a diatomic molecule (the exact energy, but also both the Hartree-Fock and Thomas-Fermi energies) in the limit of large nuclear charge of the atoms and small internuclear distances. We present calculated energies for a number...
Assessing the accuracy of Hartree-Fock-Bogoliubov calculations by use of mass relations
DEFF Research Database (Denmark)
Hove, D.; Fedorov, D. V.; Jensen, A. S.
2014-01-01
The accuracy of three different sets of Hartree-Fock-Bogoliubov calculations of nuclear binding energies is systematically evaluated. To emphasize minor fluctuations, a second order, four-point mass relation, which almost completely eliminates smooth aspects of the binding energy, is introduced...
Kuwahara, Riichi; Tadokoro, Yoichi; Ohno, Kaoru
2014-08-28
In this paper, we calculate kinetic and potential energy contributions to the electronic ground-state total energy of several isolated atoms (He, Be, Ne, Mg, Ar, and Ca) by using the local density approximation (LDA) in density functional theory, the Hartree-Fock approximation (HFA), and the self-consistent GW approximation (GWA). To this end, we have implemented self-consistent HFA and GWA routines in our all-electron mixed basis code, TOMBO. We confirm that virial theorem is fairly well satisfied in all of these approximations, although the resulting eigenvalue of the highest occupied molecular orbital level, i.e., the negative of the ionization potential, is in excellent agreement only in the case of the GWA. We find that the wave function of the lowest unoccupied molecular orbital level of noble gas atoms is a resonating virtual bound state, and that of the GWA spreads wider than that of the LDA and thinner than that of the HFA.
Janesko, Benjamin G.
2018-02-01
Parameter-free atomistic simulations of entangled solid-state paramagnetic defects may aid in the rational design of devices for quantum information science. This work applies time-dependent density functional theory (TDDFT) embedded-cluster simulations to a prototype entangled-defect system, namely two adjacent singlet-coupled F color centers in lithium fluoride. TDDFT calculations accurately reproduce the experimental visible absorption of both isolated and coupled F centers. The most accurate results are obtained by combining spin symmetry breaking to simulate strong correlation, a large fraction of exact (Hartree-Fock-like) exchange to minimize the defect electrons' self-interaction error, and a standard semilocal approximation for dynamical correlations between the defect electrons and the surrounding ionic lattice. These results motivate application of two-reference correlated ab initio approximations to the M-center, and application of TDDFT in parameter-free simulations of more complex entangled paramagnetic defect architectures.
International Nuclear Information System (INIS)
Neese, Frank; Wennmohs, Frank; Hansen, Andreas; Becker, Ute
2009-01-01
In this paper, the possibility is explored to speed up Hartree-Fock and hybrid density functional calculations by forming the Coulomb and exchange parts of the Fock matrix by different approximations. For the Coulomb part the previously introduced Split-RI-J variant (F. Neese, J. Comput. Chem. 24 (2003) 1740) of the well-known 'density fitting' approximation is used. The exchange part is formed by semi-numerical integration techniques that are closely related to Friesner's pioneering pseudo-spectral approach. Our potentially linear scaling realization of this algorithm is called the 'chain-of-spheres exchange' (COSX). A combination of semi-numerical integration and density fitting is also proposed. Both Split-RI-J and COSX scale very well with the highest angular momentum in the basis sets. It is shown that for extended basis sets speed-ups of up to two orders of magnitude compared to traditional implementations can be obtained in this way. Total energies are reproduced with an average error of <0.3 kcal/mol as determined from extended test calculations with various basis sets on a set of 26 molecules with 20-200 atoms and up to 2000 basis functions. Reaction energies agree to within 0.2 kcal/mol (Hartree-Fock) or 0.05 kcal/mol (hybrid DFT) with the canonical values. The COSX algorithm parallelizes with a speedup of 8.6 observed for 10 processes. Minimum energy geometries differ by less than 0.3 pm in the bond distances and 0.5 deg. in the bond angels from their canonical values. These developments enable highly efficient and accurate self-consistent field calculations including nonlocal Hartree-Fock exchange for large molecules. In combination with the RI-MP2 method and large basis sets, second-order many body perturbation energies can be obtained for medium sized molecules with unprecedented efficiency. The algorithms are implemented into the ORCA electronic structure system
Dziedzic, J; Hill, Q; Skylaris, C-K
2013-12-07
We present a method for the calculation of four-centre two-electron repulsion integrals in terms of localised non-orthogonal generalised Wannier functions (NGWFs). Our method has been implemented in the ONETEP program and is used to compute the Hartree-Fock exchange energy component of Hartree-Fock and Density Functional Theory (DFT) calculations with hybrid exchange-correlation functionals. As the NGWFs are optimised in situ in terms of a systematically improvable basis set which is equivalent to plane waves, it is possible to achieve large basis set accuracy in routine calculations. The spatial localisation of the NGWFs allows us to exploit the exponential decay of the density matrix in systems with a band gap in order to compute the exchange energy with a computational effort that increases linearly with the number of atoms. We describe the implementation of this approach in the ONETEP program for linear-scaling first principles quantum mechanical calculations. We present extensive numerical validation of all the steps in our method. Furthermore, we find excellent agreement in energies and structures for a wide variety of molecules when comparing with other codes. We use our method to perform calculations with the B3LYP exchange-correlation functional for models of myoglobin systems bound with O2 and CO ligands and confirm that the same qualitative behaviour is obtained as when the same myoglobin models are studied with the DFT+U approach which is also available in ONETEP. Finally, we confirm the linear-scaling capability of our method by performing calculations on polyethylene and polyacetylene chains of increasing length.
International Nuclear Information System (INIS)
Dziedzic, J.; Hill, Q.; Skylaris, C.-K.
2013-01-01
We present a method for the calculation of four-centre two-electron repulsion integrals in terms of localised non-orthogonal generalised Wannier functions (NGWFs). Our method has been implemented in the ONETEP program and is used to compute the Hartree-Fock exchange energy component of Hartree-Fock and Density Functional Theory (DFT) calculations with hybrid exchange-correlation functionals. As the NGWFs are optimised in situ in terms of a systematically improvable basis set which is equivalent to plane waves, it is possible to achieve large basis set accuracy in routine calculations. The spatial localisation of the NGWFs allows us to exploit the exponential decay of the density matrix in systems with a band gap in order to compute the exchange energy with a computational effort that increases linearly with the number of atoms. We describe the implementation of this approach in the ONETEP program for linear-scaling first principles quantum mechanical calculations. We present extensive numerical validation of all the steps in our method. Furthermore, we find excellent agreement in energies and structures for a wide variety of molecules when comparing with other codes. We use our method to perform calculations with the B3LYP exchange-correlation functional for models of myoglobin systems bound with O 2 and CO ligands and confirm that the same qualitative behaviour is obtained as when the same myoglobin models are studied with the DFT+U approach which is also available in ONETEP. Finally, we confirm the linear-scaling capability of our method by performing calculations on polyethylene and polyacetylene chains of increasing length
Exact exchange potential evaluated from occupied Kohn-Sham and Hartree-Fock solutions
International Nuclear Information System (INIS)
Cinal, M.; Holas, A.
2011-01-01
The reported algorithm determines the exact exchange potential v x in an iterative way using energy shifts (ESs) and orbital shifts (OSs) obtained with finite-difference formulas from the solutions (occupied orbitals and their energies) of the Hartree-Fock-like equation and the Kohn-Sham-like equation, the former used for the initial approximation to v x and the latter for increments of ES and OS due to subsequent changes of v x . Thus, the need for solution of the differential equations for OSs, used by Kuemmel and Perdew [Phys. Rev. Lett. 90, 043004 (2003)], is bypassed. The iterated exchange potential, expressed in terms of ESs and OSs, is improved by modifying ESs at odd iteration steps and OSs at even steps. The modification formulas are related to the optimized-effective-potential equation (satisfied at convergence) written as the condition of vanishing density shift (DS). They are obtained, respectively, by enforcing its satisfaction through corrections to approximate OSs and by determining the optimal ESs that minimize the DS norm. The proposed method, successfully tested for several closed-(sub)shell atoms, from Be to Kr, within the density functional theory exchange-only approximation, proves highly efficient. The calculations using the pseudospectral method for representing orbitals give iterative sequences of approximate exchange potentials (starting with the Krieger-Li-Iafrate approximation) that rapidly approach the exact v x so that, for Ne, Ar, and Zn, the corresponding DS norm becomes less than 10 -6 after 13, 13, and 9 iteration steps for a given electron density. In self-consistent density calculations, orbital energies of 10 -4 hartree accuracy are obtained for these atoms after, respectively, 9, 12, and 12 density iteration steps, each involving just two steps of v x iteration, while the accuracy limit of 10 -6 to 10 -7 hartree is reached after 20 density iterations.
Fortran 90 implementation of the Hartree-Fock approach within the CNDO/2 and INDO models
Sahu, Sridhar; Shukla, Alok
2009-05-01
Despite the tremendous advances made by the ab initio theory of electronic structure of atoms and molecules, its applications are still not possible for very large systems. Therefore, semi-empirical model Hamiltonians based on the zero-differential overlap (ZDO) approach such as the Pariser-Parr-Pople, CNDO, INDO, etc. provide attractive, and computationally tractable, alternatives to the ab initio treatment of large systems. In this paper we describe a Fortran 90 computer program developed by us, that uses CNDO/2 and INDO methods to solve Hartree-Fock (HF) equation for molecular systems. The INDO method can be used for the molecules containing the first-row atoms, while the CNDO/2 method is applicable to those containing both the first-, and the second-row, atoms. We have paid particular attention to computational efficiency while developing the code, and, therefore, it allows us to perform calculations on large molecules such as C 60 on small computers within a matter of seconds. Besides being able to compute the molecular orbitals and total energies, our code is also able to compute properties such as the electric dipole moment, Mulliken population analysis, and linear optical absorption spectrum of the system. We also demonstrate how the program can be used to compute the total energy per unit cell of a polymer. The applications presented in this paper include small organic and inorganic molecules, fullerene C 60, and model polymeric systems, viz., chains containing alternating boron and nitrogen atoms (BN chain), and carbon atoms (C chain). Program summaryProgram title: cindo.x Catalogue identifier: AECN_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AECN_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 23 304 No. of bytes in distributed program
International Nuclear Information System (INIS)
Almbladh, C.-O.; Ekenberg, U.; Pedroza, A.C.
1983-01-01
The authors compare the electron densities and Hartree potentials in the local density and the Hartree-Fock approximations to the corresponding quantities obtained from more accurate correlated wavefunctions. The comparison is made for a number of two-electron atoms, Li, and for Be. The Hartree-Fock approximation is more accurate than the local density approximation within the 1s shell and for the spin polarization in Li, while the local density approximation is slightly better than the Hartree-Fock approximation for charge densities in the 2s shell. The inaccuracy of the Hartree-Fock and local density approximations to the Hartree potential is substantially smaller than the inaccuracy of the local density approximation to the ground-state exchange-correlation potential. (Auth.)
A density-dependent effective interaction for relativistic Hartree-Fock calculations
International Nuclear Information System (INIS)
Marcos, S.; Mathiot, J.F.; Lopez-Quelle, M.; Niembro, R.; Bernardos, P.
1996-01-01
We present a general method to derive density-dependent effective interactions to be used in the relativistic Hartree-Fock approximation. In the non-relativistic limit (i.e. at low density), this method is identical to the usual variational ansatz with a two-body correlation function whose range is used as a variational parameter. At normal nuclear matter density, it provides a useful prescription to fit relativistic Brueckner-Hartree-Fock calculations. It provides in particular a physical way to deal with the zero-range pieces of π and ρ interactions in the medium. We apply our method to infinite symmetric nuclear matter. This effective interaction is also particularly well suited for calculations in finite nuclei. (orig.)
Efficient Computation of Hartree-Fock Exchange Using Recursive Subspace Bisection.
Gygi, François; Duchemin, Ivan
2013-01-08
We use a recursive subspace bisection approach introduced in Phys. Rev. Lett.2009, 102, 166406 to accelerate the computation of the Hartree-Fock exchange operator in plane-wave pseudopotential electronic structure calculations. Recursive subspace bisection allows for an unbiased localization of orbitals in domains of varying size and a truncation of orbitals that preserves accuracy in a controlled manner. This representation is used to accelerate the computation of the Hartree-Fock exchange operator, which in turn makes first-principles molecular dynamics simulations based on hybrid density functionals feasible for larger systems than previously possible. We describe a parallel implementation of the method and a load balancing algorithm. The efficiency and accuracy of this approach are demonstrated in electronic structure calculations of a chloride ion solvated in liquid water and calculations of the vacancy formation energy in a 512-atom silicon crystal using the PBE0 hybrid exchange-correlation functional.
Finding symmetry breaking Hartree-Fock solutions: The case of triplet instability.
Tóth, Zsuzsanna; Pulay, Peter
2016-10-28
Determining the lowest unrestricted Hartree-Fock (UHF) solution is often difficult in even-electron systems. We have developed a deterministic method for locating approximately the UHF minimum using the restricted Hartree-Fock triplet instability matrix. The current method is truncated to fourth order. The minimum energy solution for this model can be determined by solving a small linear system of equations. This solution gives a suitable starting point to determine the exact UHF solution. This should be useful for the black-box determination of active spaces spanned by the fractionally occupied charge natural orbitals of the ground-state UHF wavefunction. The results can be generalized to higher (6th and 8th) degree expansions (odd expansion orders vanish by symmetry), and to other types of instability, including complex instability. The results are illustrated by calculations on ozone, benzene, nitrobenzene, butadiene, hexatriene, octatetraene, dichromium, and nickel porphine. Further examples are given in the supplementary material.
A hierarchic sparse matrix data structure for large-scale Hartree-Fock/Kohn-Sham calculations.
Rubensson, Emanuel H; Rudberg, Elias; Sałek, Paweł
2007-12-01
A hierarchic sparse matrix data structure for Hartree-Fock/Kohn-Sham calculations is presented. The data structure makes the implementation of matrix manipulations needed for large systems faster, easier, and more maintainable without loss of performance. Algorithms for symmetric matrix square and inverse Cholesky decomposition within the hierarchic framework are also described. The presented data structure is general; in addition to its use in Hartree-Fock/Kohn-Sham calculations, it may also be used in other research areas where matrices with similar properties are encountered. The applicability of the data structure to ab initio calculations is shown with help of benchmarks on water droplets and graphene nanoribbons. (c) 2007 Wiley Periodicals, Inc.
Hartree-Fock energies of the doubly excited states of the boron isoelectronic sequence
International Nuclear Information System (INIS)
El-Sherbini, T.M.; Mansour, H.M.; Farrag, A.A.; Rahman, A.A.
1985-08-01
Hartree-Fock energies of the 1s 2 2s 2p ns( 4 P), 1s 2 2s 2p np ( 4 P, 4 D) and 1s 2 2s 2p nd ( 4 P, 4 D); n=3-6 states in the boron isoelectronic sequence are reported. The results show a fairly good agreement with the experimental data of Bromander for O IV. (author)
Near Hartree-Fock quality GTO basis sets for the first- and third-row atoms
Partridge, Harry
1989-01-01
Energy-optimized Gaussian-type-orbital (GTO) basis sets of accuracy approaching that of numerical Hartree-Fock computations are compiled for the elements of the first and third rows of the periodic table. The methods employed in calculating the sets are explained; the applicability of the sets to electronic-structure calculations is discussed; and the results are presented in tables and briefly characterized.
Can X-ray constrained Hartree-Fock wavefunctions retrieve electron correlation?
Genoni, Alessandro; Dos Santos, Leonardo H R; Meyer, Benjamin; Macchi, Piero
2017-03-01
The X-ray constrained wavefunction (XC-WF) method proposed by Jayatilaka [Jayatilaka & Grimwood (2001) ▸, Acta Cryst. A 57 , 76-86] has attracted much attention because it represents a possible third way of theoretically studying the electronic structure of atoms and molecules, combining features of the more popular wavefunction- and DFT-based approaches. In its original formulation, the XC-WF technique extracts statistically plausible wavefunctions from experimental X-ray diffraction data of molecular crystals. A weight is used to constrain the pure Hartree-Fock solution to the observed X-ray structure factors. Despite the wavefunction being a single Slater determinant, it is generally assumed that its flexibility could guarantee the capture, better than any other experimental model, of electron correlation effects, absent in the Hartree-Fock Hamiltonian but present in the structure factors measured experimentally. However, although the approach has been known for long time, careful testing of this fundamental hypothesis is still missing. Since a formal demonstration is impossible, the validation can only be done heuristically and, to accomplish this task, X-ray constrained Hartree-Fock calculations have been performed using structure factor amplitudes computed at a very high correlation level (coupled cluster) for selected molecules in isolation, in order to avoid the perturbations due to intermolecular interactions. The results show that a single-determinant XC-WF is able to capture the electron correlation effects only partially. The largest amount of electron correlation is extracted when: (i) a large external weight is used (much larger than what has normally been used in XC-WF calculations using experimental data); and (ii) the high-order reflections, which carry less information on the electron correlation, are down-weighted (or even excluded), otherwise they would bias the fitting towards the unconstrained Hartree-Fock wavefunction.
Relativistic description of nuclear systems in the Hartree-Fock approximation
International Nuclear Information System (INIS)
Bouyssy, A.; Mathiot, J.F.; Nguyen Van Giai; Marcos, S.
1986-03-01
The structure of infinite nuclear matter and finite nuclei is studied in the framework of the relativistic Hartree-Fock approximation. A particular attention is paid to the contribution of isovector mesons. (π,p). A satisfactory description of binding energies and densities can be obtained for light as well as heavy nuclei. The spin-orbit splittings are well reproduced. Connections with non-relativistic formulations are also discussed
On the NP-completeness of the Hartree-Fock method for translationally invariant systems.
Whitfield, James Daniel; Zimborás, Zoltán
2014-12-21
The self-consistent field method utilized for solving the Hartree-Fock (HF) problem and the closely related Kohn-Sham problem is typically thought of as one of the cheapest methods available to quantum chemists. This intuition has been developed from the numerous applications of the self-consistent field method to a large variety of molecular systems. However, as characterized by its worst-case behavior, the HF problem is NP-complete. In this work, we map out boundaries of the NP-completeness by investigating restricted instances of HF. We have constructed two new NP-complete variants of the problem. The first is a set of Hamiltonians whose translationally invariant Hartree-Fock solutions are trivial, but whose broken symmetry solutions are NP-complete. Second, we demonstrate how to embed instances of spin glasses into translationally invariant Hartree-Fock instances and provide a numerical example. These findings are the first steps towards understanding in which cases the self-consistent field method is computationally feasible and when it is not.
Time-dependent restricted-active-space self-consistent-field theory with space partition
Miyagi, Haruhide; Madsen, Lars Bojer
2017-02-01
Aiming at efficient numerical analysis of time-dependent (TD) many-electron dynamics of atoms involving multielectron continua, the TD restricted-active-space self-consistent-field theory with space partition (TD-RASSCF-SP) is presented. The TD-RASSCF-SP wave function is expanded in terms of TD configuration-interaction coefficients with Slater determinants composed of two kinds of TD orbitals: M ̂ orbitals are defined to be nonvanishing in the inner region (V ̂), a small volume around the atomic nucleus, and M ˇ orbitals are nonvanishing in the large outer region (V ˇ). For detailed discussion of the SP strategy, the equations of motion are derived by two different formalisms for comparison. To ensure continuous differentiability of the wave function across the two regions, one of the formalisms makes use of the property of the finite-element discrete-variable-representation (FEDVR) functions and introduces additional time-independent orbitals. The other formalism is more general and is based on the Bloch operator as in the R -matrix theory, but turns out to be less practical for numerical applications. Hence, using the FEDVR-based formalism, the numerical performance is tested by computing double-ionization dynamics of atomic beryllium in intense light fields. To achieve high accuracy, M ̂ should be set large to take into account the strong many-electron correlation around the nucleus. On the other hand, M ˇ can be set much smaller than M ̂ for capturing the weaker correlation between the two outgoing photoelectrons. As a result, compared with more accurate multiconfigurational TD Hartree-Fock (MCTDHF) method, the TD-RASSCF-SP method may achieve comparable accuracy in the description of the double-ionization dynamics. There are, however, difficulties related to the stiffness of the equations of motion of the TD-RASSCF-SP method, which makes the required time step for this method smaller than the one needed for the MCTDHF approach.
Spin-Excitation Mechanisms in Skyrme-Force Time-Dependent Hartree-Fock
Maruhn, J. A.; Reinhard, P. -G.; Stevenson, P. D.; Strayer, M. R.
2006-01-01
We investigate the role of odd-odd (with respect to time inversion) couplings in the Skyrme force on collisions of light nuclei, employing a fully three-dimensional numerical treatment without any symmetry restrictions and with modern Skyrme functionals. We demonstrate the necessity of these couplings to suppress spurious spin excitations owing to the spin-orbit force in free translational motion of a nucleus but show that in a collision situation there is a strong spin excitation even in spi...
Chiba, Mahito; Tsuneda, Takao; Hirao, Kimihiko
2006-04-14
An analytical excitation energy gradient of long-range corrected time-dependent density functional theory (LC-TDDFT) is presented. This is based on a previous analytical TDDFT gradient formalism, which avoids solving the coupled-perturbed Kohn-Sham equation for each nuclear degree of freedom. In LC-TDDFT, exchange interactions are evaluated by combining the short-range part of a DFT exchange functional with the long-range part of the Hartree-Fock exchange integral. This LC-TDDFT gradient was first examined by calculating the excited state geometries and adiabatic excitation energies of small typical molecules and a small protonated Schiff base. As a result, we found that long-range interactions play a significant role even in valence excited states of small systems. This analytical LC-TDDFT gradient was also applied to the investigations of small twisted intramolecular charge transfer (TICT) systems. By comparing with calculated ab initio multireference perturbation theory and experimental results, we found that LC-TDDFT gave much more accurate absorption and fluorescence energies of these systems than those of conventional TDDFTs using pure and hybrid functionals. For optimized excited state geometries, LC-TDDFT provided fairly different twisting and wagging angles of these small TICT systems in comparison with conventional TDDFT results.
Time dependent mean field approximation to the many-body S-matrix
International Nuclear Information System (INIS)
Alhassid, Y.; Koonin, S.E.
1980-01-01
Time-dependent Hartree-Fock (TDHF) calculations are a good description of some inclusive properties of deep inelastic heavy-ion collisions. The first steps toward a mean-field theory that approximates specific elements of the many-body S matrix are presented. A many-body system with pairwise interactions excited by an external, time-dependent one-body field is considered. The methods are used to solve the forced Lipkin model. The moduli of elastic and excitation amplitudes are plotted. 3 figures
Tensor numerical methods in quantum chemistry: from Hartree-Fock to excitation energies.
Khoromskaia, Venera; Khoromskij, Boris N
2015-12-21
We resume the recent successes of the grid-based tensor numerical methods and discuss their prospects in real-space electronic structure calculations. These methods, based on the low-rank representation of the multidimensional functions and integral operators, first appeared as an accurate tensor calculus for the 3D Hartree potential using 1D complexity operations, and have evolved to entirely grid-based tensor-structured 3D Hartree-Fock eigenvalue solver. It benefits from tensor calculation of the core Hamiltonian and two-electron integrals (TEI) in O(n log n) complexity using the rank-structured approximation of basis functions, electron densities and convolution integral operators all represented on 3D n × n × n Cartesian grids. The algorithm for calculating TEI tensor in a form of the Cholesky decomposition is based on multiple factorizations using algebraic 1D "density fitting" scheme, which yield an almost irreducible number of product basis functions involved in the 3D convolution integrals, depending on a threshold ε > 0. The basis functions are not restricted to separable Gaussians, since the analytical integration is substituted by high-precision tensor-structured numerical quadratures. The tensor approaches to post-Hartree-Fock calculations for the MP2 energy correction and for the Bethe-Salpeter excitation energies, based on using low-rank factorizations and the reduced basis method, were recently introduced. Another direction is towards the tensor-based Hartree-Fock numerical scheme for finite lattices, where one of the numerical challenges is the summation of electrostatic potentials of a large number of nuclei. The 3D grid-based tensor method for calculation of a potential sum on a L × L × L lattice manifests the linear in L computational work, O(L), instead of the usual O(L(3) log L) scaling by the Ewald-type approaches.
Alzubadi, Ali A.; Radhi, R. A.; Manie, Noori S.
2018-02-01
The nuclear structure of the 17O nucleus has been investigated using shell model and self-consistent Hartree-Fock calculations. In particular, elastic and inelastic electron scattering form factors, energy levels, and transition probabilities are calculated for positive and negative low-lying states. Two different shell model spaces have been used for this purpose. The first one is the psdpn model space for positive parity states and the second one is p1 /2s d model space for negative parity states. For all selected excited states, Skyrme interactions are adopted to generate from them a one-body potential in Hartrre-Fock theory to calculate the single-particle matrix elements. The deduced results are discussed for the longitudinal and transverse form factors and compared with the available experimental data. It has been confirmed that combining the shell model plus Hartree-Fock mean field method with the Skyrme interaction can accommodate very well the nuclear excitation properties, and work better for low lying states than for higher excitations. Furthermore, the combination can be used to reproduce the positive and negative parity states after choosing the suitable model space, effective two-body interaction, and parameterization to reach highly descriptive and predictive results.
Self-consistent Hartree-Fock approach for interacting bosons in optical lattices
Lü, Qin-Qin; Patton, Kelly R.; Sheehy, Daniel E.
2014-12-01
A theoretical study of interacting bosons in a periodic optical lattice is presented. Instead of the commonly used tight-binding approach (applicable near the Mott-insulating regime of the phase diagram), the present work starts from the exact single-particle states of bosons in a cubic optical lattice, satisfying the Mathieu equation, an approach that can be particularly useful at large boson fillings. The effects of short-range interactions are incorporated using a self-consistent Hartree-Fock approximation, and predictions for experimental observables such as the superfluid transition temperature, condensate fraction, and boson momentum distribution are presented.
Generalized Hartree-Fock-Bogoliubov approach in the description of many-body systems
International Nuclear Information System (INIS)
Janssen, D.
1979-01-01
The quantum mechanical equation for a group of states connected by large probabilities of transitions to each other, i.e. possessing common internal structure, is found. No phenomenological assumptions about the vibrational or rotational character of these states have been used. The equations obtained here can be understood as a direct generalization of the Hartree-Fock-Bogoliubov equation, this scheme including not only the ground state, but some excited states as well. The question of normalization of the density matrix in the generalized space has been solved and the additional solutions of the problem have been excluded. (author)
Half-projected Hartree-Fock calculations on several small molecules
Lengsfield, B. H., III; Phillips, D. H.; Schug, J. C.
1981-01-01
The half-projected Hartree-Fock (HPHF) method is examined with respect to its ability to obtain molecular correlation, describe molecular potential energy surfaces, and provide a one-particle basis for more elaborate treatments. The equivalence, aside from questions of efficiency, of two different HPHF algorithms is demonstrated. The results of calculations on H2O, C2, N2, and CH2 indicate that the performance of the HPHF method, with spin projection in appropriate cases, is roughly equivalent to limited MCSCF treatments. In particular, a small but important fraction of the correlation energy, qualitatively correct potential energy surfaces, and good one-particle orbital bases are obtained.
Self-consistent Pauli corrections in Brueckner-Hartree-Fock calculations
Braley, R. C.; Ford, W. F.
1972-01-01
A scheme is introduced which makes it feasible to make completely self-consistent Brueckner-Hartree-Fock (BHF) and renormalized BHF calculations for spherical, closed-shell and axially-symmetric deformed nuclei. The usual requirement or orbital self-consistency has been imposed, as well as self-consistency in the starting energies and occupation probabilities. Previously, only approximate forms were used for the Pauli operator. This approximation is removed and a method for making the necessary Pauli corrections to the reaction matrix during the approach to self-consistency is presented. A discussion of the symmetries which reduce the problem to one of manageable proportions is included.
Particle-number-projected Hartree-Fock-Bogoliubov study with effective shell model interactions
Maqbool, I.; Sheikh, J. A.; Ganai, P. A.; Ring, P.
2011-04-01
We perform the particle-number-projected mean-field study using the recently developed symmetry-projected Hartree-Fock-Bogoliubov (HFB) equations. Realistic calculations have been performed in sd- and fp-shell nuclei using the shell model empirical interactions, USD and GXPFIA. It is demonstrated that the mean-field results for energy surfaces, obtained with these shell model interactions, are quite similar to those obtained using the density functional approaches. Further, it is shown that particle-number-projected results, for neutron-rich isotopes, can lead to different ground-state shapes in comparison to bare HFB calculations.
Ab initio Hartree-Fock study on surface desorption process in tritium release
International Nuclear Information System (INIS)
Taniguchi, M.; Tanaka, S.
1998-01-01
Dissociative adsorption of hydrogen on Li 2 O (110) surface has been investigated with ab initio Hartree-Fock quantum chemical calculation technique. Heat of adsorption and surface potential energy for H 2 dissociative adsorption were evaluated by calculating the total energy of the system. The calculated results on adsorption heat indicated that H 2 adsorption is endothermic. However, when an oxygen vacancy exists adjacent to the adsorption site, the heat of adsorption became less endothermic and the activation energy required to dissociate the H-H bonding was smaller than that for the terrace site. This is considered to be caused by the excess charge localized near the defect. (orig.)
Liu, Jie; Liang, WanZhen
2011-07-07
We present the analytical expression and computer implementation for the second-order energy derivatives of the electronic excited state with respect to the nuclear coordinates in the time-dependent density functional theory (TDDFT) with Gaussian atomic orbital basis sets. Here, the Tamm-Dancoff approximation to the full TDDFT is adopted, and therefore the formulation process of TDDFT excited-state Hessian is similar to that of configuration interaction singles (CIS) Hessian. However, due to the replacement of the Hartree-Fock exchange integrals in CIS with the exchange-correlation kernels in TDDFT, many quantitative changes in the derived equations are arisen. The replacement also causes additional technical difficulties associated with the calculation of a large number of multiple-order functional derivatives with respect to the density variables and the nuclear coordinates. Numerical tests on a set of test molecules are performed. The simulated excited-state vibrational frequencies by the analytical Hessian approach are compared with those computed by CIS and the finite-difference method. It is found that the analytical Hessian method is superior to the finite-difference method in terms of the computational accuracy and efficiency. The numerical differentiation can be difficult due to root flipping for excited states that are close in energy. TDDFT yields more exact excited-state vibrational frequencies than CIS, which usually overestimates the values.
Kulesza, Alexander Jan; Titov, Evgenii; Daly, Steven; Włodarczyk, Radosław; Megow, Jörg; Saalfrank, Peter; Choi, Chang Min; MacAleese, Luke; Antoine, Rodolphe; Dugourd, Philippe
2016-10-05
Action spectroscopy has emerged as an analytical tool to probe excited states in the gas phase. Although comparison of gas-phase absorption properties with quantum-chemical calculations is, in principle, straightforward, popular methods often fail to describe many molecules of interest-such as xanthene analogues. We, therefore, face their nano- and picosecond laser-induced photofragmentation with excited-state computations by using the CC2 method and time-dependent density functional theory (TDDFT). Whereas the extracted absorption maxima agree with CC2 predictions, the TDDFT excitation energies are blueshifted. Lowering the amount of Hartree-Fock exchange in the DFT functional can reduce this shift but at the cost of changing the nature of the excited state. Additional bandwidth observed in the photofragmentation spectra is rationalized in terms of multiphoton processes. Observed fragmentation from higher-lying excited states conforms to intense excited-to-excited state transitions calculated with CC2. The CC2 method is thus suitable for the comparison with photofragmentation in xanthene analogues. © 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Elward, Jennifer M; Thallinger, Barbara; Chakraborty, Arindam
2012-03-28
The electron-hole explicitly correlated Hartree-Fock method (eh-XCHF) is presented as a general strategy for investigation of electron-hole correlation and computation of electron-hole recombination probability. The eh-XCHF method is a variational method which uses explicitly correlated wavefunction that depends on the electron-hole inter-particle distances. It is shown that the explicitly correlated ansatz provides a systematic route to variationally minimize the total energy. The parabolic quantum dot is used as the benchmark system and the eh-XCHF method is used for computation of the ground state energy and electron-hole recombination probability. The results are compared to Hartree-Fock and explicitly correlated full configuration interaction (R12-FCI) calculations. The results indicate that an accurate description of the electron-hole wavefunction at short electron-hole inter-particle distances is crucial for qualitative description of the electron-hole recombination probability. The eh-XCHF method successfully addresses this issue and comparison of eh-XCHF calculations with R12-FCI shows good agreement. The quality of the mean field approximation for electron-hole system is also investigated by comparing HF and R12-FCI energies for electron-electron and electron-hole systems. It was found that performance of the mean field approximation is worse for the electron-hole system as compared to the corresponding electron-electron system.
A correction for the Hartree-Fock density of states for jellium without screening.
Blair, Alexander I; Kroukis, Aristeidis; Gidopoulos, Nikitas I
2015-02-28
We revisit the Hartree-Fock (HF) calculation for the uniform electron gas, or jellium model, whose predictions--divergent derivative of the energy dispersion relation and vanishing density of states (DOS) at the Fermi level--are in qualitative disagreement with experimental evidence for simple metals. Currently, this qualitative failure is attributed to the lack of screening in the HF equations. Employing Slater's hyper-Hartree-Fock (HHF) equations, derived variationally, to study the ground state and the excited states of jellium, we find that the divergent derivative of the energy dispersion relation and the zero in the DOS are still present, but shifted from the Fermi wavevector and energy of jellium to the boundary between the set of variationally optimised and unoptimised HHF orbitals. The location of this boundary is not fixed, but it can be chosen to lie at arbitrarily high values of wavevector and energy, well clear from the Fermi level of jellium. We conclude that, rather than the lack of screening in the HF equations, the well-known qualitative failure of the ground-state HF approximation is an artifact of its nonlocal exchange operator. Other similar artifacts of the HF nonlocal exchange operator, not associated with the lack of electronic correlation, are known in the literature.
Bischoff, Florian A; Valeev, Edward F
2011-03-14
Here we report a formulation of the Hartree-Fock method in an adaptive multiresolution basis set of spectral element type. A key feature of our approach is the use of low-order tensor approximations for operators and wave functions to reduce the steep rise of storage and computational costs with the number of degrees of freedom that plague finite element computations. As a proof of principle we implemented Hartree-Fock method without explicit storage of the full-dimensional wave function and with guaranteed precision (microhartree precision for up to 14 electron systems is demonstrated). Even for the one-electron method the use of low-order tensor approximation reduces storage relative to the full representation, albeit with modest increase in cost. Preliminary tests for explicitly-correlated two-electron (six-dimensional) wave function suggest a factor of 50 savings in storage. At least correlated two-electron methods should be feasible with our approach on modern workstations with guaranteed precision.
Local Hartree-Fock orbitals using a three-level optimization strategy for the energy.
Høyvik, Ida-Marie; Jansik, Branislav; Kristensen, Kasper; Jørgensen, Poul
2013-06-05
Using the three-level energy optimization procedure combined with a refined version of the least-change strategy for the orbitals--where an explicit localization is performed at the valence basis level--it is shown how to more efficiently determine a set of local Hartree-Fock orbitals. Further, a core-valence separation of the least-change occupied orbital space is introduced. Numerical results comparing valence basis localized orbitals and canonical molecular orbitals as starting guesses for the full basis localization are presented. The results show that the localization of the occupied orbitals may be performed at a small computational cost if valence basis localized orbitals are used as a starting guess. For the unoccupied space, about half the number of iterations are required if valence localized orbitals are used as a starting guess compared to a canonical set of unoccupied Hartree-Fock orbitals. Different local minima may be obtained when different starting guesses are used. However, the different minima all correspond to orbitals with approximately the same locality. Copyright © 2013 Wiley Periodicals, Inc.
Effects of particle-collective state coupling on the Hartree-Fock potential in 208Pb
International Nuclear Information System (INIS)
Bernard, Veronique.
1978-01-01
The nucleon-nucleus optical potential is studied by starting from the Hartree-Fock potential and calculating the effects of the coupling of the particle to the collective states of the nucleus. The basic ingredient to derive the basis of Hartree-Fock states, the collective states (described in a self consistent RPA framework) as well as the residual particle-hole interaction is the effective Skyrme force. One thus obtains a complex and non local corrective potential whose absorptive part was more particularly studied in the case of 208 Pb and for incident neutron enegies up to 30MeV. In the case of the interaction SIII one used, this absorptive part is surface peaked, due to the particular density dependence of the coupling interaction. It has a correct energy dependence but the strengh is too weak as compared to the phenomenological potentials. This might be due in part to the fact that rearrangement channels, which not contained in these calculations, could be important [fr
von Rudorff, Guido Falk; Jakobsen, Rasmus; Rosso, Kevin M; Blumberger, Jochen
2017-05-09
Density functional theory-based molecular dynamics calculations of condensed phase systems often benefit from the use of hybrid functionals. However, their use is computationally very demanding and severely limits the system size and time scale that can be simulated. Several methods have been introduced to accelerate hybrid functional molecular dynamics including Schwarz screening and the auxiliary density matrix method (ADMM). Here we present a simple screening scheme that can be applied in addition to these methods. It works by examining Hartree-Fock exchange (HFX) integrals and subsequently excluding those that contribute very little to any nuclear force component. The resultant force error is corrected by a history-dependent extrapolation scheme. We find that for systems where the calculation of HFX forces is a major bottleneck, a large fraction of the integrals can be neglected without introducing significant errors in the nuclear forces. For instance, for a 2 × 2 × 2 unit cell of CoO, 92% of the HFX integrals that have passed Schwarz screening within the ADMM approach can be neglected leading to a performance gain of a factor of 3 at a negligible error in nuclear forces (≤5 × 10 -4 H bohr -1 ). We also show that total energy conservation and solvation structures are not adversely affected by the screening method.
Wang, Hao
2014-07-01
The metal-insulator transition of VO2 so far has evaded an accurate description by density functional theory. The screened hybrid functional of Heyd, Scuseria and Ernzerhof leads to reasonable solutions for both the low-temperature monoclinic and high-temperature rutile phases only if spin polarization is excluded from the calculations. We explore whether a satisfactory agreement with experiment can be achieved by tuning the fraction of Hartree Fock exchange (α) in the density functional. It is found that two branches of locally stable solutions exist for the rutile phase for 12.5%≤α≤20%. One is metallic and has the correct stability as compared to the monoclinic phase, the other is insulating with lower energy than the metallic branch. We discuss these observations based on the V 3d orbital occupations and conclude that α=10% is the best possible choice for spin-polarized VO2 calculations. © 2014 Elsevier B.V. All rights reserved.
Time-dependent Dyson orbital theory
Gritsenko, O.V.; Baerends, E.J.
2016-01-01
Although time-dependent density functional theory (TDDFT) has become the tool of choice for real-time propagation of the electron density ρN(t) of N-electron systems, it also encounters problems in this application. The first problem is the neglect of memory effects stemming from the, in TDDFT
Anguiano, M.; Lallena, A. M.; Co', G.; De Donno, V.
2014-02-01
In this work we test the validity of a Hartree-Fock plus Bardeen-Cooper-Schrieffer model in which a finite-range interaction is used in the two steps of the calculation by comparing the results obtained to those found in fully self-consistent Hartree-Fock-Bogoliubov calculations using the same interaction. Specifically, we consider the Gogny-type D1S and D1M forces. We study a wide range of spherical nuclei, far from the stability line, in various regions of the nuclear chart, from oxygen to tin isotopes. We calculate various quantities related to the ground state properties of these nuclei, such as binding energies, radii, charge and density distributions, and elastic electron scattering cross sections. The pairing effects are studied by direct comparison with the Hartree-Fock results. Despite its relative simplicity, in most cases, our model provides results very close to those of the Hartree-Fock-Bogoliubov calculations, and it reproduces the empirical evidence of pairing effects rather well in the nuclei investigated.
Skyrme-Hartree-Fock in the realm of nuclear mean field models
International Nuclear Information System (INIS)
Reinhard, P.G.; Reiss, C.; Maruhn, J.; Bender, M.; Buervenich, T.; Greiner, W.
2000-01-01
We discuss and compare two brands of nuclear mean field models, the Skyrme-Hartree-Fock scheme (SHF) and the relativistic mean field model (RMF). Similarities and differences are worked out on a formal basis and with respect to the models performance in describing nuclear data. The bulk observables of stable nuclei are all described very well. Differences come up when extrapolating to exotic nuclei. The typically larger asymmetry energy in RMF leads to a larger neutron skin. Superheavy nuclei are found to be very sensitive on the single particle levels particularly on the spin orbit splitting. Ground state correlations from collective surface vibrations can have a significant effect on difference observables, as two-nucleon separation energy and two-nucleon shell gap. (author)
Hartree-Fock calculation of the differential photoionization cross sections of small Li clusters.
Galitskiy, S A; Artemyev, A N; Jänkälä, K; Lagutin, B M; Demekhin, Ph V
2015-01-21
Cross sections and angular distribution parameters for the single-photon ionization of all electron orbitals of Li2-8 are systematically computed in a broad interval of the photoelectron kinetic energies for the energetically most stable geometry of each cluster. Calculations of the partial photoelectron continuum waves in clusters are carried out by the single center method within the Hartree-Fock approximation. We study photoionization cross sections per one electron and analyze in some details general trends in the photoionization of inner and outer shells with respect to the size and geometry of a cluster. The present differential cross sections computed for Li2 are in a good agreement with the available theoretical data, whereas those computed for Li3-8 clusters can be considered as theoretical predictions.
Self-consistent Hartree-Fock RPA calculations in 208Pb
Taqi, Ali H.; Ali, Mohammed S.
2018-01-01
The nuclear structure of 208Pb is studied in the framework of the self-consistent random phase approximation (SCRPA). The Hartree-Fock mean field and single particle states are used to implement a completely SCRPA with Skyrme-type interactions. The Hamiltonian is diagonalised within a model space using five Skyrme parameter sets, namely LNS, SkI3, SkO, SkP and SLy4. In view of the huge number of the existing Skyrme-force parameterizations, the question remains which of them provide the best description of data. The approach attempts to accurately describe the structure of the spherical even-even nucleus 208Pb. To illustrate our approach, we compared the binding energy, charge density distribution, excitation energy levels scheme with the available experimental data. Moreover, we calculated isoscalar and isovector monopole, dipole, and quadrupole transition densities and strength functions.
Efficient Computation of the Hartree-Fock Exchange in Real-Space with Projection Operators.
Boffi, Nicholas M; Jain, Manish; Natan, Amir
2016-08-09
We describe an efficient projection-based real-space implementation of the nonlocal single-determinant exchange operator. Through a matrix representation of the projected operator, we show that this scheme works equally well for both occupied and virtual states. Our scheme reaches a speedup of 2 orders of magnitude and has no significant loss of accuracy compared to an implementation of the full nonlocal single-determinant exchange operator. We find excellent agreement upon comparing Hartree-Fock eigenvalues, dipoles, and polarizabilities of selected molecules calculated using our method to values in the literature. To illustrate the efficiency of this scheme we perform calculations on systems with up to 240 carbon atoms.
Characterization and Generation of Local Occupied and Virtual Hartree-Fock Orbitals.
Høyvik, Ida-Marie; Jørgensen, Poul
2016-03-09
The scope of this review article is to discuss the locality of occupied and virtual orthogonal Hartree-Fock orbitals generated by localization function optimization. Locality is discussed from the stand that an orbital is local if it is confined to a small region in space. Focusing on locality measures that reflects the spatial extent of the bulk of an orbital and the thickness of orbital tails, we discuss, with numerical illustrations, how the locality may be reported for individual orbitals as well as for sets of orbitals. Traditional and more recent orbital localization functions are reviewed, and the locality measures are used to compare the locality of the orbitals generated by the different localization functions, both for occupied and virtual orbitals. Numerical illustrations are given also for large molecular systems and for cases where diffuse functions are included in the atomic orbital basis. In addition, we have included a discussion on the physical and mathematical limitations on orbital locality.
Existence of Infinitely Many Distinct Solutions to the Quasirelativistic Hartree-Fock Equations
Directory of Open Access Journals (Sweden)
M. Enstedt
2009-01-01
Full Text Available We establish existence of infinitely many distinct solutions to the semilinear elliptic Hartree-Fock equations for N-electron Coulomb systems with quasirelativistic kinetic energy −α−2Δxn+α−4−α−2 for the nth electron. Moreover, we prove existence of a ground state. The results are valid under the hypotheses that the total charge Ztot of K nuclei is greater than N−1 and that Ztot is smaller than a critical charge Zc. The proofs are based on a new application of the Fang-Ghoussoub critical point approach to multiple solutions on a noncompact Riemannian manifold, in combination with density operator techniques.
Near Hartree-Fock quality GTO basis sets for the second-row atoms
Partridge, Harry
1987-01-01
Energy optimized, near Hartree-Fock quality Gaussian basis sets ranging in size from (17s12p) to (20s15p) are presented for the ground states of the second-row atoms for Na(2P), Na(+), Na(-), Mg(3P), P(-), S(-), and Cl(-). In addition, optimized supplementary functions are given for the ground state basis sets to describe the negative ions, and the excited Na(2P) and Mg(3P) atomic states. The ratios of successive orbital exponents describing the inner part of the 1s and 2p orbitals are found to be nearly independent of both nuclear charge and basis set size. This provides a method of obtaining good starting estimates for other basis set optimizations.
Ab-initio Hartree-Fock study of tritium desorption from Li{sub 2}O
Energy Technology Data Exchange (ETDEWEB)
Taniguchi, Masaki; Tanaka, Satoru [Tokyo Univ. (Japan). Faculty of Engineering
1998-03-01
Dissociative adsorption of hydrogen on Li{sub 2}O (110) surface has been investigated with ab-initio Hartree-Fock quantum chemical calculation technique. Heat of adsorption and potential energy surface for H{sub 2} dissociative adsorption was evaluated by calculating the total energy of the system. Calculation results on adsorption heat indicated that H{sub 2} adsorption is endothermic. However, when oxygen vacancy exists adjacent to the adsorption sites, heat of adsorption energy became less endothermic and the activation energy required to dissociate the H-H bonding was smaller than that for the terrace site. This is considered to be caused by the excess charge localized near the defect. (author)
Implementation of a vector potential method in an ab initio Hartree-Fock code
Tevekeliyska, Violina; Springborg, Michael; Champagne, Benoît; Kirtman, Bernard
2012-12-01
For extended systems exposed to an external, electrostatic field, the presence of the field leads to an extra term (E⃗. P⃗) to the Hamiltonian, where E⃗ is the field vector and P⃗ is the polarization of the system of interest. In order to find out how a polymer chain responds to an external electric perturbation, a field with a charge and a current term for the polarization is added to an ab initio Hartree-Fock Hamiltonian. The polarization expression is taken from an efficient vector potential approach (VPA) [1] for calculating electronic and nuclear responses of infinite periodic systems to finite electric fields and is implemented in the ab initio LCAO-SCF algorithm [3], which computes band structure of regular or helical polymers, taking into account the one-dimensional translational symmetry. A smoothing procedure for numerical differentiation of the orbital coefficients is used in order to calculate self-consistently the charge flow contribution to the polarization.
Decoupled dirac equation in one-boson-Exchange potential model and Hartree-fock calculations
International Nuclear Information System (INIS)
Hanna, K.M.; Swelam, Sh.M.; Nafea, H.O.
2004-01-01
On the basis of a semi-relativistic decoupled Dirac equation and self consistent Hartree-Fock formulation, it is used the One-Boson-Exchange Potential (OBEP) model where each nucleon, as a Dirac particle, is considered to be a source of a scalar (a) and vector (co) fields, and is also acted upon by these fields, to get the ground state of some spherical nuclei. An important mathematical advantage gained by the assumption that each nucleon in the nucleus is moving under the influence of a common harmonic oscillator is that (as shown by Talmi) the wave function of the two nucleons is separable in their relative and center of mass (C.M) coordinates and the known Talmi-Moshinsky brackets. Three different static nucleon-nucleon interaction forms are used to predict the ground state energy for 4 He nucleus
Sirjoosingh, Andrew; Pak, Michael V; Swalina, Chet; Hammes-Schiffer, Sharon
2013-07-21
The nuclear-electronic orbital (NEO) method treats electrons and select nuclei quantum mechanically on the same level to extend beyond the Born-Oppenheimer approximation. Electron-nucleus dynamical correlation has been found to be highly significant due to the attractive Coulomb interaction. The explicitly correlated Hartree-Fock (NEO-XCHF) approach includes explicit electron-nucleus correlation with Gaussian-type geminal functions during the variational optimization of the nuclear-electronic wavefunction. Although accurate for small model systems, the NEO-XCHF method is computationally impractical for larger chemical systems. In this paper, we develop the reduced explicitly correlated Hartree-Fock approach, denoted NEO-RXCHF, where only select electronic orbitals are explicitly correlated to the nuclear orbitals. By explicitly correlating only the relevant electronic orbitals to the nuclear orbitals, the NEO-RXCHF approach avoids problems that can arise when all electronic orbitals are explicitly correlated to the nuclear orbitals in the same manner. We examine three different NEO-RXCHF methods that differ in the treatment of the exchange between the geminal-coupled electronic orbitals and the other electronic orbitals: NEO-RXCHF-fe is fully antisymmetric with respect to exchange of all electronic coordinates and includes all electronic exchange terms; NEO-RXCHF-ne neglects the exchange between the geminal-coupled electronic orbitals and the other electronic orbitals; and NEO-RXCHF-ae includes approximate exchange terms between the geminal-coupled electronic orbitals and the other electronic orbitals. The latter two NEO-RXCHF methods offer substantial computational savings over the NEO-XCHF approach. The NEO-RXCHF approach is applicable to a wide range of chemical systems that exhibit non-Born-Oppenheimer effects between electrons and nuclei, as well as positron-containing molecular systems.
International Nuclear Information System (INIS)
Ferrari, R.; I.N.F.N., Trento
1994-01-01
The formalism introduced in a previous paper is used for discussing the Coulomb interaction of many electrons moving in two space-dimensions in the presence of a strong magnetic field. The matrix element of the coulomb interaction is evaluated in the new basis, whose states are invariant under discrete translations. This paper is devoted to the case of low filling factor, thus the authors limit themselves to the lowest Landau level and to spins all oriented along the magnetic field. For the case of filling factor ν f = 1/u they give an Ansatz on the state of many electrons which provides a good approximated solution of the Hartree-Fock equation. For general filling factor ν f = u'/u a trial state is given which converges very rapidly to a solution of the self-consistent equation. They generalize the Hartree-Fock equation by considering some correlation: all quantum states are allowed for the u' electrons with the same translation quantum numbers. Numerical results are given for the mean energy and the energy bands, for some values of the filling factor (ν f = 1/2, 1/3, 2/3, 1/4, 3/4, 1/5, 2/5, 3/5, 4/5). The results agree numerically with the Charge Density Wave approach. The boundary conditions are shown to be very important: only large systems (degeneracy of Landau level over 200) are not affected by the boundaries. Therefore results obtained on small scale systems are somewhat unreliable. The relevance of the results for the Fractional Quantum Hall Effect is briefly discussed
Dyall, Kenneth G.
1993-01-01
Dirac-Hartree-Fock calculations have been carried out on the ground states of the group IV monoxides GeO, SnO and PbO. Geometries, dipole moments and infrared data are presented. For comparison, nonrelativistic, first-order perturbation and relativistic effective core potential calculations have also been carried out. Where appropriate the results are compared with the experimental data and previous calculations. Spin-orbit effects are of great importance for PbO, where first-order perturbation theory including only the mass-velocity and Darwin terms is inadequate to predict the relativistic corrections to the properties. The relativistic effective core potential results show a larger deviation from the all-electron values than for the hydrides, and confirm the conclusions drawn on the basis of the hydride calculations.
Dyall, Kenneth G.
1991-01-01
Dirac-Hartree-Fock calculations have been carried out on the ground states of the group IV monoxides GeO, SnO and PbO. Geometries, dipole moments and infrared data are presented. For comparison, nonrelativistic, first-order perturbation and relativistic effective core potential calculations have also been carried out. Where appropriate the results are compared with the experimental data and previous calculations. Spin-orbit effects are of great importance for PbO, where first-order perturbation theory including only the mass-velocity and Darwin terms is inadequate to predict the relativistic corrections to the properties. The relativistic effective core potential results show a larger deviation from the all-electron values than for the hydrides, and confirm the conclusions drawn on the basis of the hydride calculations.
Time dependent resonating Hartree-Bogoliubov theory
International Nuclear Information System (INIS)
Nishiyama, Seiya; Fukutome, Hideo.
1989-01-01
Very recently, we have developed a theory of excitations in superconducting Fermion systems with large quantum fluctuations that can be described by resonance of time dependent non-orthogonal Hartree-Bogoliubov (HB) wave functions with different correlation structures. We have derived a new kind of variation equation called the time dependent Resonating HB equation, in order to determine both the time dependent Resonating HB wave functions and coefficients of a superposition of the HB wave functions. Further we have got a new approximation for excitations from time dependent small fluctuations of the Resonating HB ground state, i.e., the Resonating HB RPA. The Res HB RPA equation is represented in a given single particle basis. It, however, has drawbacks that the constraints for the Res HB RPA amplitudes are not taken into account and the equation contains equations which are not independent. We shall derive another form of the Res HB RPA equation eliminating these drawbacks. The Res HB RPA gives a unified description of the vibrons and resonons and their interactions. (author)
International Nuclear Information System (INIS)
Rey, Ana Maria; Hu, B.L.; Roura, Albert; Calzetta, Esteban; Clark, Charles W.
2004-01-01
In this work a two-particle irreducible (2PI) closed-time-path (CTP) effective action is used to describe the nonequilibrium dynamics of a Bose-Einstein condensate selectively loaded into every third site of a one-dimensional optical lattice. The motivation of this work is the recent experimental realization of this system. Patterned loading methods may be useful for quantum computing with trapped atoms. This system also serves to illustrate many basic issues in nonequilibrium quantum-field theory pertaining to the dynamics of quantum correlations and fluctuations which goes beyond the capability of a mean-field theory. By numerically evolving in time the initial-state configuration using the Bose-Hubbard Hamiltonian an exact quantum solution is available for this system in the case of few atoms and wells. One can also use it to test various approximate methods. Under the 2PI CTP scheme with this initial configuration, three different approximations are considered: (a) the Hartree-Fock-Bogoliubov (HFB) approximation (b) the next-to-leading-order 1/N expansion of the 2PI effective action up to second order in the interaction strength, and (c) a second-order perturbative expansion in the interaction strength. We present detailed comparisons between these approximations and determine their range of validity by contrasting them with the exact many-body solution for a moderate number of atoms and wells. As a general feature we observe that because the second-order 2PI approximations include multiparticle scattering in a systematic way, they are able to capture damping effects exhibited in the exact solution, which a mean-field collisionless approach fails to produce. While the second-order approximations show a clear improvement over the HFB approximation, our numerical results show that they fail at late times, when interaction effects are significant
Dyall, Kenneth G.; Taylor, Peter R.; Faegri, Knut, Jr.; Partridge, Harry
1990-01-01
A basis-set-expansion Dirac-Hartree-Fock program for molecules is described. Bond lengths and harmonic frequencies are presented for the ground states of the group 4 tetrahydrides, CH4, SiH4, GeH4, SnH4, and PbH4. The results are compared with relativistic effective core potential (RECP) calculations, first-order perturbation theory (PT) calculations and with experimental data. The bond lengths are well predicted by first-order perturbation theory for all molecules, but non of the RECP's considered provides a consistent prediction. Perturbation theory overestimates the relativistic correction to the harmonic frequencies; the RECP calculations underestimate the correction.
Dyall, Kenneth G.; Taylor, Peter R.; Faegri, Knut, Jr.; Partridge, Harry
1991-01-01
A basis-set-expansion Dirac-Hartree-Fock program for molecules is described. Bond lengths and harmonic frequencies are presented for the ground states of the group 4 tetrahydrides, CH4, SiH4, GeH4, SnH4, and PbH4. The results are compared with relativistic effective core potential (RECP) calculations, first-order perturbation theory (PT) calculations and with experimental data. The bond lengths are well predicted by first-order perturbation theory for all molecules, but none of the RECP's considered provides a consistent prediction. Perturbation theory overestimates the relativistic correction to the harmonic frequencies; the RECP calculations underestimate the correction.
A poly-epoxy surface explored by Hartree-Fock ΔSCF simulations of C1s XPS spectra.
Gavrielides, A; Duguet, T; Esvan, J; Lacaze-Dufaure, C; Bagus, P S
2016-08-21
Whereas poly-epoxy polymers represent a class of materials with a wide range of applications, the structural disorder makes them difficult to model. In the present work, we use good experimental model samples in the sense that they are pure, fully polymerized, flat and smooth, defect-free, and suitable for ultrahigh vacuum x-ray photoelectron spectroscopy, XPS, experiments. In parallel, we perform Hartree-Fock, HF, calculations of the binding energies, BEs, of the C1s electrons in a model molecule composed of the two constituents of the poly-epoxy sample. These C1s BEs were determined using the HF ΔSCF method, which is known to yield accurate values, especially for the shifts of the BEs, ΔBEs. We demonstrate the benefits of combining rigorous theory with careful XPS measurements in order to obtain correct assignments of the C1s XPS spectra of the polymer sample. Both the relative binding energies-by the ΔSCF method-and relative intensities-in the sudden approximation, SA, are calculated. It results in an excellent match with the experimental spectra. We are able to identify 9 different chemical environments under the C1s peak, where an exclusively experimental work would have found only 3 contributions. In addition, we observe that some contributions are localized at discrete binding energies, whereas others allow a much wider range because of the variation of their second neighbor bound polarization. Therefore, HF-ΔSCF simulations significantly increase the spectral resolution of XPS and thus offer a new avenue for the exploration of the surface of polymers.
Dyall, Kenneth G.
1992-01-01
Relativistic corrections to a number of properties of the Group IV hydrides are calculated using the Dirac-Hartree-Fock method. The use of first-order perturbation theory is sufficient to obtain relativistic corrections for Ge, but the effects of spin-orbit interaction and other higher-order effects begin to show for Sn and become important for Pb. The energy of the reaction XH4 yields XH2 + H2 (X = Si, Ge, Sn, and Pb) is also calculated. The results are compared with relativistic effective core potential calculations, first-order perturbation theory calculations, and limited experimental data.
Kobayashi, Masato
2014-02-28
The analytical gradient for the atomic-orbital-based Hartree-Fock-Bogoliubov (HFB) energy functional, the modified form of which was proposed by Staroverov and Scuseria to account for the static electron correlation [J. Chem. Phys. 117, 11107 (2002)], is derived. Interestingly, the Pulay force for the HFB energy is expressed with the same formula as that for the Hartree-Fock method. The efficiency of the present HFB energy gradient is demonstrated in the geometry optimizations of conjugated and biradical systems. The geometries optimized by using the HFB method with the appropriate factor ζ, which controls the degree of static correlation included, are found to show good agreement with those obtained by using a complete active-space self-consistent field method, although they are significantly dependent on ζ.
The Hartree-Fock approximation for s-d shell even-even nuclei with N different of Z
International Nuclear Information System (INIS)
Oliveira, P.C. de.
1981-02-01
Using the Hartree-Fock approximation method for 22 Ne, 26 Mg and 30 Si nuclei with different kinds of two-body interactions, the electric quadrupole moments and projected energy levels, of angular momentum J=0,2,4,6..., are determined. The Peierls-Yoccoz projection m ethod is used to determine the wave function with well-defined angular momentum. A comparison is made, with the experimental results and the ones obtained by other authors. (Author) [pt
Systematic study of even-even nuclei with Hartree-Fock+BCS method using Skyrme SIII force
Energy Technology Data Exchange (ETDEWEB)
Tajima, Naoki; Takahara, Satoshi; Onishi, Naoki [Tokyo Univ. (Japan). Coll. of Arts and Sciences
1997-03-01
We have applied the Hartree-Fock+BCS method with Skyrme SIII force formulated in a three-dimensional Cartesian-mesh representation to even-even nuclei with 2 {<=} Z {<=} 114. We discuss the results concerning the atomic masses, the quadrupole (m=0, 2) and hexadecapole (m=0, 2, 4) deformations, the skin thicknesses, and the halo radii. We also discuss the energy difference between oblate and prolate solutions and the shape difference between protons and neutrons. (author)
Analytic energy gradient of projected Hartree-Fock within projection after variation.
Uejima, Motoyuki; Ten-No, Seiichiro
2017-03-14
We develop a geometrical optimization technique for the projection-after-variation (PAV) scheme of the recently refined projected Hartree-Fock (PHF) as a fast alternative to the variation-after-projection (VAP) approach for optimizing the structures of molecules/clusters in symmetry-adapted electronic states at the mean-field computational cost. PHF handles the nondynamic correlation effects by restoring the symmetry of a broken-symmetry single reference wavefunction and moreover enables a black-box treatment of orbital selections. Using HF orbitals instead of PHF orbitals, our approach saves the computational cost for the orbital optimization, avoiding the convergence problem that sometimes emerges in the VAP scheme. We show that PAV-PHF provides geometries comparable to those of the complete active space self-consistent field and VAP-PHF for the tested systems, namely, CH 2 , O 3 , and the [Cu 2 O 2 ] 2+ core, where nondynamic correlation is abundant. The proposed approach is useful for large systems mainly dominated by nondynamic correlation to find stable structures in many symmetry-adapted states.
Quantum treatment of protons with the reduced explicitly correlated Hartree-Fock approach.
Sirjoosingh, Andrew; Pak, Michael V; Brorsen, Kurt R; Hammes-Schiffer, Sharon
2015-06-07
The nuclear-electronic orbital (NEO) approach treats select nuclei quantum mechanically on the same level as the electrons and includes nonadiabatic effects between the electrons and the quantum nuclei. The practical implementation of this approach is challenging due to the significance of electron-nucleus dynamical correlation. Herein, we present a general extension of the previously developed reduced NEO explicitly correlated Hartree-Fock (RXCHF) approach, in which only select electronic orbitals are explicitly correlated to each quantum nuclear orbital via Gaussian-type geminal functions. Approximations of the electronic exchange between the geminal-coupled electronic orbitals and the other electronic orbitals are also explored. This general approach enables computationally tractable yet accurate calculations on molecular systems with quantum protons. The RXCHF method is applied to the hydrogen cyanide (HCN) and FHF(-) systems, where the proton and all electrons are treated quantum mechanically. For the HCN system, only the two electronic orbitals associated with the CH covalent bond are geminal-coupled to the proton orbital. For the FHF(-) system, only the four electronic orbitals associated with the two FH covalent bonds are geminal-coupled to the proton orbital. For both systems, the RXCHF method produces qualitatively accurate nuclear densities, in contrast to mean field-based NEO approaches. The development and implementation of the RXCHF method provide the framework to perform calculations on systems such as proton-coupled electron transfer reactions, where electron-proton nonadiabatic effects are important.
Nuclear Tensor Force and Effective Pions in the Relativistic Hartree-Fock Formalism
Directory of Open Access Journals (Sweden)
Marcos S.
2014-03-01
Full Text Available In the framework of nonlinear nuclear models based on the relativistic Hartree-Fock approximation, we have isolated the contribution of the tensor force of pions in the effective NN interaction, by means of two different approximate methods, recently developed by us, in order to dilucidate its role in a variety of nuclear properties. Results show that a reduction of the contribution of this tensor force considerably influences the spin-orbit splittings and magic gaps in the spin-unsaturated midweight 56Ni nucleus as well as the behaviour of the total binding energies with A in heavy nuclei. Both methods give similar results. We also study the evolution of the splitting of the proton 1d spin-orbit doublet in the chain Z=14, from N=20 to N=28, and the neutron 2p − 1f shell in the chain N=28, from the 48Ca nucleus to the 42Si nucleus. Whereas, in the first case, the pion tensor force (PTF plays an important role and its reduction is needed to reproduce the corresponding experimental results; in the second case, the quenching of the neutron 2p3/2 − 1f7/2 gap in the mentioned isotonic chain N=28 is hardly affected by the PTF.
Rosen, A.; Ellis, D. E.; Adachi, H.; Averill, F. W.
1976-01-01
A numerical-variational method for performing self-consistent molecular calculations in the Hartree-Fock-Slater (HFS) model is presented. Molecular wavefunctions are expanded in terms of basis sets constructed from numerical HFS solutions of selected one-center atomlike problems. Binding energies and wavefunctions for the molecules are generated using a discrete variational method for a given molecular potential. In the self-consistent-charge (SCC) approximation to the complete self-consistent-field (SCF) method, results of a Mulliken population analysis of the molecular eigenfunctions are used in each iteration to produce 'atomic' occupation numbers. The simplest SCC potential is then obtained from overlapping spherical atomlike charge distributions. Molecular ionization energies are calculated using the transition-state procedure; results are given for CO, H2O, H2S, AlCl, InCl, and the Ni5O surface complex. Agreement between experimental and theoretical ionization energies for the free-molecule valence levels is generally within 1 eV. The simple SCC procedure gives a reasonably good approximation to the molecular potential, as shown by comparison with experiment, and with complete SCF calculations for CO, H2O, and H2S.
Efficient method of evaluation for Gaussian Hartree-Fock exchange operator for Gau-PBE functional.
Song, Jong-Won; Hirao, Kimihiko
2015-07-14
We previously developed an efficient screened hybrid functional called Gaussian-Perdew-Burke-Ernzerhof (Gau-PBE) [Song et al., J. Chem. Phys. 135, 071103 (2011)] for large molecules and extended systems, which is characterized by the usage of a Gaussian function as a modified Coulomb potential for the Hartree-Fock (HF) exchange. We found that the adoption of a Gaussian HF exchange operator considerably decreases the calculation time cost of periodic systems while improving the reproducibility of the bandgaps of semiconductors. We present a distance-based screening scheme here that is tailored for the Gaussian HF exchange integral that utilizes multipole expansion for the Gaussian two-electron integrals. We found a new multipole screening scheme helps to save the time cost for the HF exchange integration by efficiently decreasing the number of integrals of, specifically, the near field region without incurring substantial changes in total energy. In our assessment on the periodic systems of seven semiconductors, the Gau-PBE hybrid functional with a new screening scheme has 1.56 times the time cost of a pure functional while the previous Gau-PBE was 1.84 times and HSE06 was 3.34 times.
Quantum supercharger library: hyper-parallelism of the Hartree-Fock method.
Fernandes, Kyle D; Renison, C Alicia; Naidoo, Kevin J
2015-07-05
We present here a set of algorithms that completely rewrites the Hartree-Fock (HF) computations common to many legacy electronic structure packages (such as GAMESS-US, GAMESS-UK, and NWChem) into a massively parallel compute scheme that takes advantage of hardware accelerators such as Graphical Processing Units (GPUs). The HF compute algorithm is core to a library of routines that we name the Quantum Supercharger Library (QSL). We briefly evaluate the QSL's performance and report that it accelerates a HF 6-31G Self-Consistent Field (SCF) computation by up to 20 times for medium sized molecules (such as a buckyball) when compared with mature Central Processing Unit algorithms available in the legacy codes in regular use by researchers. It achieves this acceleration by massive parallelization of the one- and two-electron integrals and optimization of the SCF and Direct Inversion in the Iterative Subspace routines through the use of GPU linear algebra libraries. © 2015 Wiley Periodicals, Inc. © 2015 Wiley Periodicals, Inc.
Projection after variation in the finite-temperature Hartree-Fock-Bogoliubov approximation
Fanto, P.
2017-11-01
The finite-temperature Hartree-Fock-Bogoliubov (HFB) approximation often breaks symmetries of the underlying many-body Hamiltonian. Restricting the calculation of the HFB partition function to a subspace with good quantum numbers through projection after variation restores some of the correlations lost in breaking these symmetries, although effects of the broken symmetries such as sharp kinks at phase transitions remain. However, the most general projection after variation formula in the finite-temperature HFB approximation is limited by a sign ambiguity. Here, I extend the Pfaffian formula for the many-body traces of HFB density operators introduced by Robledo [L. M. Robledo, Phys. Rev. C. 79, 021302(R) (2009), 10.1103/PhysRevC.79.021302] to eliminate this sign ambiguity and evaluate the more complicated many-body traces required in projection after variation in the most general HFB case. The method is validated through a proof-of-principle calculation of the particle-number-projected HFB thermal energy in a simple model.
Multi-configuration Dirac-Hartree-Fock (MCDHF) calculations for Ni XXV
Singh, Narendra; Aggarwal, Sunny
2018-03-01
We present accurate 165 fine-structure energy levels related to the configurations 1s22s2, 1s22p2, 1s2nƖn‧l‧ (n = 2, n‧ = 2, 3, 4, 5, Ɩ = s,p Ɩ‧ = s, p, d, f, g) of Ni XXV which may be useful ion for astrophysical and fusion plasma. For the calculations of energy levels and radiative rates, we have used the multiconfiguration Dirac-Hartree-Fock (MCDHF) method employed in GRASP2K code. The calculations are carried out in the active space approximation with the inclusion of the Breit interaction, the finite nuclear size effect, and quantum electrodynamic corrections. The transition wavelengths, transition probabilities, line strengths, and absorption oscillator strengths are reported for electric dipole (E1), electric quadrupole (E2), magnetic dipole (M1), magnetic quadrupole (M2) transitions from the ground state. We have compared our calculated results with available theoretical and experimental data and good agreement is achieved. We predict new energy levels, oscillator strengths, line strengths and transition probabilities, where no other experimental or theoretical results are available. The present complete set of results should be of great help in line identification and the interpretation of spectra, as well as in the modelling and diagnostics of astrophysical and fusion plasmas.
Dynamical description of the fission process using the TD-BCS theory
Energy Technology Data Exchange (ETDEWEB)
Scamps, Guillaume, E-mail: scamps@nucl.phys.tohoku.ac.jp [Department of Physics, Tohoku University, Sendai 980-8578 (Japan); Simenel, Cédric [Department of Nuclear Physics, Research School of Physics and Engineering Australian National University, Canberra, Australian Capital Territory 2601 (Australia); Lacroix, Denis [Institut de Physique Nucléaire, IN2P3-CNRS, Université Paris-Sud, F-91406 Orsay Cedex (France)
2015-10-15
The description of fission remains a challenge for nuclear microscopic theories. The time-dependent Hartree-Fock approach with BCS pairing is applied to study the last stage of the fission process. A good agreement is found for the one-body observables: the total kinetic energy and the average mass asymmetry. The non-physical dependence of two-body observables with the initial shape is discussed.
Kishi, Ryohei; Nakano, Masayoshi
2011-04-21
A novel method for the calculation of the dynamic polarizability (α) of open-shell molecular systems is developed based on the quantum master equation combined with the broken-symmetry (BS) time-dependent density functional theory within the Tamm-Dancoff approximation, referred to as the BS-DFTQME method. We investigate the dynamic α density distribution obtained from BS-DFTQME calculations in order to analyze the spatial contributions of electrons to the field-induced polarization and clarify the contributions of the frontier orbital pair to α and its density. To demonstrate the performance of this method, we examine the real part of dynamic α of singlet 1,3-dipole systems having a variety of diradical characters (y). The frequency dispersion of α, in particular in the resonant region, is shown to strongly depend on the exchange-correlation functional as well as on the diradical character. Under sufficiently off-resonant condition, the dynamic α is found to decrease with increasing y and/or the fraction of Hartree-Fock exchange in the exchange-correlation functional, which enhances the spin polarization, due to the decrease in the delocalization effects of π-diradical electrons in the frontier orbital pair. The BS-DFTQME method with the BHandHLYP exchange-correlation functional also turns out to semiquantitatively reproduce the α spectra calculated by a strongly correlated ab initio molecular orbital method, i.e., the spin-unrestricted coupled-cluster singles and doubles.
Study of superdeformation at zero spin with Skyrme-Hartree-Fock method
Energy Technology Data Exchange (ETDEWEB)
Takahara, S.; Tajima, N.; Onishi, N. [Tokyo Univ. (Japan)
1998-03-01
Superdeformed (SD) bands have been studied extensively both experimentally and theoretically in the last decade. Since the first observation in {sup 152}Dy in 1986, SD bands have been found in four mass regions, i.e., A {approx} 80, 130, 150 and 190. While these SD bands have been observed only at high spins so far, they may also be present at zero spin like fission isomers in actinide nuclei: The familiar generic argument on the strong shell effect at axis ratio 2:1 does not assume rotations. If non-fissile SD isomers exist at zero spin, they may be utilized to develop new experimental methods to study exotic states, in a similar manner as short-lived high-spin isomers are planned to be utilized as projectiles of fusion reactions in order to populate very high-spin near-yrast states. They will also be useful to test theoretical models whether the models can describe correctly the large deformations of rare-earth nuclei without further complications due to rotations. In this report, we employ the Skyrme-Hartree-Fock method to study the SD states at zero spin. First, we compare various Skyrme force parameter sets to test whether they can reproduce the extrapolated excitation energy of the SD band head of {sup 194}Hg. Second, we systematically search large-deformation solutions with the SkM{sup *} force. The feature of our calculations is that the single-particle wavefunctions are expressed in a three-dimensional-Cartesian-mesh representation. This representation enables one to obtain solutions of various shapes (including SD) without preparing a basis specific to each shape. Solving the mean-field equations in this representation requires, however, a large amount of computation which can be accomplished only with present supercomputers. (author)
Kambe, Takahide; Katayama, Tetsuya; Saito, Koichi
In the present study, using the flavor-SU(3) NJL model with the vector coupling interaction, we have calculated the equation of state (EoS) for the quark phase at high density. Furthermore, for the hadron phase at low density, we have used two kinds of the equations of state; one is a rather soft one by the QHD model, and the other is a stiff one calculated with relativistic Brueckner-Hartree-Fock approximation [1]. Using those equations of state for the two phases, we have investigated the influence of various choices of parameters concerning the crossover region on the mass and radius of a neutron star.
Lee, Hyun-Jung; Kim, Ki-Seok
2018-04-01
We investigate the role of Coulomb interaction in the multifractality of Anderson metal-insulator transition, where the Coulomb interaction is treated within the Hartree-Fock approximation, but disorder effects are taken into account exactly. An innovative technical aspect in our simulation is to utilize the Ewald-sum technique, which allows us to introduce the long-range nature of the Coulomb interaction into Hartree-Fock self-consistent equations of order parameters more accurately. This numerical simulation reproduces the Altshuler-Aronov correction in a metallic state and the Efros-Shklovskii pseudogap in an insulating phase, where the density of states ρ (ω ) is evaluated in three dimensions. Approaching the quantum critical point of a metal-insulator transition from either the metallic or insulting phase, we find that the density of states is given by ρ (ω ) ˜|ω| 1 /2 , which determines one critical exponent of the McMillan-Shklovskii scaling theory. Our main result is to evaluate the eigenfunction multifractal scaling exponent αq, given by the Legendre transformation of the fractal dimension τq, which characterizes the scaling behavior of the inverse participation ratio with respect to the system size L . Our multifractal analysis leads us to identify two kinds of mobility edges, one of which occurs near the Fermi energy and the other of which appears at a high energy, where the density of states at the Fermi energy shows the Coulomb-gap feature. We observe that the multifractal exponent at the high-energy mobility edge remains to be almost identical to that of the Anderson localization transition in the absence of Coulomb interactions. On the other hand, we find that the multifractal exponent near the Fermi energy is more enhanced than that at the high-energy mobility edge, suspected to result from interaction effects. However, both the multifractal exponents do not change even if the strength of the Coulomb interaction varies. We also show that the
Near Hartree-Fock quality Gaussian type orbital basis sets for the first- and third-row atoms
Partridge, Harry
1989-01-01
Energy-optimized, near Hartree-Fock (NHF) quality Gaussian type orbital (GTO) basis sets are reported for the second-row (Li to Ne) and fourth-row (K to Kr) atoms. The most accurate basis sets reported for the second row are (18s 13p) sets which are with 4 micro E(H) of the numerical Hartree-Fock (NHF) results. For B to Ne basis sets with more than 15s functions are quadruple zeta in the valence space. For the second-row transition metal atoms the (20s 12p 9d) basis sets are triple zeta in the valence space and are approximately equivalent to Clementi and Roetti's accurate Slater type orbital sets. Supplementing the (20s 12p 9d) basis sets optimized for the lowest state with the 4s(2)3d(n) occupation with a diffuse d function gives self-consistent-field energy separations to the 4s(1)3d(n+1) and 3d(n+2) states which are within 100 micro E(H) of the NHF results. The most accurate basis sets for the transition metal atoms are with 30 micro E(H) of the NHF results. In addition, energy optimized sets are reported for He(3P), Li(2P) and Be(3P).
International Nuclear Information System (INIS)
Lara-Castells, María Pilar de; Mitrushchenkov, Alexander O.; Stoll, Hermann
2015-01-01
A combined density functional (DFT) and incremental post-Hartree-Fock (post-HF) approach, proven earlier to calculate He-surface potential energy surfaces [de Lara-Castells et al., J. Chem. Phys. 141, 151102 (2014)], is applied to describe the van der Waals dominated Ag 2 /graphene interaction. It extends the dispersionless density functional theory developed by Pernal et al. [Phys. Rev. Lett. 103, 263201 (2009)] by including periodic boundary conditions while the dispersion is parametrized via the method of increments [H. Stoll, J. Chem. Phys. 97, 8449 (1992)]. Starting with the elementary cluster unit of the target surface (benzene), continuing through the realistic cluster model (coronene), and ending with the periodic model of the extended system, modern ab initio methodologies for intermolecular interactions as well as state-of-the-art van der Waals-corrected density functional-based approaches are put together both to assess the accuracy of the composite scheme and to better characterize the Ag 2 /graphene interaction. The present work illustrates how the combination of DFT and post-HF perspectives may be efficient to design simple and reliable ab initio-based schemes in extended systems for surface science applications
de Lara-Castells, María Pilar; Mitrushchenkov, Alexander O; Stoll, Hermann
2015-09-14
A combined density functional (DFT) and incremental post-Hartree-Fock (post-HF) approach, proven earlier to calculate He-surface potential energy surfaces [de Lara-Castells et al., J. Chem. Phys. 141, 151102 (2014)], is applied to describe the van der Waals dominated Ag2/graphene interaction. It extends the dispersionless density functional theory developed by Pernal et al. [Phys. Rev. Lett. 103, 263201 (2009)] by including periodic boundary conditions while the dispersion is parametrized via the method of increments [H. Stoll, J. Chem. Phys. 97, 8449 (1992)]. Starting with the elementary cluster unit of the target surface (benzene), continuing through the realistic cluster model (coronene), and ending with the periodic model of the extended system, modern ab initio methodologies for intermolecular interactions as well as state-of-the-art van der Waals-corrected density functional-based approaches are put together both to assess the accuracy of the composite scheme and to better characterize the Ag2/graphene interaction. The present work illustrates how the combination of DFT and post-HF perspectives may be efficient to design simple and reliable ab initio-based schemes in extended systems for surface science applications.
Arivazhagan, M; Manivel, S; Jeyavijayan, S; Meenakshi, R
2015-01-05
The FTIR and FT-Raman spectra of 2-ethylimidazole (2EIDZ) have been recorded in the region 4000-400 cm(-1) and 3500-50 cm(-1), respectively. Utilizing the observed FTIR and FT-Raman data, a complete vibrational assignment and analysis of the fundamental modes of the compound were carried out. The optimized molecular geometry, harmonic vibrational frequencies, infrared intensities and Raman scattering activities, were calculated by ab initio Hartree-Fock (HF) and density functional theory (DFT/B3LYP) methods with 6-311++G(d,p) basis set. The difference between the observed and scaled wavenumber values of most of the fundamentals is very small. A detailed interpretation of the infrared and Raman spectra of 2EIDZ is also reported based on total energy distribution (TED). The values of the total dipole moment (μ) and the first-order hyperpolarizability (β) of the compound were computed. Stability of the molecule arising from hyperconjugative interactions, charge delocalization have been analyzed using natural bond orbital (NBO) analysis. Besides, HOMO and LUMO analysis, Mulliken's charge analysis and several thermodynamic properties have been calculated. Copyright © 2014 Elsevier B.V. All rights reserved.
Energy Technology Data Exchange (ETDEWEB)
Lara-Castells, María Pilar de, E-mail: Pilar.deLara.Castells@csic.es [Instituto de Física Fundamental (C.S.I.C.), Serrano 123, E-28006 Madrid (Spain); Mitrushchenkov, Alexander O. [Université Paris-Est, Laboratoire Modélisation et Simulation Multi Echelle, MSME UMR 8208 CNRS, 5 bd Descartes, 77454 Marne-la-Vallée (France); Stoll, Hermann [Institut für Theoretische Chemie, Universität Stuttgart, D-70550 Stuttgart (Germany)
2015-09-14
A combined density functional (DFT) and incremental post-Hartree-Fock (post-HF) approach, proven earlier to calculate He-surface potential energy surfaces [de Lara-Castells et al., J. Chem. Phys. 141, 151102 (2014)], is applied to describe the van der Waals dominated Ag{sub 2}/graphene interaction. It extends the dispersionless density functional theory developed by Pernal et al. [Phys. Rev. Lett. 103, 263201 (2009)] by including periodic boundary conditions while the dispersion is parametrized via the method of increments [H. Stoll, J. Chem. Phys. 97, 8449 (1992)]. Starting with the elementary cluster unit of the target surface (benzene), continuing through the realistic cluster model (coronene), and ending with the periodic model of the extended system, modern ab initio methodologies for intermolecular interactions as well as state-of-the-art van der Waals-corrected density functional-based approaches are put together both to assess the accuracy of the composite scheme and to better characterize the Ag{sub 2}/graphene interaction. The present work illustrates how the combination of DFT and post-HF perspectives may be efficient to design simple and reliable ab initio-based schemes in extended systems for surface science applications.
Perger, W. F.; Das, B. P.
1987-01-01
The parity-nonconserving electric-dipole-transition amplitudes for the 6s1/2-7s1/2 transition in cesium and the 6p1/2-7p1/2 transition in thallium have been calculated by the Dirac-Hartree-Fock method. The effects of using different Dirac-Hartree-Fock atomic core potentials are examined and the transition amplitudes for both the length and velocity gauges are given. It is found that the parity-nonconserving transition amplitudes exhibit a greater dependence on the starting potential for thallium than for cesium.
Time-Dependent Thermal Transport Theory.
Biele, Robert; D'Agosta, Roberto; Rubio, Angel
2015-07-31
Understanding thermal transport in nanoscale systems presents important challenges to both theory and experiment. In particular, the concept of local temperature at the nanoscale appears difficult to justify. Here, we propose a theoretical approach where we replace the temperature gradient with controllable external blackbody radiations. The theory recovers known physical results, for example, the linear relation between the thermal current and the temperature difference of two blackbodies. Furthermore, our theory is not limited to the linear regime and goes beyond accounting for nonlinear effects and transient phenomena. Since the present theory is general and can be adapted to describe both electron and phonon dynamics, it provides a first step toward a unified formalism for investigating thermal and electronic transport.
Quiney, HM; Glushkov, VN; Wilson, S
2004-01-01
Using large component basis sets of distributed s-type Gaussian functions with positions and exponents optimized so as to support Hartree-Fock total energies with an accuracy approaching the sub-muhartree level, Dirac-Hartree-Fock-Coulomb calculations are reported for the ground states of the
Nonrelativistic theory of heavy-ion collisions
International Nuclear Information System (INIS)
Bertsch, G.
1984-01-01
A wide range of phenomena is observed in heavy-ion collisions, calling for a comprehensive theory based on fundamental principles of many-particle quantum mechanics. At low energies, the nuclear dynamics is controlled by the mean field, as we know from spectroscopic nuclear physics. We therefore expect the comprehensive theory of collisions to contain mean-field theory at low energies. The mean-field theory is the subject of the first lectures in this chapter. This theory can be studied quantum mechanically, in which form it is called TDHF (time-dependent Hartree-Fock), or classically, where the equation is called the Vlasov equation. 25 references, 14 figures
Nonrelativistic theory of heavy-ion collisions
Energy Technology Data Exchange (ETDEWEB)
Bertsch, G.
1984-07-17
A wide range of phenomena is observed in heavy-ion collisions, calling for a comprehensive theory based on fundamental principles of many-particle quantum mechanics. At low energies, the nuclear dynamics is controlled by the mean field, as we know from spectroscopic nuclear physics. We therefore expect the comprehensive theory of collisions to contain mean-field theory at low energies. The mean-field theory is the subject of the first lectures in this chapter. This theory can be studied quantum mechanically, in which form it is called TDHF (time-dependent Hartree-Fock), or classically, where the equation is called the Vlasov equation. 25 references, 14 figures.
Energy Technology Data Exchange (ETDEWEB)
Valsson, Omar [Department of Chemistry and Applied Biosciences, ETH Zurich and Facoltà di Informatica, Instituto di Scienze Computationali, Università della Svizzera italiana, Via Giuseppe Buffi 13, CH-6900 Lugano (Switzerland); Filippi, Claudia, E-mail: c.filippi@utwente.nl [MESA+ Institute for Nanotechnology, University of Twente, P.O. Box 217, 7500 AE Enschede (Netherlands); Casida, Mark E., E-mail: mark.casida@ujf-grenoble.fr [Laboratoire de Chimie Théorique, Département de Chimie Moléculaire (DCM), Institut de Chimie Moléculaire de Grenoble (ICMG), Université Joseph Fourier, Grenoble I, F-3801 Grenoble (France)
2015-04-14
The excited-state relaxation of retinal protonated Schiff bases (PSBs) is an important test case for biological applications of time-dependent (TD) density-functional theory (DFT). While well-known shortcomings of approximate TD-DFT might seem discouraging for application to PSB relaxation, progress continues to be made in the development of new functionals and of criteria allowing problematic excitations to be identified within the framework of TD-DFT itself. Furthermore, experimental and theoretical ab initio advances have recently lead to a revised understanding of retinal PSB photochemistry, calling for a reappraisal of the performance of TD-DFT in describing this prototypical photoactive system. Here, we re-investigate the performance of functionals in (TD-)DFT calculations in light of these new benchmark results, which we extend to larger PSB models. We focus on the ability of the functionals to describe primarily the early skeletal relaxation of the chromophore and investigate how far along the out-of-plane pathways these functionals are able to describe the subsequent rotation around formal single and double bonds. Conventional global hybrid and range-separated hybrid functionals are investigated as the presence of Hartree-Fock exchange reduces problems with charge-transfer excitations as determined by the Peach-Benfield-Helgaker-Tozer Λ criterion and by comparison with multi-reference perturbation theory results. While we confirm that most functionals cannot render the complex photobehavior of the retinal PSB, do we also observe that LC-BLYP gives the best description of the initial part of the photoreaction.
Uemura, Wataru
2011-01-01
In this paper, we introduce a new representation of many body electron wave function and a few calculation results of the ground state energies of many body systems using that representation, which is systematically better than the Hartree-Fock approximation.
Hermes, Matthew R; Hirata, So
2015-09-14
One-dimensional (1D) solids exhibit a number of striking electronic structures including charge-density wave (CDW) and spin-density wave (SDW). Also, the Peierls theorem states that at zero temperature, a 1D system predicted by simple band theory to be a metal will spontaneously dimerize and open a finite fundamental bandgap, while at higher temperatures, it will assume the equidistant geometry with zero bandgap (a Peierls transition). We computationally study these unique electronic structures and transition in polyyne and all-trans polyacetylene using finite-temperature generalizations of ab initio spin-unrestricted Hartree-Fock (UHF) and spin-restricted coupled-cluster doubles (CCD) theories, extending upon previous work [He et al., J. Chem. Phys. 140, 024702 (2014)] that is based on spin-restricted Hartree-Fock (RHF) and second-order many-body perturbation (MP2) theories. Unlike RHF, UHF can predict SDW as well as CDW and metallic states, and unlike MP2, CCD does not diverge even if the underlying RHF reference wave function is metallic. UHF predicts a gapped SDW state with no dimerization at low temperatures, which gradually becomes metallic as the temperature is raised. CCD, meanwhile, confirms that electron correlation lowers the Peierls transition temperature. Furthermore, we show that the results from all theories for both polymers are subject to a unified interpretation in terms of the UHF solutions to the Hubbard-Peierls model using different values of the electron-electron interaction strength, U/t, in its Hamiltonian. The CCD wave function is shown to encompass the form of the exact solution of the Tomonaga-Luttinger model and is thus expected to describe accurately the electronic structure of Luttinger liquids.
Xu, Ruirui; Ma, Zhongyu; Muether, Herbert; van Dalen, E. N. E.; Liu, Tinjin; Zhang, Yue; Zhang, Zhi; Tian, Yuan
2017-09-01
A relativistic microscopic optical model potential, named CTOM, for nucleon-nucleus scattering is investigated in the framework of Dirac-Brueckner-Hartree-Fock approach. The microscopic feature of CTOM is guaranteed through rigorously adopting the isospin dependent DBHF calculation within the subtracted T matrix scheme. In order to verify its prediction power, a global study n, p+ A scattering are carried out. The predicted scattering observables coincide with experimental data within a good accuracy over a broad range of targets and a large region of energies only with two free items, namely the free-range factor t in the applied improved local density approximation and minor adjustments of the scalar and vector potentials in the low-density region. In addition, to estimate the uncertainty of the theoretical results, the deterministic simple least square approach is preliminarily employed to derive the covariance of predicted angular distributions, which is also briefly contained in this paper.
Kalinowski, Jaroslaw; Wennmohs, Frank; Neese, Frank
2017-07-11
A resolution of identity based implementation of the Hartree-Fock method on graphical processing units (GPUs) is presented that is capable of handling basis functions with arbitrary angular momentum. For practical reasons, only functions up to (ff|f) angular momentum are presently calculated on the GPU, thus leaving the calculation of higher angular momenta integrals on the CPU of the hybrid CPU-GPU environment. Speedups of up to a factor of 30 are demonstrated relative to state-of-the-art serial and parallel CPU implementations. Benchmark calculations with over 3500 contracted basis functions (def2-SVP or def2-TZVP basis sets) are reported. The presented implementation supports all devices with OpenCL support and is capable of utilizing multiple GPU cards over either MPI or OpenCL itself.
Shimazaki, Tomomi; Nakajima, Takahito
2015-02-21
Dielectric-dependent screened Hartree-Fock (HF) exchange potential and Slater-formula have been reported, where the ratio of the HF exchange term mixed into potentials is inversely proportional to the dielectric constant of the target semiconductor. This study introduces a position-dependent dielectric constant method in which the dielectric constant is partitioned between the atoms in a semiconductor. These partitioned values differ depending on the electrostatic environment surrounding the atoms and lead to position-dependent atomic dielectric constants. These atomic dielectric constants provide atomic orbital-based matrix elements for the screened exchange potentials. Energy band structures of several semiconductors and insulators are also presented to validate this approach.
International Nuclear Information System (INIS)
Heinemann, D.; Rosen, A.; Fricke, B.
1990-01-01
The finite element method (FEM) is now developed to solve two-dimensional Hartree-Fock (HF) equations for atoms and diatomic molecules. The method and its implementation is described and results are presented for the atoms Be, Ne and Ar as well as the diatomic molecules LiH, BH, N 2 and CO as examples. Total energies and eigenvalues calculated with the FEM on the HF-level are compared with results obtained with the numerical standard methods used for the solution of the opne dimensional HF equations for atoms and for diatomic molecules with the traditional LCAO quantum chemical methods and the newly developed finite difference method on the HF-level. In general the accuracy increases from the LCAO - to the finite difference - to the finite element method. (orig.)
International Nuclear Information System (INIS)
Lorenzana, J.; Grynberg, M.D.; Yu, L.; Yonemitsu, K.; Bishop, A.R.
1992-11-01
The ground state energy, and static and dynamic correlation functions are investigated in the inhomogeneous Hartree-Fock (HF) plus random phase approximation (RPA) approach applied to a one-dimensional spinless fermion model showing self-trapped doping states at the mean field level. Results are compared with homogeneous HF and exact diagonalization. RPA fluctuations added to the generally inhomogeneous HF ground state allows the computation of dynamical correlation functions that compare well with exact diagonalization results. The RPA correction to the ground state energy agrees well with the exact results at strong and weak coupling limits. We also compare it with a related quasi-boson approach. The instability towards self-trapped behaviour is signaled by a RPA mode with frequency approaching zero. (author). 21 refs, 10 figs
International Nuclear Information System (INIS)
West, Aaron C.; Schmidt, Michael W.; Gordon, Mark S.; Ruedenberg, Klaus
2013-01-01
Through a basis-set-independent web of localizing orbital-transformations, the electronic wave function of a molecule is expressed in terms of a set of orbitals that reveal the atomic structure and the bonding pattern of a molecule. The analysis is based on resolving the valence orbital space in terms of an internal space, which has minimal basis set dimensions, and an external space. In the internal space, oriented quasi-atomic orbitals and split-localized molecular orbitals are determined by new, fast localization methods. The density matrix between the oriented quasi-atomic orbitals as well as the locations of the split-localized orbitals exhibit atomic populations and inter-atomic bonding patterns. A correlation-adapted quasi-atomic basis is determined in the external orbital space. The general formulations are specified in detail for Hartree-Fock wave functions. Applications to specific molecules exemplify the general scheme
Boussouf, K; Boulmene, R; Prakash, M; Komiha, N; Taleb, M; Mogren Al-Mogren, M; Hochlaf, M
2015-06-14
In the present work, we investigate the bonding, structures, stability and spectra of the Zn(q+)Im (where q = 0, 1, and 2) complexes, which are zeolitic imidazolate frameworks (ZIFs) and Zn-enzyme sub-units. Through a benchmark work, we used density functional theory (DFT) with dispersion correction and standard and explicitly correlated ab initio methods. For neutral Zn(0)Im, we found two stable weakly bound forms: (i) a stacked ferrocene-like complex and (ii) a planar σ-type complex. This is the first report of the Zn(0) organic compound with a stacked ferrocene-like structure. The most stable isomers of the ionic species consist of σ-type bonded complexes. The role of various types of covalent and noncovalent interactions within these complexes is discussed after performing vibrational, NBO, charge and orbital analyses. For neutral species, van der Waals (vdWs) and charge transfer through covalent as well as noncovalent interactions are in action; whereas the bonding is dominated by charge transfer from Zn to Im within the ionic species. These findings are important to understand, at the microscopic level, the structure and the bonding within the ZIFs and the Zn-enzymes. Moreover, we establish the ability and reliability of M05-2X and PBE0 functionals for the simultaneous correct description of covalent and noncovalent interactions since this DFT leads to a close agreement with post-Hartree-Fock methods. The newly launched M11 functional is also suited for the description of noncovalent interactions. Therefore, M05-2X and PBE0 functionals are recommended for studying the larger complexes formed by Zn and Im, such as the ZIFs and Zn-enzymes.
Time-dependent potential-functional embedding theory
International Nuclear Information System (INIS)
Huang, Chen; Libisch, Florian; Peng, Qing; Carter, Emily A.
2014-01-01
We introduce a time-dependent potential-functional embedding theory (TD-PFET), in which atoms are grouped into subsystems. In TD-PFET, subsystems can be propagated by different suitable time-dependent quantum mechanical methods and their interactions can be treated in a seamless, first-principles manner. TD-PFET is formulated based on the time-dependent quantum mechanics variational principle. The action of the total quantum system is written as a functional of the time-dependent embedding potential, i.e., a potential-functional formulation. By exploiting the Runge-Gross theorem, we prove the uniqueness of the time-dependent embedding potential under the constraint that all subsystems share a common embedding potential. We derive the integral equation that such an embedding potential needs to satisfy. As proof-of-principle, we demonstrate TD-PFET for a Na 4 cluster, in which each Na atom is treated as one subsystem and propagated by time-dependent Kohn-Sham density functional theory (TDDFT) using the adiabatic local density approximation (ALDA). Our results agree well with a direct TDDFT calculation on the whole Na 4 cluster using ALDA. We envision that TD-PFET will ultimately be useful for studying ultrafast quantum dynamics in condensed matter, where key regions are solved by highly accurate time-dependent quantum mechanics methods, and unimportant regions are solved by faster, less accurate methods
Time-dependent density functional theory for periodic systems
Kootstra, Freddie
2001-01-01
In this thesis the time-dependent version of density functional theory is described, which has been developed for crystalline non-metallic systems with periodicity in one to three dimensions. The application of this theory to the calculation of the optical reponse properties of a wide range of
International Nuclear Information System (INIS)
Sugimoto, Satoru; Ikeda, Kiyomi; Toki, Hiroshi
2004-01-01
We propose a new mean-field-type framework which can treat the strong correlation induced by the tensor force. To treat the tensor correlation we break the charge and parity symmetries of a single-particle state and restore these symmetries of the total system by the projection method. We perform the charge and parity projections before variation and obtain a Hartree-Fock-like equation, which is solved self-consistently. We apply the Hartree-Fock-like equation to the alpha particle and find that by breaking the parity and charge symmetries, the correlation induced by the tensor force is obtained in the projected mean-field framework. We emphasize that the projection before the variation is important to pick up the tensor correlation in the present framework
Wu, Zuqing; Ping, Jialun; Zong, Hongshi
2017-12-01
Three representations of Nambu-Jona-Lasinio interaction Lagrangians are constructed by Fierz transformation, and gap equation and critical end point in these three representations at finite temperature and finite chemical potential are studied. We find that the values of the quark mass and the critical end point are different in these three representations because of the consideration of Hartree-Fock approximation in our calculation.
International Nuclear Information System (INIS)
Brorsen, Kurt R.; Sirjoosingh, Andrew; Pak, Michael V.; Hammes-Schiffer, Sharon
2015-01-01
The nuclear electronic orbital (NEO) reduced explicitly correlated Hartree-Fock (RXCHF) approach couples select electronic orbitals to the nuclear orbital via Gaussian-type geminal functions. This approach is extended to enable the use of a restricted basis set for the explicitly correlated electronic orbitals and an open-shell treatment for the other electronic orbitals. The working equations are derived and the implementation is discussed for both extensions. The RXCHF method with a restricted basis set is applied to HCN and FHF − and is shown to agree quantitatively with results from RXCHF calculations with a full basis set. The number of many-particle integrals that must be calculated for these two molecules is reduced by over an order of magnitude with essentially no loss in accuracy, and the reduction factor will increase substantially for larger systems. Typically, the computational cost of RXCHF calculations with restricted basis sets will scale in terms of the number of basis functions centered on the quantum nucleus and the covalently bonded neighbor(s). In addition, the RXCHF method with an odd number of electrons that are not explicitly correlated to the nuclear orbital is implemented using a restricted open-shell formalism for these electrons. This method is applied to HCN + , and the nuclear densities are in qualitative agreement with grid-based calculations. Future work will focus on the significance of nonadiabatic effects in molecular systems and the further enhancement of the NEO-RXCHF approach to accurately describe such effects
Kim, Jaewook; Hong, Kwangwoo; Choi, Sunghwan; Hwang, Sang-Yeon; Youn Kim, Woo
2015-12-21
We developed a program code of configuration interaction singles (CIS) based on a numerical grid method. We used Kohn-Sham (KS) as well as Hartree-Fock (HF) orbitals as a reference configuration and Lagrange-sinc functions as a basis set. Our calculations show that KS-CIS is more cost-effective and more accurate than HF-CIS. The former is due to the fact that the non-local HF exchange potential greatly reduces the sparsity of the Hamiltonian matrix in grid-based methods. The latter is because the energy gaps between KS occupied and virtual orbitals are already closer to vertical excitation energies and thus KS-CIS needs small corrections, whereas HF results in much larger energy gaps and more diffuse virtual orbitals. KS-CIS using the Lagrange-sinc basis set also shows a better or a similar accuracy to smaller orbital space compared to the standard HF-CIS using Gaussian basis sets. In particular, KS orbitals from an exact exchange potential by the Krieger-Li-Iafrate approximation lead to more accurate excitation energies than those from conventional (semi-) local exchange-correlation potentials.
Spiral magnetism in the single-band Hubbard model: the Hartree-Fock and slave-boson approaches.
Igoshev, P A; Timirgazin, M A; Gilmutdinov, V F; Arzhnikov, A K; Irkhin, V Yu
2015-11-11
The ground-state magnetic phase diagram is investigated within the single-band Hubbard model for square and different cubic lattices. The results of employing the generalized non-correlated mean-field (Hartree-Fock) approximation and generalized slave-boson approach by Kotliar and Ruckenstein with correlation effects included are compared. We take into account commensurate ferromagnetic, antiferromagnetic, and incommensurate (spiral) magnetic phases, as well as phase separation into magnetic phases of different types, which was often lacking in previous investigations. It is found that the spiral states and especially ferromagnetism are generally strongly suppressed up to non-realistically large Hubbard U by the correlation effects if nesting is absent and van Hove singularities are well away from the paramagnetic phase Fermi level. The magnetic phase separation plays an important role in the formation of magnetic states, the corresponding phase regions being especially wide in the vicinity of half-filling. The details of non-collinear and collinear magnetic ordering for different cubic lattices are discussed.
Brorsen, Kurt R; Sirjoosingh, Andrew; Pak, Michael V; Hammes-Schiffer, Sharon
2015-06-07
The nuclear electronic orbital (NEO) reduced explicitly correlated Hartree-Fock (RXCHF) approach couples select electronic orbitals to the nuclear orbital via Gaussian-type geminal functions. This approach is extended to enable the use of a restricted basis set for the explicitly correlated electronic orbitals and an open-shell treatment for the other electronic orbitals. The working equations are derived and the implementation is discussed for both extensions. The RXCHF method with a restricted basis set is applied to HCN and FHF(-) and is shown to agree quantitatively with results from RXCHF calculations with a full basis set. The number of many-particle integrals that must be calculated for these two molecules is reduced by over an order of magnitude with essentially no loss in accuracy, and the reduction factor will increase substantially for larger systems. Typically, the computational cost of RXCHF calculations with restricted basis sets will scale in terms of the number of basis functions centered on the quantum nucleus and the covalently bonded neighbor(s). In addition, the RXCHF method with an odd number of electrons that are not explicitly correlated to the nuclear orbital is implemented using a restricted open-shell formalism for these electrons. This method is applied to HCN(+), and the nuclear densities are in qualitative agreement with grid-based calculations. Future work will focus on the significance of nonadiabatic effects in molecular systems and the further enhancement of the NEO-RXCHF approach to accurately describe such effects.
Shaw, Robert A; Hill, J Grant
2017-04-11
Auxiliary basis sets for use in the resolution of the identity (RI) approximation in explicitly correlated methods are presented for the elements H-Ar. These extend the cc-pVnZ-F12/OptRI (n = D-Q) auxiliary basis sets of Peterson and co-workers by the addition of a small number of s- and p-functions, optimized so as to yield the greatest complementary auxiliary basis set (CABS) singles correction to the Hartree-Fock energy. The new sets, denoted OptRI+, also lead to a reduction in errors due to the RI approximation and hence an improvement in correlation energies. The atomization energies and heats of formation for a test set of small molecules, and spectroscopic constants for 27 diatomics, calculated at the CCSD(T)-F12b level, are shown to have improved error distributions for the new auxiliary basis sets with negligible additional effort. The OptRI+ sets retain all of the desirable properties of the original OptRI, including the production of smooth potential energy surfaces, while maintaining a compact nature.
Time-dependent quantum fluid density functional theory of hydrogen ...
Indian Academy of Sciences (India)
A time-dependent generalized non-linear Schrödinger equation (GNLSE) of motion was earlier derived in our laboratory by combining density functional theory and quantum fluid dynamics in threedimensional space. In continuation of the work reported previously, the GNLSE is applied to provide additional knowledge on ...
General time-dependent formulation of quantum scattering theory
International Nuclear Information System (INIS)
Althorpe, Stuart C.
2004-01-01
We derive and explain the key ideas behind a time-dependent formulation of quantum scattering theory, applicable generally to systems with a finite-range scattering potential. The scattering is initiated and probed by plane wave packets, which are localized just outside the range of the potential. The asymptotic limits of conventional scattering theory (initiation in the remote past; detection in the remote future) are not taken. Instead, the differential cross section (DCS) is obtained by projecting the scattered wave packet onto the probe plane wave packets. The projection also yields a time-dependent version of the DCS. Cuts through the wave packet, just as it exits the scattering potential, yield time-dependent and time-independent angular distributions that give a close-up picture of the scattering which complements the DCS. We have previously applied the theory to interpret experimental cross sections of chemical reactions [e.g., S. C. Althorpe, F. Fernandez-Alonso, B. D. Bean, J. D. Ayers, A. E. Pomerantz, R. N. Zare, and E. Wrede, Nature (London) 416, 67 (2002)]. This paper gives the derivation of the theory, and explains its relation to conventional scattering theory. For clarity, the derivation is restricted to spherical-particle scattering, though it may readily be extended to general multichannel systems. We illustrate the theory using a simple application to hard-sphere scattering
Time-dependent geminal method applied to laser-driven beryllium
Lötstedt, Erik; Kato, Tsuyoshi; Yamanouchi, Kaoru
2018-01-01
We introduce the time-dependent geminal method, in which the total wave function is written as an antisymmetrized product of time-dependent geminals. A geminal is a two-electron orbital depending on the coordinates of two electrons, and each geminal is expanded as a sum of products of time-dependent one-electron orbitals. The equation of motion for the geminal coefficients similar to the time-dependent Hartree-Fock equation is derived. The evaluation of the largest eigenvalues of the second-order reduced density matrix is proposed as a way to measure the extent of the intergeminal correlation in a time-dependent wave function. Using the time-dependent geminal method, we simulate the evolution of the time-dependent wave function of a beryllium atom exposed to an intense laser pulse at two different wavelengths, 400 and 10 nm. The results are compared to those obtained by the time-dependent Hartree-Fock method and by the multiconfiguration time-dependent Hartree-Fock method.
Lewis, Cannada A; Calvin, Justus A; Valeev, Edward F
2016-12-13
We describe the clustered low-rank (CLR) framework for block-sparse and block-low-rank tensor representation and computation. The CLR framework exploits the tensor structure revealed by basis clustering; computational savings arise from low-rank compression of tensor blocks and performing block arithmetic in the low-rank form whenever beneficial. The precision is rigorously controlled by two parameters, avoiding ad-hoc heuristics, such as domains: one controls the CLR block rank truncation, and the other controls screening of small contributions in arithmetic operations on CLR tensors to propagate sparsity through expressions. As these parameters approach zero, the CLR representation and arithmetic become exact. As a pilot application, we considered the use of the CLR format for the order-2 and order-3 tensors in the context of the density fitting (DF) evaluation of the Hartree-Fock (exact) exchange (DF-K). Even for small systems and realistic basis sets, CLR-DF-K becomes more efficient than the standard DF-K approach, and it has significantly reduced asymptotic storage and computational complexities relative to the standard [Formula: see text] and [Formula: see text] DF-K figures. CLR-DF-K is also significantly more efficient-all while negligibly affecting molecular energies and properties-than the conventional (non-DF) [Formula: see text] exchange algorithm for applications to medium-sized systems (on the order of 100 atoms) with diffuse Gaussian basis sets, a necessity for applications to negatively charged species, molecular properties, and high-accuracy correlated wave functions.
Hartree Fock-type equations in relativistic quantum electrodynamics with non-linear gauge fixing
International Nuclear Information System (INIS)
Dietz, K.; Hess, B.A.
1990-08-01
Relativistic mean-field equations are obtained by minimizing the effective energy obtained from the gauge-invariant energy density by eliminating electro-magnetic degrees of freedom in certain characteristic non-linear gauges. It is shown that by an appropriate choice of gauge many-body correlations, e.g. screening, three-body 'forces' etc. can be included already at the mean-field level. The many-body perturbation theory built on the latter is then expected to show improved 'convergence'. (orig.)
Time-dependent density-functional theory concepts and applications
Ullrich, Carsten A
2011-01-01
Time-dependent density-functional theory (TDDFT) describes the quantum dynamics of interacting electronic many-body systems formally exactly and in a practical and efficient manner. TDDFT has become the leading method for calculating excitation energies and optical properties of large molecules, with accuracies that rival traditional wave-function based methods, but at a fraction of the computational cost.This book is the first graduate-level text on the concepts and applications of TDDFT, including many examples and exercises, and extensive coverage of the literature. The book begins with a s
Scattering theory for explicitely time-dependent interactions
International Nuclear Information System (INIS)
Perusch, M.
1982-01-01
Multiple ionization of hydrogen atoms has got increased attention in recent years in connection with high-power lasers. Due to the strong external electromagnetic fields, perturbation theory is no longer valid. The expression for the multiple ionization probability contains the projections of the time-dependent Hamilton operators and the Moeller operators. The main point of the present work is a proof of existence and completeness of the Moeller operators. The proof of existence and completeness is given. The final chapter contains a physical interpretation and discussion of the multiple ionization probability. (G.Q.)
Directory of Open Access Journals (Sweden)
Y. Sajeev
2015-08-01
Full Text Available The equation-of-motion coupled cluster (EOMCC method based on the excited state Hartree-Fock (ESHF solutions is shown to be appropriate for computing the entire ground state potential energy curves of strongly correlated higher-order bonds. The new approach is best illustrated for the homolytic dissociation of higher-order bonds in molecules. The required multireference character of the true ground state wavefunction is introduced through the linear excitation operator of the EOMCC method. Even at the singles and doubles level of cluster excitation truncation, the nonparallelity error of the ground state potential energy curve from the ESHF based EOMCC method is small.
Masur, Oliver; Schütz, Martin; Maschio, Lorenzo; Usvyat, Denis
2016-10-11
We present a periodic/finite-cluster interface for fragment-based direct local ring-coupled-cluster doubles (d-LrCCD) calculations embedded in the periodic mean field. The fragment is defined by a set of Wannier functions (WFs), obtained from a periodic Hartree-Fock calculation. The pair-specific virtual space is spanned by projected atomic orbitals (PAOs) truncated to pair domains. The computational procedure is initiated by a periodic local Møller-Plesset (LMP2) calculation. A subset of the WF pairs is then subsequently subjected to a finite-cluster d-LrCCD treatment using the local coupled cluster program of Molpro; this subset is specified by an interorbital cutoff distance. The orbital, pair, and domain lists, as well as other essential quantities needed for d-LrCCD such as the Fock and overlap matrices, and the electron repulsion integrals (ERIs) in the basis of WFs and PAOs are evaluated in the periodic framework and passed to Molpro via an interface. These periodic quantities provide the correct periodic mean-field embedding for the fragment d-LrCCD. Moreover, no expensive orbital transformations involving orbital coefficients related to large supporting clusters are necessary. ERIs appearing in the d-LrCCD diagrams are factorized via density fitting, which enables an efficient processing of the corresponding terms via three-index intermediates. The corresponding 3-index and the metric 2-index ERIs involving auxiliary functions are also computed and transformed to the WF-PAO basis (the 3-index ERI) on the periodic side. Although the direct ring-CCD method itself is not generally more accurate than MP2, it is more stable in the case of small band gap systems, as it sums up the ring diagrams to infinite order. Furthermore, this interface is a first step toward a high-level fragment-based quantum chemical treatment such as local CCSD(T) within a periodic embedding that is treated at a lower level. As two test examples we study the physisorption of H 2 and
Supersymmetric gauge theory with space-time-dependent couplings
Choi, Jaewang; Fernández-Melgarejo, José J.; Sugimoto, Shigeki
2018-01-01
We study deformations of N=4 supersymmetric Yang-Mills theory with couplings and masses depending on space-time. The conditions to preserve part of the supersymmetry are derived and a lot of solutions of these conditions are found. The main example is the case with ISO(1,1)× SO(3)× SO(3) symmetry, in which couplings, as well as masses and the theta parameter, can depend on two spatial coordinates. In the case in which ISO(1,1) is enhanced to ISO(1,2), it reproduces the supersymmetric Janus configuration found by Gaiotto and Witten [J. High Energy Phys. 06, 097 (2010)]. When SO(3)× SO(3) is enhanced to SO(6), it agrees with the world-volume theory of D3-branes embedded in F-theory (a background with 7-branes in type IIB string theory). We have also found the general solution of the supersymmetry conditions for the cases with ISO(1,1)× SO(2)× SO(4) symmetry. Cases with time-dependent couplings and/or masses are also considered.
Rérat, Michel; Maschio, Lorenzo; Kirtman, Bernard; Civalleri, Bartolomeo; Dovesi, Roberto
2016-01-12
The electronic second harmonic generation (SHG) tensor, d, of crystalline urea and potassium dihydrogen phosphate (KDP) is evaluated as a function of frequency using a Gaussian type basis set and the Coupled Perturbed Hartree-Fock (CPHF) and Kohn-Sham (CPKS) schemes as implemented in the CRYSTAL code. The results of various functionals, including LDA, GGA (PBE), and global and range-separated hybrids (B3LYP, PBE0, LC-BLYP), as well as Hartree-Fock, are compared. It is found that the calculated SHG intensity always decreases as the percentage of exact exchange increases. The hybrid functionals turn out to provide results that agree well with experiment. For urea and KDP the percentage of exact exchange determined by the inverse dielectric constant is too large. At 1064 nm the vibrational contribution for urea is found to be less than 5% of the total value. To the authors' knowledge, this is the first coupled (self-consistent) calculation of SHG for any periodic system.
de Cerqueira Sobrinho, Antonio Moreira; de Andrade, Micael Dias; Nascimento, Marco Antônio Chaer; Malbouisson, Luiz Augusto Carvalho
2014-08-01
In this work, we propose new double-zeta atomic bases for the Li and Be atoms. These were obtained by applying the Hartree-Fock-Gauss generalized simulated annealing (GSA) method-a modified form of the GSA algorithm. The new bases were generated through optimization of the atomic electronic energy functional with regards to the linear combination of atomic orbitals-molecular orbital (LCAO-MO) coefficients, and exponent and contraction coefficients of the primitive Gaussian functions, simultaneously. These new bases were tested by performing calculations of the ground state energy of the Be atom, and the ground state energy and permanent electrical dipole moment of the LiH molecule, using the multi-reference Hartree-Fock (HF) configuration interaction method-a multi-reference method based on multiple HF solutions. In addition, multi-reference HF configuration interaction calculations were performed for the Be atom using the standard double-zeta, triple-zeta and polarized double-zeta bases. With the new double-zeta bases and with reduced multi-reference HF bases, it was possible to obtain lower energies than those obtained with the full configuration interaction calculations using the standard double-zeta bases and dipole moment values in close agreement with experimental values.
Zheng, Xiao; Yam, ChiYung; Wang, Fan; Chen, GuanHua
2011-08-28
We present the time-dependent holographic electron density theorem (TD-HEDT), which lays the foundation of time-dependent density-functional theory (TDDFT) for open electronic systems. For any finite electronic system, the TD-HEDT formally establishes a one-to-one correspondence between the electron density inside any finite subsystem and the time-dependent external potential. As a result, any electronic property of an open system in principle can be determined uniquely by the electron density function inside the open region. Implications of the TD-HEDT on the practicality of TDDFT are also discussed.
Shimazaki, Tomomi; Asai, Yoshihiro
2010-06-14
The screening effect on the Hartree-Fock (HF) exchange term plays a key role in the investigation of solid-state materials by first-principles electronic structure calculations. We recently proposed a novel screened HF exchange potential, in which the inverse of the dielectric constant represents the fraction of the HF exchange term incorporated into the potential. We demonstrated that this approach can be used to reproduce the energy band structure of diamond well [T. Shimazaki and Y. Asai, J. Chem. Phys. 130, 164702 (2009)]. In the present paper, we report that the screened HF exchange method is applicable to other semiconductors such as silicon, AlP, AlAs, GaP, and GaAs.
Martinez, Jean-Philippe
2017-11-01
The Hartree-Fock method, one of the first applications of the new quantum mechanics in the frame of the many-body problem, had been elaborated by Rayner Douglas Hartree in 1928 and Vladimir Fock in 1930. Promptly, the challenge of tedious computations was being discussed and it is well known that the application of the method benefited greatly from the development of computers from the mid-to-late 1950s. However, the years from 1930 to 1950 were by no means years of stagnation, as the method was the object of several considerations related to its mathematical formulation, possible extension, and conceptual understanding. Thus, with a focus on the respective attitudes of Hartree and Fock, in particular with respect to the concept of quantum exchange, the present work puts forward some mathematical and conceptual clarifications, which played an important role for a better understanding of the many-body problem in quantum mechanics.
Linker, Gerrit-Jan; van Loosdrecht, Paul H M; van Duijnen, Piet Th; Broer, Ria
2015-11-11
The insulating and conducting phases of (EDO-TTF)2PF6 were studied by all electron, periodic Hartree-Fock and hybrid density functional calculations. Electronic properties, such as the electronic band structure, the density of states and the Fermi surface are discussed in relation to the metal-insulator transition in this material. The nature of conduction is confirmed in both phases from their band structures and density of states. The hybrid DFT band gaps are in good agreement with experiment. Interactions are discussed on the basis of band dispersion in the inter-stack, intra-stack and inter-sheet directions. We discuss the phase transition in terms of the Peierls mechanism and our results fully support this view.
Shimazaki, Tomomi; Nakajima, Takahito
2014-09-21
We previously reported a screened Hartree-Fock (HF) exchange potential for energy band structure calculations [T. Shimazaki and Y. Asai, J. Chem. Phys. 130, 164702 (2009); T. Shimazaki and Y. Asai, J. Chem. Phys. 132, 224105 (2010)]. In this paper, we discuss the Coulomb-hole (COH) interaction and screened Slater-formula and determine the energy band diagrams of several semiconductors, such as diamond, silicon, AlAs, AlP, GaAs, GaP, and InP, based on the screened HF exchange potential and Slater-formula with COH interaction, to demonstrate the adequacy of those theoretical concepts. The screened HF exchange potential and Slater-formula are derived from a simplified dielectric function and, therefore, include the dielectric constant in their expressions. We also present a self-consistent calculation technique to automatically determine the dielectric constant, which is incorporated into each self-consistent field step.
Time-dependent non-equilibrium dielectric response in QM/continuum approaches
Energy Technology Data Exchange (ETDEWEB)
Ding, Feizhi; Lingerfelt, David B.; Li, Xiaosong, E-mail: benedetta.mennucci@unipi.it, E-mail: li@chem.washington.edu [Department of Chemistry, University of Washington, Seattle, Washington 98195 (United States); Mennucci, Benedetta, E-mail: benedetta.mennucci@unipi.it, E-mail: li@chem.washington.edu [Dipartimento di Chimica e Chimica Industriale, Università di Pisa, Via Risorgimento 35, 56126 Pisa (Italy)
2015-01-21
The Polarizable Continuum Models (PCMs) are some of the most inexpensive yet successful methods for including the effects of solvation in quantum-mechanical calculations of molecular systems. However, when applied to the electronic excitation process, these methods are restricted to dichotomously assuming either that the solvent has completely equilibrated with the excited solute charge density (infinite-time limit), or that it retains the configuration that was in equilibrium with the solute prior to excitation (zero-time limit). This renders the traditional PCMs inappropriate for resolving time-dependent solvent effects on non-equilibrium solute electron dynamics like those implicated in the instants following photoexcitation of a solvated molecular species. To extend the existing methods to this non-equilibrium regime, we herein derive and apply a new formalism for a general time-dependent continuum embedding method designed to be propagated alongside the solute’s electronic degrees of freedom in the time domain. Given the frequency-dependent dielectric constant of the solvent, an equation of motion for the dielectric polarization is derived within the PCM framework and numerically integrated simultaneously with the time-dependent Hartree fock/density functional theory equations. Results for small molecular systems show the anticipated dipole quenching and electronic state dephasing/relaxation resulting from out-of-phase charge fluctuations in the dielectric and embedded quantum system.
Time-dependent density functional theory for multi-component systems
International Nuclear Information System (INIS)
Tiecheng Li; Peiqing Tong
1985-10-01
The Runge-Gross version of Hohenberg-Kohn-Sham's density functional theory is generalized to multi-component systems, both for arbitrary time-dependent pure states and for arbitrary time-dependent ensembles. (author)
Time-dependent quantum fluid density functional theory of hydrogen ...
Indian Academy of Sciences (India)
WINTEC
GNLSE) of motion was earlier derived in our laboratory by combining density functional theory and quantum fluid dynamics in three- dimensional space. In continuation of the work reported previously, the GNLSE is applied to provide addi-.
Time-dependent quantum fluid density functional theory of hydrogen ...
Indian Academy of Sciences (India)
dependent density; density functional theory; quantum fluid dynamics. ... (HHG) is also examined. The present approach goes beyond the linear response formalism and, in principle, calculates the TD electron density to all orders of change.
Time-dependent quantum fluid density functional theory of hydrogen ...
Indian Academy of Sciences (India)
WINTEC
derived in our laboratory by combining density functional theory and quantum fluid dynamics in three- dimensional space. In continuation of the .... repulsion, electron-nuclear Coulomb attraction, ex- change and correlation interactions, ..... Eberly J H, Grobe R, Law C K and Su Q 1992 Adv. At. Mol. Opt. Phys. Suppl. 1 301. 8.
King, Andrew W; Baskerville, Adam L; Cox, Hazel
2018-03-13
An implementation of the Hartree-Fock (HF) method using a Laguerre-based wave function is described and used to accurately study the ground state of two-electron atoms in the fixed nucleus approximation, and by comparison with fully correlated (FC) energies, used to determine accurate electron correlation energies. A variational parameter A is included in the wave function and is shown to rapidly increase the convergence of the energy. The one-electron integrals are solved by series solution and an analytical form is found for the two-electron integrals. This methodology is used to produce accurate wave functions, energies and expectation values for the helium isoelectronic sequence, including at low nuclear charge just prior to electron detachment. Additionally, the critical nuclear charge for binding two electrons within the HF approach is calculated and determined to be Z HF C =1.031 177 528.This article is part of the theme issue 'Modern theoretical chemistry'. © 2018 The Author(s).
Prasad, Viki Kumar; Otero-de-la-Roza, Alberto; DiLabio, Gino A
2018-02-13
We present a computational methodology based on atom-centered potentials (ACPs) for the efficient and accurate structural modeling of large molecular systems. ACPs are atom-centered one-electron potentials that have the same functional form as effective-core potentials. In recent works, we showed that ACPs can be used to produce a correction to the ground-state wave function and electronic energy to alleviate shortcomings in the underlying model chemistry. In this work, we present ACPs for H, C, N, and O atoms that are specifically designed to predict accurate non-covalent binding energies and inter- and intramolecular geometries when combined with dispersion-corrected Hartree-Fock (HF-D3) and a minimal basis-set (scaled MINI or MINIs). For example, the combined HF-D3/MINIs-ACP method demonstrates excellent performance, with mean absolute errors of 0.36 and 0.28 kcal/mol for the S22x5 and S66x8 benchmark sets, respectively, relative to highly correlated complete-basis-set data. The application of ACPs results in a significant decrease in error compared to uncorrected HF-D3/MINIs for all benchmark sets examined. In addition, HF-D3/MINIs-ACP, has a cost only slightly higher than a minimal-basis-set HF calculation and can be used with any electronic structure program for molecular quantum chemistry that uses Gaussian basis sets and effective-core potentials.
Directory of Open Access Journals (Sweden)
H. Mariji
2016-01-01
Full Text Available The nucleon single-particle energies (SPEs of the selected nuclei, that is, O16, Ca40, and Ni56, are obtained by using the diagonal matrix elements of two-body effective interaction, which generated through the lowest-order constrained variational (LOCV calculations for the symmetric nuclear matter with the Aυ18 phenomenological nucleon-nucleon potential. The SPEs at the major levels of nuclei are calculated by employing a Hartree-Fock inspired scheme in the spherical harmonic oscillator basis. In the scheme, the correlation influences are taken into account by imposing the nucleon effective mass factor on the radial wave functions of the major levels. Replacing the density-dependent one-body momentum distribution functions of nucleons, n(k,ρ, with the Heaviside functions, the role of n(k,ρ in the nucleon SPEs at the major levels of the selected closed shell nuclei is investigated. The best fit of spin-orbit splitting is taken into account when correcting the major levels of the nuclei by using the parameterized Wood-Saxon potential and the Aυ18 density-dependent mean field potential which is constructed by the LOCV method. Considering the point-like protons in the spherical Coulomb potential well, the single-proton energies are corrected. The results show the importance of including n(k,ρ, instead of the Heaviside functions, in the calculation of nucleon SPEs at the different levels, particularly the valence levels, of the closed shell nuclei.
López-Quelle, M.; Marcos, S.; Niembro, R.; Savushkin, L. N.
2018-03-01
Within a nonlinear relativistic Hartree-Fock approximation combined with the BCS method, we study the effect of the nucleon-nucleon tensor force of the π-exchange potential on the spin- and pseudospin-orbit doublets along the Ca and Sn isotopic chains. We show how the self-consistent tensor force effect modifies the splitting of both kinds of doublets in an interdependent form, leading, quite generally, to opposite effects in the accomplishment of the spin and pseudospin symmetries (the one is restored, the other one deteriorates and vice versa). The ordering of the single-particle energy levels is crucial to this respect. Also, we observe a mutual dependence on the evolution of the shell closure gap Z = 50 and the energy band outside the core, along the Sn chain, as due to the tensor force. In fact, when the shell gap is quenched the outside energy band is enlarged, and vice versa. A reduction of the strength of the pion tensor force with respect to its experimental value from the nucleon-nucleon scattering is needed to get results closer to the experiment. Pairing correlations act to some extent in the opposite direction of the tensor term of the one-pion-exchange force.
Energy Technology Data Exchange (ETDEWEB)
Kilin, V.A. [Tomsk Polytechnic University, Tomsk (Russian Federation); Lazarev, D.V.; Lazarev, Dm.A.; Zelichenko, V.M. [Tomsk Pedagogic University, Tomsk (Russian Federation); Amusia, M. Ya. [A.F. Ioffe Physico-Technical Institute, St. Petersburg (Russian Federation); Schartner, K.-H. [I Physikalisches Institut, Justus-Liebig-Universitaet, Giessen (Germany); Ehresmann, A.; Schmoranzer, H. [Fachbereich Physik, Universitaet Kaiserslautern, Kaiserslautern (Germany)
2001-10-28
The approach of a parametric V{sup (N-q)} Hartree-Fock potential with fractional q is developed and applied for the first time for the calculation of the double photoionization cross sections of Ne. A minimum of the squared difference between the length-form and velocity-form cross sections is used as a criterion for calculating the values of q. It is found that the minimization procedure leads to a practically exact equality of the length-form and velocity-form cross sections for the Ne III 2s{sup 2}2p{sup 4}[{sup 3}P,{sup 1}D,{sup 1}S], 2s{sup 1}2p{sup 5}[{sup 3}P,{sup 1}P] and 2s{sup 0}2p{sup 6}[{sup 1}S] states in the exciting-photon energy region from the double-ionization threshold up to 325 eV, if q is considered as a function of the exciting-photon energy. The calculated V{sup (N-q)} cross sections are in better agreement with the experimental data than those for the V{sup (N-1)} and V{sup (N-2)} potentials. (author)
Rodriguez-Bautista, Mariano; Díaz-García, Cecilia; Navarrete-López, Alejandra M; Vargas, Rubicelia; Garza, Jorge
2015-07-21
In this report, we use a new basis set for Hartree-Fock calculations related to many-electron atoms confined by soft walls. One- and two-electron integrals were programmed in a code based in parallel programming techniques. The results obtained with this proposal for hydrogen and helium atoms were contrasted with other proposals to study just one and two electron confined atoms, where we have reproduced or improved the results previously reported. Usually, an atom enclosed by hard walls has been used as a model to study confinement effects on orbital energies, the main conclusion reached by this model is that orbital energies always go up when the confinement radius is reduced. However, such an observation is not necessarily valid for atoms confined by penetrable walls. The main reason behind this result is that for atoms with large polarizability, like beryllium or potassium, external orbitals are delocalized when the confinement is imposed and consequently, the internal orbitals behave as if they were in an ionized atom. Naturally, the shell structure of these atoms is modified drastically when they are confined. The delocalization was an argument proposed for atoms confined by hard walls, but it was never verified. In this work, the confinement imposed by soft walls allows to analyze the delocalization concept in many-electron atoms.
International Nuclear Information System (INIS)
Dancer, H.
2000-01-01
This work concerns the extension of the application domain of microscopic calculations in nuclear structure to phenomena breaking the z-signature symmetry. The approach followed consists in solving the many-body problem by means of the mean-field approximation using the Hartree-Fock-Bogoliubov method. By employing the Gogny nucleon-nucleon interaction, mean-field effects as well as pairing correlations are calculated in a self-consistent way. In order to simplify the iterative resolution of the associated system of non-linear equations, the remaining symmetries of the system are explicitly taken into account. In all studies made up to now, the z-signature symmetry was imposed. The solutions of the HFB problem were eigenstates of the z-signature symmetry, a symmetry related to a rotation of π around the z axis. However, many physical phenomena, as rotational bands based on individual excitations and magnetic dipole collective excitations, break this symmetry. In this work the formalism needed to take into account this symmetry breaking is developed and results are given for the two above phenomena. Theoretical rotational bands are in good agreement with experimental data. Band-heads excitation energies as well as moment of inertia are well reproduced. Concerning magnetic dipole excitations, we show that the low-lying l + states experimentally observed, are not collective scissor excitations, the latter being found at high excitation energy. An interpretation in terms of rather non-collective hexadecapole excitations coupled to individual excitations is proposed. (author) [fr
Atomic Structure Theory Lectures on Atomic Physics
Johnson, Walter R
2007-01-01
Atomic Structure Theory is a textbook for students with a background in quantum mechanics. The text is designed to give hands-on experience with atomic structure calculations. Material covered includes angular momentum methods, the central field Schrödinger and Dirac equations, Hartree-Fock and Dirac-Hartree-Fock equations, multiplet structure, hyperfine structure, the isotope shift, dipole and multipole transitions, basic many-body perturbation theory, configuration interaction, and correlation corrections to matrix elements. Numerical methods for solving the Schrödinger and Dirac eigenvalue problems and the (Dirac)-Hartree-Fock equations are given as well. B-spline basis sets are used to carry out sums arising in higher-order many-body calculations. Illustrative problems are provided, together with solutions. FORTRAN programs implementing the numerical methods in the text are included.
Quantum theory of dynamical collective subspace for large-amplitude collective motion
International Nuclear Information System (INIS)
Sakata, Fumihiko; Marumori, Toshio; Ogura, Masanori.
1986-03-01
By placing emphasis on conceptual correspondence to the ''classical'' theory which has been developed within the framework of the time-dependent Hartree-Fock theory, a full quantum theory appropriate for describing large-amplitude collective motion is proposed. A central problem of the quantum theory is how to determine an optimal representation called a dynamical representation; the representation is specific for the collective subspace where the large-amplitude collective motion is replicated as satisfactorily as possible. As an extension of the classical theory where the concept of an approximate integral surface plays an important role, the dynamical representation is properly characterized by introducing a concept of an approximate invariant subspace of the Hamiltonian. (author)
Efficient computation of the MCTDHF approximation to the time-dependent Schrödinger equation
Directory of Open Access Journals (Sweden)
Othmar Koch
2006-01-01
Full Text Available We discuss analytical and numerical properties of the multi-configuration time-dependent Hartree-Fock method for the approximate solution of the time-dependent multi-particle (electronic Schrödinger equation which are relevant for an efficient implementation of this model reduction technique. Particularly, we focus on a discretization and low rank approximation in the evaluation of the meanfield terms occurring in the MCTDHF equations of motion, which is crucial for the computational tractability of the problem. We give error bounds for this approximation and demonstrate the achieved gain in performance.
Energy Technology Data Exchange (ETDEWEB)
Hayhurst, Thomas Laine [Univ. of California, Berkeley, CA (United States); Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
1980-08-06
Techniques for applying ab-initio calculations to the is of atomic spectra are investigated, along with the relationship between the semi-empirical and ab-initio forms of Slater-Condon theory. Slater-Condon theory is reviewed with a focus on the essential features that lead to the effective Hamiltonians associated with the semi-empirical form of the theory. Ab-initio spectroscopic parameters are calculated from wavefunctions obtained via self-consistent field methods, while multi-configuration Hamiltonian matrices are constructed and diagonalized with computer codes written by Robert Cowan of Los Alamos Scientific Laboratory. Group theoretical analysis demonstrates that wavefunctions more general than Slater determinants (i.e. wavefunctions with radial correlations between electrons) lead to essentially the same parameterization of effective Hamiltonians. In the spirit of this analysis, a strategy is developed for adjusting ab-initio values of the spectroscopic parameters, reproducing parameters obtained by fitting the corresponding effective Hamiltonian. Secondary parameters are used to "screen" the calculated (primary) spectroscopic parameters, their values determined by least squares. Extrapolations of the secondary parameters determined from analyzed spectra are attempted to correct calculations of atoms and ions without experimental levels. The adjustment strategy and extrapolations are tested on the K I sequence from K^{0+} through Fe^{7+}, fitting to experimental levels for V^{4+}, and Cr^{5+}; unobserved levels and spectra are predicted for several members of the sequence. A related problem is also discussed: Energy levels of the Uranium hexahalide complexes, (UX_{6})^{2-} for X= F, Cl, Br, and I, are fit to an effective Hamiltonian (the f^{2} configuration in O_{h} symmetry) with corrections proposed by Brian Judd.
Evaluation of time-dependent void nucleation theory under ion bombardment conditions
International Nuclear Information System (INIS)
Sprague, J.A.; Russell, K.C.; Choi, Y.H.
1975-01-01
The applicability of a steady state and time-dependent homogeneous void nucleation theory to charged-particle irradiation experiments was investigated. The steady-state theory was found to be inappropriate, since significant changes in a metal's microstructure would likely occur before the void nucleation rate could reach steady state. Two types of time dependence were examined, that of the point defect concentrations at the beginning of an irradiation and the longer-term time dependence of void nucleation. It was found that vacancy and interstitial clustering significantly reduce the relaxation time for the point defect concentrations. An efficient form of time-dependent homogeneous nucleation theory was applied to ion bombardment conditions to predict void size distributions
Figgen, Detlev
2007-01-01
In dieser Arbeit wurden energiekonsistente zweikomponentige small core-Pseudopotentiale für die 4d- und 5d-Übergangsmetalle sowie die Elemente der Gruppen 17 und 18 justiert. Diese Justierung erfolgte an Referenzdaten aus Multikonfigurations-Dirac-Hartree-Fock-Rechnungen; mit den in dieser Arbeit justierten Pseudopotentialen stehen somit Pseudopotentiale dieses Typs für alle Übergangsmetalle und post-d-Hauptgruppenelemente zur Verfügung. Zusammen mit den für diese Pseudopotentiale optimierten...
de Lara-Castells, María Pilar; Fernández-Perea, Ricardo; Madzharova, Fani; Voloshina, Elena
2016-06-01
The adsorption of noble gases on metallic surfaces represents a paradigmatic case of van-der-Waals (vdW) interaction due to the role of screening effects on the corrugation of the interaction potential [J. L. F. Da Silva et al., Phys. Rev. Lett. 90, 066104 (2003)]. The extremely small adsorption energy of He atoms on the Mg(0001) surface (below 3 meV) and the delocalized nature and mobility of the surface electrons make the He/Mg(0001) system particularly challenging, even for state-of-the-art vdW-corrected density functional-based (vdW-DFT) approaches [M. P. de Lara-Castells et al., J. Chem. Phys. 143, 194701 (2015)]. In this work, we meet this challenge by applying two different procedures. First, the dispersion-corrected second-order Möller-Plesset perturbation theory (MP2C) approach is adopted, using bare metal clusters of increasing size. Second, the method of increments [H. Stoll, J. Chem. Phys. 97, 8449 (1992)] is applied at coupled cluster singles and doubles and perturbative triples level, using embedded cluster models of the metal surface. Both approaches provide clear evidences of the anti-corrugation of the interaction potential: the He atom prefers on-top sites, instead of the expected hollow sites. This is interpreted as a signature of the screening of the He atom by the metal for the on-top configuration. The strong screening in the metal is clearly reflected in the relative contribution of successively deeper surface layers to the main dispersion contribution. Aimed to assist future dynamical simulations, a pairwise potential model for the He/surface interaction as a sum of effective He-Mg pair potentials is also presented, as an improvement of the approximation using isolated He-Mg pairs.
Theory of time-dependent intense-field collisional resonance fluorescence
Kleiber, P. D.; Cooper, J.; Burnett, K.; Kunasz, C. V.; Raymer, M. G.
1983-01-01
The time-dependent theory of Courtens and Szoke (1977) is generalized using the approach of Burnett et al. (1982) to derive time-dependent spectral intensities of resonance fluorescence from atoms driven by a pulsed laser in the presence of collisions. These results are valid both for laser detunings inside and outside the usual impact region of the spectrum, including Zeeman degeneracy effects. This theory is applied to a simple but important example (J = 0 to J = 1) to obtain quantitative predictions for the observable scattered-light spectrum which can be directly compared with recent experiments.
Schunck, N.; Dobaczewski, J.; Satuła, W.; Bączyk, P.; Dudek, J.; Gao, Y.; Konieczka, M.; Sato, K.; Shi, Y.; Wang, X. B.; Werner, T. R.
2017-07-01
We describe the new version (v2.73y) of the code HFODD which solves the nuclear Skyrme Hartree-Fock or Skyrme Hartree-Fock-Bogolyubov problem by using the Cartesian deformed harmonic-oscillator basis. In the new version, we have implemented the following new features: (i) full proton-neutron mixing in the particle-hole channel for Skyrme functionals, (ii) the Gogny force in both particle-hole and particle-particle channels, (iii) linear multi-constraint method at finite temperature, (iv) fission toolkit including the constraint on the number of particles in the neck between two fragments, calculation of the interaction energy between fragments, and calculation of the nuclear and Coulomb energy of each fragment, (v) the new version 200d of the code HFBTHO, together with an enhanced interface between HFBTHO and HFODD, (vi) parallel capabilities, significantly extended by adding several restart options for large-scale jobs, (vii) the Lipkin translational energy correction method with pairing, (viii) higher-order Lipkin particle-number corrections, (ix) interface to a program plotting single-particle energies or Routhians, (x) strong-force isospin-symmetry-breaking terms, and (xi) the Augmented Lagrangian Method for calculations with 3D constraints on angular momentum and isospin. Finally, an important bug related to the calculation of the entropy at finite temperature and several other little significant errors of the previous published version were corrected.
Stein, Tamar; Jiménez-Hoyos, Carlos A; Scuseria, Gustavo E
2014-09-04
Hartree-Fock (HF) is known to suffer from drawbacks in the description of the relative stabilities between the hemi-bonded (HB) and proton-transferred (PT) isomers of the water dimer cation, (H2O)2(+). The energy difference predicted by HF is too large, approximately 27 kcal/mol, which is lowered to 7 kcal/mol when correlation effects are added. The error in HF has been previously attributed to the large dynamic correlation effects in the HB structure as well to the large symmetry breaking this structure exhibits. In this study we use the recently developed projected Hartree-Fock (PHF) methods to study the relative stability of the two isomers of (H2O)2(+) as well as its second and third row analogs, namely, (H2S)2(+) and (H2Se)2(+). In PHF, symmetries are broken and restored in a variation-after-projection approach and thus can deal easily with systems for which HF itself spontaneously breaks symmetry. We use different flavors of PHF (SUHF, KSUHF, SGHF, and KSGHF) to explore their ability in capturing dynamic correlation effects and to compare their performance to different wave function based methods. We study the role of the symmetry-breaking in the above systems, using wave function based methods with unrestricted and restricted wave functions as well as performing a single-shot symmetry restoration (a projection-after-variation scheme).
Brorsen, Kurt R; Pak, Michael V; Hammes-Schiffer, Sharon
2017-01-19
Although the binding of a positron to a neutral atom has not been directly observed experimentally, high-level theoretical methods have predicted that a positron will bind to a neutral atom. In the present study, the binding energies of a positron to lithium, sodium, beryllium, and magnesium, as well as the electron-positron annihilation rates for these systems, are calculated using the reduced explicitly correlated Hartree-Fock (RXCHF) method within the nuclear-electronic orbital (NEO) framework. Due to the lack of explicit electron-positron correlation, NEO Hartree-Fock and full configuration interaction calculations with reasonable electronic and positronic basis sets do not predict positron binding to any of these atoms. In contrast, the RXCHF calculations predict positron binding energies and electron-positron annihilation rates in qualitative agreement with previous highly accurate but computationally expensive stochastic variational method calculations. These results illustrate that the RXCHF method can successfully describe the binding of a positron to a neutral species with no dipole moment. Moreover, the RXCHF method will be computationally tractable for calculating positron binding to molecular systems. The RXCHF approach offers a balance of accuracy and computational tractability for studying these types of positronic systems.
Unitarity Bounds and RG Flows in Time Dependent Quantum Field Theory
Energy Technology Data Exchange (ETDEWEB)
Dong, Xi; Horn, Bart; Silverstein, Eva; Torroba, Gonzalo; /Stanford U., ITP /Stanford U., Phys. Dept. /SLAC
2012-04-05
We generalize unitarity bounds on operator dimensions in conformal field theory to field theories with spacetime dependent couplings. Below the energy scale of spacetime variation of the couplings, their evolution can strongly affect the physics, effectively shifting the infrared operator scaling and unitarity bounds determined from correlation functions in the theory. We analyze this explicitly for large-N double-trace flows, and connect these to UV complete field theories. One motivating class of examples comes from our previous work on FRW holography, where this effect explains the range of flavors allowed in the dual, time dependent, field theory.
Time-evolution operators for (coupled) time-dependent oscillators and Lie algebraic structure theory
Wolf, F.; Korsch, H. J.
1988-03-01
This paper deals with the application of Lie algebraic structure theory to time-dependent quantum systems making use of the Levi-Malcev decomposition of the Lie algebra generated by the Hamiltonian and the Wei-Norman representation of the time-evolution operator. In particular, (coupled) harmonic-oscillator systems are studied. Explicit formulas for expectation values and transition probabilities are derived.
The Keldysh formalism applied to time-dependent current-density-functional theory
Gidopoulos, NI; Wilson, S
2003-01-01
In this work we demonstrate how to derive the Kohn-Sham equations of time-dependent current-density functional theory from a generating action functional defined on a Keldysh time contour. These Kohn-Sham equations contain an exchange-correlation contribution to the vector potential. For this
International Nuclear Information System (INIS)
Frank, T.D.
2006-01-01
First-order approximations of time-dependent solutions are determined for stochastic systems perturbed by time-delayed feedback forces. To this end, the theory of delay Fokker-Planck equations is applied in combination with Bayes' theorem. Applications to a time-delayed Ornstein-Uhlenbeck process and the geometric Brownian walk of financial physics are discussed
Energy Technology Data Exchange (ETDEWEB)
Kapoor, Varun; Brics, Martins; Bauer, Dieter [Institut fuer Physik, Universitaet Rostock, 18051 Rostock (Germany)
2013-07-01
Autoionizing states are inaccessible to time-dependent density functional theory (TDDFT) using known, adiabatic Kohn-Sham (KS) potentials. We determine the exact KS potential for a numerically exactly solvable model Helium atom interacting with a laser field that is populating an autoionizing state. The exact single-particle density of the population in the autoionizing state corresponds to that of the energetically lowest quasi-stationary state in the exact KS potential. We describe how this exact potential controls the decay by a barrier whose height and width allows for the density to tunnel out and decay with the same rate as in the ab initio time-dependent Schroedinger calculation. However, devising a useful exchange-correlation potential that is capable of governing such a scenario in general and in more complex systems is hopeless. As an improvement over TDDFT, time-dependent reduced density matrix functional theory has been proposed. We are able to obtain for the above described autoionization process the exact time-dependent natural orbitals (i.e., the eigenfunctions of the exact, time-dependent one-body reduced density matrix) and study the potentials that appear in the equations of motion for the natural orbitals and the structure of the two-body density matrix expanded in them.
On time-dependent perturbation theory in matrix mechanics and time averaging
International Nuclear Information System (INIS)
Casas, Fernando
2015-01-01
The time-dependent quantum perturbation theory developed by Born, Heisenberg and Jordan in 1926 is revisited. We show that it not only reproduces the standard theory formulated in the interaction picture, but also allows one to construct more accurate approximations if time averaging techniques are employed. The theory can be rendered unitary even if the expansion is truncated by using a transformation previously suggested by Heisenberg. We illustrate the main features of the procedure on a simple example which clearly shows its advantages in comparison with the standard perturbation theory. (paper)
Translationally invariant self-consistent field theories
International Nuclear Information System (INIS)
Shakin, C.M.; Weiss, M.S.
1977-01-01
We present a self-consistent field theory which is translationally invariant. The equations obtained go over to the usual Hartree-Fock equations in the limit of large particle number. In addition to deriving the dynamic equations for the self-consistent amplitudes we discuss the calculation of form factors and various other observables
Time-dependent density functional theory for many-electron systems interacting with cavity photons.
Tokatly, I V
2013-06-07
Time-dependent (current) density functional theory for many-electron systems strongly coupled to quantized electromagnetic modes of a microcavity is proposed. It is shown that the electron-photon wave function is a unique functional of the electronic (current) density and the expectation values of photonic coordinates. The Kohn-Sham system is constructed, which allows us to calculate the above basic variables by solving self-consistent equations for noninteracting particles. We suggest possible approximations for the exchange-correlation potentials and discuss implications of this approach for the theory of open quantum systems. In particular we show that it naturally leads to time-dependent density functional theory for systems coupled to the Caldeira-Leggett bath.
NATO Advanced Research Workshop on Time-Dependent Quantum Molecular Dynamics : Theory and Experiment
Lathouwers, L
1992-01-01
From March 30th to April 3rd, 1992, a NATO Advanced Research workshop entitled "Time Dependent Quantum Molecular Dynamics: Theory and Experiment" was held at Snowbird, Utah. The organizing committee consisted of J. BROECKHOVE (Antwerp, Belgium), L. CEDERBAUM (Heidelberg, Germany), L. LATHOUWERS (Antwerp, Belgium), N. OHRN (Gainesville, Florida) and J. SIMONS (Salt Lake City, Utah). Fifty-two participants from eleven different countries attended the meeting at which thirty-three talks and one poster session were held. Twenty-eight participants submitted contributions to the proceedings of the meeting, which are reproduced in this volume. The workshop brought together experts in different areas 0 f molecular quantum dynamics, all adhering to the time dependent approach. The aim was to discuss and compare methods and applications. The ~amiliarityo~ the aUdience with the concepts o~ time dependent approaches greatly facilitated topical discussions and probing towards new applications. A broad area of subject matt...
Phase space theory of Bose–Einstein condensates and time-dependent modes
International Nuclear Information System (INIS)
Dalton, B.J.
2012-01-01
A phase space theory approach for treating dynamical behaviour of Bose–Einstein condensates applicable to situations such as interferometry with BEC in time-dependent double well potentials is presented. Time-dependent mode functions are used, chosen so that one, two,…highly occupied modes describe well the physics of interacting condensate bosons in time dependent potentials at well below the transition temperature. Time dependent mode annihilation, creation operators are represented by time dependent phase variables, but time independent total field annihilation, creation operators are represented by time independent field functions. Two situations are treated, one (mode theory) is where specific mode annihilation, creation operators and their related phase variables and distribution functions are dealt with, the other (field theory) is where only field creation, annihilation operators and their related field functions and distribution functionals are involved. The field theory treatment is more suitable when large boson numbers are involved. The paper focuses on the hybrid approach, where the modes are divided up between condensate (highly occupied) modes and non-condensate (sparsely occupied) modes. It is found that there are extra terms in the Ito stochastic equations both for the stochastic phases and stochastic fields, involving coupling coefficients defined via overlap integrals between mode functions and their time derivatives. For the hybrid approach both the Fokker–Planck and functional Fokker–Planck equations differ from those derived via the correspondence rules, the drift vectors are unchanged but the diffusion matrices contain additional terms involving the coupling coefficients. Results are also presented for the combined approach where all the modes are treated as one set. Here both the Fokker–Planck and functional Fokker–Planck equations are exactly the same as those derived via the correspondence rules. However, although the Ito
Double giant resonances in time-dependent relativistic mean-field theory
International Nuclear Information System (INIS)
Ring, P.; Podobnik, B.
1996-01-01
Collective vibrations in spherical nuclei are described in the framework of time-dependent relativistic mean-field theory (RMFT). Isoscalar quadrupole and isovector dipole oscillations that correspond to giant resonances are studied, and possible excitations of higher modes are investigated. We find evidence for modes which can be interpreted as double resonances. In a quantized RMFT they correspond to two-phonon states. (orig.)
Optical properties of Al nanostructures from time dependent density functional theory
Mokkath, Junais Habeeb
2016-04-05
The optical properties of Al nanostructures are investigated by means of time dependent density functional theory, considering chains of varying length and ladders/stripes of varying aspect ratio. The absorption spectra show redshifting for increasing length and aspect ratio. For the chains the absorption is dominated by HOMO → LUMO transitions, whereas ladders and stripes reveal more complex spectra of plasmonic nature above a specific aspect ratio.
Nakajima, Yuya; Seino, Junji; Nakai, Hiromi
2016-05-10
An analytical energy gradient for the spin-dependent general Hartree-Fock method based on the infinite-order Douglas-Kroll-Hess (IODKH) method was developed. To treat realistic systems, the local unitary transformation (LUT) scheme was employed both in energy and energy gradient calculations. The present energy gradient method was numerically assessed to investigate the accuracy in several diatomic molecules containing fifth- and sixth-period elements and to examine the efficiency in one-, two-, and three-dimensional silver clusters. To arrive at a practical calculation, we also determined the geometrical parameters of fac-tris(2-phenylpyridine)iridium and investigated the efficiency. The numerical results confirmed that the present method describes a highly accurate relativistic effect with high efficiency. The present method can be a powerful scheme for determining geometries of large molecules, including heavy-element atoms.
Time-dependent density functional theory for open quantum systems with unitary propagation.
Yuen-Zhou, Joel; Tempel, David G; Rodríguez-Rosario, César A; Aspuru-Guzik, Alán
2010-01-29
We extend the Runge-Gross theorem for a very general class of open quantum systems under weak assumptions about the nature of the bath and its coupling to the system. We show that for Kohn-Sham (KS) time-dependent density functional theory, it is possible to rigorously include the effects of the environment within a bath functional in the KS potential. A Markovian bath functional inspired by the theory of nonlinear Schrödinger equations is suggested, which can be readily implemented in currently existing real-time codes. Finally, calculations on a helium model system are presented.
Regular and chaotic dynamics in time-dependent relativistic mean-field theory
International Nuclear Information System (INIS)
Vretenar, D.; Ring, P.; Lalazissis, G.A.; Poeschl, W.
1997-01-01
Isoscalar and isovector monopole oscillations that correspond to giant resonances in spherical nuclei are described in the framework of time-dependent relativistic mean-field theory. Time-dependent and self-consistent calculations that reproduce experimental data on monopole resonances in 208 Pb show that the motion of the collective coordinate is regular for isoscalar oscillations, and that it becomes chaotic when initial conditions correspond to the isovector mode. Regular collective dynamics coexists with chaotic oscillations on the microscopic level. Time histories, Fourier spectra, state-space plots, Poincare sections, autocorrelation functions, and Lyapunov exponents are used to characterize the nonlinear system and to identify chaotic oscillations. Analogous considerations apply to higher multipolarities. copyright 1997 The American Physical Society
Reactive scattering theory for molecular transitions in time-dependent fields
International Nuclear Information System (INIS)
Peskin, U.; Miller, W.H.
1995-01-01
A new approach is introduced for computing probabilities of molecular transitions in time-dependent fields. The method is based on the stationary (t,t') representation of the Schroedinger equation and is shown to be equivalent to infinite order time-dependent perturbation theory. Bound-to-bound (i.e., photoexcitation) and bound-to-continuum (i.e., photoreaction) transitions are regarded as reactive collisions with the ''time coordinate'' as the reaction coordinate in an extended Hilbert space. A numerical method based on imposing absorbing boundary conditions for the time coordinate in a discrete variable representation framework is introduced. A single operation of the Green's operator provides all the state-specific transition probabilities as well as partial state-resolved (inclusive) reaction probabilities. Illustrative numerical applications are given for model systems
Hydrodynamic perspective on memory in time-dependent density-functional theory
Thiele, M.; Kümmel, S.
2009-05-01
The adiabatic approximation of time-dependent density-functional theory is studied in the context of nonlinear excitations of two-electron singlet systems. We compare the exact time evolution of these systems to the adiabatically exact one obtained from time-dependent Kohn-Sham calculations relying on the exact ground-state exchange-correlation potential. Thus, we can show under which conditions the adiabatic approximation breaks down and memory effects become important. The hydrodynamic formulation of quantum mechanics allows us to interpret these results and relate them to dissipative effects in the Kohn-Sham system. We show how the breakdown of the adiabatic approximation can be inferred from the rate of change of the ground-state noninteracting kinetic energy.
Hydrodynamic perspective on memory in time-dependent density-functional theory
International Nuclear Information System (INIS)
Thiele, M.; Kuemmel, S.
2009-01-01
The adiabatic approximation of time-dependent density-functional theory is studied in the context of nonlinear excitations of two-electron singlet systems. We compare the exact time evolution of these systems to the adiabatically exact one obtained from time-dependent Kohn-Sham calculations relying on the exact ground-state exchange-correlation potential. Thus, we can show under which conditions the adiabatic approximation breaks down and memory effects become important. The hydrodynamic formulation of quantum mechanics allows us to interpret these results and relate them to dissipative effects in the Kohn-Sham system. We show how the breakdown of the adiabatic approximation can be inferred from the rate of change of the ground-state noninteracting kinetic energy.
Critique of the foundations of time-dependent density-functional theory
International Nuclear Information System (INIS)
Schirmer, J.; Dreuw, A.
2007-01-01
The general expectation that, in principle, the time-dependent density-functional theory (TDDFT) is an exact formulation of the time evolution of an interacting N-electron system is critically reexamined. It is demonstrated that the previous TDDFT foundation, resting on four theorems by Runge and Gross (RG) [Phys. Rev. Lett. 52, 997 (1984)], is invalid because undefined phase factors corrupt the RG action integral functionals. Our finding confirms much of a previous analysis by van Leeuwen [Int. J. Mod. Phys. B 15, 1969 (2001)]. To analyze the RG theorems and other aspects of TDDFT, an utmost simplification of the Kohn-Sham (KS) concept has been introduced, in which the ground-state density is obtained from a single KS equation for one spatial (spinless) orbital. The time-dependent (TD) form of this radical Kohn-Sham (rKS) scheme, which has the same validity status as the ordinary KS version, has proved to be a valuable tool for analysis. The rKS concept is used to clarify also the alternative nonvariational formulation of TD KS theory. We argue that it is just a formal theory, allowing one to reproduce but not predict the time development of the exact density of the interacting N-electron system. Besides the issue of the formal exactness of TDDFT, it is shown that both the static and time-dependent KS linear response equations neglect the particle-particle (p-p) and hole-hole (h-h) matrix elements of the perturbing operator. For a local (multiplicative) operator this does not lead to a loss of information due to a remarkable general property of local operators. Accordingly, no logical inconsistency arises with respect to DFT, because DFT requires any external potential to be local. For a general nonlocal operator the error resulting from the neglected matrix elements is of second order in the electronic repulsion
Time-dependent, many-body scattering theory and nuclear reaction applications
International Nuclear Information System (INIS)
Levin, F.S.
1977-01-01
The channel component state form of the channel coupling array theory of many-body scattering is briefly reviewed. These states obey a non-hermitian matrix equation whose exact solution yields the Schroedinger eigenstates, eigenvalues and scattering amplitudes. A time-dependent formulation of the theory is introduced in analogy to the time-dependent Schrodinger equation and several consequences of the development are noted. These include an interaction picture, a single (matrix) S operator, and the usual connection between the t = 0 time-dependent and the time-independent scattering states. Finally, the channel component states (psi/sub j/) are shown to have the useful property that only psi/sub j/ has (two-body) outgoing waves in channel j: psi/sub m/, m not equal to j, is asymptotically zero in two-body channel j. This formalism is then considered as a means for direct nuclear reaction analysis. Typical bound state approximations are introduced and it is shown that a DWBA amplitude occurs in only one channel. The non-time-reversal invariance of the approximate theory is noted. Results of calculations based on a realistic model for two sets of light-ion induced, one-particle transfer reactions are discussed and compared with the coupled reaction channel (CRC) results using the CRC procedure of Cotanch and Vincent. Angular distributions for the two calculational methods are found to be similar in shape and magnitude. Higher ordercorrections are small as are time-reversal non-invariant effects. Post- and prior-type CRC calculations are seen to differ; the latter are closer to the full CRC results
DEFF Research Database (Denmark)
Gavnholt, Jeppe; Rubio, Angel; Olsen, Thomas
2009-01-01
Using time-evolution time-dependent density functional theory (TDDFT) within the adiabatic local-density approximation, we study the interactions between single electrons and molecular resonances at surfaces. Our system is a nitrogen molecule adsorbed on a ruthenium surface. The surface is modeled...... at two levels of approximation, first as a simple external potential and later as a 20-atom cluster. We perform a number of calculations on an electron hitting the adsorbed molecule from inside the surface and establish a picture, where the resonance is being probed by the hot electron. This enables us...
Pernal, Katarzyna
2012-05-14
Time-dependent density functional theory (TD-DFT) in the adiabatic formulation exhibits known failures when applied to predicting excitation energies. One of them is the lack of the doubly excited configurations. On the other hand, the time-dependent theory based on a one-electron reduced density matrix functional (time-dependent density matrix functional theory, TD-DMFT) has proven accurate in determining single and double excitations of H(2) molecule if the exact functional is employed in the adiabatic approximation. We propose a new approach for computing excited state energies that relies on functionals of electron density and one-electron reduced density matrix, where the latter is applied in the long-range region of electron-electron interactions. A similar approach has been recently successfully employed in predicting ground state potential energy curves of diatomic molecules even in the dissociation limit, where static correlation effects are dominating. In the paper, a time-dependent functional theory based on the range-separation of electronic interaction operator is rigorously formulated. To turn the approach into a practical scheme the adiabatic approximation is proposed for the short- and long-range components of the coupling matrix present in the linear response equations. In the end, the problem of finding excitation energies is turned into an eigenproblem for a symmetric matrix. Assignment of obtained excitations is discussed and it is shown how to identify double excitations from the analysis of approximate transition density matrix elements. The proposed method used with the short-range local density approximation (srLDA) and the long-range Buijse-Baerends density matrix functional (lrBB) is applied to H(2) molecule (at equilibrium geometry and in the dissociation limit) and to Be atom. The method accounts for double excitations in the investigated systems but, unfortunately, the accuracy of some of them is poor. The quality of the other
Tao, Jianmin; Tretiak, Sergei; Zhu, Jian-Xin
2010-01-01
With technological advances, light-emitting conjugated oligomers and polymers have become competitive candidates in the commercial market of light-emitting diodes for display and other technologies, due to the ultralow cost, light weight, and flexibility. Prediction of excitation energies of these systems plays a crucial role in the understanding of their optical properties and device design. In this review article, we discuss the calculation of excitation energies with time-dependent density functional theory, which is one of the most successful methods in the investigation of the dynamical response of molecular systems to external perturbation, owing to its high computational efficiency.
Lehtovaara, Lauri; Havu, Ville; Puska, Martti
2009-01-01
We present for static density functional theory and time-dependent density functional theory calculations an all-electron method which employs high-order hierarchical finite-element bases. Our mesh generation scheme, in which structured atomic meshes are merged to an unstructured molecular mesh, allows a highly nonuniform discretization of the space. Thus it is possible to represent the core and valence states using the same discretization scheme, i.e., no pseudopotentials or similar treatmen...
Towards time-dependent current-density-functional theory in the non-linear regime.
Escartín, J M; Vincendon, M; Romaniello, P; Dinh, P M; Reinhard, P-G; Suraud, E
2015-02-28
Time-Dependent Density-Functional Theory (TDDFT) is a well-established theoretical approach to describe and understand irradiation processes in clusters and molecules. However, within the so-called adiabatic local density approximation (ALDA) to the exchange-correlation (xc) potential, TDDFT can show insufficiencies, particularly in violently dynamical processes. This is because within ALDA the xc potential is instantaneous and is a local functional of the density, which means that this approximation neglects memory effects and long-range effects. A way to go beyond ALDA is to use Time-Dependent Current-Density-Functional Theory (TDCDFT), in which the basic quantity is the current density rather than the density as in TDDFT. This has been shown to offer an adequate account of dissipation in the linear domain when the Vignale-Kohn (VK) functional is used. Here, we go beyond the linear regime and we explore this formulation in the time domain. In this case, the equations become very involved making the computation out of reach; we hence propose an approximation to the VK functional which allows us to calculate the dynamics in real time and at the same time to keep most of the physics described by the VK functional. We apply this formulation to the calculation of the time-dependent dipole moment of Ca, Mg and Na2. Our results show trends similar to what was previously observed in model systems or within linear response. In the non-linear domain, our results show that relaxation times do not decrease with increasing deposited excitation energy, which sets some limitations to the practical use of TDCDFT in such a domain of excitations.
Towards time-dependent current-density-functional theory in the non-linear regime
Energy Technology Data Exchange (ETDEWEB)
Escartín, J. M. [Université de Toulouse, UPS, Laboratoire de Physique Théorique, IRSAMC, F-31062 Toulouse Cedex (France); CNRS, UMR5152, F-31062 Toulouse Cedex (France); Theory of Condensed Matter Group, Cavendish Laboratory, University of Cambridge, J.J. Thomson Avenue, Cambridge CB3 0HE (United Kingdom); Vincendon, M.; Dinh, P. M.; Suraud, E. [Université de Toulouse, UPS, Laboratoire de Physique Théorique, IRSAMC, F-31062 Toulouse Cedex (France); CNRS, UMR5152, F-31062 Toulouse Cedex (France); Romaniello, P. [Laboratoire de Physique Théorique, CNRS, IRSAMC, Université Toulouse III - Paul Sabatier and European Theoretical Spectroscopy Facility, 118 Route de Narbonne, 31062 Toulouse Cedex (France); Reinhard, P.-G. [Institut für Theoretische Physik, Universität Erlangen, Staudtstraße 7, D-91058 Erlangen (Germany)
2015-02-28
Time-Dependent Density-Functional Theory (TDDFT) is a well-established theoretical approach to describe and understand irradiation processes in clusters and molecules. However, within the so-called adiabatic local density approximation (ALDA) to the exchange-correlation (xc) potential, TDDFT can show insufficiencies, particularly in violently dynamical processes. This is because within ALDA the xc potential is instantaneous and is a local functional of the density, which means that this approximation neglects memory effects and long-range effects. A way to go beyond ALDA is to use Time-Dependent Current-Density-Functional Theory (TDCDFT), in which the basic quantity is the current density rather than the density as in TDDFT. This has been shown to offer an adequate account of dissipation in the linear domain when the Vignale-Kohn (VK) functional is used. Here, we go beyond the linear regime and we explore this formulation in the time domain. In this case, the equations become very involved making the computation out of reach; we hence propose an approximation to the VK functional which allows us to calculate the dynamics in real time and at the same time to keep most of the physics described by the VK functional. We apply this formulation to the calculation of the time-dependent dipole moment of Ca, Mg and Na{sub 2}. Our results show trends similar to what was previously observed in model systems or within linear response. In the non-linear domain, our results show that relaxation times do not decrease with increasing deposited excitation energy, which sets some limitations to the practical use of TDCDFT in such a domain of excitations.
Time-Dependent Density Functional Theory for Open Systems and Its Applications.
Chen, Shuguang; Kwok, YanHo; Chen, GuanHua
2018-02-20
Photovoltaic devices, electrochemical cells, catalysis processes, light emitting diodes, scanning tunneling microscopes, molecular electronics, and related devices have one thing in common: open quantum systems where energy and matter are not conserved. Traditionally quantum chemistry is confined to isolated and closed systems, while quantum dissipation theory studies open quantum systems. The key quantity in quantum dissipation theory is the reduced system density matrix. As the reduced system density matrix is an O(M! × M!) matrix, where M is the number of the particles of the system of interest, quantum dissipation theory can only be employed to simulate systems of a few particles or degrees of freedom. It is thus important to combine quantum chemistry and quantum dissipation theory so that realistic open quantum systems can be simulated from first-principles. We have developed a first-principles method to simulate the dynamics of open electronic systems, the time-dependent density functional theory for open systems (TDDFT-OS). Instead of the reduced system density matrix, the key quantity is the reduced single-electron density matrix, which is an N × N matrix where N is the number of the atomic bases of the system of interest. As the dimension of the key quantity is drastically reduced, the TDDFT-OS can thus be used to simulate the dynamics of realistic open electronic systems and efficient numerical algorithms have been developed. As an application, we apply the method to study how quantum interference develops in a molecular transistor in time domain. We include electron-phonon interaction in our simulation and show that quantum interference in the given system is robust against nuclear vibration not only in the steady state but also in the transient dynamics. As another application, by combining TDDFT-OS with Ehrenfest dynamics, we study current-induced dissociation of water molecules under scanning tunneling microscopy and follow its time dependent
Linear-Response Time-Dependent Embedded Mean-Field Theory.
Ding, Feizhi; Tsuchiya, Takashi; Manby, Frederick R; Miller, Thomas F
2017-09-12
We present a time-dependent (TD) linear-response description of excited electronic states within the framework of embedded mean-field theory (EMFT). TD-EMFT allows for subsystems to be described at different mean-field levels of theory, enabling straightforward treatment of excited states and transition properties. We provide benchmark demonstrations of TD-EMFT for both local and nonlocal excitations in organic molecules, as well as applications to chlorophyll a, solvatochromic shifts of a dye in solution, and sulfur K-edge X-ray absorption spectroscopy (XAS). It is found that mixed-basis implementations of TD-EMFT lead to substantial errors in terms of transition properties; however, as previously found for ground-state EMFT, these errors are largely eliminated with the use of Fock-matrix corrections. These results indicate that TD-EMFT is a promising method for the efficient, multilevel description of excited-state electronic structure and dynamics in complex systems.
Time-dependent current-density functional theory for generalized open quantum systems.
Yuen-Zhou, Joel; Rodríguez-Rosario, César; Aspuru-Guzik, Alán
2009-06-14
In this article, we prove the one-to-one correspondence between vector potentials and particle and current densities in the context of master equations with arbitrary memory kernels, therefore extending time-dependent current-density functional theory (TD-CDFT) to the domain of generalized many-body open quantum systems (OQS). We also analyse the issue of A-representability for the Kohn-Sham (KS) scheme proposed by D'Agosta and Di Ventra for Markovian OQS [Phys. Rev. Lett. 2007, 98, 226403] and discuss its domain of validity. We suggest ways to expand their scheme, but also propose a novel KS scheme where the auxiliary system is both closed and non-interacting. This scheme is tested numerically with a model system, and several considerations for the future development of functionals are indicated. Our results formalize the possibility of practising TD-CDFT in OQS, hence expanding the applicability of the theory to non-Hamiltonian evolutions.
Remarks on time-dependent [current]-density functional theory for open quantum systems.
Yuen-Zhou, Joel; Aspuru-Guzik, Alán
2013-08-14
Time-dependent [current]-density functional theory for open quantum systems (OQS) has emerged as a formalism that can incorporate dissipative effects in the dynamics of many-body quantum systems. Here, we review and clarify some formal aspects of these theories that have been recently questioned in the literature. In particular, we provide theoretical support for the following conclusions: (1) contrary to what we and others had stated before, within the master equation framework, there is in fact a one-to-one mapping between vector potentials and current densities for fixed initial state, particle-particle interaction, and memory kernel; (2) regardless of the first conclusion, all of our recently suggested Kohn-Sham (KS) schemes to reproduce the current and particle densities of the original OQS, and in particular, the use of a KS closed driven system, remains formally valid; (3) the Lindblad master equation maintains the positivity of the density matrix regardless of the time-dependence of the Hamiltonian or the dissipation operators; (4) within the stochastic Schrödinger equation picture, a one-to-one mapping from stochastic vector potential to stochastic current density for individual trajectories has not been proven so far, except in the case where the vector potential is the same for every member of the ensemble, in which case, it reduces to the Lindblad master equation picture; (5) master equations may violate certain desired properties of the density matrix, such as positivity, but they remain as one of the most useful constructs to study OQS when the environment is not easily incorporated explicitly in the calculation. The conclusions support our previous work as formally rigorous, offer new insights into it, and provide a common ground to discuss related theories.
Theories of time-dependent and time-independent nearside-farside reactive scattering dynamics
Monks, Phillip David Durrant
The first application of nearside-farside (NF) theory is made to the time-dependent partial wave series (PWS) representation of the scattering amplitude for the reaction H + D[2](v = 0,j = 0, m = 0) → HD(v' = 3,j' = 0, m'= 0) + D. Time-dependent NF angular distributions and time-dependent NF local angular momenta (LAMs) are defined and used to analyse the dynamics in terms of time- direct and time-delayed reaction mechanisms. The concept of a cumulative time-evolving differential cross section (DCS) is introduced and used to provide a new method for visualising the time evolution of a chemical reaction. Time-independent NF DCS and LAM analyses of the H + D[2] reaction are presented, highlighting a distinctive "trench-ridge" feature present in the full and N LAMs. It is used to define a cut line which separates the energy-analogs of the two time- distinct reaction mechanisms. This trench-ridge feature is shown to be an interference between the time-direct (backward-scattered) and time-delayed (forward-scattered) reaction mechanisms. Resummation PWS theory is used to "clean" plots of the NF DCSs and LAMs of unphysical effects. A limitation of the resummation theory is described, whereby unphysical behaviour is sometimes introduced into the N and F subamplitudes. A technique for predicting and avoiding these undesired effects is used to further improve the usefulness of the resummation technique. The fundamental identity for NF local angular momenta is stated and derived by two methods. This identity gives rise to a CLAM plot (where CLAM denotes Cross section x LAM), which provides insight into the empirical obsei'vation that DCS and LAM analyses give consistent, yet complementary, information on the reaction dynamics. Applications are reported for the H + D[2] reaction, as well as for F + H[2](v = 0,j=0, m = 0)→ FH(v' = 3,j' = 3, m' = 0) + H. The angular time-delay for a state-to-state reactive collision often displays complicated behaviour. It is shown for the H
Andrade, Xavier; Alberdi-Rodriguez, Joseba; Strubbe, David A; Oliveira, Micael J T; Nogueira, Fernando; Castro, Alberto; Muguerza, Javier; Arruabarrena, Agustin; Louie, Steven G; Aspuru-Guzik, Alán; Rubio, Angel; Marques, Miguel A L
2012-06-13
Octopus is a general-purpose density-functional theory (DFT) code, with a particular emphasis on the time-dependent version of DFT (TDDFT). In this paper we present the ongoing efforts to achieve the parallelization of octopus. We focus on the real-time variant of TDDFT, where the time-dependent Kohn-Sham equations are directly propagated in time. This approach has great potential for execution in massively parallel systems such as modern supercomputers with thousands of processors and graphics processing units (GPUs). For harvesting the potential of conventional supercomputers, the main strategy is a multi-level parallelization scheme that combines the inherent scalability of real-time TDDFT with a real-space grid domain-partitioning approach. A scalable Poisson solver is critical for the efficiency of this scheme. For GPUs, we show how using blocks of Kohn-Sham states provides the required level of data parallelism and that this strategy is also applicable for code optimization on standard processors. Our results show that real-time TDDFT, as implemented in octopus, can be the method of choice for studying the excited states of large molecular systems in modern parallel architectures.
Andrade, Xavier; Alberdi-Rodriguez, Joseba; Strubbe, David A.; Oliveira, Micael J. T.; Nogueira, Fernando; Castro, Alberto; Muguerza, Javier; Arruabarrena, Agustin; Louie, Steven G.; Aspuru-Guzik, Alán; Rubio, Angel; Marques, Miguel A. L.
2012-06-01
Octopus is a general-purpose density-functional theory (DFT) code, with a particular emphasis on the time-dependent version of DFT (TDDFT). In this paper we present the ongoing efforts to achieve the parallelization of octopus. We focus on the real-time variant of TDDFT, where the time-dependent Kohn-Sham equations are directly propagated in time. This approach has great potential for execution in massively parallel systems such as modern supercomputers with thousands of processors and graphics processing units (GPUs). For harvesting the potential of conventional supercomputers, the main strategy is a multi-level parallelization scheme that combines the inherent scalability of real-time TDDFT with a real-space grid domain-partitioning approach. A scalable Poisson solver is critical for the efficiency of this scheme. For GPUs, we show how using blocks of Kohn-Sham states provides the required level of data parallelism and that this strategy is also applicable for code optimization on standard processors. Our results show that real-time TDDFT, as implemented in octopus, can be the method of choice for studying the excited states of large molecular systems in modern parallel architectures.
International Nuclear Information System (INIS)
Andrade, Xavier; Aspuru-Guzik, Alán; Alberdi-Rodriguez, Joseba; Rubio, Angel; Strubbe, David A; Louie, Steven G; Oliveira, Micael J T; Nogueira, Fernando; Castro, Alberto; Muguerza, Javier; Arruabarrena, Agustin; Marques, Miguel A L
2012-01-01
Octopus is a general-purpose density-functional theory (DFT) code, with a particular emphasis on the time-dependent version of DFT (TDDFT). In this paper we present the ongoing efforts to achieve the parallelization of octopus. We focus on the real-time variant of TDDFT, where the time-dependent Kohn-Sham equations are directly propagated in time. This approach has great potential for execution in massively parallel systems such as modern supercomputers with thousands of processors and graphics processing units (GPUs). For harvesting the potential of conventional supercomputers, the main strategy is a multi-level parallelization scheme that combines the inherent scalability of real-time TDDFT with a real-space grid domain-partitioning approach. A scalable Poisson solver is critical for the efficiency of this scheme. For GPUs, we show how using blocks of Kohn-Sham states provides the required level of data parallelism and that this strategy is also applicable for code optimization on standard processors. Our results show that real-time TDDFT, as implemented in octopus, can be the method of choice for studying the excited states of large molecular systems in modern parallel architectures. (topical review)
Time-dependent density functional theory with twist-averaged boundary conditions
Schuetrumpf, B.; Nazarewicz, W.; Reinhard, P.-G.
2016-05-01
Background: Time-dependent density functional theory is widely used to describe excitations of many-fermion systems. In its many applications, three-dimensional (3D) coordinate-space representation is used, and infinite-domain calculations are limited to a finite volume represented by a spatial box. For finite quantum systems (atoms, molecules, nuclei, hadrons), the commonly used periodic or reflecting boundary conditions introduce spurious quantization of the continuum states and artificial reflections from boundary; hence, an incorrect treatment of evaporated particles. Purpose: The finite-volume artifacts for finite systems can be practically cured by invoking an absorbing potential in a certain boundary region sufficiently far from the described system. However, such absorption cannot be applied in the calculations of infinite matter (crystal electrons, quantum fluids, neutron star crust), which suffer from unphysical effects stemming from a finite computational box used. Here, twist-averaged boundary conditions (TABC) have been used successfully to diminish the finite-volume effects. In this work, we extend TABC to time-dependent modes. Method: We use the 3D time-dependent density functional framework with the Skyrme energy density functional. The practical calculations are carried out for small- and large-amplitude electric dipole and quadrupole oscillations of 16O. We apply and compare three kinds of boundary conditions: periodic, absorbing, and twist-averaged. Results: Calculations employing absorbing boundary conditions (ABC) and TABC are superior to those based on periodic boundary conditions. For low-energy excitations, TABC and ABC variants yield very similar results. With only four twist phases per spatial direction in TABC, one obtains an excellent reduction of spurious fluctuations. In the nonlinear regime, one has to deal with evaporated particles. In TABC, the floating nucleon gas remains in the box; the amount of nucleons in the gas is found to be
Neuromodulated Spike-Timing-Dependent Plasticity, and Theory of Three-Factor Learning Rules
Frémaux, Nicolas; Gerstner, Wulfram
2016-01-01
Classical Hebbian learning puts the emphasis on joint pre- and postsynaptic activity, but neglects the potential role of neuromodulators. Since neuromodulators convey information about novelty or reward, the influence of neuromodulators on synaptic plasticity is useful not just for action learning in classical conditioning, but also to decide “when” to create new memories in response to a flow of sensory stimuli. In this review, we focus on timing requirements for pre- and postsynaptic activity in conjunction with one or several phasic neuromodulatory signals. While the emphasis of the text is on conceptual models and mathematical theories, we also discuss some experimental evidence for neuromodulation of Spike-Timing-Dependent Plasticity. We highlight the importance of synaptic mechanisms in bridging the temporal gap between sensory stimulation and neuromodulatory signals, and develop a framework for a class of neo-Hebbian three-factor learning rules that depend on presynaptic activity, postsynaptic variables as well as the influence of neuromodulators. PMID:26834568
Time-dependent density-functional theory in the projector augmented-wave method
DEFF Research Database (Denmark)
Walter, Michael; Häkkinen, Hannu; Lehtovaara, Lauri
2008-01-01
We present the implementation of the time-dependent density-functional theory both in linear-response and in time-propagation formalisms using the projector augmented-wave method in real-space grids. The two technically very different methods are compared in the linear-response regime where we fo...... surfaces for a set of atoms and molecules with the linear-response method and by calculating nonlinear emission spectra using the time-propagation method....... found perfect agreement in the calculated photoabsorption spectra. We discuss the strengths and weaknesses of the two methods as well as their convergence properties. We demonstrate different applications of the methods by calculating excitation energies and excited state Born–Oppenheimer potential...
Cui, Ganglong; Fang, Weihai; Yang, Weitao
2010-01-14
Time-dependent density functional theory (TDDFT) has broad application in the study of electronic response, excitation and transport. To extend such application to large and complex systems, we develop a reformulation of TDDFT equations in terms of non-orthogonal localized molecular orbitals (NOLMOs). NOLMO is the most localized representation of electronic degrees of freedom and has been used in ground state calculations. In atomic orbital (AO) representation, the sparsity of NOLMO is transferred to the coefficient matrix of molecular orbitals (MOs). Its novel use in TDDFT here leads to a very simple form of time propagation equations which can be solved with linear-scaling effort. We have tested the method for several long-chain saturated and conjugated molecular systems within the self-consistent charge density-functional tight-binding method (SCC-DFTB) and demonstrated its accuracy. This opens up pathways for TDDFT applications to large bio- and nano-systems.
Neuromodulated Spike-Timing-Dependent Plasticity and Theory of Three-Factor Learning Rules
Directory of Open Access Journals (Sweden)
Wulfram eGerstner
2016-01-01
Full Text Available Classical Hebbian learning puts the emphasis on joint pre- and postsynaptic activity, but neglects the potential role of neuromodulators. Since neuromodulators convey information about novelty or reward, the influence of neuromodulatorson synaptic plasticity is useful not just for action learning in classical conditioning, but also to decide 'when' to create new memories in response to a flow of sensory stimuli.In this review, we focus on timing requirements for pre- and postsynaptic activity in conjunction with one or several phasic neuromodulatory signals. While the emphasis of the text is on conceptual models and mathematical theories, we also discusssome experimental evidence for neuromodulation of Spike-Timing-Dependent Plasticity.We highlight the importance of synaptic mechanisms in bridging the temporal gap between sensory stimulation and neuromodulatory signals, and develop a framework for a class of neo-Hebbian three-factor learning rules that depend on presynaptic activity, postsynaptic variables as well as the influence of neuromodulators.
Neuromodulated Spike-Timing-Dependent Plasticity, and Theory of Three-Factor Learning Rules.
Frémaux, Nicolas; Gerstner, Wulfram
2015-01-01
Classical Hebbian learning puts the emphasis on joint pre- and postsynaptic activity, but neglects the potential role of neuromodulators. Since neuromodulators convey information about novelty or reward, the influence of neuromodulators on synaptic plasticity is useful not just for action learning in classical conditioning, but also to decide "when" to create new memories in response to a flow of sensory stimuli. In this review, we focus on timing requirements for pre- and postsynaptic activity in conjunction with one or several phasic neuromodulatory signals. While the emphasis of the text is on conceptual models and mathematical theories, we also discuss some experimental evidence for neuromodulation of Spike-Timing-Dependent Plasticity. We highlight the importance of synaptic mechanisms in bridging the temporal gap between sensory stimulation and neuromodulatory signals, and develop a framework for a class of neo-Hebbian three-factor learning rules that depend on presynaptic activity, postsynaptic variables as well as the influence of neuromodulators.
Time-dependent Second Order Scattering Theory for Weather Radar with a Finite Beam Width
Kobayashi, Satoru; Tanelli, Simone; Im, Eastwood; Ito, Shigeo; Oguchi, Tomohiro
2006-01-01
Multiple scattering effects from spherical water particles of uniform diameter are studied for a W-band pulsed radar. The Gaussian transverse beam-profile and the rectangular pulse-duration are used for calculation. An second-order analytical solution is derived for a single layer structure, based on a time-dependent radiative transfer theory as described in the authors' companion paper. When the range resolution is fixed, increase in footprint radius leads to increase in the second order reflectivity that is defined as the ratio of the second order return to the first order one. This feature becomes more serious as the range increases. Since the spaceborne millimeter-wavelength radar has a large footprint radius that is competitive to the mean free path, the multiple scattering effect must be taken into account for analysis.
Time-dependent density functional theory of open quantum systems in the linear-response regime.
Tempel, David G; Watson, Mark A; Olivares-Amaya, Roberto; Aspuru-Guzik, Alán
2011-02-21
Time-dependent density functional theory (TDDFT) has recently been extended to describe many-body open quantum systems evolving under nonunitary dynamics according to a quantum master equation. In the master equation approach, electronic excitation spectra are broadened and shifted due to relaxation and dephasing of the electronic degrees of freedom by the surrounding environment. In this paper, we develop a formulation of TDDFT linear-response theory (LR-TDDFT) for many-body electronic systems evolving under a master equation, yielding broadened excitation spectra. This is done by mapping an interacting open quantum system onto a noninteracting open Kohn-Sham system yielding the correct nonequilibrium density evolution. A pseudoeigenvalue equation analogous to the Casida equations of the usual LR-TDDFT is derived for the Redfield master equation, yielding complex energies and Lamb shifts. As a simple demonstration, we calculate the spectrum of a C(2 +) atom including natural linewidths, by treating the electromagnetic field vacuum as a photon bath. The performance of an adiabatic exchange-correlation kernel is analyzed and a first-order frequency-dependent correction to the bare Kohn-Sham linewidth based on the Görling-Levy perturbation theory is calculated.
Two-electron Rabi oscillations in real-time time-dependent density-functional theory.
Habenicht, Bradley F; Tani, Noriyuki P; Provorse, Makenzie R; Isborn, Christine M
2014-11-14
We investigate the Rabi oscillations of electrons excited by an applied electric field in several simple molecular systems using time-dependent configuration interaction (TDCI) and real-time time-dependent density-functional theory (RT-TDDFT) dynamics. While the TDCI simulations exhibit the expected single-electron Rabi oscillations at a single resonant electric field frequency, Rabi oscillations in the RT-TDDFT simulations are a two-electron process. The existence of two-electron Rabi oscillations is determined both by full population inversion between field-free molecular orbitals and the behavior of the instantaneous dipole moment during the simulations. Furthermore, the Rabi oscillations in RT-TDDFT are subject to an intensity threshold of the electric field, below which Rabi oscillations do not occur and above which the two-electron Rabi oscillations occur at a broad range of frequencies. It is also shown that at field intensities near the threshold intensity, the field frequency predicted to induce Rabi oscillations by linear response TDDFT only produces detuned Rabi oscillations. Instead, the field frequency that yields the full two-electron population inversion and Rabi oscillation behavior is shown to be the average of single-electron transition frequencies from the ground S0 state and the doubly-excited S2 state. The behavior of the two-electron Rabi oscillations is rationalized via two possible models. The first model is a multi-photon process that results from the electric field interacting with the three level system such that three level Rabi oscillations may occur. The second model suggests that the mean-field nature of RT-TDDFT induces paired electron propagation.
Two-electron Rabi oscillations in real-time time-dependent density-functional theory
International Nuclear Information System (INIS)
Habenicht, Bradley F.; Tani, Noriyuki P.; Provorse, Makenzie R.; Isborn, Christine M.
2014-01-01
We investigate the Rabi oscillations of electrons excited by an applied electric field in several simple molecular systems using time-dependent configuration interaction (TDCI) and real-time time-dependent density-functional theory (RT-TDDFT) dynamics. While the TDCI simulations exhibit the expected single-electron Rabi oscillations at a single resonant electric field frequency, Rabi oscillations in the RT-TDDFT simulations are a two-electron process. The existence of two-electron Rabi oscillations is determined both by full population inversion between field-free molecular orbitals and the behavior of the instantaneous dipole moment during the simulations. Furthermore, the Rabi oscillations in RT-TDDFT are subject to an intensity threshold of the electric field, below which Rabi oscillations do not occur and above which the two-electron Rabi oscillations occur at a broad range of frequencies. It is also shown that at field intensities near the threshold intensity, the field frequency predicted to induce Rabi oscillations by linear response TDDFT only produces detuned Rabi oscillations. Instead, the field frequency that yields the full two-electron population inversion and Rabi oscillation behavior is shown to be the average of single-electron transition frequencies from the ground S 0 state and the doubly-excited S 2 state. The behavior of the two-electron Rabi oscillations is rationalized via two possible models. The first model is a multi-photon process that results from the electric field interacting with the three level system such that three level Rabi oscillations may occur. The second model suggests that the mean-field nature of RT-TDDFT induces paired electron propagation
Correlated electron dynamics and memory in time-dependent density functional theory
International Nuclear Information System (INIS)
Thiele, Mark
2009-01-01
Time-dependent density functional theory (TDDFT) is an exact reformulation of the time-dependent many-electron Schroedinger equation, where the problem of many interacting electrons is mapped onto the Kohn-Sham system of noninteracting particles which reproduces the exact electronic density. In the Kohn-Sham system all non-classical many-body effects are incorporated in the exchange-correlation potential which is in general unknown and needs to be approximated. It is the goal of this thesis to investigate the connection between memory effects and correlated electron dynamics in strong and weak fields. To this end one-dimensional two-electron singlet systems are studied. At the same time these systems include the onedimensional helium atom model, which is an established system to investigate the crucial effects of correlated electron dynamics in external fields. The studies presented in this thesis show that memory effects are negligible for typical strong field processes. Here the approximation of the spatial nonlocality is of primary importance. For the photoabsorption spectra on the other hand the neglect of memory effects leads to qualitative and quantitative errors, which are shown to be connected to transitions of double excitation character. To develop a better understanding of the conditions under which memory effects become important quantum fluid dynamics has been found to be especially suitable. It represents a further exact reformulation of the quantum mechanic many-body problem which is based on hydrodynamic quantities such as density and velocity. Memory effects are shown to be important whenever the velocity field develops strong gradients and dissipative effects contribute. (orig.)
Correlated electron dynamics and memory in time-dependent density functional theory
Energy Technology Data Exchange (ETDEWEB)
Thiele, Mark
2009-07-28
Time-dependent density functional theory (TDDFT) is an exact reformulation of the time-dependent many-electron Schroedinger equation, where the problem of many interacting electrons is mapped onto the Kohn-Sham system of noninteracting particles which reproduces the exact electronic density. In the Kohn-Sham system all non-classical many-body effects are incorporated in the exchange-correlation potential which is in general unknown and needs to be approximated. It is the goal of this thesis to investigate the connection between memory effects and correlated electron dynamics in strong and weak fields. To this end one-dimensional two-electron singlet systems are studied. At the same time these systems include the onedimensional helium atom model, which is an established system to investigate the crucial effects of correlated electron dynamics in external fields. The studies presented in this thesis show that memory effects are negligible for typical strong field processes. Here the approximation of the spatial nonlocality is of primary importance. For the photoabsorption spectra on the other hand the neglect of memory effects leads to qualitative and quantitative errors, which are shown to be connected to transitions of double excitation character. To develop a better understanding of the conditions under which memory effects become important quantum fluid dynamics has been found to be especially suitable. It represents a further exact reformulation of the quantum mechanic many-body problem which is based on hydrodynamic quantities such as density and velocity. Memory effects are shown to be important whenever the velocity field develops strong gradients and dissipative effects contribute. (orig.)
Perez, R. Navarro; Schunck, N.; Lasseri, R.-D.; Zhang, C.; Sarich, J.
2017-11-01
We describe the new version 3.00 of the code HFBTHO that solves the nuclear Hartree-Fock (HF) or Hartree-Fock-Bogolyubov (HFB) problem by using the cylindrical transformed deformed harmonic oscillator basis. In the new version, we have implemented the following features: (i) the full Gogny force in both particle-hole and particle-particle channels, (ii) the calculation of the nuclear collective inertia at the perturbative cranking approximation, (iii) the calculation of fission fragment charge, mass and deformations based on the determination of the neck, (iv) the regularization of zero-range pairing forces, (v) the calculation of localization functions, (vi) a MPI interface for large-scale mass table calculations. Program Files doi:http://dx.doi.org/10.17632/c5g2f92by3.1 Licensing provisions: GPL v3 Programming language: FORTRAN-95 Journal reference of previous version: M.V. Stoitsov, N. Schunck, M. Kortelainen, N. Michel, H. Nam, E. Olsen, J. Sarich, and S. Wild, Comput. Phys. Commun. 184 (2013). Does the new version supersede the previous one: Yes Summary of revisions: 1. the Gogny force in both particle-hole and particle-particle channels was implemented; 2. the nuclear collective inertia at the perturbative cranking approximation was implemented; 3. fission fragment charge, mass and deformations were implemented based on the determination of the position of the neck between nascent fragments; 4. the regularization method of zero-range pairing forces was implemented; 5. the localization functions of the HFB solution were implemented; 6. a MPI interface for large-scale mass table calculations was implemented. Nature of problem:HFBTHO is a physics computer code that is used to model the structure of the nucleus. It is an implementation of the energy density functional (EDF) approach to atomic nuclei, where the energy of the nucleus is obtained by integration over space of some phenomenological energy density, which is itself a functional of the neutron and proton
DEFF Research Database (Denmark)
Silva-Junior, Mario R.; Schreiber, Marko; Sauer, Stephan P. A.
2008-01-01
Time-dependent density functional theory (TD-DFT) and DFT-based multireference configuration interaction (DFT/MRCI) calculations are reported for a recently proposed benchmark set of 28 medium-sized organic molecules. Vertical excitation energies, oscillator strengths, and excited-state dipole...... moments are computed using the same geometries (MP2/6-31G*) and basis set (TZVP) as in our previous ab initio benchmark study on electronically excited states. The results from TD-DFT (with the functionals BP86, B3LYP, and BHLYP) and from DFT/MRCI are compared against the previous high-level ab initio...
Wavelet-based linear-response time-dependent density-functional theory
Natarajan, Bhaarathi; Genovese, Luigi; Casida, Mark E.; Deutsch, Thierry; Burchak, Olga N.; Philouze, Christian; Balakirev, Maxim Y.
2012-06-01
Linear-response time-dependent (TD) density-functional theory (DFT) has been implemented in the pseudopotential wavelet-based electronic structure program BIGDFT and results are compared against those obtained with the all-electron Gaussian-type orbital program DEMON2K for the calculation of electronic absorption spectra of N2 using the TD local density approximation (LDA). The two programs give comparable excitation energies and absorption spectra once suitably extensive basis sets are used. Convergence of LDA density orbitals and orbital energies to the basis-set limit is significantly faster for BIGDFT than for DEMON2K. However the number of virtual orbitals used in TD-DFT calculations is a parameter in BIGDFT, while all virtual orbitals are included in TD-DFT calculations in DEMON2K. As a reality check, we report the X-ray crystal structure and the measured and calculated absorption spectrum (excitation energies and oscillator strengths) of the small organic molecule N-cyclohexyl-2-(4-methoxyphenyl)imidazo[1, 2-a]pyridin-3-amine.
Farzanehpour, Mehdi; Tokatly, Ilya; Nano-Bio Spectroscopy Group; ETSF Scientific Development Centre Team
2015-03-01
We present a rigorous formulation of the time-dependent density functional theory for interacting lattice electrons strongly coupled to cavity photons. We start with an example of one particle on a Hubbard dimer coupled to a single photonic mode, which is equivalent to the single mode spin-boson model or the quantum Rabi model. For this system we prove that the electron-photon wave function is a unique functional of the electronic density and the expectation value of the photonic coordinate, provided the initial state and the density satisfy a set of well defined conditions. Then we generalize the formalism to many interacting electrons on a lattice coupled to multiple photonic modes and prove the general mapping theorem. We also show that for a system evolving from the ground state of a lattice Hamiltonian any density with a continuous second time derivative is locally v-representable. Spanish Ministry of Economy and Competitiveness (Grant No. FIS2013-46159-C3-1-P), Grupos Consolidados UPV/EHU del Gobierno Vasco (Grant No. IT578-13), COST Actions CM1204 (XLIC) and MP1306 (EUSpec).
Optical rotation calculated with time-dependent density functional theory: the OR45 benchmark.
Srebro, Monika; Govind, Niranjan; de Jong, Wibe A; Autschbach, Jochen
2011-10-13
Time-dependent density functional theory (TDDFT) computations are performed for 42 organic molecules and three transition metal complexes, with experimental molar optical rotations ranging from 2 to 2 × 10(4) deg cm(2) dmol(-1). The performances of the global hybrid functionals B3LYP, PBE0, and BHLYP, and of the range-separated functionals CAM-B3LYP and LC-PBE0 (the latter being fully long-range corrected), are investigated. The performance of different basis sets is studied. When compared to liquid-phase experimental data, the range-separated functionals do, on average, not perform better than B3LYP and PBE0. Median relative deviations between calculations and experiment range from 25 to 29%. A basis set recently proposed for optical rotation calculations (LPol-ds) on average does not give improved results compared to aug-cc-pVDZ in TDDFT calculations with B3LYP. Individual cases are discussed in some detail, among them norbornenone for which the LC-PBE0 functional produced an optical rotation that is close to available data from coupled-cluster calculations, but significantly smaller in magnitude than the liquid-phase experimental value. Range-separated functionals and BHLYP perform well for helicenes and helicene derivatives. Metal complexes pose a challenge to first-principles calculations of optical rotation.
Time-dependent density functional theory for nonlinear properties of open-shell systems.
Rinkevicius, Zilvinas; Jha, Prakash Chandra; Oprea, Corneliu I; Vahtras, Olav; Agren, Hans
2007-09-21
This paper presents response theory based on a spin-restricted Kohn-Sham formalism for computation of time-dependent and time-independent nonlinear properties of molecules with a high spin ground state. The developed approach is capable to handle arbitrary perturbations and constitutes an efficient procedure for evaluation of electric, magnetic, and mixed properties. Apart from presenting the derivation of the proposed approach, we show results from illustrating calculations of static and dynamic hyperpolarizabilities of small Si(3n+1)H(6n+3) (n=0,1,2) clusters which mimic Si(111) surfaces with dangling bond defects. The results indicate that the first hyperpolarizability tensor components of Si(3n+1)H(6n+3) have an ordering compatible with the measurements of second harmonic generation in SiO2/Si(111) interfaces and, therefore, support the hypothesis that silicon surface defects with dangling bonds are responsible for this phenomenon. The results exhibit a strong dependence on the quality of basis set and exchange-correlation functional, showing that an appropriate set of diffuse functions is required for reliable predictions of the first hyperpolarizability of open-shell compounds.
Hilal, Rifaat
2017-06-19
We aim at providing better insight into the parameters that govern the intramolecular charge transfer (ICT) and photo-injection processes in dyes for dye-sensitised solar cells (DSSC). Density functional theory (DFT) and time-dependent DFT (TD-DFT) calculations are utilized to study the geometry, electronic structure, electrostatic potential (ESP) and absorption spectrum, for a representative donor-π bridge-acceptor (D–π–A) dye for DSSC. The coplanar geometry of the dye (D1) facilitates strong conjugation and considerable delocalization originating the π CT interaction from donor to acceptor orbitals and the hyper-conjugative interactions involving Rydberg states. A model simulating the adsorption of the dye on the TiO surface is utilized to estimate binding energies. The effect of fluorine substituents in the π-spacer on the quantum efficiency of DSSCs was investigated. Gibb’s free energy values, redox potentials, excited state lifetime, non-linear optical properties (NLO) and driving forces for D1 and its fluorinated derivatives were computed.
Energy Technology Data Exchange (ETDEWEB)
Vecharynski, Eugene [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Computational Research Division; Brabec, Jiri [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Computational Research Division; Shao, Meiyue [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Computational Research Division; Govind, Niranjan [Pacific Northwest National Lab. (PNNL), Richland, WA (United States). Environmental Molecular Sciences Lab.; Yang, Chao [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Computational Research Division
2017-12-01
We present two efficient iterative algorithms for solving the linear response eigen- value problem arising from the time dependent density functional theory. Although the matrix to be diagonalized is nonsymmetric, it has a special structure that can be exploited to save both memory and floating point operations. In particular, the nonsymmetric eigenvalue problem can be transformed into a product eigenvalue problem that is self-adjoint with respect to a K-inner product. This product eigenvalue problem can be solved efficiently by a modified Davidson algorithm and a modified locally optimal block preconditioned conjugate gradient (LOBPCG) algorithm that make use of the K-inner product. The solution of the product eigenvalue problem yields one component of the eigenvector associated with the original eigenvalue problem. However, the other component of the eigenvector can be easily recovered in a postprocessing procedure. Therefore, the algorithms we present here are more efficient than existing algorithms that try to approximate both components of the eigenvectors simultaneously. The efficiency of the new algorithms is demonstrated by numerical examples.
Electron-nuclear coupling in time-dependent multicomponent density functional theory
Butriy, Olena O.
2008-01-01
In this thesis we developed the time-dependent version of the multicomponent density functional approach to treat time-dependent electron-nuclear systems. The method enables to describe the electron-nuclear coupling fully quantum mechanically. No Born-Oppenheimer approximation is involved in the
Tokatly, I. V.
2011-11-01
It is shown that the density-potential mapping and the V-representability problems in the time-dependent current density functional theory (TDCDFT) are reduced to the solution of a certain many-body nonlinear Schrödinger equation (NLSE). The derived NLSE for TDCDFT links the earlier NLSE-based formulations of the time-dependent deformation functional theory (TDDefFT) and the time-dependent density functional theory (TDDFT). We establish a close relation between the nonlinear many-body problems which control the existence of TDCDFT, TDDFT, and TDDefFT, and thus develop a unified point of view on the whole family of the TDDFT-type theories.
Spin-adapted open-shell time-dependent density functional theory. II. Theory and pilot application.
Li, Zhendong; Liu, Wenjian; Zhang, Yong; Suo, Bingbing
2011-04-07
The excited states of open-shell systems calculated by unrestricted Kohn-Sham-based time-dependent density functional theory (U-TD-DFT) are often heavily spin-contaminated and hence meaningless. This is solved ultimately by the recently proposed spin-adapted time-dependent density functional theory (TD-DFT) (S-TD-DFT) [J. Chem. Phys. 133, 064106 (2010)]. Unlike the standard restricted open-shell Kohn-Sham-based TD-DFT (R-TD-DFT) which can only access the singlet-coupled single excitations, the S-TD-DFT can capture both the singlet- and triplet-coupled single excitations with the same computational effort as the U-TD-DFT. The performances of the three approaches (U-TD-DFT, R-TD-DFT, and S-TD-DFT) are compared for both the spin-conserving and spin-flip excitations of prototypical open-shell systems, the nitrogen (N(2)(+)) and naphthalene (C(10)H(8)(+)) cations. The results show that the S-TD-DFT gives rise to balanced descriptions of excited states of open-shell systems.
Wavelet-based linear-response time-dependent density-functional theory
International Nuclear Information System (INIS)
Natarajan, Bhaarathi; Genovese, Luigi; Casida, Mark E.; Deutsch, Thierry; Burchak, Olga N.
2012-01-01
Highlights: ► We has been implemented LR-TD-DFT in the pseudopotential wavelet-based program. ► We have compared the results against all-electron Gaussian-type program. ► Orbital energies converges significantly faster for BigDFT than for DEMON2K. ► We report the X-ray crystal structure of the small organic molecule flugi6. ► Measured and calculated absorption spectrum of flugi6 is also reported. - Abstract: Linear-response time-dependent (TD) density-functional theory (DFT) has been implemented in the pseudopotential wavelet-based electronic structure program BIGDFT and results are compared against those obtained with the all-electron Gaussian-type orbital program DEMON2K for the calculation of electronic absorption spectra of N 2 using the TD local density approximation (LDA). The two programs give comparable excitation energies and absorption spectra once suitably extensive basis sets are used. Convergence of LDA density orbitals and orbital energies to the basis-set limit is significantly faster for BIGDFT than for DEMON2K. However the number of virtual orbitals used in TD-DFT calculations is a parameter in BIGDFT, while all virtual orbitals are included in TD-DFT calculations in DEMON2K. As a reality check, we report the X-ray crystal structure and the measured and calculated absorption spectrum (excitation energies and oscillator strengths) of the small organic molecule N-cyclohexyl-2-(4-methoxyphenyl)imidazo[1, 2-a]pyridin-3-amine.
Self-consistent RPA and the time-dependent density matrix approach
Energy Technology Data Exchange (ETDEWEB)
Schuck, P. [Institut de Physique Nucleaire, Orsay (France); CNRS et Universite Joseph Fourier, Laboratoire de Physique et Modelisation des Milieux Condenses, Grenoble (France); Tohyama, M. [Kyorin University School of Medicine, Mitaka, Tokyo (Japan)
2016-10-15
The time-dependent density matrix (TDDM) or BBGKY (Bogoliubov, Born, Green, Kirkwood, Yvon) approach is decoupled and closed at the three-body level in finding a natural representation of the latter in terms of a quadratic form of two-body correlation functions. In the small amplitude limit an extended RPA coupled to an also extended second RPA is obtained. Since including two-body correlations means that the ground state cannot be a Hartree-Fock state, naturally the corresponding RPA is upgraded to Self-Consistent RPA (SCRPA) which was introduced independently earlier and which is built on a correlated ground state. SCRPA conserves all the properties of standard RPA. Applications to the exactly solvable Lipkin and the 1D Hubbard models show good performances of SCRPA and TDDM. (orig.)
Schunck, N.; Dobaczewski, J.; McDonnell, J.; Satuła, W.; Sheikh, J. A.; Staszczak, A.; Stoitsov, M.; Toivanen, P.
2012-01-01
We describe the new version (v2.49t) of the code HFODD which solves the nuclear Skyrme-Hartree-Fock (HF) or Skyrme-Hartree-Fock-Bogolyubov (HFB) problem by using the Cartesian deformed harmonic-oscillator basis. In the new version, we have implemented the following physics features: (i) the isospin mixing and projection, (ii) the finite-temperature formalism for the HFB and HF + BCS methods, (iii) the Lipkin translational energy correction method, (iv) the calculation of the shell correction. A number of specific numerical methods have also been implemented in order to deal with large-scale multi-constraint calculations and hardware limitations: (i) the two-basis method for the HFB method, (ii) the Augmented Lagrangian Method (ALM) for multi-constraint calculations, (iii) the linear constraint method based on the approximation of the RPA matrix for multi-constraint calculations, (iv) an interface with the axial and parity-conserving Skyrme-HFB code HFBTHO, (v) the mixing of the HF or HFB matrix elements instead of the HF fields. Special care has been paid to using the code on massively parallel leadership class computers. For this purpose, the following features are now available with this version: (i) the Message Passing Interface (MPI) framework, (ii) scalable input data routines, (iii) multi-threading via OpenMP pragmas, (iv) parallel diagonalization of the HFB matrix in the simplex-breaking case using the ScaLAPACK library. Finally, several little significant errors of the previous published version were corrected. New version program summaryProgram title:HFODD (v2.49t) Catalogue identifier: ADFL_v3_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADFL_v3_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU General Public Licence v3 No. of lines in distributed program, including test data, etc.: 190 614 No. of bytes in distributed program, including test data, etc.: 985 898 Distribution
Time-dependent restricted-active-space self-consistent-field theory for bosonic many-body systems
International Nuclear Information System (INIS)
Lévêque, Camille; Madsen, Lars Bojer
2017-01-01
We develop an ab initio time-dependent wavefunction based theory for the description of a many-body system of cold interacting bosons. Like the multi-configurational time-dependent Hartree method for bosons (MCTDHB), the theory is based on a configurational interaction Ansatz for the many-body wavefunction with time-dependent self-consistent-field orbitals. The theory generalizes the MCTDHB method by incorporating restrictions on the active space of the orbital excitations. The restrictions are specified based on the physical situation at hand. The equations of motion of this time-dependent restricted-active-space self-consistent-field (TD-RASSCF) theory are derived. The similarity between the formal development of the theory for bosons and fermions is discussed. The restrictions on the active space allow the theory to be evaluated under conditions where other wavefunction based methods due to exponential scaling in the numerical effort cannot, and to clearly identify the excitations that are important for an accurate description, significantly beyond the mean-field approach. For ground state calculations we find it to be important to allow a few particles to have the freedom to move in many orbitals, an insight facilitated by the flexibility of the restricted-active-space Ansatz . Moreover, we find that a high accuracy can be obtained by including only even excitations in the many-body self-consistent-field wavefunction. Time-dependent simulations of harmonically trapped bosons subject to a quenching of their noncontact interaction, show failure of the mean-field Gross-Pitaevskii approach within a fraction of a harmonic oscillation period. The TD-RASSCF theory remains accurate at much reduced computational cost compared to the MCTDHB method. Exploring the effect of changes of the restricted-active-space allows us to identify that even self-consistent-field excitations are mainly responsible for the accuracy of the method. (paper)
Stoitsov, M. V.; Schunck, N.; Kortelainen, M.; Michel, N.; Nam, H.; Olsen, E.; Sarich, J.; Wild, S.
2013-06-01
We describe the new version 2.00d of the code HFBTHO that solves the nuclear Skyrme-Hartree-Fock (HF) or Skyrme-Hartree-Fock-Bogoliubov (HFB) problem by using the cylindrical transformed deformed harmonic oscillator basis. In the new version, we have implemented the following features: (i) the modified Broyden method for non-linear problems, (ii) optional breaking of reflection symmetry, (iii) calculation of axial multipole moments, (iv) finite temperature formalism for the HFB method, (v) linear constraint method based on the approximation of the Random Phase Approximation (RPA) matrix for multi-constraint calculations, (vi) blocking of quasi-particles in the Equal Filling Approximation (EFA), (vii) framework for generalized energy density with arbitrary density-dependences, and (viii) shared memory parallelism via OpenMP pragmas. Program summaryProgram title: HFBTHO v2.00d Catalog identifier: ADUI_v2_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADUI_v2_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU General Public License version 3 No. of lines in distributed program, including test data, etc.: 167228 No. of bytes in distributed program, including test data, etc.: 2672156 Distribution format: tar.gz Programming language: FORTRAN-95. Computer: Intel Pentium-III, Intel Xeon, AMD-Athlon, AMD-Opteron, Cray XT5, Cray XE6. Operating system: UNIX, LINUX, WindowsXP. RAM: 200 Mwords Word size: 8 bits Classification: 17.22. Does the new version supercede the previous version?: Yes Catalog identifier of previous version: ADUI_v1_0 Journal reference of previous version: Comput. Phys. Comm. 167 (2005) 43 Nature of problem: The solution of self-consistent mean-field equations for weakly-bound paired nuclei requires a correct description of the asymptotic properties of nuclear quasi-particle wave functions. In the present implementation, this is achieved by using the single-particle wave functions
DEFF Research Database (Denmark)
Rotvig, J.; Smith, H.; Jauho, Antti-Pekka
1996-01-01
We present an analytical study of one-dimensional semiconductor superlattices in external electric fields, which may be time dependent. A number of general results for the (quasi)energies and eigenstates are derived. An equation of motion for the density matrix is obtained for a two-band model...
Romaniello, P; de Boeij, PL
2005-01-01
We included relativistic effects in the formulation of the time-dependent current-density-functional theory for the calculation of linear response properties of metals [P. Romaniello and P. L. de Boeij, Phys. Rev. B (to be published)]. We treat the dominant scalar-relativistic effects using the
International Nuclear Information System (INIS)
Adams, Bernhard W.
2004-01-01
A time-dependent version of the Takagi-Taupin theory of X-ray diffraction is derived in a unified space-time approach, which is particularly applicable to X-ray diffraction in a crystal that is undergoing rapid change on the subpicosecond, and even few-femtosecond, time scale. The theory is applied to the proposal of a class of X-ray optical elements for the subpicosecond manipulation of X-rays
Extended gyrokinetic field theory for time-dependent magnetic confinement fields
International Nuclear Information System (INIS)
Sugama, H.; Watanabe, T.-H.; Nunami, M.
2013-12-01
A gyrokinetic system of equations for turbulent toroidal plasmas in time-dependent axisymmetric background magnetic fields is derived from the variational principle. Besides governing equations for gyrocenter distribution functions and turbulent electromagnetic fields, the conditions which self-consistently determine the background fields varying on a transport time scale are obtained by using the Lagrangian which includes the constraint on the background fields. Conservation laws for energy and toroidal angular momentum of the whole system in the time-dependent background fields are naturally derived by applying Noether's theorem. It is shown that the ensemble-averaged transport equations of particles, energy and toroidal momentum given in the present work agree with the results from the conventional recursive formulation with the WKB representation except that collisional effects are disregarded here. (author)
Time-dependent configurations in the perturbative formalism of string theory
International Nuclear Information System (INIS)
Durin, B.
2006-01-01
In this thesis three time-dependent configurations are studied in the formalism of first-quantized string. These configurations are interesting because perturbative computation of correlation functions is possible and thus is a tool to understand the interplay between the time-dependent geometry and the quantified string. In a first chapter, we explain the reasons for studying these configurations. Then in the second chapter we describe the perturbative formalism and explain how to solve technical problem we encountered. The third chapter is devoted to the physical description of the phenomena involved in these configurations, to the specific computations we made and to the insights we gained. Eventually, we conclude and give some perspectives. (author)
Energy Technology Data Exchange (ETDEWEB)
Maitra, Neepa
2017-08-31
The first US-based summer school and workshop on Time-Dependent Density Functional Theory (TDDFT) was held July 11-21, 2017 in Telluride, CO. This grant provided funding to enable 33 students to attend the school, specifically with lodging and registration fee reductions. TDDFT is increasingly used in computational molecular and materials science to calculate electronic-excitation spectra and dynamics in a wide variety of applications, including photocatalysis, photo-controlled bond dissociation, and light-induced charge transfer. Software development in this community targets multiple software packages, many of which are open source, such as octopus, NWchem and Qb@ll, which are the ones our school focused on. The goal of this first iteration was to create a home for a national community of scholars, including users and developers, with a deep understanding of TDDFT, its capabilities, limitations, and high-performance computing context. We used this opportunity to explore interest in such an event in the future and based on overwhelmingly positive feedback from students and teachers, we intend to hold a similar school+workshop every two years in the US, in order to maintain the high level of interest that we witnessed and the enthusiasm amongst participants.
Energy Technology Data Exchange (ETDEWEB)
Lantri, T. [Laboratory of Technology and Solid’s Properties, Faculty of Sciences and Technology, Abdelhamid Ibn Badis University, BP 227, Mostaganem 27000 (Algeria); Bentata, S., E-mail: sam_bentata@yahoo.com [Laboratory of Technology and Solid’s Properties, Faculty of Sciences and Technology, Abdelhamid Ibn Badis University, BP 227, Mostaganem 27000 (Algeria); Bouadjemi, B.; Benstaali, W. [Laboratory of Technology and Solid’s Properties, Faculty of Sciences and Technology, Abdelhamid Ibn Badis University, BP 227, Mostaganem 27000 (Algeria); Bouhafs, B. [Modelling and Simulation in Materials Science Laboratory, Djillali Liabès University of Sidi Bel-Abbès, 22000 Sidi Bel-Abbes (Algeria); Abbad, A. [Laboratory of Technology and Solid’s Properties, Faculty of Sciences and Technology, Abdelhamid Ibn Badis University, BP 227, Mostaganem 27000 (Algeria); Modelling and Simulation in Materials Science Laboratory, Djillali Liabès University of Sidi Bel-Abbès, 22000 Sidi Bel-Abbes (Algeria); Zitouni, A. [Laboratory of Technology and Solid’s Properties, Faculty of Sciences and Technology, Abdelhamid Ibn Badis University, BP 227, Mostaganem 27000 (Algeria)
2016-12-01
Using the first-principle calculations, we have investigated the structural, elastic, optoelectronic and magnetic properties of Co{sub 2}MnSi Heusler alloy. Based on the density functional theory (DFT) and hiring the full-potential linearized augmented plane wave (FP-LAPW) method, we have used five approaches: the Hybrid on-site exact exchange, the Local Spin Density Approximation (LSDA), the LSDA+U, the Generalized Gradient Approximation GGA and GGA+U; where the Hubbard on-site Coulomb interaction correction U is calculated by constraint local density approximation for Co and Mn atoms. Our results show that the highly-ordered Co{sub 2}MnSi alloy is a ductile, stiff and anisotropic material. It has a half-metallic ferromagnetic character with an integer magnetic moment of 5 µB which is in good agreement with the Slater-Pauling rule. - Highlights: • Each approach gives a half magnetic compound. • EECE gives the largest gap. • Elastic properties show a stiff, ductile and anisotropic material. • Electronic properties are similar for the five approaches. • Total magnetic moment is the same for the five approaches (5 µB).
Sissay, Adonay; Abanador, Paul; Mauger, François; Gaarde, Mette; Schafer, Kenneth J; Lopata, Kenneth
2016-09-07
Strong-field ionization and the resulting electronic dynamics are important for a range of processes such as high harmonic generation, photodamage, charge resonance enhanced ionization, and ionization-triggered charge migration. Modeling ionization dynamics in molecular systems from first-principles can be challenging due to the large spatial extent of the wavefunction which stresses the accuracy of basis sets, and the intense fields which require non-perturbative time-dependent electronic structure methods. In this paper, we develop a time-dependent density functional theory approach which uses a Gaussian-type orbital (GTO) basis set to capture strong-field ionization rates and dynamics in atoms and small molecules. This involves propagating the electronic density matrix in time with a time-dependent laser potential and a spatial non-Hermitian complex absorbing potential which is projected onto an atom-centered basis set to remove ionized charge from the simulation. For the density functional theory (DFT) functional we use a tuned range-separated functional LC-PBE*, which has the correct asymptotic 1/r form of the potential and a reduced delocalization error compared to traditional DFT functionals. Ionization rates are computed for hydrogen, molecular nitrogen, and iodoacetylene under various field frequencies, intensities, and polarizations (angle-dependent ionization), and the results are shown to quantitatively agree with time-dependent Schrödinger equation and strong-field approximation calculations. This tuned DFT with GTO method opens the door to predictive all-electron time-dependent density functional theory simulations of ionization and ionization-triggered dynamics in molecular systems using tuned range-separated hybrid functionals.
Time dependence of silica optical properties during the implantation of fast hydrogen ions: Theory
Barannik, E; Zhurenko, V; Kononenko, S; Kononenko, O
2015-01-01
Formation, excitation and passivation of defects by absorbed hydrogen have been extensively reported in the literature. Here we present a basic luminescence-diffusion model to simulate creation and chemical annealing behavior of non-bridging oxygen hole centers in silica by their treatment under a long-time hydrogen implantation. The model is in a good agreement with experimental data and explains the uncommon nonmonotonic time dependence of the non-bridging oxygen hole centers luminescence during the hydrogen implantation. The proposed model establishes the quantitative relation between the intensity dependence of luminescence on its intrinsic diffusivity, hydrogen concentration, defect concentration and cross-section of their creation. Possibilities to estimate these parameters based on the experimental data for the efficiency of silica luminescence are also discussed.
Time-dependence in relativistic collisionless shocks: theory of the variable
Energy Technology Data Exchange (ETDEWEB)
Spitkovsky, A
2004-02-05
We describe results from time-dependent numerical modeling of the collisionless reverse shock terminating the pulsar wind in the Crab Nebula. We treat the upstream relativistic wind as composed of ions and electron-positron plasma embedded in a toroidal magnetic field, flowing radially outward from the pulsar in a sector around the rotational equator. The relativistic cyclotron instability of the ion gyrational orbit downstream of the leading shock in the electron-positron pairs launches outward propagating magnetosonic waves. Because of the fresh supply of ions crossing the shock, this time-dependent process achieves a limit-cycle, in which the waves are launched with periodicity on the order of the ion Larmor time. Compressions in the magnetic field and pair density associated with these waves, as well as their propagation speed, semi-quantitatively reproduce the behavior of the wisp and ring features described in recent observations obtained using the Hubble Space Telescope and the Chandra X-Ray Observatory. By selecting the parameters of the ion orbits to fit the spatial separation of the wisps, we predict the period of time variability of the wisps that is consistent with the data. When coupled with a mechanism for non-thermal acceleration of the pairs, the compressions in the magnetic field and plasma density associated with the optical wisp structure naturally account for the location of X-ray features in the Crab. We also discuss the origin of the high energy ions and their acceleration in the equatorial current sheet of the pulsar wind.
Accurate Ground-State Energies of Solids and Molecules from Time-Dependent Density-Functional Theory
DEFF Research Database (Denmark)
Olsen, Thomas; Thygesen, Kristian Sommer
2014-01-01
We demonstrate that ground-state energies approaching chemical accuracy can be obtained by combining the adiabatic-connection fluctuation-dissipation theorem with time-dependent densityfunctional theory. The key ingredient is a renormalization scheme, which eliminates the divergence of the correl......We demonstrate that ground-state energies approaching chemical accuracy can be obtained by combining the adiabatic-connection fluctuation-dissipation theorem with time-dependent densityfunctional theory. The key ingredient is a renormalization scheme, which eliminates the divergence...... and solids. We also consider examples of barrier heights in chemical reactions, molecular adsorption, and graphene interacting with metal surfaces, which are three examples where the RPA has been successful. In these cases, the renormalized kernel provides results that are of equal quality or even slightly...
Weisman, Jennifer L.; Lee, Timothy J.; Salama, Farid; Gordon-Head, Martin; Kwak, Dochan (Technical Monitor)
2002-01-01
We investigate the electronic absorption spectra of several maximally pericondensed polycyclic aromatic hydrocarbon radical cations with time dependent density functional theory calculations. We find interesting trends in the vertical excitation energies and oscillator strengths for this series containing pyrene through circumcoronene, the largest species containing more than 50 carbon atoms. We discuss the implications of these new results for the size and structure distribution of the diffuse interstellar band carriers.
Energy Technology Data Exchange (ETDEWEB)
Brics, Martins
2016-12-09
Intense, ultra-short laser pulses interacting with atoms, molecules, clusters, and solids give rise to many new fascinating phenomena, not at all accessible to quantum mechanics textbook perturbation theory. A full numerical solution of the time-dependent Schr¨odinger equation (TDSE) for such strong-field problems is also impossible for more than two electrons. Hence, powerful time-dependent quantum many-body approaches need to be developed. Unfortunately, efficient methods such as time-dependent density functional theory (TDDFT) fail in reproducing experimental observations, in particular if strong correlations are involved. In TDDFT, the approximation not only lies in the so-called exchange correlation potential but also in the density functionals for the observables of interest. In fact, with just the single-particle density alone it is unclear how to calculate, e.g., multiple-ionization probabilities or photoelectron spectra, or, even worse, correlated photoelectron spectra, as measured in nowadays experiments. In general, the simple structure of the time-dependent many-body Schroedinger equation for a highly-dimensional many-body wavefunction can only be traded for more complicated equations of motion for simpler quantities. In this thesis, a theory is examined that goes one step beyond TDDFT as far as the complexity of the propagated quantity is concerned. In time-dependent renormalized natural orbital theory (TDRNOT), the basic quantities that are propagated in time are the eigenvalues and eigenstates of the one-body reduced density matrix (1-RDM). The eigenstates are called natural orbitals (NOs), the eigenvalues are the corresponding occupation numbers (ONs). Compared to TDDFT, the knowledge of the NOs and the ONs relax the problem of calculating observables in practice because they can be used to construct the 1-RDM and the two-body reduced density matrix (2-RDM). After the derivation of the equations of motion for a combination of NOs and ONs, the so
Global Melnikov Theory in Hamiltonian Systems with General Time-Dependent Perturbations
Gidea, Marian; de la Llave, Rafael
2018-04-01
We consider a mechanical system consisting of n-penduli and a d-degree-of-freedom rotator. The phase space of the rotator defines a normally hyperbolic invariant manifold Λ _0 . We apply a time-dependent perturbation, which is not assumed to be either Hamiltonian, or periodic, or quasi-periodic, as we allow for rather general time dependence. The strength of the perturbation is given by a parameter ɛ \\in R . For all |ɛ | sufficiently small, the augmented flow—obtained by making the time into a new variable—has a normally hyperbolic locally invariant manifold \\tilde{Λ }_ɛ . For ɛ =0 , \\tilde{Λ }_0=Λ _0× R . We define a Melnikov-type vector, which gives the first-order expansion of the displacement of the stable and unstable manifolds of \\tilde{Λ }_0 under the perturbation. We provide an explicit formula for the Melnikov vector in terms of convergent improper integrals of the perturbation along homoclinic orbits of the unperturbed system. We show that if the perturbation satisfies some explicit non-degeneracy conditions, then the stable and unstable manifolds of \\tilde{Λ }_ɛ , W^s(\\tilde{Λ }_ɛ ) and W^u(\\tilde{Λ }_ɛ ) , respectively, intersect along a transverse homoclinic manifold, and, moreover, the splitting of W^s(\\tilde{Λ }_ɛ ) and W^u(\\tilde{Λ }_ɛ ) can be explicitly computed, up to the first order, in terms of the Melnikov-type vector. This implies that the excursions along some homoclinic trajectories yield a non-trivial increase of order O(ɛ ) in the action variables of the rotator, for all sufficiently small perturbations. The formulas that we obtain are independent of the unperturbed motions in Λ _0 , and give, at the same time, the effects on periodic, quasi-periodic, or general-type orbits. When the perturbation is Hamiltonian, we express the effects of the perturbation, up to the first order, in terms of a Melnikov potential. In addition, if the perturbation is periodic, we obtain that the non-degeneracy conditions on
A theory of loop formation and elimination by spike timing-dependent plasticity
Directory of Open Access Journals (Sweden)
James Kozloski
2010-03-01
Full Text Available We show that the local Spike Timing-Dependent Plasticity (STDP rule has the effect of regulating the trans-synaptic weights of loops of any length within a simulated network of neurons. We show that depending on STDP's polarity, functional loops are formed or eliminated in networks driven to normal spiking conditions by random, partially correlated inputs, where functional loops comprise synaptic weights that exceed a non-zero threshold. We further prove that STDP is a form of loop-regulating plasticity for the case of a linear network driven by noise. Thus a notable local synaptic learning rule makes a specific prediction about synapses in the brain in which standard STDP is present: that under normal spiking conditions, they should participate in predominantly feed-forward connections at all scales. Our model implies that any deviations from this prediction would require a substantial modification to the hypothesized role for standard STDP. Given its widespread occurrence in the brain, we predict that STDP could also regulate long range functional loops among individual neurons across all brain scales, up to, and including, the scale of global brain network topology.
Energy Technology Data Exchange (ETDEWEB)
Brics, Martins; Kapoor, Varun; Bauer, Dieter [Institut fuer Physik, Universitaet Rostock, 18051 Rostock (Germany)
2013-07-01
Time-dependent density functional theory (TDDFT) with known and practicable exchange-correlation potentials does not capture highly correlated electron dynamics such as single-photon double ionization, autoionization, or nonsequential ionization. Time-dependent reduced density matrix functional theory (TDRDMFT) may remedy these problems. The key ingredients in TDRDMFT are the natural orbitals (NOs), i.e., the eigenfunctions of the one-body reduced density matrix (1-RDM), and the occupation numbers (OCs), i.e., the respective eigenvalues. The two-body reduced density matrix (2-RDM) is then expanded in NOs, and equations of motion for the NOs can be derived. If the expansion coefficients of the 2-RDM were known exactly, the problem at hand would be solved. In practice, approximations have to be made. We study the prospects of TDRDMFT following a top-down approach. We solve the exact two-electron time-dependent Schroedinger equation for a model Helium atom in intense laser fields in order to study highly correlated phenomena such as the population of autoionizing states or single-photon double ionization. From the exact wave function we calculate the exact NOs, OCs, the exact expansion coefficients of the 2-RDM, and the exact potentials in the equations of motion. In that way we can identify how many NOs and which level of approximations are necessary to capture such phenomena.
Kinetic Ising model in a time-dependent oscillating external magnetic field: effective-field theory
International Nuclear Information System (INIS)
Deviren, Bayram; Canko, Osman; Keskin, Mustafa
2010-01-01
Recently, Shi et al. [2008 Phys. Lett. A 372 5922] have studied the dynamical response of the kinetic Ising model in the presence of a sinusoidal oscillating field and presented the dynamic phase diagrams by using an effective-field theory (EFT) and a mean-field theory (MFT). The MFT results are in conflict with those of the earlier work of Tomé and de Oliveira, [1990 Phys. Rev. A 41 4251]. We calculate the dynamic phase diagrams and find that our results are similar to those of the earlier work of Tomé and de Oliveira; hence the dynamic phase diagrams calculated by Shi et al. are incomplete within both theories, except the low values of frequencies for the MFT calculation. We also investigate the influence of external field frequency (ω) and static external field amplitude (h 0 ) for both MFT and EFT calculations. We find that the behaviour of the system strongly depends on the values of ω and h 0 . (general)
Li, Zhendong; Liu, Wenjian
2010-08-14
The spin-adaptation of single-reference quantum chemical methods for excited states of open-shell systems has been nontrivial. The primary reason is that the configuration space, generated by a truncated rank of excitations from only one component of a reference multiplet, is spin-incomplete. Those "missing" configurations are of higher ranks and can, in principle, be recaptured by a particular class of excitation operators. However, the resulting formalisms are then quite involved and there are situations [e.g., time-dependent density functional theory (TD-DFT) under the adiabatic approximation] that prevent one from doing so. To solve this issue, we propose here a tensor-coupling scheme that invokes all the components of a reference multiplet (i.e., a tensor reference) rather than increases the excitation ranks. A minimal spin-adapted n-tuply excited configuration space can readily be constructed by tensor products between the n-tuple tensor excitation operators and the chosen tensor reference. Further combined with the tensor equation-of-motion formalism, very compact expressions for excitation energies can be obtained. As a first application of this general idea, a spin-adapted open-shell random phase approximation is first developed. The so-called "translation rule" is then adopted to formulate a spin-adapted, restricted open-shell Kohn-Sham (ROKS)-based TD-DFT (ROKS-TD-DFT). Here, a particular symmetry structure has to be imposed on the exchange-correlation kernel. While the standard ROKS-TD-DFT can access only excited states due to singlet-coupled single excitations, i.e., only some of the singly excited states of the same spin (S(i)) as the reference, the new scheme can capture all the excited states of spin S(i)-1, S(i), or S(i)+1 due to both singlet- and triplet-coupled single excitations. The actual implementation and computation are very much like the (spin-contaminated) unrestricted Kohn-Sham-based TD-DFT. It is also shown that spin-contaminated spin
Time-dependent restricted-active-space self-consistent-field theory for bosonic many-body systems
Leveque, Camille; Madsen, Lars Bojer
2017-04-01
We have developed an ab-initio time-dependent wavefunction based theory for the description of many-body systems of bosons. The theory is based on a configurational interaction Ansatz for the many-body wavefunction with time-dependent self-consistent-field orbitals. The active space of the orbital excitations is subject to restrictions to be specified based on the physical situation at hand. The restrictions on the active space allow the theory to be evaluated under conditions where other wavefunction based methods, due to exponential scaling in the numerical efforts, cannot. The restrictions also allow us to clearly identify the excitations that are important for an accurate description, significantly beyond the mean-field approach. We first apply this theory to compute the ground-state energy of tens of trapped bosons, and second to simulate the dynamics following an instantaneous quenching of a non-contact interaction. The method provides accurate results and its computational cost is largely reduced compared with other wavefunction based many-body methods thanks to the restriction of the active orbital space. The important excitations are clearly identified and the method provides a new way to gain insight in correlation effects. This work was supported by the ERC-StG (Project No. 277767-TDMET) and the VKR center of excellence, QUSCOPE.
Tempel, David G; Aspuru-Guzik, Alán
2012-01-01
We prove that the theorems of TDDFT can be extended to a class of qubit Hamiltonians that are universal for quantum computation. The theorems of TDDFT applied to universal Hamiltonians imply that single-qubit expectation values can be used as the basic variables in quantum computation and information theory, rather than wavefunctions. From a practical standpoint this opens the possibility of approximating observables of interest in quantum computations directly in terms of single-qubit quantities (i.e. as density functionals). Additionally, we also demonstrate that TDDFT provides an exact prescription for simulating universal Hamiltonians with other universal Hamiltonians that have different, and possibly easier-to-realize two-qubit interactions. This establishes the foundations of TDDFT for quantum computation and opens the possibility of developing density functionals for use in quantum algorithms.
Energy Technology Data Exchange (ETDEWEB)
Baczewski, Andrew David; Shulenburger, Luke; Desjarlais, Michael Paul; Magyar, Rudolph J.
2014-02-01
In recent years, DFT-MD has been shown to be a useful computational tool for exploring the properties of WDM. These calculations achieve excellent agreement with shock compression experiments, which probe the thermodynamic parameters of the Hugoniot state. New X-ray Thomson Scattering diagnostics promise to deliver independent measurements of electronic density and temperature, as well as structural information in shocked systems. However, they require the development of new levels of theory for computing the associated observables within a DFT framework. The experimentally observable x-ray scattering cross section is related to the electronic density-density response function, which is obtainable using TDDFT - a formally exact extension of conventional DFT that describes electron dynamics and excited states. In order to develop a capability for modeling XRTS data and, more generally, to establish a predictive capability for rst principles simulations of matter in extreme conditions, real-time TDDFT with Ehrenfest dynamics has been implemented in an existing PAW code for DFT-MD calculations. The purpose of this report is to record implementation details and benchmarks as the project advances from software development to delivering novel scienti c results. Results range from tests that establish the accuracy, e ciency, and scalability of our implementation, to calculations that are veri ed against accepted results in the literature. Aside from the primary XRTS goal, we identify other more general areas where this new capability will be useful, including stopping power calculations and electron-ion equilibration.
Time-dependent transport phenomena
Stefanucci, Gianluca; Kurth, S.; Gross, E. K. U.; Rubio, Angel
2007-01-01
This chapter describes the ab initio theory of quantum transport. The Cini scheme can be combined with time-dependent density functional theory (TDDFT). In this theory, the time-dependent density of an interacting system moving in an external, time-dependent local potential can be calculated via a fictitious system of non-interacting electrons moving in a local, effective, and time-dependent potential. Therefore this theory is well suited for the treatment of non-equilibrium transport problem...
Romaniello, P; de Boeij, P L
2005-04-22
We included relativistic effects in the formulation of the time-dependent current-density-functional theory for the calculation of linear response properties of metals [P. Romaniello and P. L. de Boeij, Phys. Rev. B (to be published)]. We treat the dominant scalar-relativistic effects using the zeroth-order regular approximation in the ground-state density-functional theory calculations, as well as in the time-dependent response calculations. The results for the dielectric function of gold calculated in the spectral range of 0-10 eV are compared with experimental data reported in literature and recent ellipsometric measurements. As well known, relativistic effects strongly influence the color of gold. We find that the onset of interband transitions is shifted from around 3.5 eV, obtained in a nonrelativistic calculation, to around 1.9 eV when relativity is included. With the inclusion of the scalar-relativistic effects there is an overall improvement of both real and imaginary parts of the dielectric function over the nonrelativistic ones. Nevertheless some important features in the absorption spectrum are not well reproduced, but can be explained in terms of spin-orbit coupling effects. The remaining deviations are attributed to the underestimation of the interband gap (5d-6sp band gap) in the local-density approximation and to the use of the adiabatic local-density approximation in the response calculation.
Excited states of ReO4-: A comprehensive time-dependent relativistic density functional theory study
Xu, Wenhua; Ma, Jianyi; Peng, Daoling; Zou, Wenli; Liu, Wenjian; Staemmler, Volker
2009-02-01
The perrhenate anion, ReO4-, is taken as a showcase of heavy transition metal complexes, to examine the performance of time-dependent relativistic density functional linear response theory for electronic excitations, which is based on a newly proposed exact two-component Hamiltonian resulting from the symmetrized elimination of the small component. In total 30 scalar and 63 spinor excited states are investigated and the results are grossly in good agreement with those by the singles and doubles coupled-cluster linear response theory. It is found that only a few scalar states of 3T1 and 3T2 symmetries are split significantly by the spin-orbit coupling, whereas only those excited states involving the Rydberg-type virtual orbital are affected by the solvent effects. The nature of the optical absorption spectra is also highlighted.
Excited states of ReO4-: A comprehensive time-dependent relativistic density functional theory study
International Nuclear Information System (INIS)
Xu Wenhua; Ma Jianyi; Peng Daoling; Zou Wenli; Liu Wenjian; Staemmler, Volker
2009-01-01
The perrhenate anion, ReO 4 - , is taken as a showcase of heavy transition metal complexes, to examine the performance of time-dependent relativistic density functional linear response theory for electronic excitations, which is based on a newly proposed exact two-component Hamiltonian resulting from the symmetrized elimination of the small component. In total 30 scalar and 63 spinor excited states are investigated and the results are grossly in good agreement with those by the singles and doubles coupled-cluster linear response theory. It is found that only a few scalar states of 3 T 1 and 3 T 2 symmetries are split significantly by the spin-orbit coupling, whereas only those excited states involving the Rydberg-type virtual orbital are affected by the solvent effects. The nature of the optical absorption spectra is also highlighted
On the consistent solution of the gap-equation for spontaneously broken λΦ 4-theory
Nachbagauer, Herbert
1995-12-01
We present a self-consistent solution of the finite temperature gap-equation for λΦ 4 theory beyond the Hartree-Fock approximation using a composite operator effective action. We find that in a spontaneously broken theory not only the so-called daisy and superdaisy graphs contribute to the resummed mass, but also resummed non-local diagrams are of the same order.
On the consistent solution of the gap-equation for spontaneously broken {lambda}{Phi}{sup 4}-theory
Energy Technology Data Exchange (ETDEWEB)
Nachbagauer, H. [Laboratoire de Physique Theorique ENSLAPP, 74 - Annecy-le-Vieux (France)
1995-08-01
We present a self-consistent solution of the finite temperature gap-equation for {lambda}{Phi}{sup 4} theory beyond the Hartree-Fock approximation using a composite operator effective action. We find that in a spontaneously broken theory not only the so-called daisy and superdaisy graphs contribute to the resummed mass, but also resummed non-local diagrams are of the same order. (orig.). With 3 figs.
Pastore, Mariachiara; Assfeld, Xavier; Mosconi, Edoardo; Monari, Antonio; Etienne, Thibaud
2017-07-14
We report a theoretical study on the analysis of the relaxed one-particle difference density matrix characterizing the passage from the ground to the excited state of a molecular system, as obtained from time-dependent density functional theory. In particular, this work aims at using the physics contained in the so-called Z-vector, which differentiates between unrelaxed and relaxed difference density matrices to analyze excited states' nature. For this purpose, we introduce novel quantum-mechanical quantities, based on the detachment/attachment methodology, for analysing the Z-vector transformation for different molecules and density functional theory functionals. A derivation pathway of these novel descriptors is reported, involving a numerical integration to be performed in the Euclidean space on the density functions. This topological analysis is then applied to two sets of chromophores, and the correlation between the level of theory and the behavior of our descriptors is properly rationalized. In particular, the effect of range-separation on the relaxation amplitude is discussed. The relaxation term is finally shown to be system-specific (for a given level of theory) and independent of the number of electrons (i.e., the relaxation amplitude is not simply the result of a collective phenomenon).
Directory of Open Access Journals (Sweden)
Muhammad Mus-’ab Anas
2015-01-01
Full Text Available This paper presents a systematic study of the absorption spectrum of various sizes of small hydrogenated silicon quantum dots of quasi-spherical symmetry using the time-dependent density functional theory (TDDFT. In this study, real-time and real-space implementation of TDDFT involving full propagation of the time-dependent Kohn-Sham equations were used. The experimental results for SiH4 and Si5H12 showed good agreement with other earlier calculations and experimental data. Then these calculations were extended to study larger hydrogenated silicon quantum dots with diameter up to 1.6 nm. It was found that, for small quantum dots, the absorption spectrum is atomic-like while, for relatively larger (1.6 nm structure, it shows bulk-like behavior with continuous plateau with noticeable peak. This paper also studied the absorption coefficient of silicon quantum dots as a function of their size. Precisely, the dependence of dot size on the absorption threshold is elucidated. It was found that the silicon quantum dots exhibit direct transition of electron from HOMO to LUMO states; hence this theoretical contribution can be very valuable in discerning the microscopic processes for the future realization of optoelectronic devices.
Farzanehpour, M.; Tokatly, I. V.
2014-11-01
We present a rigorous formulation of the time-dependent density-functional theory for interacting lattice electrons strongly coupled to cavity photons. We start with an example of one particle on a Hubbard dimer coupled to a single photonic mode, which is equivalent to the single mode spin-boson model or the quantum Rabi model. For this system we prove that the electron-photon wave function is a unique functional of the electronic density and the expectation value of the photonic coordinate, provided the initial state and the density satisfy a set of well defined conditions. Then we generalize the formalism to many interacting electrons on a lattice coupled to multiple photonic modes and prove the general mapping theorem. We also show that for a system evolving from the ground state of a lattice Hamiltonian any density with a continuous second time derivative is locally v representable.
Energy Technology Data Exchange (ETDEWEB)
Lopata, Kenneth A.; Govind, Niranjan
2013-11-12
We present a real-time time-dependent density functional theory (RT-TDDFT) prescription for capturing near and post-ionization excitations based on non-Hermitian von Neumann density matrix propagation with atom-centered basis sets, tuned range-separated DFT, and a phenomenological imaginary molecular orbital-based absorbing potential to mimic coupling to the continuum. The computed extreme ultraviolet absorption spectra for acetylene (C2H2), water (H2O), and Freon 12 (CF2Cl2) agree well with electron energy loss spectroscopy (EELS) data over the range 0 to 50 eV. The absorbing potential removes spurious high energy finite basis artifacts, yielding correct bound to bound transitions, metastable (autoionizing) resonance states, and consistent overall absorption shapes.
Wang, RuLin; Zheng, Xiao; Kwok, YanHo; Xie, Hang; Chen, GuanHua; Yam, ChiYung
2015-04-14
Understanding electronic dynamics on material surfaces is fundamentally important for applications including nanoelectronics, inhomogeneous catalysis, and photovoltaics. Practical approaches based on time-dependent density functional theory for open systems have been developed to characterize the dissipative dynamics of electrons in bulk materials. The accuracy and reliability of such approaches depend critically on how the electronic structure and memory effects of surrounding material environment are accounted for. In this work, we develop a novel squared-Lorentzian decomposition scheme, which preserves the positive semi-definiteness of the environment spectral matrix. The resulting electronic dynamics is guaranteed to be both accurate and convergent even in the long-time limit. The long-time stability of electronic dynamics simulation is thus greatly improved within the current decomposition scheme. The validity and usefulness of our new approach are exemplified via two prototypical model systems: quasi-one-dimensional atomic chains and two-dimensional bilayer graphene.
Lian, Cheng; Zhao, Shuangliang; Liu, Honglai; Wu, Jianzhong
2016-11-28
Understanding the charging kinetics of electric double layers is of fundamental importance for the design and development of novel electrochemical devices such as supercapacitors and field-effect transistors. In this work, we study the dynamic behavior of room-temperature ionic liquids using a classical time-dependent density functional theory that accounts for the molecular excluded volume effects, the electrostatic correlations, and the dispersion forces. While the conventional models predict a monotonic increase of the surface charge with time upon application of an electrode voltage, our results show that dispersion between ions results in a non-monotonic increase of the surface charge with the duration of charging. Furthermore, we investigate the effects of van der Waals attraction between electrode/ionic-liquid interactions on the charging processes.
Bai, Zhaojun; Rocca, Dario; Li, Ren-Cang; Galli, Giulia
2012-02-01
We present a technique for the iterative diagonalization of random-phase approximation (RPA) matrices, which are encountered in the framework of time-dependent density-functional theory (TDDFT) and in the solution of the Bethe-Salpeter equation (BSE) [1]. The non-Hermitian character of these matrices does not permit a straightforward application of standard iterative techniques used, i.e., for the diagonalization of ground state Hamiltonians. We first introduce a new block variational principle for RPA matrices. We then develop an algorithm for the simultaneous calculation of multiple eigenvalues and eigenvectors, with convergence and stability properties similar to techniques used to iteratively diagonalize Hermitian matrices. The algorithm is validated by computing multiple low-lying excitation energies of molecules at both the TDDFT and BSE level.[4pt] [1] D. Rocca, Z. Bai, R.-C. Li, and G. Galli, submitted to J. Chem. Phys.
Covington, Cody; Hartig, Kara; Russakoff, Arthur; Kulpins, Ryan; Varga, Kálmán
2017-05-01
Time-dependent density-functional theory was employed to study the effects of proton and α -particle radiation on uracil and adenine. This method has the advantage of treating nuclear motion and electronic motion simultaneously, allowing for the study of electronic excitation, charge transfer, ionization, and nuclear motion. Particle energies were surveyed in the range of 15-500 keV for protons and 100-2000 keV for α particles in conjunction with impact points both on and off carbon bonds in order to investigate the electron and nuclear dynamics of irradiated molecules and the form and quantity of transferred energy. The stopping power, energy transferred, and ionization were found, and the relationship between incident particle energy and electron density of the target molecule was characterized for proton and α -particle radiation incident on adenine and uracil.
Roy, Susmita; Yashonath, Subramanian; Bagchi, Biman
2015-03-28
A self-consistent mode coupling theory (MCT) with microscopic inputs of equilibrium pair correlation functions is developed to analyze electrolyte dynamics. We apply the theory to calculate concentration dependence of (i) time dependent ion diffusion, (ii) intermediate scattering function of the constituent ions, and (iii) ion solvation dynamics in electrolyte solution. Brownian dynamics with implicit water molecules and molecular dynamics method with explicit water are used to check the theoretical predictions. The time dependence of ionic self-diffusion coefficient and the corresponding intermediate scattering function evaluated from our MCT approach show quantitative agreement with early experimental and present Brownian dynamic simulation results. With increasing concentration, the dispersion of electrolyte friction is found to occur at increasingly higher frequency, due to the faster relaxation of the ion atmosphere. The wave number dependence of intermediate scattering function, F(k, t), exhibits markedly different relaxation dynamics at different length scales. At small wave numbers, we find the emergence of a step-like relaxation, indicating the presence of both fast and slow time scales in the system. Such behavior allows an intriguing analogy with temperature dependent relaxation dynamics of supercooled liquids. We find that solvation dynamics of a tagged ion exhibits a power law decay at long times-the decay can also be fitted to a stretched exponential form. The emergence of the power law in solvation dynamics has been tested by carrying out long Brownian dynamics simulations with varying ionic concentrations. The solvation time correlation and ion-ion intermediate scattering function indeed exhibit highly interesting, non-trivial dynamical behavior at intermediate to longer times that require further experimental and theoretical studies.
National Research Council Canada - National Science Library
Pachter, Ruth; Nguyen, Kiet A; Day, Paul N
2007-01-01
We report one- and two-photon absorption excitation energies and cross sections for a series of 7-aminocoumarins using time-dependent density functional theory with various basis sets and functionals...
Goings, Joshua James
Time-dependent electronic structure theory has the power to predict and probe the ways electron dynamics leads to useful phenomena and spectroscopic data. Here we report several advances and extensions of broken-symmetry time-dependent electronic structure theory in order to capture the flexibility required to describe non-equilibrium spin dynamics, as well as electron dynamics for chiroptical properties and vibrational effects. In the first half, we begin by discussing the generalization of self-consistent field methods to the so-called two-component structure in order to capture non-collinear spin states. This means that individual electrons are allowed to take a superposition of spin-1/2 projection states, instead of being constrained to either spin-up or spin-down. The system is no longer a spin eigenfunction, and is known a a spin-symmetry broken wave function. This flexibility to break spin symmetry may lead to variational instabilities in the approximate wave function, and we discuss how these may be overcome. With a stable non-collinear wave function in hand, we then discuss how to obtain electronic excited states from the non-collinear reference, along with associated challenges in their physical interpretation. Finally, we extend the two-component methods to relativistic Hamiltonians, which is the proper setting for describing spin-orbit driven phenomena. We describe the first implementation of the explicit time propagation of relativistic two-component methods and how this may be used to capture spin-forbidden states in electronic absorption spectra. In the second half, we describe the extension of explicitly time-propagated wave functions to the simulation of chiroptical properties, namely circular dichroism (CD) spectra of chiral molecules. Natural circular dichroism, that is, CD in the absence of magnetic fields, originates in the broken parity symmetry of chiral molecules. This proves to be an efficient method for computing circular dichroism spectra
International Nuclear Information System (INIS)
Malloci, G.; Cappellini, G.; Mulas, G.; Mattoni, A.
2013-01-01
We report a comparative study of the optoelectronic properties of small acenes (benzene, anthracene, and pentacene) and their bis-triisopropylsilylethynyl (TIPS) functionalized counterparts. We computed the fundamental gap using density functional theory (DFT) in the framework of the ΔSCF scheme, and the optical absorption spectra by means of time-dependent DFT. Upon TIPS functionalization we observed a lowering of the ionization energy and a rise of the electron affinity; we consequently predict a systematic reduction of the fundamental electronic gap which decreases from ∼ 40% for benzene to ∼ 16% for pentacene. This trend is reflected in the computed optical absorption spectra: for all TIPS-molecules the onset of absorption is red-shifted as compared to their plain precursors. In the case of TIPS-pentacene, in particular, the computed spectrum agrees with the available experimental data. - Highlights: • We evaluate the effect of triisopropylsilylethynyl (TIPS)-substitution on acenes. • We compared the fundamental gap and the optical absorption as a function of size. • We found a general gap reduction following TIPS functionalization. • The gap reduction decreases at increasing size, from 40% for n = 1 to 16% for n = 5. • The onset of absorption is red-shifted as compared to TIPS precursors
Energy Technology Data Exchange (ETDEWEB)
Kühn, Michael [Institut für Physikalische Chemie, Karlsruher Institut für Technologie, Kaiserstraße 12, 76131 Karlsruhe (Germany); Weigend, Florian, E-mail: florian.weigend@kit.edu [Institut für Physikalische Chemie, Karlsruher Institut für Technologie, Kaiserstraße 12, 76131 Karlsruhe (Germany); Institut für Nanotechnologie, Karlsruher Institut für Technologie, Postfach 3640, 76021 Karlsruhe (Germany)
2014-12-14
“Spin-forbidden” transitions are calculated for an eight-membered set of iridium-containing candidate molecules for organic light-emitting diodes (OLEDs) using two-component time-dependent density functional theory. Phosphorescence lifetimes (obtained from averaging over relevant excitations) are compared to experimental data. Assessment of parameters like non-distorted and distorted geometric structures, density functionals, relativistic Hamiltonians, and basis sets was done by a thorough study for Ir(ppy){sub 3} focussing not only on averaged phosphorescence lifetimes, but also on the agreement of the triplet substate structure with experimental data. The most favorable methods were applied to an eight-membered test set of OLED candidate molecules; Boltzmann-averaged phosphorescence lifetimes were investigated concerning the convergence with the number of excited states and the changes when including solvent effects. Finally, a simple model for sorting out molecules with long averaged phosphorescence lifetimes is developed by visual inspection of computationally easily achievable one-component frontier orbitals.
Walkenhorst, Jessica; De Giovannini, Umberto; Castro, Alberto; Rubio, Angel
2016-05-01
Recent advances in laser technology allow us to follow electronic motion at its natural time-scale with ultra-fast time resolution, leading the way towards attosecond physics experiments of extreme precision. In this work, we assess the use of tailored pumps in order to enhance (or reduce) some given features of the probe absorption (for example, absorption in the visible range of otherwise transparent samples). This type of manipulation of the system response could be helpful for its full characterization, since it would allow us to visualize transitions that are dark when using unshaped pulses. In order to investigate these possibilities, we perform first a theoretical analysis of the non-equilibrium response function in this context, aided by one simple numerical model of the hydrogen atom. Then, we proceed to investigate the feasibility of using time-dependent density-functional theory as a means to implement, theoretically, this absorption-optimization idea, for more complex atoms or molecules. We conclude that the proposed idea could in principle be brought to the laboratory: tailored pump pulses can excite systems into light-absorbing states. However, we also highlight the severe numerical and theoretical difficulties posed by the problem: large-scale non-equilibrium quantum dynamics are cumbersome, even with TDDFT, and the shortcomings of state-of-the-art TDDFT functionals may still be serious for these out-of-equilibrium situations.
International Nuclear Information System (INIS)
Borovsky, J.E.; Hansen, P.J.
1991-01-01
The mechanics of the first adiabatic invariant μ of nonrelativistic charged particles in time-dependent magnetic inductions B(t) are studied by means of computer simulations and analytic theory. Linear-ramp magnetic-induction profiles B=B 0 +(ΔB/Δt)t are utilized, as well as hyperbolic-tangent ramps and sine half-wave ramps. The change in μ that results from an induction change ΔB that occurs over a time Δt is quantified for all values of ΔB and Δt, as well as for all values of the particle position. It is found that the cases fall into two categories with very different μ behavior: cases in which the change in the magnetic induction occurs over a time Δt that is exactly equal to an integer number of gyroperiods (textbook case) or cases in which the change in the induction occurs over a time Δt that is not equal to an integer number of gyroperiods (more general case). In both categories μ is an adiabatic invariant, although the conservation of μ is much poorer in the latter category. It is pointed out that, in addition to the well-known constraints on ΔB and Δt, there is a constraint on the particle's initial position in the magnetic field if the change in the adiabatic invariant is to be kept small
Simulation of X-ray absorption spectra with orthogonality constrained density functional theory.
Derricotte, Wallace D; Evangelista, Francesco A
2015-06-14
Orthogonality constrained density functional theory (OCDFT) [F. A. Evangelista, P. Shushkov and J. C. Tully, J. Phys. Chem. A, 2013, 117, 7378] is a variational time-independent approach for the computation of electronic excited states. In this work we extend OCDFT to compute core-excited states and generalize the original formalism to determine multiple excited states. Benchmark computations on a set of 13 small molecules and 40 excited states show that unshifted OCDFT/B3LYP excitation energies have a mean absolute error of 1.0 eV. Contrary to time-dependent DFT, OCDFT excitation energies for first- and second-row elements are computed with near-uniform accuracy. OCDFT core excitation energies are insensitive to the choice of the functional and the amount of Hartree-Fock exchange. We show that OCDFT is a powerful tool for the assignment of X-ray absorption spectra of large molecules by simulating the gas-phase near-edge spectrum of adenine and thymine.
Projected coupled cluster theory.
Qiu, Yiheng; Henderson, Thomas M; Zhao, Jinmo; Scuseria, Gustavo E
2017-08-14
Coupled cluster theory is the method of choice for weakly correlated systems. But in the strongly correlated regime, it faces a symmetry dilemma, where it either completely fails to describe the system or has to artificially break certain symmetries. On the other hand, projected Hartree-Fock theory captures the essential physics of many kinds of strong correlations via symmetry breaking and restoration. In this work, we combine and try to retain the merits of these two methods by applying symmetry projection to broken symmetry coupled cluster wave functions. The non-orthogonal nature of states resulting from the application of symmetry projection operators furnishes particle-hole excitations to all orders, thus creating an obstacle for the exact evaluation of overlaps. Here we provide a solution via a disentanglement framework theory that can be approximated rigorously and systematically. Results of projected coupled cluster theory are presented for molecules and the Hubbard model, showing that spin projection significantly improves unrestricted coupled cluster theory while restoring good quantum numbers. The energy of projected coupled cluster theory reduces to the unprojected one in the thermodynamic limit, albeit at a much slower rate than projected Hartree-Fock.
Li, Zhendong; Liu, Wenjian
2011-11-21
The recently proposed spin-adapted time-dependent density functional theory (S-TD-DFT) [Z. Li and W. Liu, J. Chem. Phys. 133, 064106 (2010)] resolves the spin-contamination problem in describing singly excited states of high spin open-shell systems. It is an extension of the standard restricted open-shell Kohn-Sham-based TD-DFT which can only access those excited states due to singlet-coupled single excitations. It is also far superior over the unrestricted Kohn-Sham-based TD-DFT (U-TD-DFT) which suffers from severe spin contamination for those excited states due to triplet-coupled single excitations. Nonetheless, the accuracy of S-TD-DFT for high spin open-shell systems is still inferior to TD-DFT for well-behaved closed-shell systems. The reason can be traced back to the violation of the spin degeneracy conditions (SDC) by approximate exchange-correlation (XC) functionals. Noticing that spin-adapted random phase approximation (S-RPA) can indeed maintain the SDC by virtue of the Wigner-Eckart theorem, a hybrid ansatz combining the good of S-TD-DFT and S-RPA can immediately be envisaged. The resulting formalism, dubbed as X-TD-DFT, is free of spin contamination and can also be viewed as a S-RPA correction to the XC kernel of U-TD-DFT. Compared with S-TD-DFT, X-TD-DFT leads to much improved results for the low-lying excited states of, e.g., N(2)(+), yet with much reduced computational cost. Therefore, X-TD-DFT can be recommended for routine calculations of excited states of high spin open-shell systems.
Calibration of the fine-structure constant of graphene by time-dependent density-functional theory
Sindona, A.; Pisarra, M.; Vacacela Gomez, C.; Riccardi, P.; Falcone, G.; Bellucci, S.
2017-11-01
One of the amazing properties of graphene is the ultrarelativistic behavior of its loosely bound electrons, mimicking massless fermions that move with a constant velocity, inversely proportional to a fine-structure constant αg of the order of unity. The effective interaction between these quasiparticles is, however, better controlled by the coupling parameter αg*=αg/ɛ , which accounts for the dynamic screening due to the complex permittivity ɛ of the many-valence electron system. This concept was introduced in a couple of previous studies [Reed et al., Science 330, 805 (2010) and Gan et al., Phys. Rev. B 93, 195150 (2016)], where inelastic x-ray scattering measurements on crystal graphite were converted into an experimentally derived form of αg* for graphene, over an energy-momentum region on the eV Å -1 scale. Here, an accurate theoretical framework is provided for αg*, using time-dependent density-functional theory in the random-phase approximation, with a cutoff in the interaction between excited electrons in graphene, which translates to an effective interlayer interaction in graphite. The predictions of the approach are in excellent agreement with the above-mentioned measurements, suggesting a calibration method to substantially improve the experimental derivation of αg*, which tends to a static limiting value of ˜0.14 . Thus, the ab initio calibration procedure outlined demonstrates the accuracy of perturbation expansion treatments for the two-dimensional gas of massless Dirac fermions in graphene, in parallel with quantum electrodynamics.
Energy Technology Data Exchange (ETDEWEB)
Morzan, Uriel N.; Ramírez, Francisco F.; Scherlis, Damián A., E-mail: damian@qi.fcen.uba.ar, E-mail: mcgl@qb.ffyb.uba.ar [Departamento de Química Inorgánica, Analítica y Química Física/INQUIMAE, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Pab. II, Buenos Aires (C1428EHA) (Argentina); Oviedo, M. Belén; Sánchez, Cristián G. [Departamento de Matemática y Física, Facultad de Ciencias Químicas, INFIQC, Universidad Nacional de Córdoba, Ciudad Universitaria, X5000HUA Córdoba (Argentina); Lebrero, Mariano C. González, E-mail: damian@qi.fcen.uba.ar, E-mail: mcgl@qb.ffyb.uba.ar [Instituto de Química y Fisicoquímica Biológicas, IQUIFIB, CONICET (Argentina)
2014-04-28
This article presents a time dependent density functional theory (TDDFT) implementation to propagate the Kohn-Sham equations in real time, including the effects of a molecular environment through a Quantum-Mechanics Molecular-Mechanics (QM-MM) hamiltonian. The code delivers an all-electron description employing Gaussian basis functions, and incorporates the Amber force-field in the QM-MM treatment. The most expensive parts of the computation, comprising the commutators between the hamiltonian and the density matrix—required to propagate the electron dynamics—, and the evaluation of the exchange-correlation energy, were migrated to the CUDA platform to run on graphics processing units, which remarkably accelerates the performance of the code. The method was validated by reproducing linear-response TDDFT results for the absorption spectra of several molecular species. Two different schemes were tested to propagate the quantum dynamics: (i) a leap-frog Verlet algorithm, and (ii) the Magnus expansion to first-order. These two approaches were confronted, to find that the Magnus scheme is more efficient by a factor of six in small molecules. Interestingly, the presence of iron was found to seriously limitate the length of the integration time step, due to the high frequencies associated with the core-electrons. This highlights the importance of pseudopotentials to alleviate the cost of the propagation of the inner states when heavy nuclei are present. Finally, the methodology was applied to investigate the shifts induced by the chemical environment on the most intense UV absorption bands of two model systems of general relevance: the formamide molecule in water solution, and the carboxy-heme group in Flavohemoglobin. In both cases, shifts of several nanometers are observed, consistently with the available experimental data.
Morzan, Uriel N.; Ramírez, Francisco F.; Oviedo, M. Belén; Sánchez, Cristián G.; Scherlis, Damián A.; Lebrero, Mariano C. González
2014-04-01
This article presents a time dependent density functional theory (TDDFT) implementation to propagate the Kohn-Sham equations in real time, including the effects of a molecular environment through a Quantum-Mechanics Molecular-Mechanics (QM-MM) hamiltonian. The code delivers an all-electron description employing Gaussian basis functions, and incorporates the Amber force-field in the QM-MM treatment. The most expensive parts of the computation, comprising the commutators between the hamiltonian and the density matrix—required to propagate the electron dynamics—, and the evaluation of the exchange-correlation energy, were migrated to the CUDA platform to run on graphics processing units, which remarkably accelerates the performance of the code. The method was validated by reproducing linear-response TDDFT results for the absorption spectra of several molecular species. Two different schemes were tested to propagate the quantum dynamics: (i) a leap-frog Verlet algorithm, and (ii) the Magnus expansion to first-order. These two approaches were confronted, to find that the Magnus scheme is more efficient by a factor of six in small molecules. Interestingly, the presence of iron was found to seriously limitate the length of the integration time step, due to the high frequencies associated with the core-electrons. This highlights the importance of pseudopotentials to alleviate the cost of the propagation of the inner states when heavy nuclei are present. Finally, the methodology was applied to investigate the shifts induced by the chemical environment on the most intense UV absorption bands of two model systems of general relevance: the formamide molecule in water solution, and the carboxy-heme group in Flavohemoglobin. In both cases, shifts of several nanometers are observed, consistently with the available experimental data.
Donahue, Courtney M; Pacheco, Juan S Lezama; Keith, Jason M; Daly, Scott R
2014-06-28
S K-edge X-ray absorption spectroscopy (XAS) and time-dependent density functional theory (TDDFT) calculations were performed on a series of As[S2CNR2]3 complexes, where R2 = Et2, (CH2)5 and Ph2, to determine how dithiocarbamate substituents attached to N affect As[S2CNR2]3 electronic structure. Complimentary [PPh4][S2CNR2] salts were also studied to compare dithiocarbamate bonding in the absence of As. The XAS results indicate that changing the orientation of the alkyl substituents from trans to cis (R2 = Et2vs. (CH2)5) yields subtle variations whereas differences associated with a change from alkyl to aryl are much more pronounced. For example, despite the differences in As 4p mixing, the first features in the S K-edge XAS spectra of [PPh4][S2CNPh2] and As[S2CNPh2]3 were both shifted by 0.3 eV compared to their alkyl-substituted derivatives. DFT calculations revealed that the unique shift observed for [PPh4][S2CNPh2] is due to phenyl-induced splitting of the π* orbitals delocalized over N, C and S. A similar phenomenon accounts for the shift observed for As[S2CNPh2]3, but the presence of two unique S environments (As-S and As···S) prevented reliable analysis of As-S covalency from the XAS data. In the absence of experimental values, DFT calculations revealed a decrease in As-S orbital mixing in As[S2CNPh2]3 that stems from a redistribution of electron density to S atoms participating in weaker As···S interactions. Simulated spectra obtained from TDDFT calculations reproduce the experimental differences in the S K-edge XAS data, which suggests that the theory is accurately modeling the experimental differences in As-S orbital mixing. The results highlight how S K-edge XAS and DFT can be used cooperatively to understand the electronic structure of low symmetry coordination complexes containing S atoms in different chemical environments.
Diatomic interaction potential theory applications
Goodisman, Jerry
2013-01-01
Diatomic Interaction Potential Theory, Volume 2: Applications discusses the variety of applicable theoretical material and approaches in the calculations for diatomic systems in their ground states. The volume covers the descriptions and illustrations of modern calculations. Chapter I discusses the calculation of the interaction potential for large and small values of the internuclear distance R (separated and united atom limits). Chapter II covers the methods used for intermediate values of R, which in principle means any values of R. The Hartree-Fock and configuration interaction schemes des
Fock exchange in meson theories of nuclei
International Nuclear Information System (INIS)
Bolsterli, M.
1986-01-01
The Fock exchange term in meson field theories of nuclear systems is shown to arise from a two-loop ground-state self-energy diagram. Evaluation of this diagram gives the relativistic or semirelativistic analog of the Fock exchange energy; it differs from the nucleon-nucleon Fock energy in including retardation effects. In finite meson-field theories of nuclear systems, the variational nature of the meson-field analog of the Hartree-Fock energy functional can be further elucidated. 4 refs
Density functional theory of nuclei
International Nuclear Information System (INIS)
Terasaki, Jun
2008-01-01
The density functional theory of nuclei has come to draw attention of scientists in the field of nuclear structure because the theory is expected to provide reliable numerical data in wide range on the nuclear chart. This article is organized to present an overview of the theory to the people engaged in the theory of other fields as well as those people in the nuclear physics experiments. At first, the outline of the density functional theory widely used in the electronic systems (condensed matter, atoms, and molecules) was described starting from the Kohn-Sham equation derived on the variational principle. Then the theory used in the field of nuclear physics was presented. Hartree-Fock and Hartree-Fock-Bogolyubov approximation by using Skyrme interaction was explained. Comparison of the results of calculations and experiments of binding energies and ground state mean square charge radii of some magic number nuclei were shown. The similarity and dissimilarity between the two streams were summarized. Finally the activities of the international project of Universal Nuclear Energy Density Functional (UNEDF) which was started recently lead by US scientist was reported. This project is programmed for five years. One of the applications of the project is the calculation of the neutron capture cross section of nuclei on the r-process, which is absolutely necessary for the nucleosynthesis research. (S. Funahashi)
Energy Technology Data Exchange (ETDEWEB)
Bowman, David N. [Department of Chemistry; Supercomputing Institute and Chemical Theory Center; University of Minnesota; Minneapolis; USA; Asher, Jason C. [Department of Chemistry; Supercomputing Institute and Chemical Theory Center; University of Minnesota; Minneapolis; USA; Fischer, Sean A. [William R. Wiley Environmental Molecular Sciences Laboratory; Pacific Northwest National Laboratory; P.O. Box 999; Richland; USA; Cramer, Christopher J. [Department of Chemistry; Supercomputing Institute and Chemical Theory Center; University of Minnesota; Minneapolis; USA; Govind, Niranjan [William R. Wiley Environmental Molecular Sciences Laboratory; Pacific Northwest National Laboratory; P.O. Box 999; Richland; USA
2017-01-01
Three
Gritsenko, O. V.
2017-01-01
We demonstrate a crucial role of fractional occupation numbers (FONs) of natural orbitals (NOs) in the description of double excitations in time-dependent NO functional theory (TDNOFT). An analytical dependence of the double excitation energy ωα on the ratio of the FONs is derived in a model from
Carty, G. J.; Hampshire, D. P.
2008-01-01
In polycrystalline superconducting materials optimized for high critical current density (JC) in high magnetic fields, the mechanism that determines JC has long remained uncertain because of the complicated manner in which the fluxon-fluxon and fluxon-microstructure forces combine. In this work, the time-dependent Ginzburg-Landau equations are used to produce visualizations of fluxons at JC that show the disorder in the pinned part of the flux-line lattice and the motion of those fluxons alon...
Gladis Anitha, E; Joseph Vedhagiri, S; Parimala, K
2015-02-05
The molecular structure, geometry optimization, vibrational frequencies of organic dye sensitizer 2,6-Diamino-4-chloropyrimidine (DACP) were studied based on Hartree-Fock (HF) and density functional theory (DFT) using B3LYP methods with 6-311++G(d,p) basis set. Ultraviolet-Visible (UV-Vis) spectrum was investigated by time dependent DFT (TD-DFT). Features of the electronic absorption spectrum in the UV-Visible regions were assigned based on TD-DFT calculation. The absorption bands are assigned to transitions. The interfacial electron transfer between semiconductor TiO2 electrode and dye sensitizer DACP is due to an electron injection process from excited dye to the semiconductor's conduction band. The observed and the calculated frequencies are found to be in good agreement. The energies of the frontier molecular orbitals (FMOS) have also been determined. The chemical shielding anisotropic (CSA) parameters are calculated from the NMR analysis, Stability of the molecule arising from hyperconjugative interactions and charge delocalization has been analyzed using natural bond orbital (NBO) analysis. Copyright © 2014 Elsevier B.V. All rights reserved.
Carty, George J.; Hampshire, Damian P.
2008-05-01
In polycrystalline superconducting materials optimized for high critical current density (JC) in high magnetic fields, the mechanism that determines JC has long remained uncertain because of the complicated manner in which the fluxon-fluxon and fluxon-microstructure forces combine. In this work, the time-dependent Ginzburg-Landau equations are used to produce visualizations of fluxons at JC that show the disorder in the pinned part of the flux-line lattice and the motion of those fluxons along grain boundaries that cause dissipation. Calculated values of JC are consistent with experimental data.
International Nuclear Information System (INIS)
Comelli, D.; Riotto, A.
1995-06-01
Motivated by cosmological applications like electroweak baryogenesis, we develop a field theoretic approach to the computation of particle currents on a space-time dependent and CP-violating Higgs background. We consider the Standard Model model with two Higgs doublets and CP violation in the scalar sector, and compute both fermionic and Higgs currents by means of an expansion in the background fields. We discuss the gauge dependence of the results and the renormalization of the current operators, showing that in the limit of local equilibrium, no extra renormalization conditions are needed in order to specify the system completely. (orig.)
Kang, Guo-Jun; Song, Chao; Ren, Xue-Feng
2016-11-25
The electronic geometries and optical properties of two D-π-A type zinc porphyrin dyes (NCH₃-YD2 and TPhe-YD) were systematically investigated by density functional theory (DFT) and time-dependent density functional theory (TD-DFT) to reveal the origin of significantly altered charge transfer enhancement by changing the electron donor of the famous porphyrin-based sensitizer YD2-o-C8. The molecular geometries and photophysical properties of dyes before and after binding to the TiO₂ cluster were fully investigated. From the analyses of natural bond orbital (NBO), extended charge decomposition analysis (ECDA), and electron density variations (Δρ) between the excited state and ground state, it was found that the introduction of N(CH₃)₂ and 1,1,2-triphenylethene groups enhanced the intramolecular charge-transfer (ICT) character compared to YD2-o-C8. The absorption wavelength and transition possess character were significantly influenced by N(CH₃)₂ and 1,1,2-triphenylethene groups. NCH₃-YD2 with N(CH₃)₂ groups in the donor part is an effective way to improve the interactions between the dyes and TiO₂ surface, light having efficiency (LHE), and free energy change (ΔG inject ), which is expected to be an efficient dye for use in dye-sensitized solar cells (DSSCs).
Directory of Open Access Journals (Sweden)
Guo-Jun Kang
2016-11-01
Full Text Available The electronic geometries and optical properties of two D-π-A type zinc porphyrin dyes (NCH3-YD2 and TPhe-YD were systematically investigated by density functional theory (DFT and time-dependent density functional theory (TD-DFT to reveal the origin of significantly altered charge transfer enhancement by changing the electron donor of the famous porphyrin-based sensitizer YD2-o-C8. The molecular geometries and photophysical properties of dyes before and after binding to the TiO2 cluster were fully investigated. From the analyses of natural bond orbital (NBO, extended charge decomposition analysis (ECDA, and electron density variations (Δρ between the excited state and ground state, it was found that the introduction of N(CH32 and 1,1,2-triphenylethene groups enhanced the intramolecular charge-transfer (ICT character compared to YD2-o-C8. The absorption wavelength and transition possess character were significantly influenced by N(CH32 and 1,1,2-triphenylethene groups. NCH3-YD2 with N(CH32 groups in the donor part is an effective way to improve the interactions between the dyes and TiO2 surface, light having efficiency (LHE, and free energy change (ΔGinject, which is expected to be an efficient dye for use in dye-sensitized solar cells (DSSCs.
Gritsenko, O. V.
2017-09-01
We demonstrate a crucial role of fractional occupation numbers (FONs) of natural orbitals (NOs) in the description of double excitations in time-dependent NO functional theory (TDNOFT). An analytical dependence of the double excitation energy ωα on the ratio of the FONs is derived in a model from the matrix diagonalization problem. In the large ratio Heitler-London limit the derived formula reproduces the correct asymptotics of ωα of the ionic state of double excitation character. In the small ratio Møller-Plesset, MP limit the reverse relation of static MP perturbation theory emerges in the dynamical response theory to provide ωα .
Open-ended response theory with polarizable embedding
DEFF Research Database (Denmark)
Steindal, Arnfinn Hykkerud; Beerepoot, Maarten T P; Ringholm, Magnus
2016-01-01
We present the theory and implementation of an open-ended framework for electric response properties at the level of Hartree-Fock and Kohn-Sham density functional theory that includes effects from the molecular environment modeled by the polarizable embedding (PE) model. With this new state......) properties can be studied by evaluating single residues of the response functions. The PE approach includes mutual polarization effects between the quantum and classical parts of the system through induced dipoles that are determined self-consistently with respect to the electronic density. The applicability...
Ji, Min; Hao, Ce; Wang, Dandan; Li, Hongjiang; Qiu, Jieshan
2013-03-14
We have investigated a new silver-based luminescent metal-organic framework (MOF) using density functional theory and time-dependent density functional theory methods. We theoretically demonstrated that the H...O hydrogen bond is strengthened and the Ag-O coordination bond is shortened significantly due to strengthening of the hydrogen bond in the S(1) state. When the hydrogen bond is formed, the mechanism of luminescence changes from a ligand-to-metal charge transfer (LMCT) coupled with intraligand charge transfer (LLCT) to LMCT, and the luminescence is found to be enhanced.
Structures of the mycotoxin zearalenone and its analogs were investigated using density functional theory methods to gain insight into the ground state and excited state properties related to detection. Zearalenone is an estrogenic mycotoxin that can occur in agricultural commodities, and ultraviole...
Tempel, David G.; Aspuru-Guzik, Alán
2011-11-01
The dissipative dynamics of many-electron systems interacting with a thermal environment has remained a long-standing challenge within time-dependent density functional theory (TDDFT). Recently, the formal foundations of open quantum systems time-dependent density functional theory (OQS-TDDFT) within the master equation approach were established. It was proven that the exact time-dependent density of a many-electron open quantum system evolving under a master equation can be reproduced with a closed (unitarily evolving) and non-interacting Kohn-Sham system. This potentially offers a great advantage over previous approaches to OQS-TDDFT, since with suitable functionals one could obtain the dissipative open-systems dynamics by simply propagating a set of Kohn-Sham orbitals as in usual TDDFT. However, the properties and exact conditions of such open-systems functionals are largely unknown. In the present article, we examine a simple and exactly-solvable model open quantum system: one electron in a harmonic well evolving under the Lindblad master equation. We examine two different representitive limits of the Lindblad equation (relaxation and pure dephasing) and are able to deduce a number of properties of the exact OQS-TDDFT functional. Challenges associated with developing approximate functionals for many-electron open quantum systems are also discussed.
Gholibeigian, Hassan; Amirshahkarami, Abdolazim; Gholibeigian, Kazem
2017-01-01
In special relativity theory, time dilates in velocity of near light speed. Also based on ``Substantial motion'' theory of Sadra, relative time (time flux); R = f (mv , σ , τ) , for each atom is momentum of its involved fundamental particles, which is different from the other atoms. In this way, for modification of the relativistic classical equation of string theory and getting more precise results, we should use effect of dilation and contraction of time in equation. So we propose to add two derivatives of the time's flux to the equation as follows: n.tp∂/R ∂ τ +∂2Xμ/(σ , τ) ∂τ2 = n .tp (∂/R ∂ σ ) +c2∂2Xμ/(σ , τ) ∂σ2 In which, Xμ is space-time coordinates of the string, σ & τ are coordinates on the string world sheet, respectively space and time along the string, string's mass m , velocity of string's motion v , factor n depends on geometry of each hidden extra dimension which relates to its own flux time, and tp is Planck's time. AmirKabir University of Technology, Tehran, Iran.
Hutter, Jürg
2003-03-01
An efficient formulation of time-dependent linear response density functional theory for the use within the plane wave basis set framework is presented. The method avoids the transformation of the Kohn-Sham matrix into the canonical basis and references virtual orbitals only through a projection operator. Using a Lagrangian formulation nuclear derivatives of excited state energies within the Tamm-Dancoff approximation are derived. The algorithms were implemented into a pseudo potential/plane wave code and applied to the calculation of adiabatic excitation energies, optimized geometries and vibrational frequencies of three low lying states of formaldehyde. An overall good agreement with other time-dependent density functional calculations, multireference configuration interaction calculations and experimental data was found.
Applicability of self-consistent mean-field theory
International Nuclear Information System (INIS)
Guo Lu; Sakata, Fumihiko; Zhao Enguang
2005-01-01
Within the constrained Hartree-Fock (CHF) theory, an analytic condition is derived to estimate whether a concept of the self-consistent mean field is realized in the level repulsive region. The derived condition states that an iterative calculation of the CHF equation does not converge when the quantum fluctuations coming from two-body residual interaction and quadrupole deformation become larger than a single-particle energy difference between two avoided crossing orbits. By means of numerical calculation, it is shown that the analytic condition works well for a realistic case
Kawai, Shinnosuke; Komatsuzaki, Tamiki
2009-12-14
We present a novel theory which enables us to explore the mechanism of reaction selectivity and robust functions in complex systems persisting under thermal fluctuation. The theory constructs a nonlinear coordinate transformation so that the equation of motion for the new reaction coordinate is independent of the other nonreactive coordinates in the presence of thermal fluctuation. In this article we suppose that reacting systems subject to thermal noise are described by a multidimensional Langevin equation without a priori assumption for the form of potential. The reaction coordinate is composed not only of all the coordinates and velocities associated with the system (solute) but also of the random force exerted by the environment (solvent) with friction constants. The sign of the reaction coordinate at any instantaneous moment in the region of a saddle determines the fate of the reaction, i.e., whether the reaction will proceed through to the products or go back to the reactants. By assuming the statistical properties of the random force, one can know a priori a well-defined boundary of the reaction which separates the full position-velocity space in the saddle region into mainly reactive and mainly nonreactive regions even under thermal fluctuation. The analytical expression of the reaction coordinate provides the firm foundation on the mechanism of how and why reaction proceeds in thermal fluctuating environments.
Flick, Johannes; Ruggenthaler, Michael; Appel, Heiko; Rubio, Angel
2015-12-15
The density-functional approach to quantum electrodynamics extends traditional density-functional theory and opens the possibility to describe electron-photon interactions in terms of effective Kohn-Sham potentials. In this work, we numerically construct the exact electron-photon Kohn-Sham potentials for a prototype system that consists of a trapped electron coupled to a quantized electromagnetic mode in an optical high-Q cavity. Although the effective current that acts on the photons is known explicitly, the exact effective potential that describes the forces exerted by the photons on the electrons is obtained from a fixed-point inversion scheme. This procedure allows us to uncover important beyond-mean-field features of the effective potential that mark the breakdown of classical light-matter interactions. We observe peak and step structures in the effective potentials, which can be attributed solely to the quantum nature of light; i.e., they are real-space signatures of the photons. Our findings show how the ubiquitous dipole interaction with a classical electromagnetic field has to be modified in real space to take the quantum nature of the electromagnetic field fully into account.
Correlated orbital theories with both local and non-local one-body potentials
Directory of Open Access Journals (Sweden)
Norman H. March
2010-10-01
Full Text Available After a brief survey of current density functional theory (DFT, based on an incompletely known one-body potential V(r, a method due to Cordero, March, and Alonso (CMA is summarized. This obtains the ground-state density n(r, for spherical atoms as yet, from a semi-empirical fine-tuning of Hartree-Fock (HF theory, which of course involves a non-local potential because of the presence of the Fock operator. This leads to n(r for spherical atoms of quantum Monte Carlo quality. A more recent proposal, related to CMA but different, by Bartlett, is also reviewed.
Baryonic forces and hyperons in nuclear matter from SU(3) chiral effective field theory
Energy Technology Data Exchange (ETDEWEB)
Petschauer, Stefan Karl
2016-02-12
In this work the baryon-baryon interaction is studied at next-to-leading order in SU(3) chiral effective field theory and applied to hyperon-nucleon scattering. The properties of hyperons in isospin-symmetric as well as asymmetric nuclear matter are calculated within the Bruecker-Hartree-Fock formalism. Moreover, the leading three-baryon interaction is derived and its low-energy constants are estimated from decuplet intermediate states. We conclude, that chiral effective field theory is a well-suited tool to describe the baryonic forces.
Open-system Kohn-Sham density functional theory.
Zhou, Yongxi; Ernzerhof, Matthias
2012-03-07
A simple model for electron transport through molecules is provided by the source-sink potential (SSP) method [F. Goyer, M. Ernzerhof, and M. Zhuang, J. Chem. Phys. 126, 144104 (2007)]. In SSP, the boundary conditions of having an incoming and outgoing electron current are enforced through complex potentials that are added to the Hamiltonian. Depending on the sign of the imaginary part of the potentials, current density is generated or absorbed. In this way, a finite system can be used to model infinite molecular electronic devices. The SSP has originally been developed for the Hückel method and subsequently it has been extended [F. Goyer and M. Ernzerhof, J. Chem. Phys. 134, 174101 (2011)] to the Hubbard model. Here we present a step towards its generalization for first-principles electronic structure theory methods. In particular, drawing on our earlier work, we discuss a new generalized density functional theory for complex non-Hermitian Hamiltonians. This theory enables us to combine SSP and Kohn-Sham theory to obtain a method for the description of open systems that exchange current density with their environment. Similarly, the Hartree-Fock method is extended to the realm of non-Hermitian, SSP containing Hamiltonians. As a proof of principle, we present the first applications of complex-density functional theory (CODFT) as well as non-Hermitian Hartree-Fock theory to electron transport through molecules. © 2012 American Institute of Physics
Energy Technology Data Exchange (ETDEWEB)
Castro, A., E-mail: acastro@bifi.es [Institute for Biocomputation and Physics of Complex Systems (BIFI) and Zaragoza Scientific Center for Advanced Modelling (ZCAM), University of Zaragoza, 50018 Zaragoza (Spain); Isla, M. [Departamento de Fisica Teorica, Atomica y Optica, Universidad de Valladolid, 47005 Valladolid (Spain); Martinez, Jose I. [Departamento de Fisica Teorica de la Materia Condensada, Universidad Autonoma de Madrid, ES-28049 Madrid (Spain); Alonso, J.A. [Departamento de Fisica Teorica, Atomica y Optica, Universidad de Valladolid, 47005 Valladolid (Spain)
2012-05-03
Graphical abstract: Two trajectories for the collision of a proton with the Lithium tetramer. On the left, the proton is scattered away, and a Li{sub 2} molecule plus two isolated Lithium atoms result. On the right, the proton is captured and a LiH molecule is created. Highlights: Black-Right-Pointing-Pointer Scattering of a proton with Lithium clusters described from first principles. Black-Right-Pointing-Pointer Description based on non-adiabatic molecular dynamics. Black-Right-Pointing-Pointer The electronic structure is described with time-dependent density-functional theory. Black-Right-Pointing-Pointer The method allows to discern reaction channels depending on initial parameters. - Abstract: We have employed non-adiabatic molecular dynamics based on time-dependent density-functional theory to characterize the scattering behavior of a proton with the Li{sub 4} cluster. This technique assumes a classical approximation for the nuclei, effectively coupled to the quantum electronic system. This time-dependent theoretical framework accounts, by construction, for possible charge transfer and ionization processes, as well as electronic excitations, which may play a role in the non-adiabatic regime. We have varied the incidence angles in order to analyze the possible reaction patterns. The initial proton kinetic energy of 10 eV is sufficiently high to induce non-adiabatic effects. For all the incidence angles considered the proton is scattered away, except in one interesting case in which one of the Lithium atoms captures it, forming a LiH molecule. This theoretical formalism proves to be a powerful, effective and predictive tool for the analysis of non-adiabatic processes at the nanoscale.
Nazarov, Vladimir U.
2017-06-01
We find an exact analytical solution to the exchange-only time-dependent density-functional theory (TDDFT) problem for a significant class of quasi-low-dimensional (QLD) materials: QLD electron gas with only one band filled in the direction perpendicular to the layer or wire. The theory yields the TD exchange potential as an explicit nonlocal operator of the TD spin density. The dressed interband (image states) excitation spectra of quasi-two-dimensional electron gas are obtained, while the comparison with the Kohn-Sham transitions provides insights into the qualitative and quantitative role of the many-body interactions. Important cancellations between the Hartree fH and the exchange fx kernels of TDDFT are found in the low-density regime, elucidating the interrelations between the Kohn-Sham and the many-body dynamics in mesoscopic systems.
Hu, Zhongwei; Autschbach, Jochen; Jensen, Lasse
2014-09-28
Resonance hyper-Rayleigh scattering (HRS) of molecules and metal clusters have been simulated based on a time-dependent density functional theory approach. The resonance first-order hyperpolarizability (β) is obtained by implementing damped quadratic response theory using the (2n + 1) rule. To test this implementation, the prototypical dipolar molecule para-nitroaniline (p-NA) and the octupolar molecule crystal violet are used as benchmark systems. Moreover, small silver clusters Ag 8 and Ag 20 are tested with a focus on determining the two-photon resonant enhancement arising from the strong metal transition. Our results show that, on a per atom basis, the small silver clusters possess two-photon enhanced HRS comparable to that of larger nanoparticles. This finding indicates the potential interest of using small metal clusters for designing new nonlinear optical materials.
DEFF Research Database (Denmark)
Martinez, Jose Ignacio; García Lastra, Juan Maria; Lopez, M. J.
2010-01-01
the optical properties according to specific functionality targets. The differences in the spectra could be used to identify relative abundances of isomers with different spins in experimental studies. As a salient feature, this theoretical spectroscopic analysis predicts the metallization of the infinite (Ti......The optical spectra of sandwich clusters formed by transition metal atoms (titanium, vanadium, and chromium) intercalated between parallel benzene molecules have been studied by time-dependent density functional theory (TDDFT) and many-body perturbation theory. Sandwiches with different number...... of layers, including infinite chains, are considered. The lowest excitation energy peaks in the spectra are characteristic of the robust bonding in these complexes. The excitation energies vary in a systematic way with the metal atoms and with the cluster size, and so these materials could be used to tune...
On the consistent solution of the gap-equation for spontaneously broken {lambda}{Phi}{sup 4}-theory
Energy Technology Data Exchange (ETDEWEB)
Nachbagauer, H.
1994-10-01
A self-consistent solution of the finite temperature gap-equation for {lambda}{Phi}{sup 4} theory beyond the Hartree-Fock approximation is presented using a composite operator effective action. It was found that in a spontaneously broken theory not only the so-called daisy and super daisy graphs contribute to the re summed mass, but also re summed non-local diagrams are of the same order, thus altering the effective mass for small values of the latter. (author). 10 refs., 3 figs., 1 tab.
On the consistent solution of the gap-equation for spontaneously broken λΦ4-theory
International Nuclear Information System (INIS)
Nachbagauer, H.
1994-10-01
A self-consistent solution of the finite temperature gap-equation for λΦ 4 theory beyond the Hartree-Fock approximation is presented using a composite operator effective action. It was found that in a spontaneously broken theory not only the so-called daisy and super daisy graphs contribute to the re summed mass, but also re summed non-local diagrams are of the same order, thus altering the effective mass for small values of the latter. (author). 10 refs., 3 figs., 1 tab
Energy Technology Data Exchange (ETDEWEB)
Durin, B
2006-01-15
In this thesis three time-dependent configurations are studied in the formalism of first-quantized string. These configurations are interesting because perturbative computation of correlation functions is possible and thus is a tool to understand the interplay between the time-dependent geometry and the quantified string. In a first chapter, we explain the reasons for studying these configurations. Then in the second chapter we describe the perturbative formalism and explain how to solve technical problem we encountered. The third chapter is devoted to the physical description of the phenomena involved in these configurations, to the specific computations we made and to the insights we gained. Eventually, we conclude and give some perspectives. (author)
Polidoro, B.; Iervolino, I.; Chioccarelli, E.; Giorgio, M.
2012-04-01
Probabilistic seismic hazard is usually computed trough a homogeneous Poisson process that even though it is a time-independent process it is widely used for its very convenient properties. However, when a single fault is of concern and/or the time scale is different from that of the long term, time-dependent processes are required. In this paper, different time-dependent models are reviewed with working examples. In fact, the Paganica fault (in central Italy) has been considered to compute both the probability of occurrence of at least one event in the lifespan of the structure, as well as the seismic hazard expressed in terms of probability of exceedance of an intensity value in a given time frame causing the collapse of the structure. Several models, well known or novel application to engineering hazard have been considered, limitation and issues in their applications are also discussed. The Brownian Passage Time (BPT) model is based on a stochastic modification of the deterministic stick-slip oscillator model for characteristic earthquakes; i.e., based on the addition of random perturbations (a Gaussian white noise) to the deterministic load path predicted by elastic rebound theory. This model assumes that the load state is at some ground level immediately after an event, increases steadly over time, reaches a failure threshold and relaxes instantaneously back to the ground level. For this model also a variable threshold has been considered to take into account the uncertainty of the threshold value. For the slip-predictable model it is assumed that the stress accumulates at a constant rate starting from some initial stress level. Stress is assumed to accumulate for a random period of time until an earthquake occurs. The size of the earthquake is governed by the stress release and it is a function of the elapsed time since the last event. In the time-predictable model stress buildup occurs at a constant rate until the accumulated stress reaches a threshold
International Nuclear Information System (INIS)
Passos, E.M.J. de
1976-01-01
The relationship between the Johnson-Baranger time-dependent folded diagram (JBFD) expansion, and the time independent methods of perturbation theory, are investigated. In the nondegenerate case, the JBFD expansion and the Rayleigh-Schroedinger perturbation expansion, for the ground state energy, are identical. On the other hand, in the degenerate case, for the nonhermitian effective interaction considered, the JBFD expansion, of the effective interaction, is equal to the perturbative expansion of the effective interaction of the nonhermitian eigenvalue problem of Bloch and Brandow-Des Cloizeaux. For the two hermitian effective interactions, the JBFD expansion of the effective interaction differs from the perturbation expansion of the effective interaction of the hermitian eigenvalue problem of Des Cloizeaux [pt
Yu, W.; Gao, C.-Z.; Zhang, Y.; Zhang, F. S.; Hutton, R.; Zou, Y.; Wei, B.
2018-03-01
We calculate electron capture and ionization cross sections of N2 impacted by the H+ projectile at keV energies. To this end, we employ the time-dependent density-functional theory coupled nonadiabatically to molecular dynamics. To avoid the explicit treatment of the complex density matrix in the calculation of cross sections, we propose an approximate method based on the assumption of constant ionization rate over the period of the projectile passing the absorbing boundary. Our results agree reasonably well with experimental data and semi-empirical results within the measurement uncertainties in the considered energy range. The discrepancies are mainly attributed to the inadequate description of exchange-correlation functional and the crude approximation for constant ionization rate. Although the present approach does not predict the experiments quantitatively for collision energies below 10 keV, it is still helpful to calculate total cross sections of ion-molecule collisions within a certain energy range.
Hassouneh, Ola; Salah, Wa'el
2017-07-01
We report the results of an accurate computation of the energy levels, oscillator strengths f_{ij}, the radiative transition rates A_{ij}, the Landé g-factor, the magnetic dipole and the electric quadrupole hyperfine constants of the intermediate Rydberg series nf[K]J (n = 4, 5), nd[K]J (n = 5, 6), np[K]J (n = 6, 7) and ns[K]J (n = 7, 8) relative to the ground state 3p6 1S0 for neutral argon atom spectra based on the multiconfiguration Dirac-Hartree-Fock (MCDHF) approach. In this approach, the quantum electrodynamics (QED) effects with transverse photon Breit interaction and vacuum photon polarization self-energy corrections are included. Moreover, the perturbation due to the core-polarization and electron correlation effects are taken into account. We also reported the oscillator strengths and transition rates in Coulomb and Babushkin gauges for the 3p5(2P)3d-3p5(2P)4f, 3p5(2P)3d-3p5(2P)5f, 3p5(2P)4d-3p5(2P)4f, 3p5(2P)4d-3p5(2P)5f, 3p5(2P)5d-3p5(2P)4f, 3p5(2P)5d-3p5(2P)5f, 3p5(2P)6d-3p5(2P)4f and 3p5(2P)6d-3p5(2P)5f transition arrays as well as the 3p5(2P)5d-3p5(2P)6p, 3p5(2P)7s-3p5(2P)6p, 3p5(2P)7s-3p5(2P)7p and 3p5(2P)8s-3p5(2P)7p transition arrays. Insofar as experimental or theoretical values by other authors exist, comparison is made with those values; it turns out that, for most of the levels, a rather satisfying agreement with these experimental and theoretical results is obtained, thus confirming the reliability of our data.
Metropolis Evaluation of the Hartree-Fock Exchange Energy.
Cytter, Yael; Neuhauser, Daniel; Baer, Roi
2014-10-14
We examine the possibility of using a Metropolis algorithm for computing the exchange energy in a large molecular system. Following ideas set forth in a recent publication (Baer, Neuhauser, and Rabani, Phys. Rev. Lett. 111, 106402 (2013)) we focus on obtaining the exchange energy per particle (ExPE, as opposed to the total exchange energy) to a predefined statistical error and on determining the numerical scaling of the calculation achieving this. For this we assume that the occupied molecular orbitals (MOs) are known and given in terms of a standard Gaussian atomic basis set. The Metropolis random walk produces a sequence of pairs of three-dimensional points (x,x'), which are distributed in proportion to ρ(x,x')(2), where ρ(x,x') is the density matrix. The exchange energy per particle is then simply the average of the Coulomb repulsion energy υC(|x-x'|) over these pairs. To reduce the statistical error we separate the exchange energy into a short-range term that can be calculated deterministically in a linear scaling fashion and a long-range term that is treated by the Metropolis method. We demonstrate the method on water clusters and silicon nanocrystals showing the magnitude of the ExPE standard deviation is independent of system size. In the water clusters a longer random walk was necessary to obtain full ergodicity as Metropolis walkers tended to get stuck for a while in localized regions. We developed a diagnostic tool that can alert a user when such a situation occurs. The calculation effort scales linearly with system size if one uses an atom screening procedure that can be made numerically exact. In systems where the MOs can be localized efficiently the ExPE can even be computed with "sublinear scaling" as the MOs themselves can be screened.
Integral processing in beyond-Hartree-Fock calculations
Taylor, P. R.
1986-01-01
The increasing rate at which improvements in processing capacity outstrip improvements in input/output performance of large computers has led to recent attempts to bypass generation of a disk-based integral file. The direct self-consistent field (SCF) method of Almlof and co-workers represents a very successful implementation of this approach. This paper is concerned with the extension of this general approach to configuration interaction (CI) and multiconfiguration-self-consistent field (MCSCF) calculations. After a discussion of the particular types of molecular orbital (MO) integrals for which -- at least for most current generation machines -- disk-based storage seems unavoidable, it is shown how all the necessary integrals can be obtained as matrix elements of Coulomb and exchange operators that can be calculated using a direct approach. Computational implementations of such a scheme are discussed.
Giant resonances in the deformed continuum
International Nuclear Information System (INIS)
Nakatsukasa, T.; Yabana, K.
2004-01-01
Giant resonances in the continuum for deformed nuclei are studied with the time-dependent Hartree-Fock (TDHF) theory in real time and real space. The continuum effect is effectively taken into account by introducing a complex Absorbing Boundary Condition (ABC). (orig.)
Ito; Adachi; Hikosaka; Motoki; Soejima; Yagishita; Raseev; Cherepkov
2000-07-03
The dynamical information (ten dipole matrix elements and eight phase differences) has been deduced from the measured angular distributions of photoelectrons from O K shell of oriented CO molecules near the ionization threshold in the region of a sigma(*) shape resonance. Light polarization parallel and perpendicular to the molecular axis has been used. An important contribution of six lsigma partial waves with 0Hartree-Fock approximation reveals only a qualitative agreement, therefore a more advanced theory is needed.
Fransson, Thomas; Burdakova, Daria; Norman, Patrick
2016-05-21
X-ray absorption spectra of carbon, silicon, germanium, and sulfur compounds have been investigated by means of damped four-component density functional response theory. It is demonstrated that a reliable description of relativistic effects is obtained at both K- and L-edges. Notably, an excellent agreement with experimental results is obtained for L2,3-spectra-with spin-orbit effects well accounted for-also in cases when the experimental intensity ratio deviates from the statistical one of 2 : 1. The theoretical results are consistent with calculations using standard response theory as well as recently reported real-time propagation methods in time-dependent density functional theory, and the virtues of different approaches are discussed. As compared to silane and silicon tetrachloride, an anomalous error in the absolute energy is reported for the L2,3-spectrum of silicon tetrafluoride, amounting to an additional spectral shift of ∼1 eV. This anomaly is also observed for other exchange-correlation functionals, but it is seen neither at other silicon edges nor at the carbon K-edge of fluorine derivatives of ethene. Considering the series of molecules SiH4-XFX with X = 1, 2, 3, 4, a gradual divergence from interpolated experimental ionization potentials is observed at the level of Kohn-Sham density functional theory (DFT), and to a smaller extent with the use of Hartree-Fock. This anomalous error is thus attributed partly to difficulties in correctly emulating the electronic structure effects imposed by the very electronegative fluorines, and partly due to inconsistencies in the spurious electron self-repulsion in DFT. Substitution with one, or possibly two, fluorine atoms is estimated to yield small enough errors to allow for reliable interpretations and predictions of L2,3-spectra of more complex and extended silicon-based systems.
Energy Technology Data Exchange (ETDEWEB)
Rebolini, Elisa, E-mail: elisa.rebolini@kjemi.uio.no; Toulouse, Julien, E-mail: julien.toulouse@upmc.fr [Laboratoire de Chimie Théorique, Sorbonne Universités, UPMC Univ Paris 06, CNRS, 4 place Jussieu, F-75005 Paris (France)
2016-03-07
We present a range-separated linear-response time-dependent density-functional theory (TDDFT) which combines a density-functional approximation for the short-range response kernel and a frequency-dependent second-order Bethe-Salpeter approximation for the long-range response kernel. This approach goes beyond the adiabatic approximation usually used in linear-response TDDFT and aims at improving the accuracy of calculations of electronic excitation energies of molecular systems. A detailed derivation of the frequency-dependent second-order Bethe-Salpeter correlation kernel is given using many-body Green-function theory. Preliminary tests of this range-separated TDDFT method are presented for the calculation of excitation energies of the He and Be atoms and small molecules (H{sub 2}, N{sub 2}, CO{sub 2}, H{sub 2}CO, and C{sub 2}H{sub 4}). The results suggest that the addition of the long-range second-order Bethe-Salpeter correlation kernel overall slightly improves the excitation energies.
Cao, Yixiang; Hughes, Thomas; Giesen, Dave; Halls, Mathew D; Goldberg, Alexander; Vadicherla, Tati Reddy; Sastry, Madhavi; Patel, Bhargav; Sherman, Woody; Weisman, Andrew L; Friesner, Richard A
2016-06-15
We have developed and implemented pseudospectral time-dependent density-functional theory (TDDFT) in the quantum mechanics package Jaguar to calculate restricted singlet and restricted triplet, as well as unrestricted excitation energies with either full linear response (FLR) or the Tamm-Dancoff approximation (TDA) with the pseudospectral length scales, pseudospectral atomic corrections, and pseudospectral multigrid strategy included in the implementations to improve the chemical accuracy and to speed the pseudospectral calculations. The calculations based on pseudospectral time-dependent density-functional theory with full linear response (PS-FLR-TDDFT) and within the Tamm-Dancoff approximation (PS-TDA-TDDFT) for G2 set molecules using B3LYP/6-31G*(*) show mean and maximum absolute deviations of 0.0015 eV and 0.0081 eV, 0.0007 eV and 0.0064 eV, 0.0004 eV and 0.0022 eV for restricted singlet excitation energies, restricted triplet excitation energies, and unrestricted excitation energies, respectively; compared with the results calculated from the conventional spectral method. The application of PS-FLR-TDDFT to OLED molecules and organic dyes, as well as the comparisons for results calculated from PS-FLR-TDDFT and best estimations demonstrate that the accuracy of both PS-FLR-TDDFT and PS-TDA-TDDFT. Calculations for a set of medium-sized molecules, including Cn fullerenes and nanotubes, using the B3LYP functional and 6-31G(**) basis set show PS-TDA-TDDFT provides 19- to 34-fold speedups for Cn fullerenes with 450-1470 basis functions, 11- to 32-fold speedups for nanotubes with 660-3180 basis functions, and 9- to 16-fold speedups for organic molecules with 540-1340 basis functions compared to fully analytic calculations without sacrificing chemical accuracy. The calculations on a set of larger molecules, including the antibiotic drug Ramoplanin, the 46-residue crambin protein, fullerenes up to C540 and nanotubes up to 14×(6,6), using the B3LYP functional and 6-31G
Li, Junfeng; Rinkevicius, Zilvinas; Cao, Zexing
2014-07-07
Time-dependent density-functional theory (TD-DFT) and complete active space multiconfiguration self-consistent field (CASSCF) calculations have been used to determine equilibrium structures and vibrational frequencies of the ground state and several singlet low-lying excited states of coumarin. Vertical and adiabatic transition energies of S1, S2, and S3 have been estimated by TD-B3LYP and CASSCF/PT2. Calculations predict that the dipole-allowed S1 and S3 states have a character of (1)(ππ*), while the dipole-forbidden (1)(nπ*) state is responsible for S2. The vibronic absorption and emission spectra of coumarin have been simulated by TD-B3LYP and CASSCF calculations within the Franck-Condon approximation, respectively. The simulated vibronic spectra show good agreement with the experimental observations available, which allow us to reasonably interpret vibronic features in the S0→S1 and S0→S3 absorption and the S0←S1 emission spectra. Based on the calculated results, activity, intensity, and density of the vibronic transitions and their contribution to the experimental spectrum profile have been discussed.
Landau, Arie
2013-07-07
This paper presents a new method for calculating spectroscopic properties in the framework of response theory utilizing a sequence of similarity transformations (STs). The STs are preformed using the coupled cluster (CC) and Fock-space coupled cluster operators. The linear and quadratic response functions of the new similarity transformed CC response (ST-CCR) method are derived. The poles of the linear response yield excitation-energy (EE) expressions identical to the ones in the similarity transformed equation-of-motion coupled cluster (STEOM-CC) approach. ST-CCR and STEOM-CC complement each other, in analogy to the complementarity of CC response (CCR) and equation-of-motion coupled cluster (EOM-CC). ST-CCR/STEOM-CC and CCR/EOM-CC yield size-extensive and size-intensive EEs, respectively. Other electronic-properties, e.g., transition dipole strengths, are also size-extensive within ST-CCR, in contrast to STEOM-CC. Moreover, analysis suggests that in comparison with CCR, the ST-CCR expressions may be confined to a smaller subspace, however, the precise scope of the truncation can only be determined numerically. In addition, reformulation of the time-independent STEOM-CC using the same parameterization as in ST-CCR, as well as an efficient truncation scheme, is presented. The shown convergence of the time-dependent and time-independent expressions displays the completeness of the presented formalism.
Fry, Nicole L; Rose, Michael J; Rogow, David L; Nyitray, Crystal; Kaur, Manpreet; Mascharak, Pradip K
2010-02-15
In order to examine the role(s) of designed ligands on the NO photolability of {Ru-NO}(6) nitrosyls, a set of three nitrosyls with ligands containing two carboxamide groups along with a varying number of phenolates have been synthesized. The nitrosyls namely, (NEt(4))(2)[(hybeb)Ru(NO)(OEt)] (1), (PPh(4))[(hypyb)Ru(NO)(OEt)] (2), and [(bpb)Ru(NO)(OEt)] (3) have been characterized by X-ray crystallography. Complexes 1-3 are diamagnetic, exhibit nu(NO) in the range 1780-1840 cm(-1) and rapidly release NO in solution upon exposure to low power UV light (7 mW/cm(2)). Density Functional Theory (DFT) and Time Dependent DFT (TDDFT) calculations on 1-3 indicate considerable contribution of ligand orbitals in the MOs involved in transitions leading to NO photolability. The results of the theoretical studies match well with the experimental absorption spectra as well as the parameters for NO photorelease and provide insight into the transition(s) associated with loss of NO.
Miyamoto, Yoshiyuki; Zhang, Hong; Cheng, Xinlu; Rubio, Angel
2017-09-01
We use time-dependent density functional theory to study laser-pulse induced decomposition of H2O molecules above the two-dimensional (2D) materials graphene, hexagonal boron nitride, and graphitic carbon nitride. We examine femtosecond-laser pulses with a full width at half maximum of 10 or 20 fs for laser-field intensity and wavelengths of 800 or 400 nm by varying the intensity of the laser field from 5 to 9 V/Å, with the corresponding range of fluence per pulse up to 10.7 J /cm2 . For a H2O molecule above the graphitic sheets, the threshold for laser-field H2O decomposition is reduced by more than 20% compared with that of an isolated H2O molecule. We also show that hole doping enhances the water adsorption energy above graphene. The present results indicate that the graphitic materials should support laser-induced chemistry and that other 2D materials that can enhance laser-induced H2O decomposition should be investigated.
Energy Technology Data Exchange (ETDEWEB)
Su, Xiaoxing; Jiang, Lan [Beijing Institute of Technology, Laser Micro/Nano Fabrication Laboratory, School of Mechanical Engineering, Beijing (China); Wang, Feng [Beijing Institute of Technology, School of Physics, Beijing (China); Su, Gaoshi [Beijing Institute of Technology, School of Mechatronical Engineering, Beijing (China); Qu, Liangti [Beijing Institute of Technology, Key Laboratory of Cluster Science, Ministry of Education, School of Chemistry, Beijing (China); Lu, Yongfeng [University of Nebraska-Lincoln, Department of Electrical Engineering, Lincoln, NE (United States)
2017-07-15
In this study, we adopted time-dependent density functional theory to investigate the optical properties of monolayer MoS{sub 2} and the effect of intense few-cycle femtosecond laser pulses on these properties. The electron dynamics of monolayer MoS{sub 2} under few-cycle and multi-cycle laser irradiation were described. The polarization direction of the laser had a marked effect on the energy absorption and electronic excitation of monolayer MoS{sub 2} because of anisotropy. Change in the polarization direction of few-cycle pulse changed the absorbed energy by a factor over 4000. Few-cycle pulse showed a higher sensitivity to the electronic property of material than multi-cycle pulse. The modulation of the dielectric properties of the material was observed on the femtosecond time scale. The negative divergence appeared in the real part of the function at low frequencies and photoinduced blue shift occurred due to Burstein-Moss effect. The irradiation of femtosecond laser caused the dielectric response within the infrared region and introduced anisotropy to the in-plane optical properties. Laser-based engineering of optical properties through controlling transient electron dynamics expands the functionality of MoS{sub 2} and has potential applications in direction-dependent optoelectronic devices. (orig.)
Espinosa-García, W. F.; Pérez-Walton, S.; Osorio-Guillén, J. M.; Moyses Araujo, C.
2018-01-01
We have studied, by means of first-principles calculations, the electronic and optical properties of the sulvanite family: Cu3MX4 (M = V, Nb, Ta and X = S, Se), which, due to its broad range of gaps and chemical stability, have emerged as promising materials for technological applications such as photovoltaics and transparent conductivity. To address the reliability of those properties we have used semi-local and hybrid functionals (PBEsol, HSE06), many-body perturbation theory (G0W0 approximation and Bethe–Salpeter equation), and time-dependent density functional theory (revised bootstrap kernel) to calculate the quasi-particle dispersion relation, band gaps, the imaginary part of the macroscopic dielectric function and the absorption coefficient. The calculated valence band maximum and the conduction band minimum are located at the R and X-points, respectively. The calculated gaps using PBEsol are between 0.81 and 1.88 eV, with HSE06 into 1.73 and 2.94 eV, whereas the G0W0 values fall into the 1.91–3.19 eV range. The calculated dielectric functions and absorption coefficients show that all these compounds present continuous excitonic features when the Bethe–Salpeter equation is used. Contrarily, the revised bootstrap kernel is incapable of describing the excitonic spectra. The calculated optical spectra show that Cu3VS4 and Cu3MSe4 have good absorption in the visible, whereas Cu3NbS4 and Cu3TaS4 have it on the near ultraviolet.
Dorner, Reinhard
2014-05-01
We will discuss experimental studies of ICD in van der Vaals dimers of rare gas atoms and small molecules using the COLTRIMS technique. The talk will cover ICD after resonant Auger excitation (Nature 505, 664 (2014)) and two studies unveiling the time dependence of ICD in the energy (PRL 111, 233004 (2013)) and in the time domain (PRL 111, 093401 (2013)). A new technique to make ultrafast movies without the use of short pulses will be discussed.
Computational strong-field quantum dynamics intense light-matter interactions
2017-01-01
This graduate textbook introduces the computational techniques to study ultra-fast quantum dynamics of matter exposed to strong laser fields. Coverage includes methods to propagate wavefunctions according to the time-dependent Schrödinger, Klein-Gordon or Dirac equation, the calculation of typical observables, time-dependent density functional theory, multi-configurational time-dependent Hartree-Fock, time-dependent configuration interaction singles, the strong-field approximation, and the microscopic particle-in-cell approach.
Computational strong-field quantum dynamics. Intense light-matter interactions
Energy Technology Data Exchange (ETDEWEB)
Bauer, Dieter (ed.) [Rostock Univ. (Germany). Inst. fuer Physik
2017-09-01
This graduate textbook introduces the computational techniques to study ultra-fast quantum dynamics of matter exposed to strong laser fields. Coverage includes methods to propagate wavefunctions according to the time dependent Schroedinger, Klein-Gordon or Dirac equation, the calculation of typical observables, time-dependent density functional theory, multi configurational time-dependent Hartree-Fock, time-dependent configuration interaction singles, the strong-field approximation, and the microscopic particle-in-cell approach.
Energy Technology Data Exchange (ETDEWEB)
Balint-Kurti, G.G.; Dixon, R.N.; Marston, C.C.; Mulholland, A.J. (Bristol Univ. (UK). School of Chemistry)
1991-02-01
A new method of analyzing the results of multidimensional time-dependent quantum dynamical wavepacket calculations in terms of the product quantum state distributions is presented. The method requires knowledge only of the time-dependent projection coefficients of the wavepacket onto individual product quantum states along a cut in the exit valley of the photodissociation or reaction process. The squares of the Fourier transforms of these coefficients then directly yield the cross-sections of interest. The great advantage of time-dependent quantum dynamics, namely that a single wavepacket calculation yields the cross-sections at all energies of interest, is fully exploited. (orig.).
Energy Technology Data Exchange (ETDEWEB)
Zuehlsdorff, T. J., E-mail: tjz21@cam.ac.uk; Payne, M. C. [Cavendish Laboratory, J. J. Thomson Avenue, Cambridge CB3 0HE (United Kingdom); Hine, N. D. M. [Department of Physics, University of Warwick, Coventry CV4 7AL (United Kingdom); Haynes, P. D. [Department of Materials, Imperial College London, Exhibition Road, London SW7 2AZ (United Kingdom); Department of Physics, Imperial College London, Exhibition Road, London SW7 2AZ (United Kingdom); Thomas Young Centre for Theory and Simulation of Materials, Imperial College London, Exhibition Road, London SW7 2AZ (United Kingdom)
2015-11-28
We present a solution of the full time-dependent density-functional theory (TDDFT) eigenvalue equation in the linear response formalism exhibiting a linear-scaling computational complexity with system size, without relying on the simplifying Tamm-Dancoff approximation (TDA). The implementation relies on representing the occupied and unoccupied subspaces with two different sets of in situ optimised localised functions, yielding a very compact and efficient representation of the transition density matrix of the excitation with the accuracy associated with a systematic basis set. The TDDFT eigenvalue equation is solved using a preconditioned conjugate gradient algorithm that is very memory-efficient. The algorithm is validated on a small test molecule and a good agreement with results obtained from standard quantum chemistry packages is found, with the preconditioner yielding a significant improvement in convergence rates. The method developed in this work is then used to reproduce experimental results of the absorption spectrum of bacteriochlorophyll in an organic solvent, where it is demonstrated that the TDA fails to reproduce the main features of the low energy spectrum, while the full TDDFT equation yields results in good qualitative agreement with experimental data. Furthermore, the need for explicitly including parts of the solvent into the TDDFT calculations is highlighted, making the treatment of large system sizes necessary that are well within reach of the capabilities of the algorithm introduced here. Finally, the linear-scaling properties of the algorithm are demonstrated by computing the lowest excitation energy of bacteriochlorophyll in solution. The largest systems considered in this work are of the same order of magnitude as a variety of widely studied pigment-protein complexes, opening up the possibility of studying their properties without having to resort to any semiclassical approximations to parts of the protein environment.
Jamshidi, Zahra; Kaveei, Elham; Mohammadpour, Mozhdeh
2015-08-13
The effects of the weak interactions of rare gas atoms on the UV-visible absorption spectra of gold dimer and tetramer clusters are investigated. The time-dependent density functional theory based on the two-component relativistic zeroth-order regular approximation that considered spin-orbit coupling is performed to estimate the absorption spectra of Au2,4-Rgn (Rg = Ne-Xe, and n = 1-6) complexes. Using spin-orbit, including the appropriate functional, shows a close correlation between experiment and our calculations. It is also demonstrated that the weak interactions between rare gas atoms and gold clusters affect the UV-vis spectra of Au2,4 clusters by shifting the electronic transition toward the blue. Moreover, we find that the order of change in peak position, Δν̃, is proportional to the strength of interactions: Δν̃Au2,4-Xe > Δν̃Au2,4-Kr > Δν̃Au2,4-Ar > Δν̃Au2,4-Ne. In addition, comparing the UV-visible spectra of Au2,4-Rgn complexes with those of isolated Au2 and Au4 clusters shows that for Au2,4-Rg2,4,6 complexes in which Rg atoms interacted symmetrically with gold clusters no additional peaks are observed compared to isolated clusters; however, for Au2,4-Rg1,3,5 complexes, extra peaks appear because of the decrease in symmetry.
Van Kuiken, Benjamin E; Valiev, Marat; Daifuku, Stephanie L; Bannan, Caitlin; Strader, Matthew L; Cho, Hana; Huse, Nils; Schoenlein, Robert W; Govind, Niranjan; Khalil, Munira
2013-05-30
Ruthenium L3-edge X-ray absorption (XA) spectroscopy probes unoccupied 4d orbitals of the metal atom and is increasingly being used to investigate the local electronic structure in ground and excited electronic states of Ru complexes. The simultaneous development of computational tools for simulating Ru L3-edge spectra is crucial for interpreting the spectral features at a molecular level. This study demonstrates that time-dependent density functional theory (TDDFT) is a viable and predictive tool for simulating ruthenium L3-edge XA spectroscopy. We systematically investigate the effects of exchange correlation functional and implicit and explicit solvent interactions on a series of Ru(II) and Ru(III) complexes in their ground and electronic excited states. The TDDFT simulations reproduce all of the experimentally observed features in Ru L3-edge XA spectra within the experimental resolution (0.4 eV). Our simulations identify ligand-specific charge transfer features in complicated Ru L3-edge spectra of [Ru(CN)6](4-) and Ru(II) polypyridyl complexes illustrating the advantage of using TDDFT in complex systems. We conclude that the B3LYP functional most accurately predicts the transition energies of charge transfer features in these systems. We use our TDDFT approach to simulate experimental Ru L3-edge XA spectra of transition metal mixed-valence dimers of the form [(NC)5M(II)-CN-Ru(III)(NH3)5](-) (where M = Fe or Ru) dissolved in water. Our study determines the spectral signatures of electron delocalization in Ru L3-edge XA spectra. We find that the inclusion of explicit solvent molecules is necessary for reproducing the spectral features and the experimentally determined valencies in these mixed-valence complexes. This study validates the use of TDDFT for simulating Ru 2p excitations using popular quantum chemistry codes and providing a powerful interpretive tool for equilibrium and ultrafast Ru L3-edge XA spectroscopy.
Li, Zhendong; Liu, Wenjian
2016-06-14
Compared with closed-shell systems, open-shell systems place three additional challenges to time-dependent density functional theory (TD-DFT) for electronically excited states: (a) the spin-contamination problem is a serious issue; (b) the exchange-correlation (XC) kernel may be numerically instable; and (c) the single-determinant description of open-shell ground states readily becomes energetically instable. Confined to flip-up single excitations, the spin-contamination problem can largely be avoided by using the spin-flip TD-DFT (SF-TD-DFT) formalism, provided that a noncollinear XC kernel is employed. As for the numerical instabilities associated with such a kernel, only an ad hoc scheme has been proposed so far, viz., the ALDA0 kernel, which amounts to setting the divergent components (arising from density gradients and kinetic energy density) simply to zero. The ground-state instability problem can effectively be avoided by introducing the Tamm-Dancoff approximation (TDA) to TD-DFT. Therefore, on a general basis, the SF-TDA/ALDA0 Ansatz is so far the only promising means within the TD-DFT framework for flip-up single excitations of open-shell systems. To assess systematically the performance of SF-TDA/ALDA0, in total 61 low-lying quartet excited states of the benchmark set of 11 small radicals [J. Chem. Theory Comput. 2016, 12, 238] are investigated with various XC functionals. Taking the MRCISD+Q (multireference configuration interaction with singles and doubles plus the Davidson correction) results as benchmark, it is found that the mean absolute errors of SF-TDA/ALDA0 with the SAOP (statistical averaging of model orbital potentials), global hybrid, and range-separated hybrid functionals are in the range of 0.2-0.4 eV. This is in line not only with the typical accuracy of TD-DFT for singlet and triplet excited states of closed-shell systems but also with the gross accuracy of spin-adapted TD-DFT for spin-conserving excited states of open-shell systems.
Minasian, Stefan G; Keith, Jason M; Batista, Enrique R; Boland, Kevin S; Kozimor, Stosh A; Martin, Richard L; Shuh, David K; Tyliszczak, Tolek; Vernon, Louis J
2013-10-02
Metal-carbon covalence in (C5H5)2MCl2 (M = Ti, Zr, Hf) has been evaluated using carbon K-edge X-ray absorption spectroscopy (XAS) as well as ground-state and time-dependent hybrid density functional theory (DFT and TDDFT). Differences in orbital mixing were determined experimentally using transmission XAS of thin crystalline material with a scanning transmission X-ray microscope (STXM). Moving down the periodic table (Ti to Hf) has a marked effect on the experimental transition intensities associated with the low-lying antibonding 1a1* and 1b2* orbitals. The peak intensities, which are directly related to the M-(C5H5) orbital mixing coefficients, increase from 0.08(1) and 0.26(3) for (C5H5)2TiCl2 to 0.31(3) and 0.75(8) for (C5H5)2ZrCl2, and finally to 0.54(5) and 0.83(8) for (C5H5)2HfCl2. The experimental trend toward increased peak intensity for transitions associated with 1a1* and 1b2* orbitals agrees with the calculated TDDFT oscillator strengths [0.10 and 0.21, (C5H5)2TiCl2; 0.21 and 0.73, (C5H5)2ZrCl2; 0.35 and 0.69, (C5H5)2HfCl2] and with the amount of C 2p character obtained from the Mulliken populations for the antibonding 1a1* and 1b2* orbitals [8.2 and 23.4%, (C5H5)2TiCl2; 15.3 and 39.7%, (C5H5)2ZrCl2; 20.1 and 50.9%, (C5H5)2HfCl2]. The excellent agreement between experiment, theory, and recent Cl K-edge XAS and DFT measurements shows that C 2p orbital mixing is enhanced for the diffuse Hf (5d) and Zr (4d) atomic orbitals in relation to the more localized Ti (3d) orbitals. These results provide insight into how changes in M-Cl orbital mixing within the metallocene wedge are correlated with periodic trends in covalent bonding between the metal and the cyclopentadienide ancillary ligands.
Energy Technology Data Exchange (ETDEWEB)
Kozimor, S.A.; Yang, P.; Batista, E.R.; Boland, K.S.; Burns, C.J.; Christensen, C.N.; Clark, D.L.; Conradson, S.D.; Hay, P.J.; Lezama, J.S.; Martin, R.L.; Schwarz, D.E.; Wilkerson, M.P.; Wolfsberg, L.E.
2009-05-20
For 3-5d transition-metal ions, the (C{sub 5}R{sub 5}){sub 2}MCl{sub 2} (R = H, Me for M = Ti, Zr, Hf) bent metallocenes represent a series of compounds that have been central in the development of organometallic chemistry and homogeneous catalysis. Here, we evaluate how changes in the principal quantum number for the group IV (C{sub 5}H{sub 5}){sub 2}MCl{sub 2} (M = Ti, Zr, Hf; 1-3, respectively) complexes affects the covalency of M-Cl bonds through application of Cl K-edge X-ray Absorption Spectroscopy (XAS). Spectra were recorded on solid samples dispersed as a thin film and encapsulated in polystyrene matrices to reliably minimize problems associated with X-ray self-absorption. The data show that XAS pre-edge intensities can be quantitatively reproduced when analytes are encapsulated in polystyrene. Cl K-edge XAS data show that covalency in M-Cl bonding changes in the order Ti > Zr > Hf and demonstrates that covalency slightly decreases with increasing principal quantum number in 1-3. The percent Cl 3p character was experimentally determined to be 26, 23, and 18% per M-Cl bond in the thin-film samples for 1-3 respectively and was indistinguishable from the polystyrene samples, which analyzed as 25, 25, and 19% for 1-3, respectively. To aid in interpretation of Cl K-edge XAS, 1-3 were also analyzed by ground-state and time-dependent density functional theory (TD-DFT) calculations. The calculated spectra and percent chlorine character are in close agreement with the experimental observations, and show 20, 18, and 17% Cl 3p character per M-Cl bond for 1-3, respectively. Polystyrene matrix encapsulation affords a convenient method to safely contain radioactive samples to extend our studies to include actinide elements, where both 5f and 6d orbitals are expected to play a role in M-Cl bonding and where transition assignments must rely on accurate theoretical calculations.
Rudberg, Elias
2012-02-01
Self-consistency-based Kohn-Sham density functional theory (KS-DFT) electronic structure calculations with Gaussian basis sets are reported for a set of 17 protein-like molecules with geometries obtained from the Protein Data Bank. It is found that in many cases such calculations do not converge due to vanishing HOMO-LUMO gaps. A sequence of polyproline I helix molecules is also studied and it is found that self-consistency calculations using pure functionals fail to converge for helices longer than six proline units. Since the computed gap is strongly correlated to the fraction of Hartree-Fock exchange, test calculations using both pure and hybrid density functionals are reported. The tested methods include the pure functionals BLYP, PBE and LDA, as well as Hartree-Fock and the hybrid functionals BHandHLYP, B3LYP and PBE0. The effect of including solvent molecules in the calculations is studied, and it is found that the inclusion of explicit solvent molecules around the protein fragment in many cases gives a larger gap, but that convergence problems due to vanishing gaps still occur in calculations with pure functionals. In order to achieve converged results, some modeling of the charge distribution of solvent water molecules outside the electronic structure calculation is needed. Representing solvent water molecules by a simple point charge distribution is found to give non-vanishing HOMO-LUMO gaps for the tested protein-like systems also for pure functionals.
Study of spontaneous fission lifetimes using nuclear density functional theory
Directory of Open Access Journals (Sweden)
Sadhukhan Jhilam
2013-12-01
Full Text Available The spontaneous fission lifetimes have been studied microscopically by minimizing the collective action integral in a two-dimensional collective space of quadrupole moments (Q20, Q22 representing elongation and triaxiality. The microscopic collective potential and inertia tensor are obtained by solving the self-consistent Hartree-Fock-Bogoliubov (HFB equations with the Skyrme energy density functional and mixed pairing interaction. The mass tensor is computed within the perturbative Adiabatic Time-Dependent HFB (ATDHFB approach in the cranking approximation. The dynamic fission trajectories have been obtained by minimizing the collective action using two different numerical techniques. The values of spontaneous fission lifetimes obtained in this way are compared with the static results.
Density functional approaches to nuclear dynamics
Nakatsukasa, T.; Ebata, S.; Avogadro, P.; Guo, L.; Inakura, T.; Yoshida, K.
2012-01-01
We present background concepts of the nuclear density functional theory (DFT) and applications of the time-dependent DFT with the Skyrme energy functional for nuclear response functions. Practical methods for numerical applications of the time-dependent Hartree-Fock-Bogoliubov theory (TDHFB) are proposed; finite amplitude method and canonical-basis TDHFB. These approaches are briefly reviewed and some numerical applications are shown to demonstrate their feasibility.
International Nuclear Information System (INIS)
Loibl, Stefan; Schütz, Martin
2014-01-01
In this paper, we present theory and implementation of an efficient program for calculating magnetizabilities and rotational g tensors of closed-shell molecules at the level of local second-order Møller-Plesset perturbation theory (MP2) using London orbitals. Density fitting is employed to factorize the electron repulsion integrals with ordinary Gaussians as fitting functions. The presented program for the calculation of magnetizabilities and rotational g tensors is based on a previous implementation of NMR shielding tensors reported by S. Loibl and M. Schütz [J. Chem. Phys. 137, 084107 (2012)]. Extensive test calculations show (i) that the errors introduced by density fitting are negligible, and (ii) that the errors of the local approximation are still rather small, although larger than for nuclear magnetic resonance (NMR) shielding tensors. Electron correlation effects for magnetizabilities are tiny for most of the molecules considered here. MP2 appears to overestimate the correlation contribution of magnetizabilities such that it does not constitute an improvement over Hartree-Fock (when comparing to higher-order methods like CCSD(T)). For rotational g tensors the situation is different and MP2 provides a significant improvement in accuracy over Hartree-Fock. The computational performance of the new program was tested for two extended systems, the larger comprising about 2200 basis functions. It turns out that a magnetizability (or rotational g tensor) calculation takes about 1.5 times longer than a corresponding NMR shielding tensor calculation
Reconstructive approaches to one- and two-electron density matrix theory
Herbert, John Michael
Novel computational methods for electronic structure theory are explored, in which the fundamental variable is either the one- or the two-electron reduced density matrix (1- or 2-RDM), rather than the electronic wavefunction. A unifying theme among these methods is density matrix reconstruction, that is, decoupling approximations that express higher-order density matrices as functionals of lower-order ones. On the 2-RDM side, a connected (extensive) version of the Contracted Schrodinger Equation (CSE) is developed, in which the basic unknowns are the RDM cumulants through order four. Reconstruction functionals that neglect the 3- and 4-RDM cumulants are examined and revealed to be significantly less accurate than suggested by previous minimal-basis results. Exact 3-RDM cumulants for some four-electron systems are calculated and found to be comparable in importance to unconnected products of lower-order cumulants. Decoupling approximations for the 3- and 4-RDM cumulants are developed based upon a renormalized, diagrammatic perturbation theory for the three- and four-particle Green's functions, in which the effective, pairwise interaction is extracted from the two-particle cumulant. Diagram rules suitable for both the time-dependent and time-independent versions of this perturbation theory are derived. Reconstructive approaches to natural orbital (1-RDM) functional theory are also examined, wherein the 2-RDM is parametrized in terms of the natural orbitals and their (generally fractional) occupancies. It is demonstrated, at the theorem level, that proposed "corrected Hartree" and "corrected Hartree-Fock" natural orbital functionals necessarily violate positivity of the 2-RDM, which is closely related to their failure to respect antisymmetry. Calculations demonstrate that negative eigenvalues of the 2-RDM are associated with a large, stabilizing (but ultimately spurious) contribution to the energy. Nevertheless, a partially self-interaction-corrected version of the
Directory of Open Access Journals (Sweden)
Seiya Nishiyama
2009-01-01
Full Text Available The maximally-decoupled method has been considered as a theory to apply an basic idea of an integrability condition to certain multiple parametrized symmetries. The method is regarded as a mathematical tool to describe a symmetry of a collective submanifold in which a canonicity condition makes the collective variables to be an orthogonal coordinate-system. For this aim we adopt a concept of curvature unfamiliar in the conventional time-dependent (TD self-consistent field (SCF theory. Our basic idea lies in the introduction of a sort of Lagrange manner familiar to fluid dynamics to describe a collective coordinate-system. This manner enables us to take a one-form which is linearly composed of a TD SCF Hamiltonian and infinitesimal generators induced by collective variable differentials of a canonical transformation on a group. The integrability condition of the system read the curvature C = 0. Our method is constructed manifesting itself the structure of the group under consideration. To go beyond the maximaly-decoupled method, we have aimed to construct an SCF theory, i.e., υ (external parameter-dependent Hartree-Fock (HF theory. Toward such an ultimate goal, the υ-HF theory has been reconstructed on an affine Kac-Moody algebra along the soliton theory, using infinite-dimensional fermion. An infinite-dimensional fermion operator is introduced through a Laurent expansion of finite-dimensional fermion operators with respect to degrees of freedom of the fermions related to a υ-dependent potential with a Υ-periodicity. A bilinear equation for the υ-HF theory has been transcribed onto the corresponding τ-function using the regular representation for the group and the Schur-polynomials. The υ-HF SCF theory on an infinite-dimensional Fock space F∞ leads to a dynamics on an infinite-dimensional Grassmannian Gr∞ and may describe more precisely such a dynamics on the group manifold. A finite-dimensional Grassmannian is identified with a Gr
Sharma, Divya; Paterson, Martin J
2014-11-01
DFT and MP2 calculations are performed to obtain optimized ground state geometries and binding energies of the cage and the prism conformers of water W6 clusters and Bz-W6 clusters using the aug-cc-pVDZ basis set. The cage conformer of Bz-W6 system is found to be more stable than prism conformer for all range of DFT functionals and MP2. Time dependent-DFT is then used to study UV spectroscopy of Bz, water W6 clusters and Bz-W6 clusters at both the MP2 and wB97XD optimized ground state geometries using the B3LYP, CAM-B3LYP and M06-2X functionals with 6-31++G(d,p) and aug-cc-pVTZ basis sets. Our results predict minor differences in the UV spectroscopy of cage and prism conformers W6 and Bz-W6 clusters that may be observable with high-resolution spectroscopy. The M06-2X and CAM-B3LYP functionals perform consistently with each other. Benzene-mediated excitations of the water W6 cluster towards longer wavelengths above 170 nm are noticed in both the cage and prism geometries of Bz-W6. Benzene is found to be influenced after interacting with the cage and prism W6 geometries, and is seen to undergo a red shift in the main π→π* electronic transition, in which the degeneracy is slightly broken. Charge transfer (CT) states and diffuse Rydberg-type states are also found to play an important role in the spectroscopy of such systems.
Energy Technology Data Exchange (ETDEWEB)
Keim, M.
2005-07-01
In the present thesis response effects in interatomic collisions with two active electrons are studied in the range of non-relativistic collision energies. The starting point is the mapping of the time-dependent interacting many-electron sytem on an effective one-particle picture on the base of the time-dependent density functional theory (TDDFT). By means of the basis generator method the one-particle equations aring in the framework of the TDDFT concept are solved in a finite-dimensional model space. In the study of ionization cross section in the collisional systeem anti p+He it is shown that by response effects an essential diminuishing of the cross sections in comparison to the no-response case is reached. Analoguously the ionization cross sections for the collisional systems p-He, He{sup 2+}-He, Li{sup 3+}-He and p-Li{sup +} behave.
Casida, Mark E; Huix-Rotllant, Miquel
2016-01-01
In their famous paper, Kohn and Sham formulated a formally exact density-functional theory (DFT) for the ground-state energy and density of a system of N interacting electrons, albeit limited at the time by certain troubling representability questions. As no practical exact form of the exchange-correlation (xc) energy functional was known, the xc-functional had to be approximated, ideally by a local or semilocal functional. Nowadays, however, the realization that Nature is not always so nearsighted has driven us up Perdew's Jacob's ladder to find increasingly nonlocal density/wavefunction hybrid functionals. Time-dependent (TD-) DFT is a younger development which allows DFT concepts to be used to describe the temporal evolution of the density in the presence of a perturbing field. Linear response (LR) theory then allows spectra and other information about excited states to be extracted from TD-DFT. Once again the exact TD-DFT xc-functional must be approximated in practical calculations and this has historically been done using the TD-DFT adiabatic approximation (AA) which is to TD-DFT very similar to what the local density approximation (LDA) is to conventional ground-state DFT. Although some of the recent advances in TD-DFT focus on what can be done within the AA, others explore ways around the AA. After giving an overview of DFT, TD-DFT, and LR-TD-DFT, this chapter focuses on many-body corrections to LR-TD-DFT as one way to build hybrid density-functional/wavefunction methodology for incorporating aspects of nonlocality in time not present in the AA.
Ab initio theory of magnetic interactions at surfaces
International Nuclear Information System (INIS)
Sousa, C; Graaf, C de; Lopez, N; Harrison, N M; Illas, F
2004-01-01
The low to high spin energy transition of Ni adsorbed on regular and defective sites of MgO(100) and the relative strengths of bulk and surface magnetic coupling constants of first row transition metal oxides (MnO, FeO, CoO, NiO and CuO) are taken as examples to illustrate some deficiencies of density functional theory (DFT). For these ionic systems a cluster/periodic comparison within the same computational method (either DFT or Hartree-Fock) is used to establish that embedded cluster models provide an adequate representation. The cluster model approach is then used to obtain accurate values for the magnetic properties of interest by using explicitly correlated wavefunction methods which handle the electronic open shell rigorously as spin eigenfunctions
Kasper, Joseph M; Lestrange, Patrick J; Stetina, Torin F; Li, Xiaosong
2018-03-29
X-ray absorption spectroscopy is a powerful technique to probe local electronic and nuclear structure. There has been extensive theoretical work modeling K-edge spectra from first principles. However, modeling L-edge spectra directly with density functional theory poses a unique challenge requiring further study. Spin-orbit coupling must be included in the model, and a noncollinear density functional theory is required. Using the real-time exact two-component method, we are able to variationally include one-electron spin-orbit coupling terms when calculating the absorption spectrum. The abilities of different basis sets and density functionals to model spectra for both closed- and open-shell systems are investigated using SiCl 4 and three transition metal complexes, TiCl 4 , CrO 2 Cl 2 , and [FeCl 6 ] 3- . Although we are working in the real-time framework, individual molecular orbital transitions can still be recovered by projecting the density onto the ground state molecular orbital space and separating contributions to the time evolving dipole moment.
Evolution in time-dependent fitness landscapes
Wilke, Claus O.
1998-01-01
Evolution in changing environments is an important, but little studied aspect of the theory of evolution. The idea of adaptive walks in fitness landscapes has triggered a vast amount of research and has led to many important insights about the progress of evolution. Nevertheless, the small step to time-dependent fitness landscapes has most of the time not been taken. In this work, some elements of a theory of adaptive walks on changing fitness landscapes are proposed, and are subsequently app...
Realistic nuclear shell theory and the doubly-magic 132Sn region
International Nuclear Information System (INIS)
Vary, J.P.
1978-01-01
After an introduction discussing the motivation and interest in results obtained with isotope separators, the fundamental problem in realistic nuclear shell theory is posed in the context of renormalization theory. Then some of the important developments that have occurred over the last fifteen years in the derivation of the effective Hamiltonian and application of realistic nuclear shell theory are briefly reviewed. Doubly magic regions of the periodic table and the unique advantages of the 132 Sn region are described. Then results are shown for the ground-state properties of 132 Sn as calculated from the density-dependent Hartree-Fock approach with the Skyrme Hamiltonian. A single theoretical Hamiltonian for all nuclei from doubly magic 132 Sn to doubly magic 208 Pb is presented; single-particle energies are graphed. Finally, predictions of shell-model level-density distributions obtained with spectral distribution methods are discussed; calculated level densities are shown for 136 Xe. 10 figures
Roy, A. K.; Chu, Shih-I.
2002-05-01
We extend the quantum hydrodynamical (QFD) formulation of time-dependent density functional theory (TDDFT) to the study of multiphoton processes of many-electron atomic systems in intense laser fields (A. K. Roy and S. I. Chu, Phys. Rev. A (in press).). The QFD-TDDFT formulation results in a single generalized nonlinear Schrodinger equation (GNLSE) and includes the many-body effects through a local time-dependent exchange-correlation (xc) potential. The GNLSE is solved by the time- dependent generalized pseudospectral method (X. M. Tong and S.I. Chu, Chem. Phys. 217) (1997) 119. (X. Chu and S. I. Chu, Phys. Rev. A 63) (2001) 023411.. The procedure is applied to the study of multiphoton ionization (MPI) and high harmonic generation (HHG) of He and Ne in intense laser fields. Four different xc energy functionals are used in the study with an aim to explore the roles of exchange and correlation ovn MPI/HHG processes in details ^1.
Halasinski, Thomas M.; Weisman, Jennifer L.; Lee, Timothy J.; Salama, Farid; Head-Gordon, Martin; Kwak, Dochan (Technical Monitor)
2002-01-01
We present a full experimental and theoretical study of an interesting series of polycyclic aromatic hydrocarbons, the oligorylenes. The absorption spectra of perylene, terrylene and quaterrylene in neutral, cationic and anionic charge states are obtained by matrix-isolation spectroscopy in Ne. The experimental spectra are dominated by a bright state that red shifts with growing molecular size. Excitation energies and state symmetry assignments are supported by calculations using time dependent density functional theory methods. These calculations also provide new insight into the observed trends in oscillator strength and excitation energy for the bright states: the oscillator strength per unit mass of carbon increases along the series.
Yokogawa, D.
2016-09-01
Theoretical approach to design bright bio-imaging molecules is one of the most progressing ones. However, because of the system size and computational accuracy, the number of theoretical studies is limited to our knowledge. To overcome the difficulties, we developed a new method based on reference interaction site model self-consistent field explicitly including spatial electron density distribution and time-dependent density functional theory. We applied it to the calculation of indole and 5-cyanoindole at ground and excited states in gas and solution phases. The changes in the optimized geometries were clearly explained with resonance structures and the Stokes shift was correctly reproduced.
One-Body Potential Theory of Molecules and Solids Modified Semiempirically for Electron Correlation
International Nuclear Information System (INIS)
March, N.H.
2010-08-01
The study of Cordero, March and Alonso (CMA) for four spherical atoms, Be,Ne,Mg and Ar, semiempirically fine-tunes the Hartree-Fock (HF) ground-state electron density by inserting the experimentally determined ionization potentials. The present Letter, first of all, relates this approach to the very recent work of Bartlett 'towards an exact correlated orbital theory for electrons'. Both methods relax the requirement of standard DFT that a one-body potential shall generate the exact ground-state density, though both work with high quality approximations. Unlike DFT, the CMA theory uses a modified HF non-local potential. It is finally stressed that this potential generates also an idempotent Dirac density matrix. The CMA approach is thereby demonstrated to relate, albeit approximately, to the DFT exchange-correlation potential. (author)
Energy decomposition analysis of single bonds within Kohn-Sham density functional theory.
Levine, Daniel S; Head-Gordon, Martin
2017-11-28
An energy decomposition analysis (EDA) for single chemical bonds is presented within the framework of Kohn-Sham density functional theory based on spin projection equations that are exact within wave function theory. Chemical bond energies can then be understood in terms of stabilization caused by spin-coupling augmented by dispersion, polarization, and charge transfer in competition with destabilizing Pauli repulsions. The EDA reveals distinguishing features of chemical bonds ranging across nonpolar, polar, ionic, and charge-shift bonds. The effect of electron correlation is assessed by comparison with Hartree-Fock results. Substituent effects are illustrated by comparing the C-C bond in ethane against that in bis(diamantane), and dispersion stabilization in the latter is quantified. Finally, three metal-metal bonds in experimentally characterized compounds are examined: a [Formula: see text]-[Formula: see text] dimer, the [Formula: see text]-[Formula: see text] bond in dizincocene, and the Mn-Mn bond in dimanganese decacarbonyl.
Self-consistent theory of finite Fermi systems and radii of nuclei
International Nuclear Information System (INIS)
Saperstein, E. E.; Tolokonnikov, S. V.
2011-01-01
Present-day self-consistent approaches in nuclear theory were analyzed from the point of view of describing distributions of nuclear densities. The generalized method of the energy density functional due to Fayans and his coauthors (this is the most successful version of the self-consistent theory of finite Fermi systems) was the first among the approaches under comparison. The second was the most successful version of the Skyrme-Hartree-Fock method with the HFB-17 functional due to Goriely and his coauthors. Charge radii of spherical nuclei were analyzed in detail. Several isotopic chains of deformed nuclei were also considered. Charge-density distributions ρ ch (r) were calculated for several spherical nuclei. They were compared with model-independent data extracted from an analysis of elastic electron scattering on nuclei.
Energy Technology Data Exchange (ETDEWEB)
Ringholm, Magnus; Ruud, Kenneth [Centre for Theoretical and Computational Chemistry, Department of Chemistry, University of Tromsø – The Arctic University of Norway, 9037 Tromsø (Norway); Bast, Radovan [Theoretical Chemistry and Biology, School of Biotechnology, Royal Institute of Technology, AlbaNova University Center, S-10691 Stockholm (Sweden); PDC Center for High Performance Computing, Royal Institute of Technology, S-10044 Stockholm (Sweden); Oggioni, Luca [Centre for Theoretical and Computational Chemistry, Department of Chemistry, University of Tromsø – The Arctic University of Norway, 9037 Tromsø (Norway); Department of Physics G. Occhialini, University of Milano Bicocca, Piazza della scienza 3, 20126 Milan (Italy); Ekström, Ulf [Centre for Theoretical and Computational Chemistry, Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, 0315 Oslo (Norway)
2014-10-07
We present the first analytic calculations of the geometrical gradients of the first hyperpolarizability tensors at the density-functional theory (DFT) level. We use the analytically calculated hyperpolarizability gradients to explore the importance of electron correlation effects, as described by DFT, on hyper-Raman spectra. In particular, we calculate the hyper-Raman spectra of the all-trans and 11-cis isomers of retinal at the Hartree-Fock (HF) and density-functional levels of theory, also allowing us to explore the sensitivity of the hyper-Raman spectra on the geometrical characteristics of these structurally related molecules. We show that the HF results, using B3LYP-calculated vibrational frequencies and force fields, reproduce the experimental data for all-trans-retinal well, and that electron correlation effects are of minor importance for the hyper-Raman intensities.
Liakos, Dimitrios G; Neese, Frank
2015-09-08
The recently developed domain-based local pair natural orbital coupled cluster theory with single, double, and perturbative triple excitations (DLPNO-CCSD(T)) delivers results that are closely approaching those of the parent canonical coupled cluster method at a small fraction of the computational cost. A recent extended benchmark study established that, depending on the three main truncation thresholds, it is possible to approach the canonical CCSD(T) results within 1 kJ (default setting, TightPNO), 1 kcal/mol (default setting, NormalPNO), and 2-3 kcal (default setting, LoosePNO). Although thresholds for calculations with TightPNO are 2-4 times slower than those based on NormalPNO thresholds, they are still many orders of magnitude faster than canonical CCSD(T) calculations, even for small and medium sized molecules where there is little locality. The computational effort for the coupled cluster step scales nearly linearly with system size. Since, in many instances, the coupled cluster step in DLPNO-CCSD(T) is cheaper or at least not much more expensive than the preceding Hartree-Fock calculation, it is useful to compare the method against modern density functional theory (DFT), which requires an effort comparable to that of Hartree-Fock theory (at least if Hartree-Fock exchange is part of the functional definition). Double hybrid density functionals (DHDF's) even require a MP2-like step. The purpose of this article is to evaluate the cost vs accuracy ratio of DLPNO-CCSD(T) against modern DFT (including the PBE, B3LYP, M06-2X, B2PLYP, and B2GP-PLYP functionals and, where applicable, their van der Waals corrected counterparts). To eliminate any possible bias in favor of DLPNO-CCSD(T), we have chosen established benchmark sets that were specifically proposed for evaluating DFT functionals. It is demonstrated that DLPNO-CCSD(T) with any of the three default thresholds is more accurate than any of the DFT functionals. Furthermore, using the aug-cc-pVTZ basis set and
Quantized TDHF for isoscalar giant quadrupole resonances in spherical nuclei
International Nuclear Information System (INIS)
Drozdz, S.; Okolowicz, J.; Ploszajczak, M.; Caurier, E.
1988-01-01
The time-dependent Hartree-Fock theory supplemented with the regularity and single-valuedness quantization condition for the gauge invariant component of the wavefunction is applied to the description of the centroid energy and escape width of isoscalar giant quadrupole resonances in 16 O, 40 Ca and 110 Zr. Calculations are performed using the Skyrme SIII effective interaction. An important role of the finite oscillation amplitude in the mean-field dynamics is emphasized. (orig.)
Scissors mode with a simple Hamiltonians
International Nuclear Information System (INIS)
Bal'butsev, E.B.; ); Shuk, P.
2002-01-01
The system of the motion bound equation for the nucleus angular moment and its quadrupole moments in the coordinate and pulse spaces is derived from the equation of the Hartree-Fock time-dependent theory. The formulae for the energy, B(M1)- and B(E2)-factors of the scissors mode are obtained in the approximation of low amplitudes; the physical nature of the event is explained. The calculation results qualitatively agree with the experiment [ru
Rocca, Dario; Lu, Deyu; Galli, Giulia
2010-10-28
We describe an ab initio approach to compute the optical absorption spectra of molecules and solids, which is suitable for the study of large systems and gives access to spectra within a wide energy range. In this approach, the quantum Liouville equation is solved iteratively within first order perturbation theory, with a Hamiltonian containing a static self-energy operator. This procedure is equivalent to solving the statically screened Bethe-Salpeter equation. Explicit calculations of single particle excited states and inversion of dielectric matrices are avoided using techniques based on density functional perturbation theory. In this way, full absorption spectra may be obtained with a computational workload comparable to ground state Hartree-Fock calculations. We present results for small molecules, for the spectra of a 1 nm Si cluster in a wide energy range (20 eV), and for a dipeptide exhibiting charge transfer excitations.
Murakami, Mitsuko; Zhang, G. P.; Chu, Shih-I.
2017-05-01
We present the photoelectron momentum distributions (PMDs) of helium, neon, and argon atoms driven by a linearly polarized, visible (527-nm) or near-infrared (800-nm) laser pulse (20 optical cycles in duration) based on the time-dependent density-functional theory (TDDFT) under the local-density approximation with a self-interaction correction. A set of time-dependent Kohn-Sham equations for all electrons in an atom is numerically solved using the generalized pseudospectral method. An effect of the electron-electron interaction driven by a visible laser field is not recognizable in the helium and neon PMDs except for a reduction of the overall photoelectron yield, but there is a clear difference between the PMDs of an argon atom calculated with the frozen-core approximation and TDDFT, indicating an interference of its M -shell wave functions during the ionization. Furthermore, we find that the PMDs of degenerate p states are well separated in intensity when driven by a near-infrared laser field, so that the single-active-electron approximation can be adopted safely.
Ab initio theory of the equation of state for compressed rare gas crystals
Pilipenko, E. A.; Troitskaya, E. P.; Gorbenko, Ie. Ie.
2018-01-01
Nonempirical equations of state of compressed rare gas crystals Ne, Ar, Kr, and Xe are studied on the basis of the earlier-obtained ab initio adiabatic potential. The paired and three-body short-range repulsive potentials are calculated by the Hartree-Fock method in the basis of localized functions with their exact mutual orthogonalization and do not contain experimentally determined parameters. The theory is compared with the experiment and results of calculations by other authors. Analysis of the proposed equations of state for large compressions has shown the importance of taking into account the three-body interaction and the terms of the higher order in the overlap integral in compressed neon and the sufficiency of the quadratic approximation in the orthogonalization of functions in heavy rare gas crystals.