Extension of Hartree-Fock theory including tensor correlation in nuclear matter

Science.gov (United States)

Hu, Jinniu; Toki, Hiroshi; Ogawa, Yoko

2013-10-01

We study the properties of nuclear matter in the extension of Hartree-Fock theory including tensor correlation using a realistic nucleon-nucleon (NN) interaction. The nuclear wave function consists of the Hartree-Fock and two-particle-two-hole (2p-2h) states, following the concept of the tensor-optimized shell model (TOSM) for light nuclei. The short range repulsion and strong tensor force of realistic NN interaction provide high momentum components, which are taken into account in a many-body framework by introducing 2p-2h states. Single particle states are determined by the variational principle of the total energy with respect to 2p-2h amplitudes and Hartree-Fock (HF) single-particle states. The resulting differential equation is almost identical with that of Brueckner-Hartree-Fock (BHF) theory by taking two-body scattering terms only. We calculate the equation of state (EOS) of nuclear matter in this framework with the Bonn potential as a realistic NN interaction. We found similar results to BHF theory with slightly repulsive effects in the total energy. The relativistic effect is discussed for the EOSs of nuclear matter in both non-relativistic and relativistic frameworks. The momentum distribution has large components at high momenta due to 2p-2h excitations. We also obtain the EOSs of pure neutron matter, where the tensor effect is small in the iso-vector channel.

Relativistic hadrodynamics with field-strength dependent coupling of the scalar fields in Hartree and Hartree-Fock approximation

International Nuclear Information System (INIS)

Lindner, J.

1992-09-01

In this thesis in the framework of our model of the field-strength dependent coupling the properties of infinitely extended, homogeneous, static, spin- and isospin-saturated nuclear matter are studied. Thereby we use the Hartree-Mean-Field and the Hartree-Fock approximation, whereby the influence of the antiparticle states in the Fermi sea is neglected. In chapter 2 the Lagrangian density basing to our model is fixed. Starting from the Walecka model we modify in the Lagrangian density the Linear coupling of the scalar field to the scalar density as follows g S φanti ψψ→g S f(φ) anti ψψ. In chapter 3 we fix three different functions f(φ). For these three cases and for the Walecka model with f(φ)=φ nuclear-matter calculations are performed. In chapter 4 for the Hartree-Fock calculations, but also very especially regarding the molecular-dynamics calculations, the properties of the Dirac spinors in the plane-wave representation are intensively studied. (orig.)

Molecular wave function and effective adiabatic potentials calculated by extended multi-configuration time-dependent Hartree-Fock method

Energy Technology Data Exchange (ETDEWEB)

Kato, Tsuyoshi; Ide, Yoshihiro; Yamanouchi, Kaoru [Department of Chemistry, School of Science, The University of Tokyo, 7-3-1, Hongo Bunkyo-ku, Tokyo, 113-0033 (Japan)

2015-12-31

We first calculate the ground-state molecular wave function of 1D model H{sub 2} molecule by solving the coupled equations of motion formulated in the extended multi-configuration time-dependent Hartree-Fock (MCTDHF) method by the imaginary time propagation. From the comparisons with the results obtained by the Born-Huang (BH) expansion method as well as with the exact wave function, we observe that the memory size required in the extended MCTDHF method is about two orders of magnitude smaller than in the BH expansion method to achieve the same accuracy for the total energy. Second, in order to provide a theoretical means to understand dynamical behavior of the wave function, we propose to define effective adiabatic potential functions and compare them with the conventional adiabatic electronic potentials, although the notion of the adiabatic potentials is not used in the extended MCTDHF approach. From the comparison, we conclude that by calculating the effective potentials we may be able to predict the energy differences among electronic states even for a time-dependent system, e.g., time-dependent excitation energies, which would be difficult to be estimated within the BH expansion approach.

A constrained Hartree-Fock-Bogoliubov equation derived from the double variational method

International Nuclear Information System (INIS)

Onishi, Naoki; Horibata, Takatoshi.

1980-01-01

The double variational method is applied to the intrinsic state of the generalized BCS wave function. A constrained Hartree-Fock-Bogoliubov equation is derived explicitly in the form of an eigenvalue equation. A method of obtaining approximate overlap and energy overlap integrals is proposed. This will help development of numerical calculations of the angular momentum projection method, especially for general intrinsic wave functions without any symmetry restrictions. (author)

Density-dependent Hartree-Fock response functions in quasi-elastic electron scattering on 12C and related sum rules

International Nuclear Information System (INIS)

Kohno, M.

1983-01-01

We report fully consistent calculations of the longitudinal and transverse response functions of the inclusive quasi-elastic electron scattering on 12 C in the Hartree-Fock approximation. The distorted wave for the outgoing nucleon is constructed from the same non-local Hartree-Fock field as in the ground-state description. Thus the orthogonality and Pauli principle requirements are naturally satisfied. The theoretical prediction, based on the standard density-dependent effective interaction (GO force), shows a good correspondence to the experimental data. Since the calculated response functions automatically satisfy the relevant sum rule, this work illuminates the well-known puzzle concerning the longitudinal part, which remains to be solved. We study the energy-weighted sum rules and discuss effects beyond the mean-field approximation. Meson-exchange-current contributions to the transverse response function are also estimated and found to be small due to cancellations among them. (orig.)

Method of renormalization potential for one model of Hartree-Fock-Slater type

CERN Document Server

Zasorin, Y V

2002-01-01

A new method of the potential renormalization for the quasiclassical model of the Hartree-Fock-Slater real potential is proposed. The method makes it possible to easily construct the wave functions and contrary to the majority od similar methods it does not require the knowledge of the real-type potential

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

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

Hartree-Fock implementation using a Laguerre-based wave function for the ground state and correlation energies of two-electron atoms.

Science.gov (United States)

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).

Hartree-Fock theory for the equilibrium shape of light nuclei; Theorie Hartree-Fock de la forme d'equilibre des noyaux legers

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 fonctions d'onde SU3 de J

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.)

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

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

Hartree-Fock theory for the equilibrium shape of light nuclei; Theorie Hartree-Fock de la forme d'equilibre des noyaux legers

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

Multiconfiguration Hartree-Fock calculations for complex atoms

International Nuclear Information System (INIS)

Fischer, C.F.

1984-01-01

The Hartree-Fock method has become a standard in atomic structure theory. Simpler methods are often compared with it when accessing their reliability or worth and the notion of correlation, which intuitively may be thought of as the correction needed to account for the fact that electrons do not move independently in a central field, is defined with respect to the Hartree-Fock method rather than some other independent-particle model. In fact, in an earlier article in this series, Fricke (Progress in Atomic Spectroscopy, Part A, Plenum Press (1978)), states, ''The so-called HF method is the basis of all good atomic calculations.'' In some sense, the Hartree-Fock method is the best method. The author briefly reviews its properties here. 67 references, 2 figures

Derivative discontinuity with localized Hartree-Fock potential

Energy Technology Data Exchange (ETDEWEB)

Nazarov, V. U. [Research Center for Applied Sciences, Academia Sinica, Taipei 11529, Taiwan (China); Vignale, G. [Department of Physics, University of Missouri-Columbia, Columbia, Missouri 65211 (United States)

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{sub ↑} and c{sub ↓} of the spin-components of the potential at integer particle numbers N{sub ↑} and N{sub ↓} satisfy the condition c{sub ↑}N{sub ↑} + c{sub ↓}N{sub ↓} = 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.

Positron and electron energy bands in several ionic crystals using restricted Hartree-Fock method

Science.gov (United States)

Kunz, A. B.; Waber, J. T.

1981-08-01

Using a restricted Hartree-Fock formalism and suitably localized and symmetrized wave functions, both the positron and electron energy bands were calculated for NaF, MgO and NiO. The lowest positron state at Γ 1 lies above the vacuum level and negative work functions are predicted. Positron annihilation rates were calculated and found to be in good agreement with measured lifetimes.

Time-dependent Hartree-Fock dynamics and phase transition in Lipkin-Meshkov-Glick model

International Nuclear Information System (INIS)

Kan, K.; Lichtner, P.C.; Dworzecka, M.; Griffin, J.J.

1980-01-01

The time-dependent Hartree-Fock solutions of the two-level Lipkin-Meshkov-Glick model are studied by transforming the time-dependent Hartree-Fock equations into Hamilton's canonical form and analyzing the qualitative structure of the Hartree-Fock energy surface in the phase space. It is shown that as the interaction strength increases these time-dependent Hartree-Fock solutions undergo a qualitative change associated with the ground state phase transition previously studied in terms of coherent states. For two-body interactions stronger than the critical value, two types of time-dependent Hartree-Fock solutions (the ''librations'' and ''rotations'' in Hamilton's mechanics) exist simultaneously, while for weaker interactions only the rotations persist. It is also shown that the coherent states with the maximum total pseudospin value are determinants, so that time-dependent Hartree-Fock analysis is equivalent to the coherent state method

Efficient, approximate and parallel Hartree-Fock and hybrid DFT calculations. A 'chain-of-spheres' algorithm for the Hartree-Fock exchange

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

Decomposition of the configuration-interaction coefficients in the multiconfiguration time-dependent Hartree-Fock method

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.

Hartree-Fock (HF) method and density functional theory calculations of Methanol to Gasoline (MTG) reaction

International Nuclear Information System (INIS)

Seddigi, Z.S.

2004-01-01

We found interesting results regarding some thermodynamical parameters (Delta H, Delta G and Delta S of the MTG Reaction and FTIR Spectra of methanol and dimethylether, using the Hartree-Fock method and Density Functional Theory (DFT) calculations at different computational levels. It is the aim of this paper to highlight these results. The GAUSSIAN 98 program was used to carry out the LCAO-MO-SCF calculations at the following levels: RHF/3-21g, RHF/6-31g and DFT/B3LYP/d95**. Calculations at the restricted Hartree-Fock levels (FHR/3-22 g and RHF/6-31g) were performed since they are expensive as other levels (DFT/B3LYP/d95**. In case of the HF method, working with larger basis set (6-31g) has improved the values slightly, which is as expected. We have noticed that performing calculations at higher levels (DFT/B3LY/D95**) than the Hartree-Fock method does not dramatically improve the situation. Indeed RHF is a reasonable approximation for many single gas phase molecular calculations. HF calculations at relatively small basis sets are adequate. The theoretical vibrational spectra of both methanol and dimethylether were compared with experimental results. (author)

Equilibration in the time-dependent Hartree-Fock approach probed with the Wigner distribution function

International Nuclear Information System (INIS)

Loebl, N.; Maruhn, J. A.; Reinhard, P.-G.

2011-01-01

By calculating the Wigner distribution function in the reaction plane, we are able to probe the phase-space behavior in the time-dependent Hartree-Fock scheme during a heavy-ion collision in a consistent framework. Various expectation values of operators are calculated by evaluating the corresponding integrals over the Wigner function. In this approach, it is straightforward to define and analyze quantities even locally. We compare the Wigner distribution function with the smoothed Husimi distribution function. Different reaction scenarios are presented by analyzing central and noncentral 16 O + 16 O and 96 Zr + 132 Sn collisions. Although we observe strong dissipation in the time evolution of global observables, there is no evidence for complete equilibration in the local analysis of the Wigner function. Because the initial phase-space volumes of the fragments barely merge and mean values of the observables are conserved in fusion reactions over thousands of fm/c, we conclude that the time-dependent Hartree-Fock method provides a good description of the early stage of a heavy-ion collision but does not provide a mechanism to change the phase-space structure in a dramatic way necessary to obtain complete equilibration.

Hartree--Fock time-dependent problem

Energy Technology Data Exchange (ETDEWEB)

Bove, A; Fano, G [Bologna Univ. (Italy). Istituto di Fisica; Istituto Nazionale di Fisica Nucleare, Bologna (Italy)); Da Prato, G [Rome Univ. (Italy). Istituto di Matematica

1976-06-01

A previous result is generalized. An existence and uniqueness theorem is proved for the Hartree--Fock time-dependent problem in the case of a finite Fermi system interacting via a two body potential which is supposed to be dominated by the kinetic energy part of the one-particle Hamiltonian.

Testing the multi-configuration time-dependent Hartree-Fock method

International Nuclear Information System (INIS)

Zanghellini, Juergen; Kitzler, Markus; Brabec, Thomas; Scrinzi, Armin

2004-01-01

We test the multi-configuration time-dependent Hartree-Fock method as a new approach towards the numerical calculation of dynamical processes in multi-electron systems using the harmonic quantum dot and one-dimensional helium in strong laser pulses as models. We find rapid convergence for quantities such as ground-state population, correlation coefficient and single ionization towards the exact results. The method converges, where the time-dependent Hartree-Fock method fails qualitatively

Constant resolution of time-dependent Hartree--Fock phase ambiguity

International Nuclear Information System (INIS)

Lichtner, P.C.; Griffin, J.J.; Schultheis, H.; Schultheis, R.; Volkov, A.B.

1978-01-01

The customary time-dependent Hartree--Fock problem is shown to be ambiguous up to an arbitrary function of time additive to H/sub HF/, and, consequently, up to an arbitrary time-dependent phase for the solution, PHI(t). The ''constant'' (H)'' phase is proposed as the best resolution of this ambiguity. It leads to the following attractive features: (a) the time-dependent Hartree--Fock (TDHF) Hamiltonian, H/sub HF/, becomes a quantity whose expectation value is equal to the average energy and, hence, constant in time; (b) eigenstates described exactly by determinants, have time-dependent Hartree--Fock solutions identical with the exact time-dependent solutions; (c) among all possible TDHF solutions this choice minimizes the norm of the quantity (H--i dirac constant delta/delta t) operating on the ket PHI, and guarantees optimal time evolution over an infinitesimal period; (d) this choice corresponds both to the stationary value of the absolute difference between (H) and (i dirac constant delta/delta t) and simultaneously to its absolute minimal value with respect to choice of the time-dependent phase. The source of the ambiguity is discussed. It lies in the time-dependent generalization of the freedom to transform unitarily among the single-particle states of a determinant at the (physically irrelevant for stationary states) cost of altering only a factor of unit magnitude

Spatial and Spin Symmetry Breaking in Semidefinite-Programming-Based Hartree-Fock Theory.

Science.gov (United States)

Nascimento, Daniel R; DePrince, A Eugene

2018-05-08

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.

Genealogical electronic coupling procedure incorporating the Hartree--Fock interacting space and suitable for degenerate point groups. Application to excited states of BH3

International Nuclear Information System (INIS)

Swope, W.C.; Schaefer, H.F. III; Yarkony, D.R.

1980-01-01

The use of Clebsch--Gordan-type coupling coefficients for finite point groups is applied to the problem of constructing symmetrized N-electron wave functions (configurations) for use by the Hartree--Fock SCF and CI methods of determining electronic wave functions for molecular systems. The configurations are eigenfunctions of electronic spin operators, and transform according to a particular irreducible representation of the relevant group of spatial operations which leave the Born--Oppenheimer Hamiltonian invariant. The method proposed for constructing the configurations involves a genealogical coupling procedure. It is particularly useful for studies of molecules which belong to a group which has multiply degenerate irreducible representations. The advantage of the method is that it results in configurations which are real linear combinations of determinants of real symmetry orbitals. This procedure for constructing configurations also allows for the identification of configurations which have no matrix element of the Hamiltonian with a reference configuration. It is therefore possible to construct a Hartree--Fock interacting space of configurations which can speed the convergence of a CI wave function. The coupling method is applied to a study of the ground and two excited electronic states of BH 3 in its D/sub 3h/ geometry. The theoretical approach involved Hartree--Fock SCF calculations followed by single and double substitution CI calculations, both of which employed double-zeta plus polarization quality basis sets

Study on formalism of Griffin-Wheeler-Hartree-Fock equations and a propose for its variational discretization; Estudo sobre o formalismo das equacoes Griffin-Wheeler-Hartree-Fock e uma proposta para sua discretizacao variacional

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

Matrix Methods for Solving Hartree-Fock Equations in Atomic Structure Calculations and Line Broadening

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.

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

The total Hartree-Fock energy-eigenvalue sum relationship in atoms

International Nuclear Information System (INIS)

Sen, K.D.

1979-01-01

Using the well known relationships for the isoelectronic changes in the total Hartree-Fock energy, nucleus-electron attraction energy and electron-electron repulsion energy in atoms a simple polynomial expansion in Z is obtained for the sum of the eigenvalues which can be used to calculate the total Hartree-Fock energy. Numerical results are presented for 2-10 electron series to show that the present relationship is a better approximation than the other available energy-eigenvalue relationships. (author)

A finite difference Hartree-Fock program for atoms and diatomic molecules

Science.gov (United States)

Kobus, Jacek

2013-03-01

. The lowest energy eigenstates of a given irreducible representation and spin can be obtained. The program can be used to perform one-particle calculations with (smooth) Coulomb and Krammers-Henneberger potentials and also DFT-type calculations using LDA or B88 exchange functionals and LYP or VWN correlations ones or the self-consistent multiplicative constant method. Solution method: Single-particle two-dimensional numerical functions (orbitals) are used to construct an antisymmetric many-electron wave function of the restricted open-shell Hartree-Fock model. The orbitals are obtained by solving the Hartree-Fock equations as coupled two-dimensional second-order (elliptic) partial differential equations (PDEs). The Coulomb and exchange potentials are obtained as solutions of the corresponding Poisson equations. The PDEs are discretized by the eighth-order central difference stencil on a two-dimensional single grid, and the resulting large and sparse system of linear equations is solved by the (multicolour) successive overrelaxation ((MC)SOR) method. The self-consistent-field iterations are interwoven with the (MC)SOR ones and orbital energies and normalization factors are used to monitor the convergence. The accuracy of solutions depends mainly on the grid and the system under consideration, which means that within double precision arithmetic one can obtain orbitals and energies having up to 12 significant figures. If more accurate results are needed, quadruple-precision floating-point arithmetic can be used. Reasons for new version: Additional features, many modifications and corrections, improved convergence rate, overhauled code and documentation. Summary of revisions: see ChangeLog found in tar.gz archive Restrictions: The present version of the program is restricted to 60 orbitals. The maximum grid size is determined at compilation time. Unusual features: The program uses two C routines for allocating and deallocating memory. Several BLAS (Basic Linear Algebra

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

Parallel scalability of Hartree-Fock calculations

Science.gov (United States)

Chow, Edmond; Liu, Xing; Smelyanskiy, Mikhail; Hammond, Jeff R.

2015-03-01

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.

Study on formalism of Griffin-Wheeler-Hartree-Fock equations and a propose for its variational discretization

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

Tensor numerical methods in quantum chemistry: from Hartree-Fock to excitation energies.

Science.gov (United States)

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.

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....

Accuracy of the Hartree-Fock and local density approximations for electron densities: a study for light atoms

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.)

Instability of the cranked Hartree-Fock-Bogoliubov field in backbending region

International Nuclear Information System (INIS)

Horibata, Takatoshi; Onishi, Naoki.

1982-01-01

The stability condition of the cranked Hartree-Fock-Bogoliubov field is examined explicitly by solving the eigenvalue equation for the second order variation of the energy, which is reduced to an algebraic equation through a coupled dispersion formula. We confirm that the Hartree-Fock-Bogoliubov field is unstable in the backbending region of an irregular rotational band, even though the frequency of the softest random phase approximation mode always has a positive value. We investigate properties of the softest mode in detail. (author)

Application of the resonating Hartree-Fock random phase approximation to the Lipkin model

International Nuclear Information System (INIS)

Nishiyama, S.; Ishida, K.; Ido, M.

1996-01-01

We have applied the resonating Hartree-Fock (Res-HF) approximation to the exactly solvable Lipkin model by utilizing a newly developed orbital-optimization algorithm. The Res-HF wave function was superposed by two Slater determinants (S-dets) which give two corresponding local energy minima of monopole ''deformations''. The self-consistent Res-HF calculation gives an excellent ground-state correlation energy. There exist excitations due to small vibrational fluctuations of the orbitals and mixing coefficients around their stationary values. They are described by a new approximation called the resonating Hartree-Fock random phase approximation (Res-HF RPA). Matrices of the second-order variation of the Res-HF energy have the same structures as those of the Res-HF RPA's matrices. The quadratic steepest descent of the Res-HF energy in the orbital optimization is considered to include certainly both effects of RPA-type fluctuations up to higher orders and their mode-mode couplings. It is a very important and interesting task to apply the Res-HF RPA to the Lipkin model with the use of the stationary values and to prove the above argument. It turns out that the Res-HF RPA works far better than the usual HF RPA and the renormalized one. We also show some important features of the Res-HF RPA. (orig.)

Time-Dependent Hartree-Fock Approach to Nuclear Pasta at Finite Temperature

International Nuclear Information System (INIS)

Schuetrumpf, B; Maruhn, J A; Klatt, M A; Mecke, K; Reinhard, P-G; Iida, K

2013-01-01

We present simulations of neutron-rich matter at subnuclear densities, like supernova matter, with the time-dependent Hartree-Fock approximation at temperatures of several MeV. The initial state consists of α particles randomly distributed in space that have a Maxwell-Boltzmann distribution in momentum space. Adding a neutron background initialized with Fermi distributed plane waves the calculations reflect a reasonable approximation of astrophysical matter. This matter evolves into spherical, rod-like, and slab-like shapes and mixtures thereof. The simulations employ a full Skyrme interaction in a periodic three-dimensional grid. By an improved morphological analysis based on Minkowski functionals, all eight pasta shapes can be uniquely identified by the sign of only two valuations, namely the Euler characteristic and the integral mean curvature.

Time-Dependent Hartree-Fock Approach to Nuclear Pasta at Finite Temperature

Science.gov (United States)

Schuetrumpf, B.; Klatt, M. A.; Iida, K.; Maruhn, J. A.; Mecke, K.; Reinhard, P.-G.

2013-03-01

We present simulations of neutron-rich matter at subnuclear densities, like supernova matter, with the time-dependent Hartree-Fock approximation at temperatures of several MeV. The initial state consists of α particles randomly distributed in space that have a Maxwell-Boltzmann distribution in momentum space. Adding a neutron background initialized with Fermi distributed plane waves the calculations reflect a reasonable approximation of astrophysical matter. This matter evolves into spherical, rod-like, and slab-like shapes and mixtures thereof. The simulations employ a full Skyrme interaction in a periodic three-dimensional grid. By an improved morphological analysis based on Minkowski functionals, all eight pasta shapes can be uniquely identified by the sign of only two valuations, namely the Euler characteristic and the integral mean curvature.

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

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

Oscillator strength of partially ionized high-Z atom on Hartree-Fock Slater model

International Nuclear Information System (INIS)

Nakamura, S.; Nishikawa, T.; Takabe, H.; Mima, K.

1991-01-01

The Hartree-Fock Slater (HFS) model has been solved for the partially ionized gold ions generated when an intense laser light is irradiated on a gold foil target. The resultant energy levels are compared with those obtained by a simple screened hydrogenic model with l-splitting effect (SHML). It is shown that the energy levels are poorly model by SHML as the ionization level becomes higher. The resultant wave functions are used to evaluate oscillator strength of important line radiations and compared with those obtained by a simple model using hydrogenic wave functions. Its demonstrated that oscillator strength of the 4p-4d and 4d-4f lines are well modeled by the simple method, while the 4-5 transitions such as 4f-5g, 4d-5f, 4p-5d, and 4f-5p forming the so-called N-band emission are poorly modeled and HFS results less strong line emissions. (author)

A study of self-consistent Hartree-Fock plus Bardeen-Cooper-Schrieffer calculations with finite-range interactions

Science.gov (United States)

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.

Finite-temperature coupled-cluster, many-body perturbation, and restricted and unrestricted Hartree-Fock study on one-dimensional solids: Luttinger liquids, Peierls transitions, and spin- and charge-density waves.

Science.gov (United States)

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.

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

Semiclassical expansions of the nuclear relativistic Hartree-Fock theory

International Nuclear Information System (INIS)

Weigel, M.K.; Haddad, S.

1991-01-01

Semiclassical expansions for Green functions, self-energy, phase-space density and density are given and discussed. The many-body problem was treated in the relativistic Hartree-Fock approximation with a Lagrangian with a standard OBE potential structure including the possibility of space-dependent couplings. The expansions are obtained by formulating the many-body problem in the mixed position-momentum (Wigner) representation and application of the (h/2π)-Wigner-Kirkwood expansion scheme. The resulting self-consistency problems for the zeroth and second order are formulated in three versions. (author)

Time-dependent Hartree-Fock approach to nuclear ``pasta'' at finite temperature

Science.gov (United States)

Schuetrumpf, B.; Klatt, M. A.; Iida, K.; Maruhn, J. A.; Mecke, K.; Reinhard, P.-G.

2013-05-01

We present simulations of neutron-rich matter at subnuclear densities, like supernova matter, with the time-dependent Hartree-Fock approximation at temperatures of several MeV. The initial state consists of α particles randomly distributed in space that have a Maxwell-Boltzmann distribution in momentum space. Adding a neutron background initialized with Fermi distributed plane waves the calculations reflect a reasonable approximation of astrophysical matter. This matter evolves into spherical, rod-like, and slab-like shapes and mixtures thereof. The simulations employ a full Skyrme interaction in a periodic three-dimensional grid. By an improved morphological analysis based on Minkowski functionals, all eight pasta shapes can be uniquely identified by the sign of only two valuations, namely the Euler characteristic and the integral mean curvature. In addition, we propose the variance in the cell density distribution as a measure to distinguish pasta matter from uniform matter.

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.

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.

Multiconfiguration hartree-fock theory for pseudorelativistic systems: The time-dependent case

KAUST Repository

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.

Hartree-Fock-Bogoliubov model: a theoretical and numerical perspective

International Nuclear Information System (INIS)

Paul, S.

2012-01-01

This work is devoted to the theoretical and numerical study of Hartree-Fock-Bogoliubov (HFB) theory for attractive quantum systems, which is one of the main methods in nuclear physics. We first present the model and its main properties, and then explain how to get numerical solutions. We prove some convergence results, in particular for the simple fixed point algorithm (sometimes called Roothaan). We show that it converges, or oscillates between two states, none of them being a solution. This generalizes to the HFB case previous results of Cances and Le Bris for the simpler Hartree-Fock model in the repulsive case. Following these authors, we also propose a relaxed constraint algorithm for which convergence is guaranteed. In the last part of the thesis, we illustrate the behavior of these algorithms by some numerical experiments. We first consider a system where the particles only interact through the Newton potential. Our numerical results show that the pairing matrix never vanishes, a fact that has not yet been proved rigorously. We then study a very simplified model for protons and neutrons in a nucleus. (author)

Dispersion correction derived from first principles for density functional theory and Hartree-Fock theory.

Science.gov (United States)

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.

Analysis of the half-projected Hartree--Fock function: density matrix, natural orbitals, and configuration interaction equivalence

International Nuclear Information System (INIS)

Smeyers, Y.G.; Delgado-Barrio, G.

1976-01-01

The half-projected Hartree--Fock function for singlet states (HPHF) is analyzed in terms of natural electronic configurations. For this purpose the HPHF spinless density matrix and its natural orbitals are first deduced. It is found that the HPHF function does not contain any contribution from odd-times excited configurations. It is seen in addition, in the case of the singlet ground states, this function is approximately equivalent to two closed-shell configurations, although the nature of the excited one depends on the nuclear geometry. An example is given in the case of the LiH ground state. Finally, the application of this model for studying systems of more than two atoms is criticized

General multi-configuration Hartree--Fock program: MCHF77

International Nuclear Information System (INIS)

Fischer, C.F.

1977-11-01

This technical report contains a listing of a general program for multi-configuration Hartree--Fock (MCHF) calculations, including its documentation. Several examples are given showing how the program may be used. Typical output for several cases is also presented. This program has been tested over an extended period of time for a large variety of cases. This program is written for the IBM 360 or 370 in double-precision arithmetic

Molecular Structure And Vibrational Frequencies of Tetrafluoro isophthalonitrile By Hartree-Fock And Density Functional Theory Calculations

International Nuclear Information System (INIS)

Ayikoglu, A.

2008-01-01

The molecular structure, vibrational frequencies and corresponding vibrational assignments of tetrafluoro isophthalonitrile (TFPN) in the ground state have been calculated using the Hartree-Fock (HF) and density functional methods (B3LYP) with 6-311++G (d, p) basis set. The calculations were utilized in the CS symmetry of TFPN. The obtained vibrational frequencies and optimized geometric parameters (bond lengths and bond angles) were seen to be in good agreement with the experimental data. The comparison of the observed and calculated results showed that the B3LYP method is superior to the HF method for both the vibrational frequencies and geometric parameters

Damping of monopole vibrations in time dependent Hartree-Fock theory

International Nuclear Information System (INIS)

Vautherin, D.; Stringari, S.

1979-01-01

Monopole vibrations in oxygen-16 and calcium-40 have been investigated in time-dependent Hartree-Fock theory. The characteristic damping time obtained is tau approximately 1.5x10 -22 sec. This value is in good agreement with the width of the monopole mode calculated in the random phase approximation

Cluster modeling of solid state defects and adsorbates: Beyond the Hartree-Fock level

International Nuclear Information System (INIS)

Kunz, A.B.

1990-01-01

The use of finite clusters of atoms to represent the physically interesting portion of a condensed matter system has been an accepted technique for the past two decades. Physical systems have been studied in this way using both density functional and Hartree-Fock methodologies, as well as a variety of empirical or semiempirical techniques. In this article, the author concentrates on the Hartree-Fock based methods. The attempt here is to construct a theoretical basis for the inclusion of correlation corrections in such an approach, as well as a strategy by which the limits of a finite cluster may be transcended in such a study. The initial appeal will be to a modeling approach, but methods to convert the model to a self-contained theory will be described. It will be seen for the case of diffusion of large ions in solids that such an approach is quite useful. A further study of the case of adsorption of rare gas atoms on simple metals will demonstrate the value of inclusion of electron correlation

The time-dependent Hartree-Fock equations with Coulomb two-body interaction

International Nuclear Information System (INIS)

Chadam, J.M.; Glassey, R.T.

1975-06-01

The existence and uniqueness of global solutions to the Cauchy problem is proved in the space of ''smooth'' density matrices for the time-dependent Hartree-Fock equations describing the motion of finite Fermi systems interacting via a Coulomb two-body potential [fr

Spin contamination analogy, Kramers pairs symmetry and spin density representations at the 2-component unrestricted Hartree-Fock level of theory

KAUST Repository

Bučinský , Luká š; Malček, Michal; Biskupič, Stanislav; Jayatilaka, Dylan; Bü chel, Gabriel E.; Arion, Vladimir B.

2015-01-01

"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

Obtaining Hartree-Fock and density functional theory doubly excited states with Car-Parrinello density matrix search

Science.gov (United States)

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.

Wave functions and two-electron probability distributions of the Hooke's-law atom and helium

International Nuclear Information System (INIS)

O'Neill, Darragh P.; Gill, Peter M. W.

2003-01-01

The Hooke's-law atom (hookium) provides an exactly soluble model for a two-electron atom in which the nuclear-electron Coulombic attraction has been replaced by a harmonic one. Starting from the known exact position-space wave function for the ground state of hookium, we present the momentum-space wave function. We also look at the intracules, two-electron probability distributions, for hookium in position, momentum, and phase space. These are compared with the Hartree-Fock results and the Coulomb holes (the difference between the exact and Hartree-Fock intracules) in position, momentum, and phase space are examined. We then compare these results with analogous results for the ground state of helium using a simple, explicitly correlated wave function

Spin contamination analogy, Kramers pairs symmetry and spin density representations at the 2-component unrestricted Hartree-Fock level of theory

KAUST Repository

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

Dirac-Hartree-Fock studies of X-ray transitions in meitnerium

International Nuclear Information System (INIS)

Thierfelder, C.; Schwerdtfeger, P.; Hessberger, F.P.; Hofmann, S.

2008-01-01

The K -shell and L -shell ionizations potentials for 268 109 Mt were calculated at the Dirac-Hartree-Fock level taking into account quantum electrodynamic and finite nuclear-size effects. The K α1 transition energies for different ionization states are accurately predicted and compared with recent experiments in the α -decay of 272 111 Rg. (orig.)

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 Swiatecki’s 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.

Comparison of model Hartree-Fock type calculation schemes involving various non-degenerate and quasi-degenerate intrinsic Hamiltonians

International Nuclear Information System (INIS)

Amusa, A.

1983-03-01

Different Hamiltonians and their corresponding rotationally degenerate intrinsic counterparts are employed in the study of 18 O nucleus under the normal Hartree-Fock, as well as under six other Hartree-Fock type variational calculation schemes. The results are compared and then assessed in the light of their closeness or otherwise to the full 1s-0d basis shell model calculations for this nucleus. The use of these schemes for other shells is also considered. (author)

Hartree-Fock-Bogolubov approximation in the models with general four-fermion interaction

International Nuclear Information System (INIS)

Bogolubov, N.N. Jr.; Soldatov, A.V.

1995-12-01

The foundation of this work was established by the lectures of Prof. N.N. Bogolubov (senior) written in the beginning of 1990. We should like to develop some of his ideas connected with Hartree-Fock-Bogolubov method and to show how this approximation works in connection with general equations for Green's functions with source terms for sufficiently general model Hamiltonian of four-fermion interaction type and how, for example, to get some results of superconductivity theory by means of this method. (author). 5 refs

Ab initio calculation atomics ground state wave function for interactions Ion- Atom

International Nuclear Information System (INIS)

Shojaee, F.; Bolori zadeh, M. A.

2007-01-01

Ab initio calculation atomics ground state wave function for interactions Ion- Atom Atomic wave function expressed in a Slater - type basis obtained within Roothaan- Hartree - Fock for the ground state of the atoms He through B. The total energy is given for each atom.

Uniform in N global well-posedness of the time-dependent Hartree-Fock-Bogoliubov equations in R^{1+1}

Science.gov (United States)

Chong, Jacky Jia Wei

2018-04-01

We prove the global well-posedness of the time-dependent Hartree-Fock-Bogoliubov (TDHFB) equations in R^{1+1} with two-body interaction potential of the form N^{-1}v_N(x) = N^{β -1} v(N^β x) where v≥0 is a sufficiently regular radial function, i.e., v \\in L^1(R)\\cap C^∞ (R) . In particular, using methods of dispersive PDEs similar to the ones used in Grillakis and Machedon (Commun Partial Differ Equ 42:24-67, 2017), we are able to show for any scaling parameter β >0 the TDHFB equations are globally well-posed in some Strichartz-type spaces independent of N, cf. (Bach et al. in The time-dependent Hartree-Fock-Bogoliubov equations for Bosons, 2016. arXiv:1602.05171).

The spectrum of 12C in a multi-configuration Hartree-Fock Basis

International Nuclear Information System (INIS)

Amos, K.; Morrison, I.; Smith, R.; Schmid, K.W.

1981-01-01

The energy level spectrum of 12 C is calculated in a truncated but large shell model space of projected one particle-one hole Hartree Fock determinants using a realistic G-matrix. Predictions of electromagnetic decays and electron scattering form factors are compared with experimental values

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

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

Dynamic and static correlation functions in the inhomogeneous Hartree-Fock-state approach with random-phase-approximation fluctuations

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

Equivalence of classical spins and Hartree-Fock-Bogoliubov approximation of the Fermionic Anharmonic Oscillator

International Nuclear Information System (INIS)

Thomaz, M.T.; Toledo Piza, A.F.R. de

1994-01-01

We show that the Hartree-Fock-Bogoliubov (alias Gaussian) approximation of the initial condition problem of the Fermionic Anharmonic Oscillator i equivalent to a bosonic Hamiltonian system of two classical spin. (author)

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

Relativity and pseudopotentials in the Hartree-Fock-Slater method

International Nuclear Information System (INIS)

Snijders, J.G.

1979-01-01

The methodological problems involved in electronic structure determinations of compounds containing heavy elements by the Hartree-Fock-Slater scheme are investigated. It is shown that the effect of the inner electrons can be simulated by a so called pseudopotential, so that only the valence electrons have to be treated explicitly which constitutes a considerable reduction of computation time. It is further shown that a pseudopotential calculation is able to achieve an accuracy that is comparable to the results of a calculation including the core. (Auth.)

Approximate relativistic corrections to atomic radial wave functions

International Nuclear Information System (INIS)

Cowan, R.D.; Griffin, D.C.

1976-01-01

The mass-velocity and Darwin terms of the one-electron-atom Pauli equation have been added to the Hartree-Fock differential equations by using the HX formula to calculate a local central field potential for use in these terms. Introduction of the quantum number j is avoided by omitting the spin-orbit term of the Pauli equation. The major relativistic effects, both direct and indirect, are thereby incorporated into the wave functions, while allowing retention of the commonly used nonrelativistic formulation of energy level calculations. The improvement afforded in calculated total binding energies, excitation energies, spin-orbit parameters, and expectation values of r/sub m/ is comparable with that provided by fully relativistic Dirac-Hartree-Fock calculations

Self-consistent Hartree-Fock RPA calculations in 208Pb

Science.gov (United States)

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.

A Hartree-Fock-Slater-Boltzmann-Saha method for detailed atomic structure and equation of state of plasmas

International Nuclear Information System (INIS)

Jiang Minhao; Meng Xujun

2005-01-01

The effect of the free electron background in plasmas is introduced in Hartree-Fock-Slater self-consistent field atomic model to correct the single electron energies for each electron configuration, and to provide accurate atomic data for Boltzmann-Saha equation. In the iteration process chemical potential is adjusted to change the free electron background to satisfy simultaneously the conservation of the free electrons in Saha equation as well as in Hartree-Fock-Slater self-consistent field atomic model. As examples the equations of state of the carbon and aluminum plasmas are calculated to show the applicability of this method. (authors)

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

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

Vibrational spectroscopic investigation of p-, m- and o-nitrobenzonitrile by using Hartree-Fock and density functional theory

Science.gov (United States)

Sert, Y.; Ucun, F.

2013-08-01

In the present work, the theoretical vibrational spectra of p-, m- and o-nitrobenzonitrile molecules have been analyzed. The harmonic vibrational frequencies and geometric parameters (bond lengths and bond angles) of these molecules have been calculated using ab initio Hartree-Fock and density functional theory methods with 6-311++G(d,p) basis set by Gaussian 03 W, for the first time. Assignments of the vibrational frequencies have been performed by potential energy distribution by using VEDA 4 program. The optimized geometric parameters and harmonic vibrational frequencies have been compared with the corresponding experimental data and seen to be in a good agreement with each other. Also, the highest occupied molecular orbital and lowest unoccupied molecular orbital energies have been obtained.

Fractional quantum Hall effect: Construction of the Hartree-Fock state by using translational covariance

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

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

The role of the form factor and short-range correlation in the relativistic Hartree-Fock model for nuclear matter

Science.gov (United States)

Hu, J.; Toki, H.; Wen, W.; Shen, H.

2010-03-01

The role of the form factor and short-range correlation in nuclear matter is studied within the relativistic Hartree-Fock approximation. We take, first, the mean-field approximation for meson fields and obtain the fluctuation terms of mesons to be used for the Fock energies. We introduce form factors in the meson-nucleon coupling vertices to take into account the finite-size effect of the nucleon. We use further the unitary correlation operator method for the treatment of the short-range correlation. The form factors of the size ( Λ ˜ 1.0 -2.0GeV) of the nucleon-nucleon interaction cut down largely the contribution of the ρ -meson in the Fock term. The short-range correlation effect is not large but has a significant effect on the pion and ρ -meson energies in the relativistic Hartree-Fock approximation for nuclear matter.

Nuclear Pasta at Finite Temperature with the Time-Dependent Hartree-Fock Approach

Science.gov (United States)

Schuetrumpf, B.; Klatt, M. A.; Iida, K.; Maruhn, J. A.; Mecke, K.; Reinhard, P.-G.

2016-01-01

We present simulations of neutron-rich matter at sub-nuclear densities, like supernova matter. With the time-dependent Hartree-Fock approximation we can study the evolution of the system at temperatures of several MeV employing a full Skyrme interaction in a periodic three-dimensional grid [1]. The initial state consists of α particles randomly distributed in space that have a Maxwell-Boltzmann distribution in momentum space. Adding a neutron background initialized with Fermi distributed plane waves the calculations reflect a reasonable approximation of astrophysical matter. The matter evolves into spherical, rod-like, connected rod-like and slab-like shapes. Further we observe gyroid-like structures, discussed e.g. in [2], which are formed spontaneously choosing a certain value of the simulation box length. The ρ-T-map of pasta shapes is basically consistent with the phase diagrams obtained from QMD calculations [3]. By an improved topological analysis based on Minkowski functionals [4], all observed pasta shapes can be uniquely identified by only two valuations, namely the Euler characteristic and the integral mean curvature. In addition we propose the variance in the cell-density distribution as a measure to distinguish pasta matter from uniform matter.

Nuclear Pasta at Finite Temperature with the Time-Dependent Hartree-Fock Approach

International Nuclear Information System (INIS)

Schuetrumpf, B; Maruhn, J A; Klatt, M A; Mecke, K; Reinhard, P-G; Iida, K

2016-01-01

We present simulations of neutron-rich matter at sub-nuclear densities, like supernova matter. With the time-dependent Hartree-Fock approximation we can study the evolution of the system at temperatures of several MeV employing a full Skyrme interaction in a periodic three-dimensional grid [1].The initial state consists of α particles randomly distributed in space that have a Maxwell-Boltzmann distribution in momentum space. Adding a neutron background initialized with Fermi distributed plane waves the calculations reflect a reasonable approximation of astrophysical matter.The matter evolves into spherical, rod-like, connected rod-like and slab-like shapes. Further we observe gyroid-like structures, discussed e.g. in [2], which are formed spontaneously choosing a certain value of the simulation box length. The ρ-T-map of pasta shapes is basically consistent with the phase diagrams obtained from QMD calculations [3]. By an improved topological analysis based on Minkowski functionals [4], all observed pasta shapes can be uniquely identified by only two valuations, namely the Euler characteristic and the integral mean curvature.In addition we propose the variance in the cell-density distribution as a measure to distinguish pasta matter from uniform matter. (paper)

Molecular Structure And Vibrational Frequencies of 2,3,4 Nitro anilines By Hartree-Fock And Density Functional Theory Calculations

International Nuclear Information System (INIS)

Sert, Y.

2008-01-01

The optimised molecular structure, vibrational frequencies and corresponding vibrational assignments of 2-, 3- and 4- nitro anilines have been calculated using the Hartree-Fock (HF) and density functional methods (B3LYP) with 6-311++G (d, p) basis set. The calculations were adapted to the C S symmetries of all the molecules. The calculated vibrational frequencies and geometric parameters (bond lengths and bond angles) were seen to be in good agreement with the experimental data. The comparison of the experimental and theoretical results showed that the HF method is superior to the B3LYP method for both the vibrational frequencies and geometric parameters

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.

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

Dispersion corrected hartree-fock and density functional theory for organic crystal structure prediction.

Science.gov (United States)

Brandenburg, Jan Gerit; Grimme, Stefan

2014-01-01

We present and evaluate dispersion corrected Hartree-Fock (HF) and Density Functional Theory (DFT) based quantum chemical methods for organic crystal structure prediction. The necessity of correcting for missing long-range electron correlation, also known as van der Waals (vdW) interaction, is pointed out and some methodological issues such as inclusion of three-body dispersion terms are discussed. One of the most efficient and widely used methods is the semi-classical dispersion correction D3. Its applicability for the calculation of sublimation energies is investigated for the benchmark set X23 consisting of 23 small organic crystals. For PBE-D3 the mean absolute deviation (MAD) is below the estimated experimental uncertainty of 1.3 kcal/mol. For two larger π-systems, the equilibrium crystal geometry is investigated and very good agreement with experimental data is found. Since these calculations are carried out with huge plane-wave basis sets they are rather time consuming and routinely applicable only to systems with less than about 200 atoms in the unit cell. Aiming at crystal structure prediction, which involves screening of many structures, a pre-sorting with faster methods is mandatory. Small, atom-centered basis sets can speed up the computation significantly but they suffer greatly from basis set errors. We present the recently developed geometrical counterpoise correction gCP. It is a fast semi-empirical method which corrects for most of the inter- and intramolecular basis set superposition error. For HF calculations with nearly minimal basis sets, we additionally correct for short-range basis incompleteness. We combine all three terms in the HF-3c denoted scheme which performs very well for the X23 sublimation energies with an MAD of only 1.5 kcal/mol, which is close to the huge basis set DFT-D3 result.

The role of the form factor and short-range correlation in the relativistic Hartree-Fock model for nuclear matter

International Nuclear Information System (INIS)

Hu, J.; Toki, H.; Wen, W.; Shen, H.

2010-01-01

The role of the form factor and short-range correlation in nuclear matter is studied within the relativistic Hartree-Fock approximation. We take, first, the mean-field approximation for meson fields and obtain the fluctuation terms of mesons to be used for the Fock energies. We introduce form factors in the meson-nucleon coupling vertices to take into account the finite-size effect of the nucleon. We use further the unitary correlation operator method for the treatment of the short-range correlation. The form factors of the size (Λ∝1.0 -2.0 GeV) of the nucleon-nucleon interaction cut down largely the contribution of the ρ-meson in the Fock term. The short-range correlation effect is not large but has a significant effect on the pion and ρ-meson energies in the relativistic Hartree-Fock approximation for nuclear matter. (orig.)

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

On the problem of representability and the Bogolyubov-Hartree-Fock theory

International Nuclear Information System (INIS)

Knoerr, Hans Konrad

2013-01-01

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

Contribution to the projected Hartree-Fock method and microscopic theory of coupling between rotation bands

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

Ground state hydrogen conformations and vibrational analysis of 1,2-dihdroxyanthraquinone (alizarin) molecule by AB initio Hartree-Fock and density functional theory calculations

International Nuclear Information System (INIS)

Delta, E.; Ucun, F.; Saglam, A.

2010-01-01

The ground state hydrogen conformations of 1,2-dihydroxyanthraquinone (alizarin) molecule have been investigated using ab initio Hartree-Fock (HF) and density functional theory (B3LYP) methods with 6-31G(d,p) basis set. The calculations indicate that the compound in the ground state exist with the doubly bonded O atom linked intra molecularly by the two hydrogen bonds. The vibrational analyses of the ground state conformation of the compound were also made and its optimized geometry parameters were given.

Hartree-Fock calculation of nuclear binding energy of sodium isotopes

International Nuclear Information System (INIS)

Campi, X.; Flocard, H.

1975-01-01

Mass spectrometer measurements of the neutron rich sodium isotopes show a sudden increase at 31 Na in the values of the two neutron separation energies. The spherical shell model naturally predicts a sudden decrease at 32 Na after the N=20 shell closure. It is proposed that the explanation for this disagreement lies in the fact that sodium isotopes in this mass region are strongly deformed due to the filling of negative parity orbitals from the 1f(7/2) shell. Hartree-Fock calculations are presented in support of this conjecture [fr

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.)

Influence of the Dirac-Hartree-Fock starting potential on the parity-nonconserving electric-dipole-transition amplitudes in cesium and thallium

Science.gov (United States)

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.

Basic and heavy ion scattering in time dependent Hartree-Fock Theory

International Nuclear Information System (INIS)

Weiss, M.S.

1984-01-01

Time Dependent Hartree-Fock theory, TDHF, is the most sophisticated, microscopic approach to nuclear dynamics yet practiced. Although it is far from a description of nature it does allow us to examine multiply interactive many-body systems semi quantum mechanically and to visualize otherwise covert processes. Some of the properties of the TDHF equations are stated leaving the interested reader to one of several excellent review articles for the derivations. Some of the applications to the collision of heavy ions are briefly described

Electronic correlation without double counting via a combination of spin projected Hartree-Fock and density functional theories

Energy Technology Data Exchange (ETDEWEB)

Garza, Alejandro J.; Jiménez-Hoyos, Carlos A. [Department of Chemistry, Rice University, Houston, Texas 77251-1892 (United States); Scuseria, Gustavo E. [Department of Chemistry and Department of Physics and Astronomy, Rice University, Houston, Texas 77251-1892, USA and Chemistry Department, Faculty of Science, King Abdulaziz University, Jeddah 21589 (Saudi Arabia)

2014-06-28

Several schemes to avoid the double counting of correlations in methods that merge multireference wavefunctions with density functional theory (DFT) are studied and here adapted to a combination of spin-projected Hartree-Fock (SUHF) and DFT. The advantages and limitations of the new method, denoted SUHF+f{sub c}DFT, are explored through calculations on benchmark sets in which the accounting of correlations is challenging for pure SUHF or DFT. It is shown that SUHF+f{sub c}DFT can greatly improve the description of certain molecular properties (e.g., singlet-triplet energy gaps) which are not improved by simple addition of DFT dynamical correlation to SUHF. However, SUHF+f{sub c}DFT is also shown to have difficulties dissociating certain types of bonds and describing highly charged ions with static correlation. Possible improvements to the current SUHF+f{sub c}DFT scheme are discussed in light of these results.

Classic Multi-Configuration-Dirac-Fock and Hartree-Fock-Relativistic methods integrated into a program package for the RAL-IBM mainframe with automatic comparative output

International Nuclear Information System (INIS)

Cowan, R.D.; Grant, I.P.; Fawcett, B.C.; Rose, S.J.

1985-11-01

A Multi-Configuration-Dirac-Fock (MCDF) computer program is adapted to interface with the Hartree-Fock-Relativistic (HFR) program for the RAL IBM mainframe computer. The two codes are integrated into a package which includes the Zeeman Laboratory Slater parameter optimisation routines as well as new RAL routines to further process the HFR and MCDF output. A description of the adaptions to MCDF and new output extensions is included in this report, and details are given regarding HFR FORTRAN subroutines, and lists of Job Control Language (JCL) files for the complete package. (author)

Conformational and vibrational analysis of 5-hydroxy 2-nitrobenzaldehyde by AB initio hartree-fock, density functional theory calculations

International Nuclear Information System (INIS)

Cinakli, S.; Sert, Y.; Boeyuekata, M.; Ucun, F.

2010-01-01

The vibrational spectra of benzaldehyde and its derivatives have been studied earlier. The substitution of a functional group changes the spectra markedly. Recent spectroscopic studies of the benzaldehyde and their derivatives have been motivated because the vibrational spectra are very useful for understanding of specific biological process and in the analysis of relatively complex systems. The optimized molecular structure, vibrational frequencies and corresponding vibrational assignments, the total energy calculations, relative energies, the mean vibrational deviations of the two planar O-cis and O-trans roomers of 5-Hydroxy 2-nitrobenzaldehydes have been calculated using ab initio Hartree Fock (HF) and Density Functional Theory (B3LYP) with 6-311++G(d,p) basis set. All computations have been performed on personal computer using the Gaussian 03 program package. The calculations were adapted to Cs symmetries of all the molecules. The O-trans rotomers with lower energy of all the molecules have been found as preferential rotomers in the ground state.

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)

Spin Hartree-Fock approach to studying quantum Heisenberg antiferromagnets in low dimensions

Science.gov (United States)

Werth, A.; Kopietz, P.; Tsyplyatyev, O.

2018-05-01

We construct a new mean-field theory for a quantum (spin-1/2) Heisenberg antiferromagnet in one (1D) and two (2D) dimensions using a Hartree-Fock decoupling of the four-point correlation functions. We show that the solution to the self-consistency equations based on two-point correlation functions does not produce any unphysical finite-temperature phase transition, in accord with the Mermin-Wagner theorem, unlike the common approach based on the mean-field equation for the order parameter. The next-neighbor spin-spin correlation functions, calculated within this approach, reproduce closely the strong renormalization by quantum fluctuations obtained via a Bethe ansatz in 1D and a small renormalization of the classical antiferromagnetic state in 2D. The heat capacity approximates with reasonable accuracy the full Bethe ansatz result at all temperatures in 1D. In 2D, we obtain a reduction of the peak height in the heat capacity at a finite temperature that is accessible by high-order 1 /T expansions.

Approximate energy correction for particle number summetry breaking in constrained Hartree-Fock plus BCS calculations

International Nuclear Information System (INIS)

Redon, N.; Meyer, J.; Meyer, M.

1989-01-01

An approximate restoration of the particle number symmetry, a la Lipkin-Nogami, is numerically investigated in the context of Constrained Hartree-Fock plus BCS calculations. Its effect is assessed in a variety of physical situations like potential energy landscapes in transitional nuclei, shape isomerism at low spin and fission barriers of actinide nuclei

Analytic formulae for the Hartree-Fock order parameter at arbitrary p/q filling factors for the 2DEG in a magnetic field

International Nuclear Information System (INIS)

Cabo Monte Oca, A. de.

1994-07-01

Analytic expressions for order parameters are given for the previously introduced general class of Hartree Fock states at arbitrary filling factors ν=p/q for odd q values. The order parameters are expressed as sums of magnetic translations eigenvalues over the filled single electron states. Simple summation formulae for the band spectra in terms of the same eigenvalues are also presented. The energy per particle at ν=1/3 is calculated for various states differing in the way of filling of the 1/3 of the orbitals. The calculated energies are not competing with the usual CDW results. However the high degree of electron overlapping allows for the next corrections to modify this situation. The discussion suggests these Hartree-Fock Slater determinants as interesting alternatives for the Tao-Thouless parent states which may correct their anomalous symmetry and correlation functions properties. (author). 28 refs

The deuteron bound state wave function with tensor forces

International Nuclear Information System (INIS)

Takemasa, Tadashi

1991-01-01

A FORTRAN program named DEUTERON is developed to calculate the binding energy and wave function of a deuteron, when the interaction between two nucleons is described in terms of central, tensor, spin-orbit, and quadratic LS potentials with or without a hard core. An important use of the program is to provide the deuteron wave function required in nuclear reaction calculations involving a deuteron. Also, this program may be employed in nuclear Hartree-Fock calculations using an effective nucleon-nucleon interaction with a tensor component. (author)

Theories of the nuclear ground state beyond Hartree-Fock

International Nuclear Information System (INIS)

Gogny, D.

1979-01-01

Intensive efforts have been invested toward defining a microscopic approach, simple enough to render feasible systematic calculations of nuclear structure and of the some time sufficiently rich in information as to serve for updating traditional microscopic approaches to the collective excitations. Our starting point is the mean field approximation with density dependent effective forces. To describe the collective excitations we use the two well known extensions based on the H.F. theory namely the random phase approximation and the adiabatic approximation to the time dependent Hartree-Fock theory. The purpose of this paper is to show what sort of calculations can be effectively carried out in the frame of such fully self consistent approaches. (KBE) 891 KBE/KBE 892 ARA

A correction for the Hartree-Fock density of states for jellium without screening

International Nuclear Information System (INIS)

Blair, Alexander I.; Kroukis, Aristeidis; Gidopoulos, Nikitas I.

2015-01-01

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

Application of an effective gauge-invariant model to nuclear matter in the relativistic Hartree-Fock approximation

Energy Technology Data Exchange (ETDEWEB)

Bernardos, P. [Universidad de Cantabria, Departamento de Matematica Aplicada y Ciencias de la Computacion, 39005, Santander (Spain); Fomenko, V.N. [St Petersburg University for Railway Engineering, Department of Mathematics, 190031, St Petersburg (Russian Federation); Marcos, S.; Niembro, R. [Universidad de Cantabria, Departamento de Fisica Moderna, 39005, Santander (Spain); Lopez-Quelle, M. [Universidad de Cantabria, Departamento de Fisica Aplicada, 39005, Santander (Spain); Savushkin, L.N. [St Petersburg University for Telecommunications, Department of Physics, 191186, St Petersburg (Russian Federation)

2001-02-01

An effective nuclear model describing {omega}-, {rho}- and axial-mesons as gauge fields is applied to nuclear matter in the relativistic Hartree-Fock approximation. The isoscalar two-pion exchange is simulated by a scalar field s similar to that used in the conventional relativistic mean-field approach. Two more scalar fields are essential ingredients of the present treatment: the {sigma}-field, the chiral partner of the pion, and the {sigma}-field, the Higgs field for the {omega}-meson. Two versions of the model are used depending on whether the {sigma}-field is considered as a dynamical variable or 'frozen', by taking its mass as infinite. The model contains four free parameters in the first case and three in the second one which are fitted to the nuclear matter saturation conditions. The nucleon and meson effective masses, compressibility modulus and symmetry energy are calculated. The results prove the reliability of the Dirac-Hartree-Fock approach within the linear realization of the chiral symmetry. (author)

Coupled Hartree-Fock calculation of {sup 13} C shielding tensors in acetylene clusters

Energy Technology Data Exchange (ETDEWEB)

Craw, John Simon; Nascimento, Marco Antonio Chaer [Universidade Federal, Rio de Janeiro, RJ (Brazil). Inst. de Quimica

1992-12-31

The coupled Hartree Fock method has been used to calculate ab-initio carbon magnetic shielding tensors for small clusters of acetylene molecules. The chemical shift increases from the monomer to the dimer and trimer. This is mainly due increased diamagnetism, which is imperfectly cancelled by increased paramagnetism due to loss of axial symmetry. Anisotropic effects are shown to be small in both the dimer the and trimer. (author) 21 refs., 2 tabs.

Charge- and parity-projected Hartree-Fock method for the strong tensor correlation and its application to the alpha particle

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

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)

On the solution of the Hartree-Fock-Bogoliubov equations by the conjugate gradient method

International Nuclear Information System (INIS)

Egido, J.L.; Robledo, L.M.

1995-01-01

The conjugate gradient method is formulated in the Hilbert space for density and non-density dependent Hamiltonians. We apply it to the solution of the Hartree-Fock-Bogoliubov equations with constraints. As a numerical application we show calculations with the finite range density dependent Gogny force. The number of iterations required to reach convergence is reduced by a factor of three to four as compared with the standard gradient method. (orig.)

Ground-state properties of axially deformed Sr isotopes in Skyrme-Hartree-Fock-Bogolyubov method

International Nuclear Information System (INIS)

Yilmaz, A.H.; Bayram, T.; Demirci, M.; Engin, B.; Bayram, T.

2010-01-01

Binding energies, the mean-square nuclear radii, neutron radii, quadrupole moments and deformation parameters to axially deformed Strontium isotopes were evaluated using Hartree-Fock-Bogolyubov method. Shape coexistence was also discussed. The results were compared with experimental data and some estimates obtained within some nuclear models. The calculations were performed for SIy4 set of Skyrme forces and for wide range of the neutron numbers of Sr isotopes

Projection after variation in the finite-temperature Hartree-Fock-Bogoliubov approximation

Science.gov (United States)

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.

Hartree-Fock limit values of multipole moments, polarizabilities, and hyperpolarizabilities for atoms and diatomic molecules

Science.gov (United States)

Kobus, Jacek

2015-02-01

Recently it has been demonstrated that the finite difference Hartree-Fock method can be used to deliver highly accurate values of electric multipole moments together with polarizabilities αz z,Az ,z z , and hyperpolarizabilities βz z z, γz z z,Bz z ,z z , for the ground states of various atomic and diatomic systems. Since these results can be regarded as de facto Hartree-Fock limit values their quality is of the utmost importance. This paper reexamines the use of the finite field method to calculate these electric properties, discusses its accuracy, and presents an updated list of the properties for the following atoms and diatomic molecules: H-, He, Li, Li+,Li2 +,Li-,Be2 + , Be, B+,C2 + , Ne, Mg2 +, Mg, Al+,Si2 + , Ar, K+,Ca2 +,Rb+,Sr2 +,Zr4 +,He2 , Be2,N2,F2,O2 , HeNe, LiH2 +, LiCl, LiBr, BH, CO, FH, NaCl, and KF. The potential energy curves and the dependence of the electric properties on the internuclear distance is also studied for He2,LiH+,Be2 , and HeNe systems.

Time-dependent Hartree--Fock method: description of heavy-ion collisions and allowance for correlations

International Nuclear Information System (INIS)

Maedler, P.

1984-01-01

The review describes the application of the time-dependent Hartree--Fock method to the description of heavy-ion interactions at energies of order 10 MeV/nucleon. The fundamentals of the method are presented and qualitative properties of its results are discussed. Realistic calculations of fusion reactions, deep inelastic collisions, and particle emission are presented and compared with the corresponding experimental data. Various approaches that generalize the method by taking into account correlations are considered

Extended Hartree-Fock-Bogoliubov theory for degenerate Bose systems

International Nuclear Information System (INIS)

Tommasini, Paolo; Passos, E J V de; Pires, M O C; Piza, A F R de Toledo

2005-01-01

An extension of the Hartree-Fock-Bogoliubov (HFB) theory of degenerate Bose systems in which the coupling between one and two quasi-particles is taken into account is developed. The excitation operators are written as linear combinations of one and two HFB quasi-particles. Excitation energies and quasi-particle amplitudes are given by generalized Bogoliubov equations. The excitation spectrum has two branches. The first one is a discrete branch which is gapless and has a phonon character at large wavelength and, contrarily to HFB, is always stable. This branch is detached from a second, continuum branch whose threshold, at fixed total momentum, coincides with the two quasi-particle threshold of the HFB theory. The gap between the two branches at P = 0 is twice the HFB gap, which thus provides for the relevant energy scale. Numerical results for a specific case are given

Comparison of the surface friction model with the time-dependent Hartree-Fock method

International Nuclear Information System (INIS)

Froebrich, P.

1984-01-01

A comparison is made between the classical phenomenological surface friction model and a time-dependent Hartree-Fock study by Dhar for the system 208 Pb+ 74 Ge at E/sub lab/(Pb) = 1600 MeV. The general trends for energy loss, mean values for charge and mass, interaction times and energy-angle correlations turn out to be fairly similar in both methods. However, contrary to Dhar, the events close to capture are interpreted as normal deep-inelastic, i.e., not as fast fission processes

Physically asymptotic Hartree-Fock stationary-phase approximant to the many-body S-matrix

International Nuclear Information System (INIS)

Griffin, J.J.; Dworzecka, M.

1982-01-01

The Asymptotic Hartree-Fock Approximant replaces the physically non-asymptotic (and dynamically nontrivial) external translation of the FISP result with the asymptotic and dynamically trivial translational evolution of Dirac-TDHF by adding an explicit restriction upon the acceptable channel states. It is therefore preferable under the principle of commensurability, which judges the expected output of physical descriptions in terms of the physical assumptions they incorporate. Further insight into the relationship between the TDSHF and FISP methods will reward careful comparison of the respective expressions, in specific cases

Relativistic many-body perturbation-theory calculations based on Dirac-Fock-Breit wave functions

International Nuclear Information System (INIS)

Ishikawa, Y.; Quiney, H.M.

1993-01-01

A relativistic many-body perturbation theory based on the Dirac-Fock-Breit wave functions has been developed and implemented by employing analytic basis sets of Gaussian-type functions. The instantaneous Coulomb and low-frequency Breit interactions are treated using a unified formalism in both the construction of the Dirac-Fock-Breit self-consistent-field atomic potential and in the evaluation of many-body perturbation-theory diagrams. The relativistic many-body perturbation-theory calculations have been performed on the helium atom and ions of the helium isoelectronic sequence up to Z=50. The contribution of the low-frequency Breit interaction to the relativistic correlation energy is examined for the helium isoelectronic sequence

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)

Adaptive multi-resolution 3D Hartree-Fock-Bogoliubov solver for nuclear structure

Science.gov (United States)

Pei, J. C.; Fann, G. I.; Harrison, R. J.; Nazarewicz, W.; Shi, Yue; Thornton, S.

2014-08-01

Background: Complex many-body systems, such as triaxial and reflection-asymmetric nuclei, weakly bound halo states, cluster configurations, nuclear fragments produced in heavy-ion fusion reactions, cold Fermi gases, and pasta phases in neutron star crust, are all characterized by large sizes and complex topologies in which many geometrical symmetries characteristic of ground-state configurations are broken. A tool of choice to study such complex forms of matter is an adaptive multi-resolution wavelet analysis. This method has generated much excitement since it provides a common framework linking many diversified methodologies across different fields, including signal processing, data compression, harmonic analysis and operator theory, fractals, and quantum field theory. Purpose: To describe complex superfluid many-fermion systems, we introduce an adaptive pseudospectral method for solving self-consistent equations of nuclear density functional theory in three dimensions, without symmetry restrictions. Methods: The numerical method is based on the multi-resolution and computational harmonic analysis techniques with a multi-wavelet basis. The application of state-of-the-art parallel programming techniques include sophisticated object-oriented templates which parse the high-level code into distributed parallel tasks with a multi-thread task queue scheduler for each multi-core node. The internode communications are asynchronous. The algorithm is variational and is capable of solving coupled complex-geometric systems of equations adaptively, with functional and boundary constraints, in a finite spatial domain of very large size, limited by existing parallel computer memory. For smooth functions, user-defined finite precision is guaranteed. Results: The new adaptive multi-resolution Hartree-Fock-Bogoliubov (HFB) solver madness-hfb is benchmarked against a two-dimensional coordinate-space solver hfb-ax that is based on the B-spline technique and a three-dimensional solver

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

Hartree-Fock+BCS approach to unstable nuclei with the Skyrme force

International Nuclear Information System (INIS)

Tajima, Naoki

2001-01-01

We reanalyze the results of our extensive Hartree-Fock+BCS calculation from new points of view paying attention to the properties of unstable nuclei. The calculation has been done with the Skyrme SIII force for the ground and shape isomeric states of 1029 even-even nuclei ranging 2≤Z≤114. We also discuss the advantages of the employed three-dimensional Cartesian-mesh representation, especially on its remarkably high precision with apparently coarse meshes when applied to atomic nuclei. In Appendices we give the coefficients of finite-point numerical differentiation and integration formulae suitable for Cartesian mesh representation and elucidate the features of each formula and the differences from a method based on the Fourier transformation. (author)

A multiconfigurational time-dependent Hartree-Fock method for excited electronic states. I. General formalism and application to open-shell states.

Science.gov (United States)

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.

The semi-classical limit of the time dependent Hartree-Fock equation. II. The Wick symbol of the solution

OpenAIRE

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.

Application of the gradient method to Hartree-Fock-Bogoliubov theory

International Nuclear Information System (INIS)

Robledo, L. M.; Bertsch, G. F.

2011-01-01

A computer code is presented for solving the equations of the Hartree-Fock-Bogoliubov (HFB) theory by the gradient method, motivated by the need for efficient and robust codes to calculate the configurations required by extensions of the HFB theory, such as the generator coordinate method. The code is organized with a separation between the parts that are specific to the details of the Hamiltonian and the parts that are generic to the gradient method. This permits total flexibility in choosing the symmetries to be imposed on the HFB solutions. The code solves for both even and odd particle-number ground states, with the choice determined by the input data stream. Application is made to the nuclei in the sd shell using the universal sd-shell interaction B (USDB) shell-model Hamiltonian.

Automatic Differentiation in Quantum Chemistry with Applications to Fully Variational Hartree-Fock.

Science.gov (United States)

Tamayo-Mendoza, Teresa; Kreisbeck, Christoph; Lindh, Roland; Aspuru-Guzik, Alán

2018-05-23

Automatic differentiation (AD) is a powerful tool that allows calculating derivatives of implemented algorithms with respect to all of their parameters up to machine precision, without the need to explicitly add any additional functions. Thus, AD has great potential in quantum chemistry, where gradients are omnipresent but also difficult to obtain, and researchers typically spend a considerable amount of time finding suitable analytical forms when implementing derivatives. Here, we demonstrate that AD can be used to compute gradients with respect to any parameter throughout a complete quantum chemistry method. We present DiffiQult , a Hartree-Fock implementation, entirely differentiated with the use of AD tools. DiffiQult is a software package written in plain Python with minimal deviation from standard code which illustrates the capability of AD to save human effort and time in implementations of exact gradients in quantum chemistry. We leverage the obtained gradients to optimize the parameters of one-particle basis sets in the context of the floating Gaussian framework.

A importância do método de Hartree no ensino de química quântica

Directory of Open Access Journals (Sweden)

Silmar A. do Monte

2011-01-01

Full Text Available Hartree's original ideas are described. Its connection with electrostatics can be explored in order to decrease the gap between teaching of Physics and Chemistry. As a consequence of its simplicity and connection with electrostatics, it is suggested that Hartree's method should be presented before the Hartree-Fock method. Besides, since the fundamental concepts of indistinguishibility of electrons along with the antissimetry of the wave function are missing in the Hartree's product, the method itself can be used to introduce these concepts. Despite the fact that these features are not included in the trial wavefunction, important qualitatively correct results can be obtained.

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)

Assessing the role of Hartree-Fock exchange, correlation energy and long range corrections in evaluating ionization potential, and electron affinity in density functional theory.

Science.gov (United States)

Vikramaditya, Talapunur; Lin, Shiang-Tai

2017-06-05

Accurate determination of ionization potentials (IPs), electron affinities (EAs), fundamental gaps (FGs), and HOMO, LUMO energy levels of organic molecules play an important role in modeling and predicting the efficiencies of organic photovoltaics, OLEDs etc. In this work, we investigate the effects of Hartree Fock (HF) Exchange, correlation energy, and long range corrections in predicting IP and EA in Hybrid Functionals. We observe increase in percentage of HF exchange results in increase of IPs and decrease in EAs. Contrary to the general expectations inclusion of both HF exchange and correlation energy (from the second order perturbation theory MP2) leads to poor prediction. Range separated Hybrid Functionals are found to be more reliable among various DFT Functionals investigated. DFT Functionals predict accurate IPs whereas post HF methods predict accurate EAs. © 2017 Wiley Periodicals, Inc. © 2017 Wiley Periodicals, Inc.

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.)

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)

Properties of nuclear and neutron matter in a relativistic Hartree-Fock theory

International Nuclear Information System (INIS)

Horowitz, C.J.; Serot, B.D.

1983-01-01

Relativistic-Hartree-Fock (HF) equations are derived for an infinite system of mesons and baryons in the framework of a renormalizable relativistic quantum field theory. The derivation is based on a diagrammatic approach and Dyson's equation for the baryon propagator. The result is a set of coupled, nonlinear integral equations for the baryon self-energy with a self-consistency condition on the single-particle spectrum. The HF equations are solved for nuclear and neutron matter in the Walecka model, which contains neutral scalar and vector mesons. After renormalizing model parameters to reproduce nuclear matter saturation properties, HF results at low to moderate densities are similar to those in the mean-field (Hartree) approximation. Self-consistent exchange corrections to the Hartree equation of state become negligible at high densities. Rho- and pi-meson exchanges are incorporated using a renormalizable gauge-theory model. A chiral transformation of the lagrangian is used to replace the pseudoscalar πN coupling with a pseudovector coupling, for which one-pion exchange is a reasonable first approximation. This transformation maintains the model's renormalizability so that corrections may be evaluated. Pion exchange has a small effect on the HF results of the Walecka model and brings HF results in closer in closer agreement with the mean-field theory. The diagrammatic techniques used here retain the mesonic degrees of freedom and are simple enough to be extended to more refined self-consistent approximations. (orig.)

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

Combining density functional and incremental post-Hartree-Fock approaches for van der Waals dominated adsorbate-surface interactions: Ag2/graphene

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

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)

Molecular structures and vibrational frequencies of xanthine and its methyl derivatives (caffeine and theobromine) by ab initio Hartree-Fock and density functional theory calculations

Science.gov (United States)

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.

Long-range corrected density functional theory with accelerated Hartree-Fock exchange integration using a two-Gaussian operator [LC-ωPBE(2Gau)].

Science.gov (United States)

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.

Restricted Hartree Fock using complex-valued orbitals: A long-known but neglected tool in electronic structure theory

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.

Spin Density Distribution in Open-Shell Transition Metal Systems: A Comparative Post-Hartree-Fock, Density Functional Theory, and Quantum Monte Carlo Study of the CuCl2 Molecule.

Science.gov (United States)

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.

Combining density functional and incremental post-Hartree-Fock approaches for van der Waals dominated adsorbate-surface interactions: Ag{sub 2}/graphene

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.

Adiabatic time-dependent Hartree-Fock theory of collective motion in finite systems

International Nuclear Information System (INIS)

Baranger, M.; Veneroni, M.

1978-01-01

We show how to derive the parameters of a phenomenological collective model from a microscopic theory. The microscopic theory is Hartree-Fock, and we start from the time-dependent Hartree-Fock equation. To this we add the adiabatic approximation, which results in a collective kinetic energy quadratic in the velocities, with coefficients depending on the coordinates, as in the phenomenological models. The crucial step is the decomposition of the single-particle density matrix p in the form exp(i/sub chi/) rho/sub omicron/exp(-i/sub chi/), where rho/sub omicron/ represents a time-even Slater determinant and plays the role of coordinate. Then chi plays the role of momentum, and the adiabatic assumption is that chi is small. The energy is expanded in powers of chi, the zeroth-order being the collective potential energy. The analogy with classical mechanics is stressed and studied. The same adiabatic equations of motion are derived in three different ways (directly, from the Lagrangian, from the Hamiltonian), thus proving the consistency of the theory. The dynamical equation is not necessary for writing the energy or for the subsequent quantization which leads to a Schroedinger equation, but it must be used to check the validity of various approximation schemes, particularly to reduce the problem to a few degrees of freedom. The role of the adiabatic hypothesis, its definition, and range of validity, are analyzed in great 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. For a quadrupole two-body force, the Baranger-Kumar formalism is recovered. The self-consistency brings additional terms to the Inglis cranking formula. Comparison is also made with generator coordinate methods

On minimal energy Hartree-Fock states for the 2DEG at fractional fillings

International Nuclear Information System (INIS)

Cabo Montes Oca, A. de.

1995-08-01

Approximate minimal energy solutions of the previously discussed general class of Hartree-Fock (HF) states of the 2DEG at 1/3 and 2/3 filling factors are determined. Their selfenergy spectrum is evaluated. Wannier states associated to the filled Bloch states are introduced in a lattice having three flux quanta per cell. They allow to rewrite approximately the ν = 1/3 HF Hamiltonian as sum of three independent tight-binding model Hamiltonians, one describing the dynamics in the band of occupied states and the other ones in the tow bands of excited states. The magnitude of the hopping integral indicates the enhanced role which should have the correlation energy in the present situation with respect to the case of the Yoshioka and Lee second order energy calculation for the lowest energy HF state. Finally, the discussion also suggests the Wannier function, which spreads an electron into a three quanta area, as a physical model for the composite fermion mean field one particle state. (author). 11 refs, 5 figs

Multiconfiguration Dirac-Hartree-Fock calculations of energy levels and radiative rates of Fe VII

Science.gov (United States)

Li, Yang; Xu, Xiaokai; Li, Bowen; Jönsson, Per; Chen, Ximeng

2018-06-01

Detailed calculations are performed for 134 fine-structure levels of the 3p63d2, 3p63d4s, 3p53d3 and 3p63d4p configurations in Fe VII using the multiconfiguration Dirac-Hartree-Fock (MCDHF) and relativistic configuration interaction (RCI) methods. Important electron correlation effects are systematically accounted for through active space (AS) expansions. Our results compare well with experimental measurements, emphasizing the importance of a careful treatment of electron correlation, and provide some missing data in the NIST atomic database. The data obtained are expected to be useful in astrophysical applications, particularly for the research of the solar coronal plasma.

Description of plasmon-like band in silver clusters: the importance of the long-range Hartree-Fock exchange in time-dependent density-functional theory simulations.

Science.gov (United States)

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.

Self-consistent field description of high spin states in rare earth nuclei. [Hartree-Fock-Bogolyubov Theory

Energy Technology Data Exchange (ETDEWEB)

Goodman, A L [Carnegie-Mellon Univ., Pittsburgh, Pa. (USA)

1976-07-12

The Hartree-Fock-Bogolyubov cranking equations are solved for /sup 168/ /sup 170/Yb and /sup 174/Hf. Deformation and pairing properties are both obtained with a G-matrix derived from the Reid soft-core potential. The high spin anomalies are attributed to the disappearance of the neutron pair gap in /sup 168/Yb, the realignment of an isub(13/2) neutron pair in /sup 170/Yb, and a combination of these two mechanisms in /sup 174/Hf. Two bands intersecting at high spin are found for /sup 174/Hf.

Energy Levels and B(E2) transition rates in the Hartree-Fock approximation with the Skyrme force

International Nuclear Information System (INIS)

Oliveira, D.R. de; Mizrahi, S.S.

1976-11-01

The Hartree-Fock approximation with the Skyrme force is applied to the A = 4n type of nuclei in the s-d shell. Energy levels and electric quadrupole transition probabilities within the ground states band are calculated from the projected states of good angular momentum. Strong approximations are made but the results concerning the spectra are better than those obtained with more sophisticated density independent two-body interactions. The transition rates are less sensitive to the interaction, as previously verified

Effect of Hartree-Fock exact exchange on intramolecular magnetic coupling constants of organic diradicals

Science.gov (United States)

Cho, Daeheum; Ko, Kyoung Chul; Ikabata, Yasuhiro; Wakayama, Kazufumi; Yoshikawa, Takeshi; Nakai, Hiromi; Lee, Jin Yong

2015-01-01

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.

Effect of Hartree-Fock exact exchange on intramolecular magnetic coupling constants of organic diradicals

Energy Technology Data Exchange (ETDEWEB)

Cho, Daeheum; Ko, Kyoung Chul; Lee, Jin Yong, E-mail: jinylee@skku.edu [Department of Chemistry, Sungkyunkwan University, Suwon 440-746 (Korea, Republic of); Ikabata, Yasuhiro; Wakayama, Kazufumi; Yoshikawa, Takeshi [Department of Chemistry and Biochemistry, School of Advanced Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555 (Japan); Nakai, Hiromi, E-mail: nakai@waseda.jp [Department of Chemistry and Biochemistry, School of Advanced Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555 (Japan); Research Institute for Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555 (Japan); CREST, Japan Science and Technology Agency, Tokyo 102-0075 (Japan); Elements Strategy Initiative for Catalysts and Batteries (ESICB), Kyoto University, Katsura, Kyoto 615-8520 (Japan)

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 and 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.

Iterative scheme for electronic systems: using one-electron Green's functions

International Nuclear Information System (INIS)

Hyslop, J.; Rees, D.

1976-01-01

An iterative generalization of the minimum principle proposed for electronic systems by Hall, Hyslop, and Rees is investigated. It is shown that this generalization still retains the advantage of using members of a larger class of trial wave functions, for example those with discontinuities, as initial approximations to the wave functions. This scheme has the advantage that, at each stage of iteration, an upper bound is obtained which is at least as good as that obtained previously. The theory is first applied to the hydrogen atom. It is then adapted to estimate the Hartree--Fock energy of the helium atom, the Hartree--Fock limit being obtained after a relatively small number of iterations

The Strutinsky method and its foundation from the Hartree-Fock-Bogoliubov approximation at finite temperature

International Nuclear Information System (INIS)

Brack, M.

1981-01-01

Strutinsky's shell-correction method is investigated in the framework of the microscopial Hartree-Fock-Bogoliubov method at finite temperature HFBT. Applying the Strutinsky energy averaging consistently to the normal and abnormal density matrices and to the entropy, we define a self-consistently average HFBT system as the solution of a variational problem. From the latter we derive the generalized Strutinsky energy theorem and the explicit expressions for the shell correction of a statistically excited system of BCS quasiparticles. Using numerical results of HF calculations, we demonstrate the convergence of the Strutinsky expansion and estimate the validity of the partical shell-correction approach. We also discuss the close connections of the Strutinsky energy averaging with semiclassical expansions and their usefulness for solving the average nuclear self-consistency problem. In particular we argue that the Hohenberg-Kohn theorem should hold for the averaged HFBT system and we thus provide a justification of the use of semiclassical density functionals. (orig.)

Toward a muon-specific electronic structure theory: effective electronic Hartree-Fock equations for muonic molecules.

Science.gov (United States)

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.

Axially deformed solution of the Skyrme-Hartree-Fock-Bogolyubov equations using the transformed harmonic oscillator basis (III) HFBTHO (v3.00): A new version of the program

Science.gov (United States)

Perez, R. Navarro; Schunck, N.; Lasseri, R.-D.; Zhang, C.; Sarich, J.

2017-11-01

intrinsic densities. In the present version of HFBTHO, the energy density derives either from the zero-range Skyrme or the finite-range Gogny effective two-body interaction between nucleons. Nuclear super-fluidity is treated at the Hartree-Fock-Bogolyubov (HFB) approximation. Constraints on the nuclear shape allows probing the potential energy surface of the nucleus as needed e.g., for the description of shape isomers or fission. The implementation of a local scale transformation of the single-particle basis in which the HFB solutions are expanded provide a tool to properly compute the structure of weakly-bound nuclei. Solution method: The program uses the axial Transformed Harmonic Oscillator (THO) single-particle basis to expand quasiparticle wave functions. It iteratively diagonalizes the Hartree-Fock-Bogolyubov Hamiltonian based on generalized Skyrme-like energy densities and zero-range pairing interactions or the finite-range Gogny force until a self-consistent solution is found. A previous version of the program was presented in M.V. Stoitsov, N. Schunck, M. Kortelainen, N. Michel, H. Nam, E. Olsen, J. Sarich, and S. Wild, Comput. Phys. Commun. 184 (2013) 1592-1604 with much of the formalism presented in the original paper M.V. Stoitsov, J. Dobaczewski, W. Nazarewicz, P. Ring, Comput. Phys. Commun. 167 (2005) 43-63. Additional comments: The user must have access to (i) the LAPACK subroutines DSYEEVR, DSYEVD, DSYTRF and DSYTRI, and their dependencies, which compute eigenvalues and eigenfunctions of real symmetric matrices, (ii) the LAPACK subroutines DGETRI and DGETRF, which invert arbitrary real matrices, and (iii) the BLAS routines DCOPY, DSCAL, DGEMM and DGEMV for double-precision linear algebra (or provide another set of subroutines that can perform such tasks). The BLAS and LAPACK subroutines can be obtained from the Netlib Repository at the University of Tennessee, Knoxville: http://netlib2.cs.utk.edu/.

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

Spin polarization, orbital occupation and band gap opening in vanadium dioxide: The effect of screened Hartree-Fock exchange

KAUST Repository

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.

Expansion of X-ray form factor for close shell using uncorrelated wave function

Energy Technology Data Exchange (ETDEWEB)

AL-Robayi, Enas M. [Babylon University , College of Science for Women, laser Physics Department, Hilla (Iraq)

2013-12-16

The atomic scattering factor has been studied for Be+ve, and B+2ve ions using the uncorrelated wave function (Hartree-Fock (HF)) for inter particle electronic shells. The physical importance of this factor appears in its relation to several important atomic properties as, the coherent scattering intensity, the total scattering intensity, the incoherent scattering function, the coherent scattering cross section, the total incoherent cross section, the nuclear magnetic shielding constant, the geometrical structure factor. Also there is one atomic properties the one particle radial density distribution function D(r)has been studied using the partitioning technique.

Efficient exact-exchange time-dependent density-functional theory methods and their relation to time-dependent Hartree-Fock.

Science.gov (United States)

Hesselmann, Andreas; Görling, Andreas

2011-01-21

A recently introduced time-dependent exact-exchange (TDEXX) method, i.e., a response method based on time-dependent density-functional theory that treats the frequency-dependent exchange kernel exactly, is reformulated. In the reformulated version of the TDEXX method electronic excitation energies can be calculated by solving a linear generalized eigenvalue problem while in the original version of the TDEXX method a laborious frequency iteration is required in the calculation of each excitation energy. The lowest eigenvalues of the new TDEXX eigenvalue equation corresponding to the lowest excitation energies can be efficiently obtained by, e.g., a version of the Davidson algorithm appropriate for generalized eigenvalue problems. Alternatively, with the help of a series expansion of the new TDEXX eigenvalue equation, standard eigensolvers for large regular eigenvalue problems, e.g., the standard Davidson algorithm, can be used to efficiently calculate the lowest excitation energies. With the help of the series expansion as well, the relation between the TDEXX method and time-dependent Hartree-Fock is analyzed. Several ways to take into account correlation in addition to the exact treatment of exchange in the TDEXX method are discussed, e.g., a scaling of the Kohn-Sham eigenvalues, the inclusion of (semi)local approximate correlation potentials, or hybrids of the exact-exchange kernel with kernels within the adiabatic local density approximation. The lowest lying excitations of the molecules ethylene, acetaldehyde, and pyridine are considered as examples.

Structure of single-particle nuclear densities from Hartree-Fock theory and model independent analysis

International Nuclear Information System (INIS)

Starodubskij, V.E.; Shaginyan, V.R.

1979-01-01

Friar-Negele method is applied to determine the static densities of neutrons and nuclear matter from the fast proton-nuclei elastic scattering data. This model-independent analysis (MIA) has been carried out for 28 Si, sup(32,34)S, sup(40,42,44,48)Ca, 48 Ti, sup(58,60)Ni, 90 Zr, 208 Pb nuclei. The binding energies, rms radii, densities and scattering cross sections of 1 GeV-proton are calculated in the framework of the Hartree-Fock theory (HF) with Skyrme's interaction. The HF and MIA densities and cross sections have been compared to draw a conclusion on the quality of the HF densities. Calculation of the cross sections has included the spin-orbit interaction with parameters taken from the polarization data

Publisher Correction: Imaging the square of the correlated two-electron wave function of a hydrogen molecule.

Science.gov (United States)

Waitz, M; Bello, R Y; Metz, D; Lower, J; Trinter, F; Schober, C; Keiling, M; Lenz, U; Pitzer, M; Mertens, K; Martins, M; Viefhaus, J; Klumpp, S; Weber, T; Schmidt, L Ph H; Williams, J B; Schöffler, M S; Serov, V V; Kheifets, A S; Argenti, L; Palacios, A; Martín, F; Jahnke, T; Dörner, R

2018-06-05

The original version of this Article contained an error in the fifth sentence of the first paragraph of the 'Application on H 2 ' section of the Results, which incorrectly read 'The role of electron correlation is quite apparent in this presentation: Fig. 1a is empty for the uncorrelated Hartree-Fock wave function, since projection of the latter wave function onto the 2pσ u orbital is exactly zero, while this is not the case for the fully correlated wave function (Fig. 1d); also, Fig. 1b, c for the uncorrelated description are identical, while Fig. 1e, f for the correlated case are significantly different.' The correct version replaces 'Fig. 1e, f' with 'Fig. 2e and f'.

A comparison between the adiabatic time dependent Hartree-Fock and the generator coordinate methods for the description of nuclear collective motion

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

Multi-configuration Dirac-Hartree-Fock (MCDHF) calculations for Ni XXV

Science.gov (United States)

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.

Microscopic descriptions of the superdeformed bands in the region A 190: Bohr and Routhian Hamiltonians in the Hartree-Fock-Bogolyubov approximation

International Nuclear Information System (INIS)

Libert, J.; Girod, M.; Delaroche, J-P.; Berger, J-F.; Romain, P.; Peru, S.

1997-01-01

The superdeformed bands of the nuclei in the region A = 190 were described by two microscopic approaches using Gogny D1 finite range interaction. The first one consists in building a Bohr Hamiltonian in the framework of Gauss overlap approximation (GOA) of the generator-coordinate method, starting from Hartree-Fock-Bogolyubov solutions under quadrupole constraints. This collective Hamiltonian microscopically determined for five quadrupolar variables is then diagonalized by a projection method on a collective based adapted to the large variety of the deformations to be considered. A special attention was given to the precise definition of the under-barrier collective wavefunctions (for which an original method of solving the collective Schroedinger equation was developed) in order to described correctly the lifetime of the shape isomeric states. The other approach, that of Routhian is based also on the Hartree-Fock-Bogolyubov approximation. The calculations are carried out with and without restoring the broken symmetry associated to the particle numbers (as given by Lipkin-Nogami). The results (excitation energies, moments of inertia, etc...) of the two calculation methods are compared with most recent experimental data. The existence of the superdeformed bands corresponding to vibrational excitations similar to those appearing in β and γ bands is proposed

A density functional study of backbone structures of polydiacetylene: destabilization of butatriene structure

International Nuclear Information System (INIS)

Katagiri, Hideki; Shimoi, Yukihiro; Abe, Shuji

2004-01-01

Backbone structures of polydiacetylene are studied with first-principles electronic structure method using plane-waves within generalized gradient approximation (GGA) of density functional theory. In spin-restricted calculations a coarse k-point sampling gives a potential energy curve with two local minima corresponding to acetylene and butatriene structures. However, the potential barrier between the two structures rapidly decreases with increasing number of k-points, which results in destabilization of the butatriene structure. Spin polarization effects also destabilize the butatriene structure, inducing atom-centered spin-density-wave state. These potential energies were compared with those obtained by Hartree-Fock, density functional within local density approximation (LDA) and GGA, and hybrid density functional methods using a gaussian basis set. The comparison shows that the density functional methods within LDA and GGA favor the destabilization of the butatriene structure in contrast to the Hartree-Fock method

Quantum treatment of protons with the reduced explicitly correlated Hartree-Fock approach

Energy Technology Data Exchange (ETDEWEB)

Sirjoosingh, Andrew; Pak, Michael V.; Brorsen, Kurt R.; Hammes-Schiffer, Sharon, E-mail: shs3@illinois.edu [Department of Chemistry, University of Illinois at Urbana-Champaign, 600 South Mathews Ave., Urbana, Illinois 61801 (United States)

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{sup −} 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{sup −} 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.

The Calculation of Single-Nucleon Energies of Nuclei by Considering Two-Body Effective Interaction, n(k,ρ, and a Hartree-Fock Inspired Scheme

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.

Two-body Schrödinger wave functions in a plane-wave basis via separation of dimensions

Science.gov (United States)

Jerke, Jonathan; Poirier, Bill

2018-03-01

Using a combination of ideas, the ground and several excited electronic states of the helium atom and the hydrogen molecule are computed to chemical accuracy—i.e., to within 1-2 mhartree or better. The basic strategy is very different from the standard electronic structure approach in that the full two-electron six-dimensional (6D) problem is tackled directly, rather than starting from a single-electron Hartree-Fock approximation. Electron correlation is thus treated exactly, even though computational requirements remain modest. The method also allows for exact wave functions to be computed, as well as energy levels. From the full-dimensional 6D wave functions computed here, radial distribution functions and radial correlation functions are extracted—as well as a 2D probability density function exhibiting antisymmetry for a single Cartesian component. These calculations support a more recent interpretation of Hund's rule, which states that the lower energy of the higher spin-multiplicity states is actually due to reduced screening, rather than reduced electron-electron repulsion. Prospects for larger systems and/or electron dynamics applications appear promising.

Charge transfer excitations from excited state Hartree-Fock subsequent minimization scheme

International Nuclear Information System (INIS)

Theophilou, Iris; Tassi, M.; Thanos, S.

2014-01-01

Photoinduced charge-transfer processes play a key role for novel photovoltaic phenomena and devices. Thus, the development of ab initio methods that allow for an accurate and computationally inexpensive treatment of charge-transfer excitations is a topic that nowadays attracts a lot of scientific attention. In this paper we extend an approach recently introduced for the description of single and double excitations [M. Tassi, I. Theophilou, and S. Thanos, Int. J. Quantum Chem. 113, 690 (2013); M. Tassi, I. Theophilou, and S. Thanos, J. Chem. Phys. 138, 124107 (2013)] to allow for the description of intermolecular charge-transfer excitations. We describe an excitation where an electron is transferred from a donor system to an acceptor one, keeping the excited state orthogonal to the ground state and avoiding variational collapse. These conditions are achieved by decomposing the space spanned by the Hartree-Fock (HF) ground state orbitals into four subspaces: The subspace spanned by the occupied orbitals that are localized in the region of the donor molecule, the corresponding for the acceptor ones and two more subspaces containing the virtual orbitals that are localized in the neighborhood of the donor and the acceptor, respectively. Next, we create a Slater determinant with a hole in the subspace of occupied orbitals of the donor and a particle in the virtual subspace of the acceptor. Subsequently we optimize both the hole and the particle by minimizing the HF energy functional in the corresponding subspaces. Finally, we test our approach by calculating the lowest charge-transfer excitation energies for a set of tetracyanoethylene-hydrocarbon complexes that have been used earlier as a test set for such kind of excitations

Study of the tensor correlation in a neutron-rich sd-shell region with the charge- and parity-projected Hartree-Fock method

International Nuclear Information System (INIS)

Sugimoto, Satoru; Toki, Hiroshi; Ikeda, Kiyomi

2008-01-01

We study the effect of the tensor force on nuclear structure with mean-field and beyond-mean-field methods. An important correlation induced by the tensor force is two-particle-two-hole (2p2h) correlation, which cannot be treated with a usual mean-filed method. To treat the 2p2h tensor correlation, we develop a new framework (charge- and parity-projected Hartree-Fock (CPPHF) method), which is a beyond-mean-field method. In the CPPHF method, we introduce single-particle states with parity and charge mixing. The parity and charge projections are performed on a total wave function before variation. We apply the CPPHF method to oxygen isotopes including neutron-rich ones. The potential energy from the tensor force has the same order of magnitude with that from the LS force and becomes smaller with neutron number, which indicates that excess neutrons do not contribute to the 2p2h tensor correlation significantly. We also study the effect of the tensor force on spin-orbit-splitting (ls-splitting) in a neutron-rich fluorine isotope 23 F. The tensor force reduces the ls-splitting for the proton d-orbits by about 3 MeV. This effect is important to reproduce the experimental value. We also find that the 2p2h tensor correlation does not affect the ls-splitting in 23 F

The contribution of Skyrme Hartree-Fock calculations to the understanding of the shell model

International Nuclear Information System (INIS)

Zamick, L.

1984-01-01

The authors present a detailed comparison of Skyrme Hartree-Fock and the shell model. The H-F calculations are sensitive to the parameters that are chosen. The H-F results justify the use of effective charges in restricted model space calculations by showing that the core contribution can be large. Further, the H-F results roughly justify the use of a constant E2 effective charge, but seem to yield nucleus dependent E4 effective charges. The H-F can yield results for E6 and higher multipoles, which would be zero in s-d model space calculations. On the other side of the coin in H-F the authors can easily consider only the lowest rotational band, whereas in the shell model one can calculate the energies and properties of many more states. In the comparison some apparent problems remain, in particular E4 transitions in the upper half of the s-d shell

Dirac-Fock atomic electronic structure calculations using different nuclear charge distributions

NARCIS (Netherlands)

Visscher, L; Dyall, KG

1997-01-01

Numerical Hartree-Fock calculations based on the Dirac-Coulomb Hamiltonian for the first 109 elements of the periodic table are presented. The results give the total electronic energy, as a function of the nuclear model that is used, for four different models of the nuclear charge distribution. The

Relativistic Hartree-Bogoliubov description of thorium and uranium isotopes

International Nuclear Information System (INIS)

Naz, Tabassum; Ahmad, Shakeb

2016-01-01

The relativistic Hartree-Bogoliubov (RHB) theory is a relativistic extension of the Hartree-Fock- Bogoliubov theory. It is a unified description of mean-field and pairing correlations and successfully describe the various phenomenon of nuclear structure. In the present work, RHB is applied to study the thorium and uranium isotopes

Investigation of the hyperfine properties of deoxy hemoglobin based on its electronic structure obtained by Hartree-Fock-Roothan procedure

Energy Technology Data Exchange (ETDEWEB)

Lata, K. Ramani [State University of New York at Albany, Department of Physics (United States); Sahoo, N. [University of Texas M.D. Anderson Cancer Center, Department of Radiation Physics (United States); Dubey, Archana [University of Central Florida, Department of Physics (United States); Scheicher, R. H. [Uppsala University, Condensed Matter Theory Group, Department of Physics and Materials Science (Sweden); Badu, S. R.; Pink, R. H.; Mahato, Dip N. [State University of New York at Albany, Department of Physics (United States); Schulte, A. F.; Saha, H. P. [University of Central Florida, Department of Physics (United States); Maharjan, N. B. [State University of New York at Albany, Department of Physics (United States); Chow, Lee [University of Central Florida, Department of Physics (United States); Das, T. P., E-mail: tpd56@albany.edu [State University of New York at Albany, Department of Physics (United States)

2008-01-15

The electronic structure of the heme unit of deoxyhemoglobin including the proximal imidazole has been studied using the first-principles Hartree-Fock procedure. Our results for the {sup 57m}Fe isomer shift and asymmetry parameter are in very good agreement with the values obtained from Moessbauer spectroscopy measurements. The {sup 57m}Fe nuclear quadrupole coupling constant is smaller than the experimental result and possible ways to improve the agreement in the future are discussed. Improved analysis of the Moessbauer data, removing some approximations made for deriving the magnetic hyperfine tensor for the {sup 57m}Fe nucleus, is suggested to allow quantitative comparison with our results in the future.

Models including electron correlation in relation to Fock's proposed expansion of the ground-state wave function of He-like atomic ions

Energy Technology Data Exchange (ETDEWEB)

Glasser, M. L.; March, N. H.; Nieto, L. M. [Departamento de Fisica Teorica, Atomica y Optica, Universidad de Valladolid, ES-47011 Valladolid, Spain and Department of Physics, Clarkson University, Potsdam, New York 13699 (United States); Department of Physics, University of Antwerp, BE-2020 Antwerp, Belgium and Department of Theoretical Chemistry, University of Oxford, Oxford OX1 2JD (United Kingdom); Departamento de Fisica Teorica, Atomica y Optica, Universidad de Valladolid, ES-47011 Valladolid (Spain)

2011-12-15

Here attention is first drawn to the importance of gaining insight into Fock's early proposal for expanding the ground-state wave function for He-like atomic ions in hyperspherical coordinates. We approach the problem via two solvable models, namely, (i) the s-term model put forth by Temkin [Phys. Rev. 126, 130 (1962)] and (ii) the Hookean atom model proposed by Kestner and Sinanoglu [Phys. Rev. 128, 2687 (1962)]. In both cases the local kinetic energy can be obtained explicitly in hyperspherical coordinates. Separation of variables occurs in both model wave functions, though in a different context in the two cases. Finally, a k-space formulation is proposed that should eventually result in distinctive identifying characteristics of Fock's nonanalyticities for He-like atomic ions when both electrons are close to the nucleus.

Spiral magnetism in the single-band Hubbard model: the Hartree-Fock and slave-boson approaches.

Science.gov (United States)

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.

Koopmans' theorem in the Hartree-Fock method. General formulation

Science.gov (United States)

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.

Application of the RPA method based on the cranked Hartree-Fock-Bogolyubov model in 168Er and 158Dy

International Nuclear Information System (INIS)

Kvasil, J.; Khariev, M.M.; Cwiok, S.; Mikhajlov, I.N.; Khoriev, B.

1984-01-01

The Random Phase Approximation (RPA) based on the Cranked Hartree-Fock-Bogolyubov (CHFB) model is used for the study of low-lying nuclear states near the yrast line in 158 Dy and 168 Er. The relation of the spurious unphysical states connected with the nucleus centre of mass rotational motion to the solutions of RPA equations of motion is cleared up. The calculated level energies and reduced probabilities B(E2) are compared with experimental ones. The dependence of the residual interaction strength constants and the nucleus moment of inertia on the angular momentum is discussed. The experimental characteristics of low-lying states up to approx. 2 MeV are reproduced by the CHFB+RPA model. (author)

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.)

Nuclear-electronic orbital reduced explicitly correlated Hartree-Fock approach: Restricted basis sets and open-shell systems

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

Nuclear-electronic orbital reduced explicitly correlated Hartree-Fock approach: Restricted basis sets and open-shell systems

Energy Technology Data Exchange (ETDEWEB)

Brorsen, Kurt R.; Sirjoosingh, Andrew; Pak, Michael V.; Hammes-Schiffer, Sharon, E-mail: shs3@illinois.edu [Department of Chemistry, University of Illinois at Urbana-Champaign, 600 South Mathews Ave., Urbana, Illinois 61801 (United States)

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{sup −} 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{sup +}, 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.

Nucleon and isobar properties in a relativistic Hartree-Fock calculation with vector Richardson potential and various radial forms for scalar mass terms

International Nuclear Information System (INIS)

Dey, J.; Dey, M.; Mukhopadhyay, G.; Samanta, B.C.

1989-01-01

Mean field models of the nucleon and the delta are established with the two-quark vector Richardson potential along with various prescriptions for a running quark mass. This is taken to be a one-particle operator in the Dirac-Hartree Fock formalism. An effective density dependent one body potential U(ρ) for quarks at a given density ρ inside the nucleon is derived. It shows an interesting structure. Asymptotic freedom and confinement properties are built-in at high and low densities in U (ρ) and the model dependence is restricted to the intermediate desnsities. (author) [pt

Higher Fock states and power counting in exclusive P-wave quarkonium decays

CERN Document Server

Bolz, J; Schuler, G A; Bolz, Jan; Kroll, Peter; Schuler, Gerhard A.

1998-01-01

Exclusive processes at large momentum transfer Q factor into perturbatively calculable short-distance parts and long-distance hadronic wave functions. Usually, only contributions from the leading Fock states have to be included to leading order in 1/Q. We show that for exclusive decays of P-wave quarkonia the contribution from the next-higher Fock state |Q Qbar g> contributes at the same order in 1/Q. We investigate how the constituent gluon attaches to the hard process in order to form colour-singlet final-state hadrons and argue that a single additional long-distance factor is sufficient to parametrize the size of its contribution. Incorporating transverse degrees of freedom and Sudakov factors, our results are perturbatively stable in the sense that soft phase-space contributions are largely suppressed. Explicit calculations yield good agreement with data on chi_{c J} decays into pairs of pions, kaons, and etas. We also comment on J/psi decays into two pions.

Ab Initio periodic Hartree-Fock study of group IA cations in ANA-type zeolites

International Nuclear Information System (INIS)

Anchell, J.L.; White, J.C.; Thompson, M.R.; Hess, A.C.

1994-01-01

This study investigates the electronic structure of Group IA cations intercalated into zeolites with the analcime (ANA) framework using ab initio periodic Hartree-Fock theory. The purpose of the study is to gain a better understanding of the role played by electron-donating species in zeolites in general, with specific applications to materials that have been suggested as storage matrices for radioactive materials. The effect of the intercalated species (Na, K, Rb, and Cs) on the electronic structure of the zeolite is presented on the basis of an analysis of the total and projected density of states, Mulliken charges, and charge density differences. The results of those analyses indicate that, relative to a charge neutral atomic state, the Group IA species donate an electron to the zeolite lattice and interact most strongly with the s and p atomic states of oxygen as the species are moved through the lattice. In addition, estimates of the self-diffusion constants of Na, K, Rb, and Cs based upon a one-dimensional diffusion model parameterized from the ab initio total energy data will be presented. 24 refs., 8 figs., 4 tabs

Axially deformed solution of the Skyrme-Hartree-Fock-Bogoliubov equations using the transformed harmonic oscillator basis (II) HFBTHO v2.00d: A new version of the program

Science.gov (United States)

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

Microscopic descriptions of the superdeformed bands in the region A 190: Bohr and Routhian Hamiltonians in the Hartree-Fock-Bogolyubov approximation; Descriptions microscopiques des bandes superdeformees dans la region A 190: Hamiltonien de Bohr et Routhian a l`approximation de Hartee-Fock-Bogolyubov

Energy Technology Data Exchange (ETDEWEB)

Libert, J. [Centre d`Etudes Nucleaires, Bordeaux-1 Univ., 33 Gradignan (France); Girod, M.; Delaroche, J-P.; Berger, J-F.; Romain, P.; Peru, S. [CEA Centre d`Etudes de Bruyeres-le-Chatel, 91 (France)

1997-06-01

The superdeformed bands of the nuclei in the region A = 190 were described by two microscopic approaches using Gogny D1 finite range interaction. The first one consists in building a Bohr Hamiltonian in the framework of Gauss overlap approximation (GOA) of the generator-coordinate method, starting from Hartree-Fock-Bogolyubov solutions under quadrupole constraints. This collective Hamiltonian microscopically determined for five quadrupolar variables is then diagonalized by a projection method on a collective based adapted to the large variety of the deformations to be considered. A special attention was given to the precise definition of the under-barrier collective wavefunctions (for which an original method of solving the collective Schroedinger equation was developed) in order to described correctly the lifetime of the shape isomeric states. The other approach, that of Routhian is based also on the Hartree-Fock-Bogolyubov approximation. The calculations are carried out with and without restoring the broken symmetry associated to the particle numbers (as given by Lipkin-Nogami). The results (excitation energies, moments of inertia, etc...) of the two calculation methods are compared with most recent experimental data. The existence of the superdeformed bands corresponding to vibrational excitations similar to those appearing in {beta} and {gamma} bands is proposed

Correlation corrections to the Hartree-Fock perturbation theory of atomic and molecular properties. Dipole polarizabilities of He, Be and Ne

International Nuclear Information System (INIS)

Sadlej, A.J.

1980-01-01

The problem of the most efficient perturbation calculation of the correlation contributions to atomic and molecular properties is discussed. The method which is based on the coupled Hartree-Fock (CHF) perturbation theory appears to be the most promising one. The CHF-based perturbation theory of correlation effects is applied to the calculation of the second-order correlation contributions to the electric dipole polarizabilities of He, Be and Ne. The numerical approach employed in this paper consists in computing first the electric-field-dependent SCF functions. Then, the field dependent second-order correlation energy is calculated. The electric dipole polarizabilities, accurate through the second-order in correlation, are obtained via the numerical differentiation of the field-dependent energies with respect to the external electric field strength. In order to avoid the use of very large basis sets the so-called electric-field-variant (EFV) orbitals are employed in the present study. The CHF results obtained in this paper are of the same accuracy as the best literature data. In addition of the second-order correlation correction the final values of the electric dipole polarizability differ from the accurate or experimental results by less than a few per cent. (author)

The molecular structure and vibrational spectra of N-(2,2-diphenylacetyl)- N'-(naphthalen-1yl)-thiourea by Hartree-Fock and density functional methods

Science.gov (United States)

Arslan, Hakan; Mansuroglu, Demet Sezgin; VanDerveer, Don; Binzet, Gun

2009-04-01

N-(2,2-Diphenylacetyl)- N'-(naphthalen-1yl)-thiourea (PANT) has been synthesized and characterized by elemental analysis, IR spectroscopy and 1H NMR spectroscopy. The crystal and molecular structure of the title compound has been determined from single crystal X-ray diffraction data. It crystallizes in the triclinic space group P-1, Z = 2 with a = 10.284(2) Å, b = 10.790(2) Å, c = 11.305(2) Å, α = 64.92(3)°, β = 89.88(3)°, γ = 62.99(3)°, V = 983.7(3) Å 3 and Dcalc = 1.339 Mg/m 3. The molecular structure, vibrational frequencies and infrared intensities of PANT were calculated by the Hartree-Fock and density functional theory methods (BLYP and B3LYP) using the 6-31G* basis set. The calculated geometric parameters were compared to the corresponding X-ray structure of the title compound. We obtained 22 stable conformers for the title compound; however Conformer 1 is approximately 9.53 kcal/mol more stable than Conformer 22. The comparison of the theoretical and experimental geometry of the title compound shows that the X-ray parameters fairly well reproduce the geometry of Conformer 17. The harmonic vibrations computed for this compound by the B3LYP/6-31G* method are in good agreement with the observed IR spectral data. Theoretical vibrational spectra of the title compound were interpreted by means of PEDs using the VEDA 4 program. A general better performance of the investigated methods was calculated by PAVF 1.0 program.

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)

A simple and efficient dispersion correction to the Hartree-Fock theory (2): Incorporation of a geometrical correction for the basis set superposition error.

Science.gov (United States)

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.

Solution of the Skyrme-Hartree-Fock-Bogolyubov equations in the Cartesian deformed harmonic-oscillator basis. (VII) HFODD (v2.49t): A new version of the program

International Nuclear Information System (INIS)

Schunck, Nicolas F.; McDonnell, J.; Sheikh, J.A.; Staszczak, A.; Stoitsov, Mario; Dobaczewski, J.; 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.

On the physical interpretation of the nuclear molecular orbital energy.

Science.gov (United States)

Charry, Jorge; Pedraza-González, Laura; Reyes, Andrés

2017-06-07

Recently, several groups have extended and implemented molecular orbital (MO) schemes to simultaneously obtain wave functions for electrons and selected nuclei. Many of these schemes employ an extended Hartree-Fock approach as a first step to find approximate electron-nuclear wave functions and energies. Numerous studies conducted with these extended MO methodologies have explored various effects of quantum nuclei on physical and chemical properties. However, to the best of our knowledge no physical interpretation has been assigned to the nuclear molecular orbital energy (NMOE) resulting after solving extended Hartree-Fock equations. This study confirms that the NMOE is directly related to the molecular electrostatic potential at the position of the nucleus.

Dynamic equations for gauge-invariant wave functions

International Nuclear Information System (INIS)

Kapshaj, V.N.; Skachkov, N.B.; Solovtsov, I.L.

1984-01-01

The Bethe-Salpeter and quasipotential dynamic equations for wave functions of relative quark motion, have been derived. Wave functions are determined by the gauge invariant method. The V.A. Fock gauge condition is used in the construction. Despite the transl tional noninvariance of the gauge condition the standard separation of variables has been obtained and wave function doesn't contain gauge exponents

Direct Quantum Dynamics Using Grid-Based Wave Function Propagation and Machine-Learned Potential Energy Surfaces.

Science.gov (United States)

Richings, Gareth W; Habershon, Scott

2017-09-12

We describe a method for performing nuclear quantum dynamics calculations using standard, grid-based algorithms, including the multiconfiguration time-dependent Hartree (MCTDH) method, where the potential energy surface (PES) is calculated "on-the-fly". The method of Gaussian process regression (GPR) is used to construct a global representation of the PES using values of the energy at points distributed in molecular configuration space during the course of the wavepacket propagation. We demonstrate this direct dynamics approach for both an analytical PES function describing 3-dimensional proton transfer dynamics in malonaldehyde and for 2- and 6-dimensional quantum dynamics simulations of proton transfer in salicylaldimine. In the case of salicylaldimine we also perform calculations in which the PES is constructed using Hartree-Fock calculations through an interface to an ab initio electronic structure code. In all cases, the results of the quantum dynamics simulations are in excellent agreement with previous simulations of both systems yet do not require prior fitting of a PES at any stage. Our approach (implemented in a development version of the Quantics package) opens a route to performing accurate quantum dynamics simulations via wave function propagation of many-dimensional molecular systems in a direct and efficient manner.

2nd derivatives of the electronic energy in density functional theory

Energy Technology Data Exchange (ETDEWEB)

Dam, H. van

2001-08-01

This document details the equations needed to implement the calculation of vibrational frequencies within the density functional formalism of electronic structure theory. This functionality has been incorporated into the CCP1 DFT module and the required changes to the application programmers interface are outlined. Throughout it is assumed that an implementation of Hartree-Fock vibrational frequencies is available that can be modified to incorporate the density functional formalism. Employing GAMESS-UK as an example the required changes to the Hartree-Fock code are outlined. (author)

Test of a q-fractional V{sup (N-q)} Hartree-Fock potential for the calculation of double photoionization cross sections of neon

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)

Structure factors for tunneling ionization rates of molecules: General Hartree-Fock-based integral representation

Science.gov (United States)

Madsen, Lars Bojer; Jensen, Frank; Dnestryan, Andrey I.; Tolstikhin, Oleg I.

2017-07-01

In the leading-order approximation of the weak-field asymptotic theory (WFAT), the dependence of the tunneling ionization rate of a molecule in an electric field on its orientation with respect to the field is determined by the structure factor of the ionizing molecular orbital. The WFAT yields an expression for the structure factor in terms of a local property of the orbital in the asymptotic region. However, in general quantum chemistry approaches molecular orbitals are expanded in a Gaussian basis which does not reproduce their asymptotic behavior correctly. This hinders the application of the WFAT to polyatomic molecules, which are attracting increasing interest in strong-field physics. Recently, an integral-equation approach to the WFAT for tunneling ionization of one electron from an arbitrary potential has been developed. The structure factor is expressed in an integral form as a matrix element involving the ionizing orbital. The integral is not sensitive to the asymptotic behavior of the orbital, which resolves the difficulty mentioned above. Here, we extend the integral representation for the structure factor to many-electron systems treated within the Hartree-Fock method and show how it can be implemented on the basis of standard quantum chemistry software packages. We validate the methodology by considering noble-gas atoms and the CO molecule, for which accurate structure factors exist in the literature. We also present benchmark results for CO2 and for NH3 in the pyramidal and planar geometries.

A geometrical correction for the inter- and intra-molecular basis set superposition error in Hartree-Fock and density functional theory calculations for large systems

Science.gov (United States)

Kruse, Holger; Grimme, Stefan

2012-04-01

A semi-empirical counterpoise-type correction for basis set superposition error (BSSE) in molecular systems is presented. An atom pair-wise potential corrects for the inter- and intra-molecular BSSE in supermolecular Hartree-Fock (HF) or density functional theory (DFT) calculations. This geometrical counterpoise (gCP) denoted scheme depends only on the molecular geometry, i.e., no input from the electronic wave-function is required and hence is applicable to molecules with ten thousands of atoms. The four necessary parameters have been determined by a fit to standard Boys and Bernadi counterpoise corrections for Hobza's S66×8 set of non-covalently bound complexes (528 data points). The method's target are small basis sets (e.g., minimal, split-valence, 6-31G*), but reliable results are also obtained for larger triple-ζ sets. The intermolecular BSSE is calculated by gCP within a typical error of 10%-30% that proves sufficient in many practical applications. The approach is suggested as a quantitative correction in production work and can also be routinely applied to estimate the magnitude of the BSSE beforehand. The applicability for biomolecules as the primary target is tested for the crambin protein, where gCP removes intramolecular BSSE effectively and yields conformational energies comparable to def2-TZVP basis results. Good mutual agreement is also found with Jensen's ACP(4) scheme, estimating the intramolecular BSSE in the phenylalanine-glycine-phenylalanine tripeptide, for which also a relaxed rotational energy profile is presented. A variety of minimal and double-ζ basis sets combined with gCP and the dispersion corrections DFT-D3 and DFT-NL are successfully benchmarked on the S22 and S66 sets of non-covalent interactions. Outstanding performance with a mean absolute deviation (MAD) of 0.51 kcal/mol (0.38 kcal/mol after D3-refit) is obtained at the gCP-corrected HF-D3/(minimal basis) level for the S66 benchmark. The gCP-corrected B3LYP-D3/6-31G* model

A geometrical correction for the inter- and intra-molecular basis set superposition error in Hartree-Fock and density functional theory calculations for large systems.

Science.gov (United States)

Kruse, Holger; Grimme, Stefan

2012-04-21

A semi-empirical counterpoise-type correction for basis set superposition error (BSSE) in molecular systems is presented. An atom pair-wise potential corrects for the inter- and intra-molecular BSSE in supermolecular Hartree-Fock (HF) or density functional theory (DFT) calculations. This geometrical counterpoise (gCP) denoted scheme depends only on the molecular geometry, i.e., no input from the electronic wave-function is required and hence is applicable to molecules with ten thousands of atoms. The four necessary parameters have been determined by a fit to standard Boys and Bernadi counterpoise corrections for Hobza's S66×8 set of non-covalently bound complexes (528 data points). The method's target are small basis sets (e.g., minimal, split-valence, 6-31G*), but reliable results are also obtained for larger triple-ζ sets. The intermolecular BSSE is calculated by gCP within a typical error of 10%-30% that proves sufficient in many practical applications. The approach is suggested as a quantitative correction in production work and can also be routinely applied to estimate the magnitude of the BSSE beforehand. The applicability for biomolecules as the primary target is tested for the crambin protein, where gCP removes intramolecular BSSE effectively and yields conformational energies comparable to def2-TZVP basis results. Good mutual agreement is also found with Jensen's ACP(4) scheme, estimating the intramolecular BSSE in the phenylalanine-glycine-phenylalanine tripeptide, for which also a relaxed rotational energy profile is presented. A variety of minimal and double-ζ basis sets combined with gCP and the dispersion corrections DFT-D3 and DFT-NL are successfully benchmarked on the S22 and S66 sets of non-covalent interactions. Outstanding performance with a mean absolute deviation (MAD) of 0.51 kcal/mol (0.38 kcal/mol after D3-refit) is obtained at the gCP-corrected HF-D3/(minimal basis) level for the S66 benchmark. The gCP-corrected B3LYP-D3/6-31G* model

An exactly soluble Hartree problem in an external potential

International Nuclear Information System (INIS)

Gunn, J.C.; Gunn, J.M.F.

1987-09-01

The problem of N bosons interacting with each other via repulsive delta function interactions and with an external, attractive, delta function potential is solved within the Hartree approximation, exactly. It is found that if the interparticle interactions are above a certain value, there is no bound state. Thus the bound state does not just expand to compensate for the increase in the repulsive Hartree potential. Moreover as the interaction strength is increased to that value, the ground state wave function develops a pole at the position of the attractive potential. (author)

Similarity transformed equation of motion coupled-cluster theory based on an unrestricted Hartree-Fock reference for applications to high-spin open-shell systems.

Science.gov (United States)

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.

Similarity transformed equation of motion coupled-cluster theory based on an unrestricted Hartree-Fock reference for applications to high-spin open-shell systems

Science.gov (United States)

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.

Lattice Dynamics of Beryllium from a First-Principles Nonlocal Pseudopotential Approach

DEFF Research Database (Denmark)

Walter, F. King; Cutler, P. H.

1970-01-01

dielectric-screening function employing the Kohn-Sham approximation for exchange among the conduction electrons. The energy-wave-number characteristic F(q) is constructed from the Hartree-Fock-Slater (HFS) wave function for Be++; this is used to calculate the phonon dispersion relations in the [0001], [011̅...

Application of the weak-field asymptotic theory to the analysis of tunneling ionization of linear molecules

DEFF Research Database (Denmark)

Madsen, Lars Bojer; Tolstikhin, Oleg I.; Morishita, Toru

2012-01-01

The recently developed weak-field asymptotic theory [ Phys. Rev. A 84 053423 (2011)] is applied to the analysis of tunneling ionization of a molecular ion (H2+), several homonuclear (H2, N2, O2) and heteronuclear (CO, HF) diatomic molecules, and a linear triatomic molecule (CO2) in a static...... electric field. The dependence of the ionization rate on the angle between the molecular axis and the field is determined by a structure factor for the highest occupied molecular orbital. This factor is calculated using a virtually exact discrete variable representation wave function for H2+, very accurate...... Hartree-Fock wave functions for the diatomics, and a Hartree-Fock quantum chemistry wave function for CO2. The structure factors are expanded in terms of standard functions and the associated structure coefficients, allowing the determination of the ionization rate for any orientation of the molecule...

Local-scaling density-functional method: Intraorbit and interorbit density optimizations

International Nuclear Information System (INIS)

Koga, T.; Yamamoto, Y.; Ludena, E.V.

1991-01-01

The recently proposed local-scaling density-functional theory provides us with a practical method for the direct variational determination of the electron density function ρ(r). The structure of ''orbits,'' which ensures the one-to-one correspondence between the electron density ρ(r) and the N-electron wave function Ψ({r k }), is studied in detail. For the realization of the local-scaling density-functional calculations, procedures for intraorbit and interorbit optimizations of the electron density function are proposed. These procedures are numerically illustrated for the helium atom in its ground state at the beyond-Hartree-Fock level

Transferability and accuracy by combining dispersionless density functional and incremental post-Hartree-Fock theories: Noble gases adsorption on coronene/graphene/graphite surfaces

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

Studies of the electron density in the highest occupied molecular orbitals of PH 3, PF 3 and P(CH 3) 3 by electron momentum spectroscopy and Hartree-Fock, MRSD-CI and DFT calculations

Science.gov (United States)

Rolke, J.; Brion, C. E.

1996-06-01

The spherically averaged momentum profiles for the highest occupied molecular orbitals of PF 3 and P(CH 3) 3 have been obtained by electron momentum spectroscopy. The measurements provide a stringent test of basis set effects and the quality of ab-initio methods in the description of these larger molecular systems. As in previous work on the methyl-substituted amines, intuitive arguments fail to predict the correct amount of s- and p-type contributions to the momentum profile while delocalized molecular orbital concepts provide a more adequate description of the HOMOs. The experimental momentum profiles have been compared with theoretical momentum profiles calculated at the level of the target Hartree-Fock approximation with a range of basis sets. New Hartree-Fock calculations are also presented for the HOMO of PH 3 and compared to previously published experimental and theoretical momentum profiles. The experimental momentum profiles have further been compared to calculations at the level of the target Kohn-Sham approximation using density functional theory with the local density approximation and also with gradient corrected (non-local) exchange correlation potentials. In addition, total energies and dipole moments have been calculated for all three molecules by the various theoretical methods and compared to experimental values. Calculated 'density difference maps' show the regions where the HOMO momentum and position electron densities of PF 3 and P(CH 3) 3 change relative to the corresponding HOMO density of PH 3. The results suggest that methyl groups have an electron-attracting effect (relative to H) on the HOMO charge density in trimethyl phosphines. These conclusions are supported by a consideration of dipole moments and the 31P NMR chemical shifts for PH 3, PF 3 and P(CH 3) 3.

Application of the graphical unitary group approach to the energy second derivative for CI wave functions via the coupled perturbed CI equations

International Nuclear Information System (INIS)

Fox, D.J.

1983-10-01

Analytic derivatives of the potential energy for Self-Consistent-Field (SCF) wave functions have been developed in recent years and found to be useful tools. The first derivative for configuration interaction (CI) wave functions is also available. This work details the extension of analytic methods to energy second derivatives for CI wave functions. The principal extension required for second derivatives is evaluation of the first order change in the CI wave function with respect to a nuclear perturbation. The shape driven graphical unitary group approach (SDGUGA) direct CI program was adapted to evaluate this term via the coupled-perturbed CI equations. Several iterative schemes are compared for use in solving these equations. The pilot program makes no use of molecular symmetry but the timing results show that utilization of molecular symmetry is desirable. The principles for defining and solving a set of symmetry adapted equations are discussed. Evaluation of the second derivative also requires the solution of the second order coupled-perturbed Hartree-Fock equations to obtain the correction to the molecular orbitals due to the nuclear perturbation. This process takes a consistently higher percentage of the computation time than for the first order equations alone and a strategy for its reduction is discussed

Hartree-Fock study of the Anderson metal-insulator transition in the presence of Coulomb interaction: Two types of mobility edges and their multifractal scaling exponents

Science.gov (United States)

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

Orbital stability of standing waves of a class of fractional Schrödinger equations with Hartree-type nonlinearity

KAUST Repository

Cho, Yonggeun

2016-05-04

This paper is devoted to the mathematical analysis of a class of nonlinear fractional Schrödinger equations with a general Hartree-type integrand. We show the well-posedness of the associated Cauchy problem and prove the existence and stability of standing waves under suitable assumptions on the nonlinearity. Our proofs rely on a contraction argument in mixed functional spaces and the concentration-compactness method. © 2015 World Scientific Publishing Company

Roothaan approach in the thermodynamic limit

Science.gov (United States)

Gutierrez, G.; Plastino, A.

1982-02-01

A systematic method for the solution of the Hartree-Fock equations in the thermodynamic limit is presented. The approach is seen to be a natural extension of the one usually employed in the finite-fermion case, i.e., that developed by Roothaan. The new techniques developed here are applied, as an example, to neutron matter, employing the so-called V1 Bethe "homework" potential. The results obtained are, by far, superior to those that the ordinary plane-wave Hartree-Fock theory yields. NUCLEAR STRUCTURE Hartree-Fock approach; nuclear and neutron matter.

On the description of electronic final states in the K-shell ionization by protons

International Nuclear Information System (INIS)

Aashamar, O.; Kocbach, L.

1976-06-01

The choice of free electronic wave functions in the description of K-shell ionization by protons is discussed. The previously known discrepancies between PWBA and SCA results are shown to be entirely due to two different choices of electronic wave functions. Calculations in the SCA framework with Hartree-Fock-Slater wave functions are reported. Some general features of the SCA calculations are discussed. (Auth.)

Effects of valence nucleon orbits and charge symmetry breaking interaction on the Nolen-Schiffer anomaly of mirror nuclei

International Nuclear Information System (INIS)

Suzuki, T.; Sagawa, H.; Arima, A.

1992-01-01

Coulomb energy differences (Nolen-Schiffer anomalies) of mirror nuclei 17 O- 17 F and 41 Ca- 41 Sc are studied by using realistic Hartree-Fock and Woods-Saxon single-particle wave functions which are determined precisely through the analysis of the magnetic form factors of electron scattering. These single-particle wave functions are used to evaluate the Coulomb energy differences due to charge symmetry breaking forces, with new coupling constants determined by the analysis of the scattering lengths of pp and nn system which have been successfully applied to the Coulomb energy difference of 3 He- 3 H. We also evaluated the effects of the charge symmetry breaking forces using Hartree-Fock wave functions. Together with various other contributions, our calculated values of the Coulomb energy differences, which showed deviations of 3-9% from the experimental values in the previous analysis of Nolen and Schiffer, agree with the experimental values within 1% (2%) accuracy for A=17 (41). (orig.)

Ab initio Hartree-Fock and density functional theory investigations on the conformational stability, molecular structure and vibrational spectra of 5-chloro-3-(2-(4-methylpiperazin-1-yl)-2-oxoethyl)benzo[d]thiazol-2(3H)-one drug molecule.

Science.gov (United States)

Taşal, Erol; Kumalar, Mustafa

2012-09-01

In this work, the experimental and theoretical spectra of 5-chloro-3-(2-(4-methylpiperazin-1-yl)-2-oxoethyl)benzo[d]thiazol-2(3H)-one molecule (abbreviated as 5CMOT) are studied. The molecular geometry and vibrational frequencies are calculated in the ground state of molecule using ab initio Hartree-Fock (HF) and Density Function Theory (DFT) methods with 6-311++G(d,p), 6-31G++(d,p), 6-31G(d,p), 6-31G(d) and 6-31G basis sets. Three staggered stable conformers were observed on the torsional potential energy surfaces. The complete assignments were performed on the basis of the total energy distribution (TED) of the vibrational modes calculated. The comparison of the theoretical and experimental geometries of the title compound indicated that the X-ray parameters fairly well agree with the theoretically obtained values for the most stable conformer. The theoretical results showed an excellent agreement with the experimental values. The calculated HOMO and LUMO energies show that the charge transfer occurs within the molecule. Copyright © 2012 Elsevier B.V. All rights reserved.

On the XFEL Schrödinger Equation: Highly Oscillatory Magnetic Potentials and Time Averaging

KAUST Repository

Antonelli, Paolo; Athanassoulis, Agisillaos; Hajaiej, Hichem; Markowich, Peter A.

2014-01-01

We analyse a nonlinear Schrödinger equation for the time-evolution of the wave function of an electron beam, interacting selfconsistently through a Hartree-Fock nonlinearity and through the repulsive Coulomb interaction of an atomic nucleus

Competition between spin, charge, and bond waves in a Peierls-Hubbard model

International Nuclear Information System (INIS)

Venegas, P.A.; Henriquez, C.; Roessler, J.

1996-01-01

We study a one-dimensional extended Peierls-Hubbard model coupled to intracell and intercell phonons for a half-filled band. The calculations are made using the Hartree-Fock and adiabatic approximations for arbitrary temperature. In addition to static spin, charge, and bond density waves, we predict intermediate phases that lack inversion symmetry, and phase transitions that reduce symmetry on increasing temperature. copyright 1996 The American Physical Society

Ab initio effective core potentials for molecular calculations. Potentials for main group elements Na to Bi

International Nuclear Information System (INIS)

Wadt, W.R.; Hay, P.J.

1985-01-01

A consistent set of ab initio effective core potentials (ECP) has been generated for the main group elements from Na to Bi using the procedure originally developed by Kahn. The ECP's are derived from all-electron numerical Hartree--Fock atomic wave functions and fit to analytical representations for use in molecular calculations. For Rb to Bi the ECP's are generated from the relativistic Hartree--Fock atomic wave functions of Cowan which incorporate the Darwin and mass--velocity terms. Energy-optimized valence basis sets of (3s3p) primitive Gaussians are presented for use with the ECP's. Comparisons between all-electron and valence-electron ECP calculations are presented for NaF, NaCl, Cl 2 , Cl 2 - , Br 2 , Br 2 - , and Xe 2 + . The results show that the average errors introduced by the ECP's are generally only a few percent

Dependence of Excited State Potential Energy Surfaces on the Spatial Overlap of the Kohn-Sham Orbitals and the Amount of Nonlocal Hartree-Fock Exchange in Time-Dependent Density Functional Theory.

Science.gov (United States)

Plötner, Jürgen; Tozer, David J; Dreuw, Andreas

2010-08-10

Time-dependent density functional theory (TDDFT) with standard GGA or hybrid exchange-correlation functionals is not capable of describing the potential energy surface of the S1 state of Pigment Yellow 101 correctly; an additional local minimum is observed at a twisted geometry with substantial charge transfer (CT) character. To investigate the influence of nonlocal exact orbital (Hartree-Fock) exchange on the shape of the potential energy surface of the S1 state in detail, it has been computed along the twisting coordinate employing the standard BP86, B3LYP, and BHLYP xc-functionals as well as the long-range separated (LRS) exchange-correlation (xc)-functionals LC-BOP, ωB97X, ωPBE, and CAM-B3LYP and compared to RI-CC2 benchmark results. Additionally, a recently suggested Λ-parameter has been employed that measures the amount of CT in an excited state by calculating the spatial overlap of the occupied and virtual molecular orbitals involved in the transition. Here, the error in the calculated S1 potential energy curves at BP86, B3LYP, and BHLYP can be clearly related to the Λ-parameter, i.e., to the extent of charge transfer. Additionally, it is demonstrated that the CT problem is largely alleviated when the BHLYP xc-functional is employed, although it still exhibits a weak tendency to underestimate the energy of CT states. The situation improves drastically when LRS-functionals are employed within TDDFT excited state calculations. All tested LRS-functionals give qualitatively the correct potential energy curves of the energetically lowest excited states of P. Y. 101 along the twisting coordinate. While LC-BOP and ωB97X overcorrect the CT problem and now tend to give too large excitation energies compared to other non-CT states, ωPBE and CAM-B3LYP are in excellent agreement with the RI-CC2 results, with respect to both the correct shape of the potential energy curve as well as the absolute values of the calculated excitation energies.

The positronium and the dipositronium in a Hartree-Fock approximation of quantum electrodynamics

Science.gov (United States)

Sok, Jérémy

2016-02-01

The Bogoliubov-Dirac-Fock (BDF) model is a no-photon approximation of quantum electrodynamics. It allows to study relativistic electrons in interaction with the Dirac sea. A state is fully characterized by its one-body density matrix, an infinite rank non-negative projector. We prove the existence of the para-positronium, the bound state of an electron and a positron with antiparallel spins, in the BDF model represented by a critical point of the energy functional in the absence of an external field. We also prove the existence of the dipositronium, a molecule made of two electrons and two positrons that also appears as a critical point. More generally, for any half integer j ∈ 1/2 + Z + , we prove the existence of a critical point of the energy functional made of 2j + 1 electrons and 2j + 1 positrons.

Construction of the Fock Matrix on a Grid-Based Molecular Orbital Basis Using GPGPUs.

Science.gov (United States)

Losilla, Sergio A; Watson, Mark A; Aspuru-Guzik, Alán; Sundholm, Dage

2015-05-12

We present a GPGPU implementation of the construction of the Fock matrix in the molecular orbital basis using the fully numerical, grid-based bubbles representation. For a test set of molecules containing up to 90 electrons, the total Hartree-Fock energies obtained from reference GTO-based calculations are reproduced within 10(-4) Eh to 10(-8) Eh for most of the molecules studied. Despite the very large number of arithmetic operations involved, the high performance obtained made the calculations possible on a single Nvidia Tesla K40 GPGPU card.

Determination of the molecular structure via the medium energy electrons (500 eV-1,5 KeV) Ar, N2, Co e HCl

International Nuclear Information System (INIS)

Nogueira, J.C.

1977-01-01

Elastic Differential and Total Differential Cross Sections are measured for electron collision in medium-energy range (500 eV - 1,5 KeV) with argon, nitrogen, carbon monoxide and hydrogen chloride, all in their electronic ground state. Theoretical calculation for the Elastic Differential Cross Sections by atoms were done employing Hartree-Fock-Clementy wave function, and making use of Partial Wave and WKBJ Methods. Exchange effect is included in the case of argon. Independent Atom Model, Half Molecule Model and a new model, the Ionic Model were utilized for the molecular calculations. The Ionic Model is suggested for the interaction between HCl and electrons. Inelastic Differential Cross Section were also computed, making use of the First Born Approximation and Hartree-Fock-Clementi wave function. It is also demonstrated, for the first time, that medium energy electrons (500 eV - 1,5 Kev) can be used to determine molecular structure parameters, in gas phase [pt

Method and basis set dependence of anharmonic ground state nuclear wave functions and zero-point energies: Application to SSSH

Science.gov (United States)

Kolmann, Stephen J.; Jordan, Meredith J. T.

2010-02-01

One of the largest remaining errors in thermochemical calculations is the determination of the zero-point energy (ZPE). The fully coupled, anharmonic ZPE and ground state nuclear wave function of the SSSH radical are calculated using quantum diffusion Monte Carlo on interpolated potential energy surfaces (PESs) constructed using a variety of method and basis set combinations. The ZPE of SSSH, which is approximately 29 kJ mol-1 at the CCSD(T)/6-31G∗ level of theory, has a 4 kJ mol-1 dependence on the treatment of electron correlation. The anharmonic ZPEs are consistently 0.3 kJ mol-1 lower in energy than the harmonic ZPEs calculated at the Hartree-Fock and MP2 levels of theory, and 0.7 kJ mol-1 lower in energy at the CCSD(T)/6-31G∗ level of theory. Ideally, for sub-kJ mol-1 thermochemical accuracy, ZPEs should be calculated using correlated methods with as big a basis set as practicable. The ground state nuclear wave function of SSSH also has significant method and basis set dependence. The analysis of the nuclear wave function indicates that SSSH is localized to a single symmetry equivalent global minimum, despite having sufficient ZPE to be delocalized over both minima. As part of this work, modifications to the interpolated PES construction scheme of Collins and co-workers are presented.

Method and basis set dependence of anharmonic ground state nuclear wave functions and zero-point energies: application to SSSH.

Science.gov (United States)

Kolmann, Stephen J; Jordan, Meredith J T

2010-02-07

One of the largest remaining errors in thermochemical calculations is the determination of the zero-point energy (ZPE). The fully coupled, anharmonic ZPE and ground state nuclear wave function of the SSSH radical are calculated using quantum diffusion Monte Carlo on interpolated potential energy surfaces (PESs) constructed using a variety of method and basis set combinations. The ZPE of SSSH, which is approximately 29 kJ mol(-1) at the CCSD(T)/6-31G* level of theory, has a 4 kJ mol(-1) dependence on the treatment of electron correlation. The anharmonic ZPEs are consistently 0.3 kJ mol(-1) lower in energy than the harmonic ZPEs calculated at the Hartree-Fock and MP2 levels of theory, and 0.7 kJ mol(-1) lower in energy at the CCSD(T)/6-31G* level of theory. Ideally, for sub-kJ mol(-1) thermochemical accuracy, ZPEs should be calculated using correlated methods with as big a basis set as practicable. The ground state nuclear wave function of SSSH also has significant method and basis set dependence. The analysis of the nuclear wave function indicates that SSSH is localized to a single symmetry equivalent global minimum, despite having sufficient ZPE to be delocalized over both minima. As part of this work, modifications to the interpolated PES construction scheme of Collins and co-workers are presented.

A single-electron picture based on the multiconfiguration time-dependent Hartree-Fock method: application to the anisotropic ionization and subsequent high-harmonic generation of the CO molecule

Science.gov (United States)

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.

Some implications of the Hartree product treatment of the quantum nuclei in the ab initio nuclear–electronic orbital methodology

Energy Technology Data Exchange (ETDEWEB)

Gharabaghi, Masumeh [Faculty of Chemical and Petroleum Sciences, Shahid Beheshti University, G. C., Evin, Tehran, 19839, P.O. Box 19395-4716 (Iran, Islamic Republic of); Shahbazian, Shant, E-mail: chemist_shant@yahoo.com [Department of Physics, Shahid Beheshti University, G. C., Evin, Tehran, 19839, P.O. Box 19395-4716 (Iran, Islamic Republic of)

2016-12-09

In this letter the conceptual and computational implications of the Hartree product type nuclear wavefunction introduced recently within the context of the ab initio non-Born–Oppenheimer Nuclear–electronic orbital (NEO) methodology are considered. It is demonstrated that this wavefunction may imply a pseudo-adiabatic separation of the nuclei and electrons and each nucleus is conceived as a quantum oscillator while a non-Coulombic effective Hamiltonian is deduced for electrons. Using the variational principle this Hamiltonian is employed to derive a modified set of single-component Hartree–Fock equations which are equivalent to the multi-component version derived previously within the context of the NEO and, easy to be implemented computationally. - Highlights: • The Hartree product wavefunction is used for the quantum nuclei of a molecule. • With this wavefunction quantum nuclei may be conceived as quantum oscillators. • Using variational integral, non-Coulomb effective electronic Hamiltonian was derived. • A set of modified Hartree–Fock equations were derived from this Hamiltonian. • The derived equations are equivalent to the multi-component Hartree–Fock equations.

Collapse of the random-phase approximation: Examples and counter-examples from the shell model

International Nuclear Information System (INIS)

Johnson, Calvin W.; Stetcu, Ionel

2009-01-01

The Hartree-Fock approximation to the many-fermion problem can break exact symmetries, and in some cases by changing a parameter in the interaction one can drive the Hartree-Fock minimum from a symmetry-breaking state to a symmetry-conserving state (also referred to as a 'phase transition' in the literature). The order of the transition is important when one applies the random-phase approximation (RPA) to the of the Hartree-Fock wave function: if first order, RPA is stable through the transition, but if second-order, then the RPA amplitudes become large and lead to unphysical results. The latter is known as 'collapse' of the RPA. While the difference between first- and second-order transitions in the RPA was first pointed out by Thouless, we present for the first time nontrivial examples of both first- and second-order transitions in a uniform model, the interacting shell-model, where we can compare to exact numerical results.

Relativistic Hartree-Bogoliubov description of the halo nuclei

Energy Technology Data Exchange (ETDEWEB)

Meng, J.; Ring, P. [Universitaet Muenchen, Garching (Germany)

1996-12-31

Here the authors report the development of the relativistic Hartree-Bogoliubov theory in coordinate space. Pairing correlations are taken into account by both density dependent force of zero range and finite range Gogny force. As a primary application the relativistic HB theory is used to describe the chain of Lithium isotopes reaching from {sup 6}Li to {sup 11}Li. In contrast to earlier investigations within a relativistic mean field theory and a density dependent Hartree Fock theory, where the halo in {sup 11}Li could only be reproduced by an artificial shift of the 1p{sub 1/2} level close to the continuum limit, the halo is now reproduced in a self-consistent way without further modifications using the scattering of Cooper pairs to the 2s{sub 1/2} level in the continuum. Excellent agreement with recent experimental data is observed.

Calibration of Sn-119 isomer shift using ab initio wave function methods

NARCIS (Netherlands)

Kurian, Reshmi; Filatov, Michael

2009-01-01

The isomer shift for the 23.87 keV M1 resonant transition in the Sn-119 nucleus is calibrated with the help of ab initio calculations. The calibration constant alpha(Sn-119) obtained from Hartree-Fock (HF) calculations (alpha(HF)(Sn-119)=(0.081 +/- 0.002)a(0)(-3) mm/s) and from second-order

Tensor force effect on the evolution of single-particle energies in some isotopic chains in the relativistic Hartree-Fock approximation

Science.gov (United States)

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.

QCD Phenomenology and Light-Front Wave Functions

International Nuclear Information System (INIS)

Brodsky, St.J.

2001-01-01

A natural calculus for describing the bound-state structure of relativistic composite systems in quantum field theory is the light-front Fock expansion which encodes the properties of a hadrons in terms of a set of frame-independent n-particle wave functions. Light-front quantization in the doubly-transverse light-cone gauge has a number of remarkable advantages, including explicit unitarity, a physical Fock expansion, the absence of ghost degrees of freedom, and the decoupling properties needed to prove factorization theorems in high momentum transfer inclusive and exclusive reactions. A number of applications are discussed in these lectures, including semileptonic B decays, two-photon exclusive reactions, diffractive dissociation into jets, and deeply virtual Compton scattering. The relation of the intrinsic sea to the light-front wave functions is discussed. Light-front quantization can also be used in the Hamiltonian form to construct an event generator for high energy physics reactions at the amplitude level. The light-cone partition function, summed over exponentially-weighted light-cone energies, has simple boost properties which may be useful for studies in heavy ion collisions. I also review recent work which shows that the structure functions measured in deep inelastic lepton scattering are affected by final-state rescattering, thus modifying their connection to light-front probability distributions. In particular, the shadowing of nuclear structure functions is due to destructive interference effects from leading-twist diffraction of the virtual photon, physics not included in the nuclear light-cone wave functions. (author)

Calculation of transition probabilities using the multiconfiguration Dirac-Fock method

International Nuclear Information System (INIS)

Kim, Yong Ki; Desclaux, Jean Paul; Indelicato, Paul

1998-01-01

The performance of the multiconfiguration Dirac-Fock (MCDF) method in calculating transition probabilities of atoms is reviewed. In general, the MCDF wave functions will lead to transition probabilities accurate to ∼ 10% or better for strong, electric-dipole allowed transitions for small atoms. However, it is more difficult to get reliable transition probabilities for weak transitions. Also, some MCDF wave functions for a specific J quantum number may not reduce to the appropriate L and S quantum numbers in the nonrelativistic limit. Transition probabilities calculated from such MCDF wave functions for nonrelativistically forbidden transitions are unreliable. Remedies for such cases are discussed

Symbolic computation of the Hartree-Fock energy from a chiral EFT three-nucleon interaction at N2LO

International Nuclear Information System (INIS)

Gebremariam, B.; Bogner, S.K.; Duguet, T.

2010-01-01

We present the first of a two-part Mathematica notebook collection that implements a symbolic approach for the application of the density matrix expansion (DME) to the Hartree-Fock (HF) energy from a chiral effective field theory (EFT) three-nucleon interaction at N 2 LO. The final output from the notebooks is a Skyrme-like energy density functional that provides a quasi-local approximation to the non-local HF energy. In this paper, we discuss the derivation of the HF energy and its simplification in terms of the scalar/vector-isoscalar/isovector parts of the one-body density matrix. Furthermore, a set of steps is described and illustrated on how to extend the approach to other three-nucleon interactions. Program summary: Program title: SymbHFNNN; Catalogue identifier: AEGC v 1 0 ; Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEGC_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.: 96 666; No. of bytes in distributed program, including test data, etc.: 378 083; Distribution format: tar.gz; Programming language: Mathematica 7.1; Computer: Any computer running Mathematica 6.0 and later versions; Operating system: Windows Xp, Linux/Unix; RAM: 256 Mb; Classification: 5, 17.16, 17.22; Nature of problem: The calculation of the HF energy from the chiral EFT three-nucleon interaction at N 2 LO involves tremendous spin-isospin algebra. The problem is compounded by the need to eventually obtain a quasi-local approximation to the HF energy, which requires the HF energy to be expressed in terms of scalar/vector-isoscalar/isovector parts of the one-body density matrix. The Mathematica notebooks discussed in this paper solve the latter issue. Solution method: The HF energy from the chiral EFT three-nucleon interaction at N 2 LO is cast into a form suitable for an automatic

Gauge origin independent calculations of molecular magnetisabilities in relativistic four-component theory

DEFF Research Database (Denmark)

Iliaš, M.; Jensen, Hans Jørgen Aagaard; Bast, R.

2013-01-01

of the four-component relativistic linear response method at the self-consistent field single reference level. Benefits of employing the London atomic orbitals in relativistic calculations are illustrated with Hartree-Fock wave functions on the XF3 (X = N, P, As, Sb, Bi) series of molecules. Significantly...

Quantities Ts[n] and Tc[n] in density-functional theory

International Nuclear Information System (INIS)

Zhao, Q.; Parr, R.G.

1992-01-01

Levy's constrained-search procedure [Proc. Natl. Acad. Sci. U.S, North 76, 6062 (1979)] is employed to show how to determine Kohn-Sham and Hartree-Fock-Kohn-Sham orbitals and kinetic energies T s and T c , for the two-electron, four-electron, and the general case starting from the electron density. Numerical results are presented for the species H - through F 7+ and the atom Be. The Pauli potential is also determined for Be. The small differences among Kohn-Sham, Hartree-Fock, and Hartree-Fock-Kohn-Sham orbitals suggest that determination of Kohn-Sham orbitals from the density in this way is an attractive procedure for getting an orbital description from an electron density

The positronium and the dipositronium in a Hartree-Fock approximation of quantum electrodynamics

DEFF Research Database (Denmark)

Sok, Jérémy Vithya

2016-01-01

The Bogoliubov-Dirac-Fock (BDF) model is a no-photon approximation of quantum electrodynamics. It allows to study relativistic electrons in interaction with the Dirac sea. A state is fully characterized by its one-body density matrix, an infinite rank non-negative projector. We prove the existence...

Solution of the Skyrme-Hartree-Fock-Bogolyubov equations in the Cartesian deformed harmonic-oscillator basis.. (VII) HFODD (v2.49t): A new version of the program

Science.gov (United States)

Schunck, N.; Dobaczewski, J.; McDonnell, J.; Satuła, W.; Sheikh, J. A.; Staszczak, A.; Stoitsov, M.; Toivanen, P.

2012-01-01

-consistent Hartree-Fock equations, even for heavy nuclei, and for various nucleonic ( n-particle- n-hole) configurations, deformations, excitation energies, or angular momenta. Similarly, Local Density Approximation in the particle-particle channel, which is equivalent to using a zero-range interaction, allows for a simple implementation of pairing effects within the Hartree-Fock-Bogolyubov method. Solution method: The program uses the Cartesian harmonic oscillator basis to expand single-particle or single-quasiparticle wave functions of neutrons and protons interacting by means of the Skyrme effective interaction and zero-range pairing interaction. The expansion coefficients are determined by the iterative diagonalization of the mean-field Hamiltonians or Routhians which depend non-linearly on the local neutron and proton densities. Suitable constraints are used to obtain states corresponding to a given configuration, deformation or angular momentum. The method of solution has been presented in: [J. Dobaczewski, J. Dudek, Comput. Phys. Commun. 102 (1997) 166]. Reasons for new version: Version 2.49s of HFODD provides a number of new options such as the isospin mixing and projection of the Skyrme functional, the finite-temperature HF and HFB formalism and optimized methods to perform multi-constrained calculations. It is also the first version of HFODD to contain threading and parallel capabilities. Summary of revisions: Isospin mixing and projection of the HF states has been implemented. The finite-temperature formalism for the HFB equations has been implemented. The Lipkin translational energy correction method has been implemented. Calculation of the shell correction has been implemented. The two-basis method for the solution to the HFB equations has been implemented. The Augmented Lagrangian Method (ALM) for calculations with multiple constraints has been implemented. The linear constraint method based on the cranking approximation of the RPA matrix has been implemented. An

Functional approach to a time-dependent self-consistent field theory

International Nuclear Information System (INIS)

Reinhardt, H.

1979-01-01

The time-dependent Hartree-Fock approximation is formulated within the path integral approach. It is shown that by a suitable choice of the collective field the classical equation of motion of the collective field coincides with the time-dependent Hartree (TDH) equation. The consideration is restricted to the TDH equation, since the exchange terms do not appear in the functional approach on the same footing as the direct terms

Roothaan's approach to solve the Hartree-Fock equations for atoms confined by soft walls: Basis set with correct asymptotic behavior.

Science.gov (United States)

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.

Finite-field evaluation of the Lennard-Jones atom-wall interaction constant C3 for alkali-metal atoms

International Nuclear Information System (INIS)

Johnson, W.R.; Dzuba, V.A.; Safronova, U.I.; Safronova, M.S.

2004-01-01

A finite-field scaling method is applied to evaluate the Lennard-Jones interaction constant C 3 for alkali-metal atoms. The calculations are based on the relativistic single-double approximation in which single and double excitations of Dirac-Hartree-Fock wave functions are included to all orders in perturbation theory

Densities, form factors, transitions and multipole moments in the s-d shell, with the Skyrme force

International Nuclear Information System (INIS)

Oliveira, D.R. de; Mizrahi, S.S.

1977-09-01

The nuclear densities, radii, multipole moments, form-factors and transition probabilities obtained for the A = 4n type of nuclei in the s-d shell are reported, using the Hartree-Fock wave functions calculated with the Skyrme force. Experimental data and theoretical values derived by others are shown for comparison [pt

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)

Recent developments and applications of multi-configuration Hartree-Fock methods. NRCC proceedings No. 10

Energy Technology Data Exchange (ETDEWEB)

Dupuis, M. (ed.)

1981-02-01

Twenty-seven papers are included in four sessions titled: generalized Fock operator methods, annihilation of single excitations methods, second-order MCSCF methods, and applications of MCHF methods. Separate abstracts were prepared for eight papers; one of the remaining had been previously abstracted. (DLC)

Recent developments and applications of multi-configuration Hartree-Fock methods. NRCC proceedings No. 10

International Nuclear Information System (INIS)

Dupuis, M.

1981-02-01

Twenty-seven papers are included in four sessions titled: generalized Fock operator methods, annihilation of single excitations methods, second-order MCSCF methods, and applications of MCHF methods. Separate abstracts were prepared for eight papers; one of the remaining had been previously abstracted

Application of potential

International Nuclear Information System (INIS)

Petris, L.

1979-01-01

This report summarizes the results obtained with the nucleon-nucleon potential presented previously for: 1) the deuteron properties and wave function, 2) a Hartree-Fock calculation on O 16 , and 3) the perturbation V-matrix and G-matrix results for the potential in relation to the results of other potentials and to saturation

Hartree and Exchange in Ensemble Density Functional Theory: Avoiding the Nonuniqueness Disaster.

Science.gov (United States)

Gould, Tim; Pittalis, Stefano

2017-12-15

Ensemble density functional theory is a promising method for the efficient and accurate calculation of excitations of quantum systems, at least if useful functionals can be developed to broaden its domain of practical applicability. Here, we introduce a guaranteed single-valued "Hartree-exchange" ensemble density functional, E_{Hx}[n], in terms of the right derivative of the universal ensemble density functional with respect to the coupling constant at vanishing interaction. We show that E_{Hx}[n] is straightforwardly expressible using block eigenvalues of a simple matrix [Eq. (14)]. Specialized expressions for E_{Hx}[n] from the literature, including those involving superpositions of Slater determinants, can now be regarded as originating from the unifying picture presented here. We thus establish a clear and practical description for Hartree and exchange in ensemble systems.

Roothaan’s approach to solve the Hartree-Fock equations for atoms confined by soft walls: Basis set with correct asymptotic behavior

Energy Technology Data Exchange (ETDEWEB)

Rodriguez-Bautista, Mariano; Díaz-García, Cecilia; Navarrete-López, Alejandra M.; Vargas, Rubicelia; Garza, Jorge, E-mail: jgo@xanum.uam.mx [Departamento de Química, División de Ciencias Básicas e Ingeniería, Universidad Autónoma Metropolitana-Iztapalapa, San Rafael Atlixco 186, Col. Vicentina, Iztapalapa C. P. 09340, México D. F., México (Mexico)

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.

Comment on "Density functional theory is straying from the path toward the exact functional"

DEFF Research Database (Denmark)

Kepp, Kasper Planeta

2017-01-01

Medvedev et al (Reports, 6 January 2017, p. 49) argue that recent density functionals stray from the path toward exactness. This conclusion rests on very compact 1s2 and 1s22s2 systems favored by the Hartree-Fock picture. Comparison to actual energies for the same systems indicates that the "stra...

Calculation of the valence charge density and binding energy in a simple metal according to the neutral atom method: the Hartree-Fock ionic potential

International Nuclear Information System (INIS)

Dagens, L.

1975-01-01

The neutral atom method is generalized in order to deal with a Hartree-Fock nonlocal ionic potential. It is used to test the following metal potential, based upon a theoretical analysis due to Hedin and Lundquist. The true HF potential is used to describe the ionic part and a simple local density scheme (the Gaspar-Kohn-Sham approximation) is used for the valence part. The method is first applied to the calculation of the rigid neutral atom valence density of a few simple metals and the corresponding form factor n(q). The choice of the ionic potential (HF or GKS) is found to have a small but significant effect as far as n(q) is concerned. A comparison with experiment is made for Al and Be, using the available X-rays structure factor measurements. Good agreement is obtained for Al with the recent results of Raccah and Heinrich. No agreement is obtained with the Be results of Brown, although the general behavior of the observed and theoretical n(g) as function of g (reciprocal vector length) are found to be quite similar. The binding energy is calculated for Li, Be, Na, Mg and Al, using the Nozieres-Pines formula for the valence-valence correlation energy. The agreement with observed values is improved considerably when the present (HF+GKS) scheme is used, instead of the HFS completely local density scheme used in a previous work. The remaining discrepancies may be ascribed to the inaccuracy of the NP formula and to the neglect of the whole valence-core correlation energy [fr

Roothaan approach in the thermodynamic limit

International Nuclear Information System (INIS)

Gutierrez, G.; Plastino, A.

1982-01-01

A systematic method for the solution of the Hartree-Fock equations in the thermodynamic limit is presented. The approach is seen to be a natural extension of the one usually employed in the finite-fermion case, i.e., that developed by Roothaan. The new techniques developed here are applied, as an example, to neutron matter, employing the so-called V 1 Bethe homework potential. The results obtained are, by far, superior to those that the ordinary plane-wave Hartree-Fock theory yields

Z-dependent perturbation theory and its application to polyatomic molecules

International Nuclear Information System (INIS)

Galvan, D.H.

1986-01-01

Z-dependent perturbation theory is applied to study the ground states of simple diatomic and triatomic molecules in order to calculate the total third-order energies for these systems. The systems studied are H 2 + , H 2 , H 3 + , HeH +2 , HeH + , and HeH 2 +2 . The total energies are compared with exact energy values, as well as Hartree-Fock values, and the author's results are a considerable improvement over second-order energies for most internuclear distances, and consistently better than Hartree-Fock calculations for all internuclear distances. Compared with variational methods, this method is simpler and more efficient. In order to calculate total energies up to third order, the wave functions necessary will be two-center, one electron or one-center, two-electron wave functions, at most. Hence, the most complicated integrals that have to be performed are three-center, two-electron integrals, and four-center, one-electron integrals, no matter how complex the molecular system. More importantly, the results obtained for the one-electron diatomic molecular ion are directly incorporated into the calculations for polyatomic systems

Hadronic wave functions and high momentum transfer interactions in quantum chromodynamics

International Nuclear Information System (INIS)

Brodsky, S.J.; Huang, T.; Lepage, G.P.

1983-01-01

This chapter emphasizes the utility of a Fock state representation of the meson and baryon wave functions as a means not only to parametrize the effects of bound state dynamics in QCD phenomena, but also to interrelate exclusive, inclusive, and higher twist processes. Discusses hadronic wave functions in QCD, measures of hadronic wave functions (form factors of composite systems, form factors of mesons, the meson distribution amplitude); large momentum transfer exclusive processes (two-photon processes); deep inelastic lepton scattering; and the phenomenology of hadronic wave functions (measures of hadron wave functions, constraints on the pion and proton valence wave function, quark jet diffraction excitation, the ''unveiling'' of the hadronic wave function and intrinsic charm). Finds that the testing ground of perturbative QCD where rigorous, definitive tests of the theory can be made can now be extended throughout a large domain of large momentum transfer exclusive and inclusive lepton, photon, and hadron reactions

Calculations of transitions in singly ionised iron

International Nuclear Information System (INIS)

Donnelly, M.P.

1999-04-01

The thesis gives a general overview of the atomic structure, introducing the relevant quantum mechanical concepts. Theoretical methods for determining the wave functions, like the Hartree-Fock Methode and the Hylleraas-Undheim Principle are discussed. Methods for obtaining atomic data by theoretical and by experimental means are discussed. Finally sextet transitions in FeII are treated in some detail

Symplectic manifolds, coadjoint orbits, and Mean Field Theory

International Nuclear Information System (INIS)

Rosensteel, G.

1986-01-01

Mean field theory is given a geometrical interpretation as a Hamiltonian dynamical system. The Hartree-Fock phase space is the Grassmann manifold, a symplectic submanifold of the projective space of the full many-fermion Hilbert space. The integral curves of the Hartree-Fock vector field are the time-dependent Hartree-Fock solutions, while the critical points of the energy function are the time-independent states. The mean field theory is generalized beyond determinants to coadjoint orbit spaces of the unitary group; the Grassmann variety is the minimal coadjoint orbit

Molecular-crystal approach to accounting of correlation corrections in the chemical bond theory in crystals: electronic structure of Ti2O3 crystal

International Nuclear Information System (INIS)

Ehvarestov, R.A.; Panin, A.I.

2000-01-01

The problem on the possibility of partial accounting for the electron correlation effects within the frames of the Hartree-Fock unlimited method (HF). The local characteristic of the electron structure of the molecular systems for the case of the multi-determinant wave functions, configurational interaction methods and multiconfigurational self-consistent field (MCSCF) are determined. The molecular-crystalline approach is applied to studies on the electron correlation effects in the Ti 2 O 3 crystal. It is shown on the basis of the [Ti 2 O 9 ] 12- cluster electron structure calculation, that the Hartree-Fock unlimited method accounts in a number of cases for an essential part of statistical correlation effects. The energy values and local characteristics of the [Ti 2 O 9 ] 12- cluster, calculated through the HF and MCSCF methods, are presented [ru

Theoretical investigation of molecular structure and vibrational spectra of 4,5-bis-(2-isopropyl-5- methylphenoxy) phthalonitrile molecule

International Nuclear Information System (INIS)

Avci, D.

2005-01-01

The molecular geometry and vibrational frequencies of 4,5-bis-(2-isopropyl-5- methylphenoxy) phthalonitrile in the ground state have been calculated using the Hartree- Fock (HF) and density functional method (B3LYP) with 6-31G(d) basis set. The optimized geometric bond lengths and bond angles obtained by using HF and DFT (B3LYP) show the best agreement with the experimental data. Comparison of the observed fundamental vibrational frequencies of 4,5-bis-(2-isopropyl-5-methylphenoxy) phthalonitrile with calculated results by density functional B3LYP and Hartree-Fock methods indicate that B3LYP is superior to the scaled Hartree-Fock approach for molecular vibrational problems

Molecular structure and vibrational spectra of 6-methylquinoline and 8-methylquinoline molecules by quantum mechanical methods

International Nuclear Information System (INIS)

Kurt, M.

2005-01-01

The molecular geometry and vibrational frequencies of 6-methylquinoline(6MQ) and 8-methylquinolines(8MQ) in the ground state have been calculated by using the Hartree-Fock and density functional methods (B3LYP and BLYP) with 6-31G (d) as the basis set. The optimized geometric bond lengths obtained by using B3LYP and bond angles obtained by BLYP were given corresponding experimental values of similar molecule. Comparison of the observed fundamental vibrational frequencies of these molecules and calculated results by density functional B3LYP, BLYP and Hartree-Fock methods indicates that B3LYP is superior to the scaled Hartree- Fock and BLYP approach for molecular vibrational problems

The technique of the modified hamiltonian for construction of the spin-projected wave function

International Nuclear Information System (INIS)

Tsaune, A.Ya.; Glushkov, V.N.

1991-01-01

A method is suggested to construct the wave function, which is an eigenfunction for operator S 2 . A combination of Lowdin's projection operators and the method of taking into account the orthogonality conditions in variational problems previously developed by the authors is used for determination of the spin-current wave functions component. It is shown that the suggested method gives better results for the energies that the traditional restricted Hartee-Fock scheme

Improvement of one-nucleon removal and total reaction cross sections in the Liège intranuclear-cascade model using Hartree-Fock-Bogoliubov calculations

Science.gov (United States)

Rodríguez-Sánchez, Jose Luis; David, Jean-Christophe; Mancusi, Davide; Boudard, Alain; Cugnon, Joseph; Leray, Sylvie

2017-11-01

The prediction of one-nucleon-removal cross sections by the Liège intranuclear-cascade model has been improved using a refined description of the matter and energy densities in the nuclear surface. Hartree-Fock-Bogoliubov calculations with the Skyrme interaction are used to obtain a more realistic description of the radial-density distributions of protons and neutrons, as well as the excitation-energy uncorrelation at the nuclear surface due to quantum effects and short-range correlations. The results are compared with experimental data covering a large range of nuclei, from carbon to uranium, and projectile kinetic energies. We find that the new approach is in good agreement with experimental data of one-nucleon-removal cross sections covering a broad range in nuclei and energies. The new ingredients also improve the description of total reaction cross sections induced by protons at low energies, the production cross sections of heaviest residues close to the projectile, and the triple-differential cross sections for one-proton removal. However, other observables such as quadruple-differential cross sections of coincident protons do not present any sizable sensitivity to the new approach. Finally, the model is also tested for light-ion-induced reactions. It is shown that the new parameters can give a reasonable description of the nucleus-nucleus total reaction cross sections at high energies.

Microscopic approach to subthreshold pion production in heavy-ion collisions

International Nuclear Information System (INIS)

Tohyama, M.; Kaps, R.; Masak, D.; Mosel, U.

1985-01-01

A microscopic approach to subthreshold pion production in heavy-ion collisions is proposed, in which the wave function of the nucleon system is approximated in the time-dependent Hartree-Fock theory and an effective interaction for the pion-production process is taken from (p,π) reaction theories. The model is applied to pion production in 16 O + 16 O collisions. (orig.)

Generalized Population Analysis of Three-Center Two-Electron Bonding

Czech Academy of Sciences Publication Activity Database

Ponec, Robert; Cooper, D. L.

2004-01-01

Roč. 97, č. 6 (2004), s. 1002-1011 ISSN 0020-7608 R&D Projects: GA AV ČR IAA4072006; GA MŠk OC D9.20 Institutional research plan: CEZ:AV0Z4072921 Keywords : multicenter bonding * generalized population analysis * post-Hartree Fock wave functions Subject RIV: CF - Physical ; The oretical Chemistry Impact factor: 1.392, year: 2004

Density functional study of molecular interactions in secondary structures of proteins.

Science.gov (United States)

Takano, Yu; Kusaka, Ayumi; Nakamura, Haruki

2016-01-01

Proteins play diverse and vital roles in biology, which are dominated by their three-dimensional structures. The three-dimensional structure of a protein determines its functions and chemical properties. Protein secondary structures, including α-helices and β-sheets, are key components of the protein architecture. Molecular interactions, in particular hydrogen bonds, play significant roles in the formation of protein secondary structures. Precise and quantitative estimations of these interactions are required to understand the principles underlying the formation of three-dimensional protein structures. In the present study, we have investigated the molecular interactions in α-helices and β-sheets, using ab initio wave function-based methods, the Hartree-Fock method (HF) and the second-order Møller-Plesset perturbation theory (MP2), density functional theory, and molecular mechanics. The characteristic interactions essential for forming the secondary structures are discussed quantitatively.

Scaling function, spectral function and nucleon momentum distribution in nuclei

International Nuclear Information System (INIS)

Antonov, A.N.; Ivanov, M.V.; Caballero, J.A.; Barbaro, M.B.; Udias, J.M.; Moya de Guerra, E.; Donnelly, T.W.

2010-01-01

The aim of the study is to find a good simultaneous description of the spectral function and the momentum distribution in relation to the realistic scaling function obtained from inclusive electron-nuclei scattering experiments. We start with a modified Hartree-Fock spectral function in which the energy dependent part (δ-function) is replaced by the Gaussian distributions with hole state widths as free parameters. We calculate the scaling function and the nucleon momentum distribution on the basis of the spectral function constructed in this way, trying to find a good description of the experimental data. The obtained scaling function has a weak asymmetry and the momentum distribution has not got a high-momentum tail in the case when harmonic-oscillator single-particle wave functions are used. So, to improve the behavior of the momentum distribution we used the basis of natural orbitals (NO) in which short-range correlations are partly incorporated. The results for the scaling function show again a weak asymmetry, but in this case the momentum distribution has a high-momentum tail. As a next step we include final-state interactions (FSI) in the calculations to reproduce the experimentally observed asymmetry of the scaling function. (author)

Hartree--Slater calculation of the cross section for L-shell ionization of argon by simple heavy charged particles

International Nuclear Information System (INIS)

Choi, B.

1975-01-01

The cross sections for L-shell and subshell ionization by direct Coulomb excitation of argon by incident heavy charged particles are evaluated. Incident particles are described in the plane-wave Born approximation, and nonrelativistic Hartree-Slater (HS) wave functions are used for the atomic electrons. Form factors, energy distributions, and ionization cross sections are compared with those obtained from screened hydrogenic wave functions. At most incident energies, the HS results for the total ionization cross section are only slightly smaller than those obtained with screened hydrogenic wave functions, but considerable discrepancies are found for form factors and energy distributions near the ionization threshold

Compton profiles and electronic structure of HgBr{sub 2} and HgI{sub 2}

Energy Technology Data Exchange (ETDEWEB)

Ahmed, G.; Dashora, Alpa [Department of Physics, University College of Science, M.L. Sukhadia University, Udaipur, 313001 Rajasthan (India); Sharma, M. [Physics Division, State Forensic Science Laboratory, Jaipur, 302016 Rajasthan (India); Ahuja, B.L. [Department of Physics, University College of Science, M.L. Sukhadia University, Udaipur, 313001 Rajasthan (India)], E-mail: blahuja@yahoo.com

2010-02-15

In this paper, we present the first-ever experimental Compton line shapes of HgBr{sub 2} and HgI{sub 2} using {sup 137}Cs Compton spectrometer. To compare our experimental momentum densities, we have computed the Compton profiles using Hartree-Fock and density functional theory within linear combination of atomic orbitals. We have also computed the energy bands and density of states using the linear combination of atomic orbitals and full potential linearized augmented plane wave method. On the basis of equal-valence-electron-density profiles, it is seen that HgI{sub 2} is more covalent than HgBr{sub 2} which is in agreement with the valence charge densities. The experimental isotropic profiles are found to be relatively in better agreement with the Hartree-Fock data. We have also discussed the photoluminescence and detection properties of both the halides.

Relativistic approach to nuclear structure

International Nuclear Information System (INIS)

Nguyen Van Giai; Bouyssy, A.

1987-03-01

Some recent works related with relativistic models of nuclear structure are briefly reviewed. The Dirac-Hartree-Fock and Dirac-Brueckner-Hartree-Fock are recalled and illustrated by some examples. The problem of isoscalar current and magnetic moments of odd nuclei is discussed. The application of the relativistic model to the nuclear response function is examined

A study on the multiple solutions of the Martree-Fock-Roothaan equation for closed shell systems

International Nuclear Information System (INIS)

Malbouisson, L.A.C.

1985-01-01

An analysis of the multiple solutions of the Hartree-Fock-Roothaan equation for closed shell systems is done. The meaning of these solutions is discussed as self-consistent solutions of the pseudo-eingen-value equation and a general method for obtaining them is proposed. It is developed a criterion of stability for classifying the solutions depending on the type of the extremum point of the electronic energy function that the solution represent. It is also shown the existence of a correspondence between the multiple solutions and the several ordering rules that can be introduced for the usual iterative procedure of resolution of the equation. All the analysis and procedures developed are applied to the systems LiH, BH, Be and He. (author) [pt

Electron impact ionization of heavy ions: some surprises

International Nuclear Information System (INIS)

Younger, S.M.

1986-01-01

This paper reports the results of calculations of electron impact ionization cross sections for a variety of heavy ions using a distorted wave Born-exchange approximation. The target is described by a Hartree-Fock wavefunction. The scattering matrix element is represented by a triple partial wave expansion over incident, scattered, and ejected (originally bound) continuum states. These partial waves are computed in the potentials associated with the initial target (incident and scattered waves) and the residual ion (ejected waves). A Gauss integration was performed over the distribution of energy between the two final state continuum electrons. For ionization of closed d- and f-subshells, the ejected f-waves were computed in frozen-core term-dependent Hartree-Fock potentials, which include the strong repulsive contribution in singlet terms which arises from the interaction of an excited orbital with an almost closed shell. Ground state correlation was included in some calculations of ionization of d 10 subshells

A possible form of the pion's structure function

International Nuclear Information System (INIS)

Long Ming; Huang Tao

1986-01-01

The pion's structure function behaviour is discussed by using the Fock state expansion of the hadronic wave function in QCD in this paper. As an example, we employ a model wave function of the Fock state in the light-cone and assume a Regge behaviour of a weight function for higher Fock states, and we get a possible form of the pion's structure function. This form is consistent with experimental data of the pion's structure function

A constrained approximation for nuclear barrier penetration and fission

International Nuclear Information System (INIS)

Tang, H.H.K.; Negele, J.W.; Massachusetts Inst. of Tech., Cambridge; Massachusetts Inst. of Tech., Cambridge

1983-01-01

An approximation to the time-dependent mean-field theory for barrier penetration by a nucleus is obtained in terms of constrained Hartree-Fock wave functions and a coherent velocity field. A discrete approximation to the continuum theory suitable for practical numerical calculations is presented and applied to three illustrative models. Potential application of the theory to the study of nuclear fission is discussed. (orig.)

A microscopic study of the S band in the generator co-ordinate approach

International Nuclear Information System (INIS)

Wuest, E.; Ansari, A.

1985-04-01

Using particle number and spin projected cranked Hartree-Fock-Bogolubov (CHFB) wave functions in the generator co-ordinate method (GCM) with the cranking frequency as a GC the shortcomings of the usual CHFB theory are removed and the ground as well as the s band are studied simultaneously. In particular, low-spin properties of the s band are discussed for a backbending nucleus 158 Dy. (author)

Electron distributions of the first-row homonuclear diatomic molecules, A2

International Nuclear Information System (INIS)

Ramirez, B.I.; Bielefeld Univ.

1982-08-01

Electron momentum density contour maps of the first-row homonuclear diatomic molecules, A 2 , are obtained from near Hartree-Fock wave functions. Both the total momentum density and momentum density difference (molecule - isolated atoms) maps present trends that may be related to the binding in the molecules. These results are compared with the corresponding charge density maps in position space (Bader, Henneker and Cade 1967). (author)

Hankel transforms in generalized Fock spaces

Directory of Open Access Journals (Sweden)

John Schmeelk

1994-01-01

Full Text Available A classical Fock space consists of functions of the form,ϕ↔(ϕ0,ϕ1,…,ϕq,where ϕ0∈ℂ and ϕq∈Lp(ℝq, q≥1. We will replace the ϕq, q≥1 with test functions having Hankel transforms. This space is a natural generalization of a classical Fock space as seen by expanding functionals having abstract Taylor Series. The particular coefficients of such series are multilinear functionals having distributions as their domain. Convergence requirements set forth are somewhat in the spirit of ultra differentiable functions and ultra distribution theory. The Hankel transform oftentimes implemented in Cauchy problems will be introduced into this setting. A theorem will be proven relating the convergence of the transform to the inductive limit parameter, s, which sweeps out a scale of generalized Fock spaces.

Stiffness-constant variation in nickel-based alloys: Experiment and theory

International Nuclear Information System (INIS)

Hennion, M.; Hennion, B.

1979-01-01

Recent measurements of the spin-wave stiffness constant in several nickel alloys at various concentrations are interpreted within a random-phase approximation, coherent-potential approximation (RPA-CPA) band model which uses the Hartree-Fock approximation to treat the intraatomic correlations. We give a theoretical description of the possible impurity states in the Hartree-Fock approximation. This allows the determination of the Hartree-Fock solutions which can account for the stiffness-constant behavior and the magnetic moment on the impurity for all the investigated alloys. For alloys such as NiCr, NiV, NiMo, and NiRu, the magnetizations of which deviate from the Slater-Pauling curve, our determination does not correspond to previous works and is consequently discussed. The limits of the model appear mainly due to local-environment effects; in the case of NiMn, it is found that a ternary-alloy model with some Mn atoms in the antiferromagnetic state can account for both stiffness-constant and magnetization behaviors

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

Compton scattering study of electron momentum distribution in lithium fluoride using 662 keV gamma radiations

Science.gov (United States)

Vijayakumar, R.; Shivaramu; Ramamurthy, N.; Ford, M. J.

2008-12-01

Here we report the first ever 137Cs Compton spectroscopy study of lithium fluoride. The spherical average Compton profiles of lithium fluoride are deduced from Compton scattering measurements on poly crystalline sample at gamma ray energy of 662 keV. To compare the experimental data, we have computed the spherical average Compton profiles using self-consistent Hartree-Fock wave functions employed on linear combination of atomic orbital (HF-LCAO) approximation. The directional Compton profiles and their anisotropic effects are also calculated using the same HF-LCAO approximation. The experimental spherical average profiles are found to be in good agreement with the corresponding HF-LCAO calculations and in qualitative agreement with Hartree-Fock free atom values. The present experimental isotropic and calculated directional profiles are also compared with the available experimental isotropic and directional Compton profiles using 59.54 and 159 keV γ-rays.

Isoelectronic sequence fits to configuration-averaged photoionization cross sections and ionization energies

International Nuclear Information System (INIS)

Clark, R.E.H.; Cowan, R.D.; Bobrowicz, F.W.

1986-01-01

Hartree--Fock wave functions have been used to calculate configuration -averaged photoionization cross sections and ionization energies for orbitals 1s< or =nl< or =5g in He-like through Al-like isoelectroni csequences. The photoionization cross sections have been fitted as a function of the nuclear charge, Z, and photon energy, X, in threshold units, with average error of less than 10%. The ionization energies have been fitted as a function of Z with errors of less than 0.5%

GAUSSIAN 76: an ab initio molecular orbital program

International Nuclear Information System (INIS)

Binkley, J.S.; Whiteside, R.; Hariharan, P.C.; Seeger, R.; Hehre, W.J.; Lathan, W.A.; Newton, M.D.; Ditchfield, R.; Pople, J.A.

Gaussian 76 is a general-purpose computer program for ab initio Hartree-Fock molecular orbital calculations. It can handle basis sets involving s, p and d-type gaussian functions. Certain standard sets (STO-3G, 4-31G, 6-31G*, etc.) are stored internally for easy use. Closed shell (RHF) or unrestricted open shell (UHF) wave functions can be obtained. Facilities are provided for geometry optimization to potential minima and for limited potential surface scans

On the classification of the spectrally stable standing waves of the Hartree problem

Science.gov (United States)

Georgiev, Vladimir; Stefanov, Atanas

2018-05-01

We consider the fractional Hartree model, with general power non-linearity and arbitrary spatial dimension. We construct variationally the "normalized" solutions for the corresponding Choquard-Pekar model-in particular a number of key properties, like smoothness and bell-shapedness are established. As a consequence of the construction, we show that these solitons are spectrally stable as solutions to the time-dependent Hartree model. In addition, we analyze the spectral stability of the Moroz-Van Schaftingen solitons of the classical Hartree problem, in any dimensions and power non-linearity. A full classification is obtained, the main conclusion of which is that only and exactly the "normalized" solutions (which exist only in a portion of the range) are spectrally stable.

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)

Elementary quantum chemistry

CERN Document Server

Pilar, Frank L

2003-01-01

Useful introductory course and reference covers origins of quantum theory, Schrödinger wave equation, quantum mechanics of simple systems, electron spin, quantum states of atoms, Hartree-Fock self-consistent field method, more. 1990 edition.

The effect of basis set and exchange-correlation functional on time-dependent density functional theory calculations within the Tamm-Dancoff approximation of the x-ray emission spectroscopy of transition metal complexes.

Science.gov (United States)

Roper, Ian P E; Besley, Nicholas A

2016-03-21

The simulation of X-ray emission spectra of transition metal complexes with time-dependent density functional theory (TDDFT) is investigated. X-ray emission spectra can be computed within TDDFT in conjunction with the Tamm-Dancoff approximation by using a reference determinant with a vacancy in the relevant core orbital, and these calculations can be performed using the frozen orbital approximation or with the relaxation of the orbitals of the intermediate core-ionised state included. Both standard exchange-correlation functionals and functionals specifically designed for X-ray emission spectroscopy are studied, and it is shown that the computed spectral band profiles are sensitive to the exchange-correlation functional used. The computed intensities of the spectral bands can be rationalised by considering the metal p orbital character of the valence molecular orbitals. To compute X-ray emission spectra with the correct energy scale allowing a direct comparison with experiment requires the relaxation of the core-ionised state to be included and the use of specifically designed functionals with increased amounts of Hartree-Fock exchange in conjunction with high quality basis sets. A range-corrected functional with increased Hartree-Fock exchange in the short range provides transition energies close to experiment and spectral band profiles that have a similar accuracy to those from standard functionals.

Nuclear structure for the crust of neutron stars and exotic nuclei

International Nuclear Information System (INIS)

Goegelein, Peter

2007-01-01

In this work the Skyrme Hartree-Fock and Relativistic Hartree--Fock approaches have been considered to describe the structure of nuclear systems ranging from finite nuclei, structures in the crust of neutron stars to homogeneous matter. Effects of pairing correlations and finite temperature are also taken into account. The numerical procedure in the cubic box is described for the Skyrme Hartree-Fock as well as the relativistic Hartree-Fock approach. And finally, results for the crust of neutron stars and exotic nuclei are presented and discussed. (orig.)

Nuclear structure for the crust of neutron stars and exotic nuclei

Energy Technology Data Exchange (ETDEWEB)

Goegelein, Peter

2007-07-01

In this work the Skyrme Hartree-Fock and Relativistic Hartree--Fock approaches have been considered to describe the structure of nuclear systems ranging from finite nuclei, structures in the crust of neutron stars to homogeneous matter. Effects of pairing correlations and finite temperature are also taken into account. The numerical procedure in the cubic box is described for the Skyrme Hartree-Fock as well as the relativistic Hartree-Fock approach. And finally, results for the crust of neutron stars and exotic nuclei are presented and discussed. (orig.)

Quantum tunneling in the periodically driven SU(2) model

International Nuclear Information System (INIS)

Arvieu, R.

1991-01-01

The tunneling rate is investigated in the quantum and classical limits using an exactly soluble, periodically driven SU(2) model. The tunneling rate is obtained by solving the time-dependent Schroedinger equation and projecting the exact wave-function on the space of coherent states using the Husimi distribution. The oscillatory, coherent tunneling of the wave-function between two Hartree-Fock minima is observed. The driving plays an important role increasing the tunneling rate by orders of magnitude as compared to the semiclassical results. This is due to the dominant role of excited states in the driven quantum tunneling. (author) 15 refs., 4 figs

Calculation of wave-functions with frozen orbitals in mixed quantum mechanics/molecular mechanics methods. Part I. Application of the Huzinaga equation.

Science.gov (United States)

Ferenczy, György G

2013-04-05

Mixed quantum mechanics/quantum mechanics (QM/QM) and quantum mechanics/molecular mechanics (QM/MM) methods make computations feasible for extended chemical systems by separating them into subsystems that are treated at different level of sophistication. In many applications, the subsystems are covalently bound and the use of frozen localized orbitals at the boundary is a possible way to separate the subsystems and to ensure a sensible description of the electronic structure near to the boundary. A complication in these methods is that orthogonality between optimized and frozen orbitals has to be warranted and this is usually achieved by an explicit orthogonalization of the basis set to the frozen orbitals. An alternative to this approach is proposed by calculating the wave-function from the Huzinaga equation that guaranties orthogonality to the frozen orbitals without basis set orthogonalization. The theoretical background and the practical aspects of the application of the Huzinaga equation in mixed methods are discussed. Forces have been derived to perform geometry optimization with wave-functions from the Huzinaga equation. Various properties have been calculated by applying the Huzinaga equation for the central QM subsystem, representing the environment by point charges and using frozen strictly localized orbitals to connect the subsystems. It is shown that a two to three bond separation of the chemical or physical event from the frozen bonds allows a very good reproduction (typically around 1 kcal/mol) of standard Hartree-Fock-Roothaan results. The proposed scheme provides an appropriate framework for mixed QM/QM and QM/MM methods. Copyright © 2012 Wiley Periodicals, Inc.

The soliton solution of the PHI24 field theory in the Hartree approximation

International Nuclear Information System (INIS)

Altenbokum, M.

1984-01-01

In this thesis in a simple model which possesses at the classical level a soliton solution a quantum-mechanical soliton sector shall be constructed in a Hartree-Fock approximation without application of semiclassical procedures. To this belongs beside the determination of the excitation spectrum of the applied Hamiltonian the knowledge of the corresponding infinitely-much eigenfunctions. The existing translational invariance of a classical soliton solution which implies the existence of a degenerated ground state by presence of a massless excitation is removed by quantum fluctuations. By removing of this degeneration conventional approximation procedures for this sector of the Hilbert space become for the first time immediately possible. (HSI) [de

Coherent states in the fermionic Fock space

International Nuclear Information System (INIS)

Oeckl, Robert

2015-01-01

We construct the coherent states in the sense of Gilmore and Perelomov for the fermionic Fock space. Our treatment is from the outset adapted to the infinite-dimensional case. The fermionic Fock space becomes in this way a reproducing kernel Hilbert space of continuous holomorphic functions. (paper)

Numerical studies of the g-hartree density functional in the Thomas-Fermi scaling limit

International Nuclear Information System (INIS)

Millack, T.; Weymans, G.

1986-02-01

Methods of finite temperature quantum field theory are used to construct the g-Hartree density functional for atoms. Low and high temperature expansions are discussed in detail. Numerical studies for atomic ground-state configurations are presented in the Thomas-Fermi-Scaling limit. (orig.)

Collective gyromagnetic ratio and moment of inertia from density-dependent Hartree-Fock calculations

International Nuclear Information System (INIS)

Sprung, D.W.L.; Lie, S.G.; Vallieres, M.; Quentin, P.

1979-01-01

The collective gyromagnetic ratio and moment of inertia of deformed even-even axially symmetric nuclei are calculated in the cranking approximation using wave functions obtained with the Skyrme force S-III. Good agreement is found for gsub(R), while the moment of inertia is about 20% too small. The cranking formula leads to better agreement than the projection method. (Auth.)

Covariant density functional theory: predictive power and first attempts of a microscopic derivation

Science.gov (United States)

Ring, Peter

2018-05-01

We discuss systematic global investigations with modern covariant density functionals. The number of their phenomenological parameters can be reduced considerable by using microscopic input from ab-initio calculations in nuclear matter. The size of the tensor force is still an open problem. Therefore we use the first full relativistic Brueckner-Hartree-Fock calculations in finite nuclear systems in order to study properties of such functionals, which cannot be obtained from nuclear matter calculations.

Cross-sections for neutrino-nucleus interactions on $^{12}C$ and $^{16}O$

CERN Document Server

Jachowicz, N; Heyde, Kris L G

1998-01-01

We calculate cross sections for neutral current quasi-elastic neutrino-nucleus scattering within a continuum RPA model, based on a Green's function approach. As residual interaction a Skyrme force is used. The unperturbed single particle wave functions are generated using either a Woods-Saxon potential or a Hartree-Fock calculation. These calculations have interesting applications. Neutrinos play an important role in supernova nucleosynthesis. To obtain more information about these processes, cross sections are folded with a Fermi-Dirac distribution with temperatures of approximately 10 9 K.

Cross-sections for neutral-current neutrino-nucleus interactions applications for $^{12}$C and $^{16}$O

CERN Document Server

Jachowicz, N; Heyde, Kris L G; Ryckebusch, J

1999-01-01

We calculate cross sections for neutral current quasi-elastic neutrino-nucleus scattering within a continuum RPA model, based on a Green's function approach. As residual interaction a Skyrme force is used. The unperturbed single particle wave functions are generated using either a Woods-Saxon potential or a Hartree-Fock calculation. These calculations have interesting applications. Neutrinos play an important role in supernova nucleosynthesis. To obtain more information about these processes, cross sections are folded with a Fermi-Dirac distribution with temperatures of approximately 10$^9$ K.

Strong semiclassical approximation of Wigner functions for the Hartree dynamics

KAUST Repository

Athanassoulis, Agissilaos; Paul, Thierry; Pezzotti, Federica; Pulvirenti, Mario

2011-01-01

We consider the Wigner equation corresponding to a nonlinear Schrödinger evolution of the Hartree type in the semiclassical limit h → 0. Under appropriate assumptions on the initial data and the interaction potential, we show that the Wigner function is close in L 2 to its weak limit, the solution of the corresponding Vlasov equation. The strong approximation allows the construction of semiclassical operator-valued observables, approximating their quantum counterparts in Hilbert-Schmidt topology. The proof makes use of a pointwise-positivity manipulation, which seems necessary in working with the L 2 norm and the precise form of the nonlinearity. We employ the Husimi function as a pivot between the classical probability density and the Wigner function, which - as it is well known - is not pointwise positive in general.

Exact-exchange time-dependent density-functional theory for static and dynamic polarizabilities

International Nuclear Information System (INIS)

Hirata, So; Ivanov, Stanislav; Bartlett, Rodney J.; Grabowski, Ireneusz

2005-01-01

Time-dependent density-functional theory (TDDFT) employing the exact-exchange functional has been formulated on the basis of the optimized-effective-potential (OEP) method of Talman and Shadwick for second-order molecular properties and implemented into a Gaussian-basis-set, trial-vector algorithm. The only approximation involved, apart from the lack of correlation effects and the use of Gaussian-type basis functions, was the consistent use of the adiabatic approximation in the exchange kernel and in the linear response function. The static and dynamic polarizabilities and their anisotropy predicted by the TDDFT with exact exchange (TDOEP) agree accurately with the corresponding values from time-dependent Hartree-Fock theory, the exact-exchange counterpart in the wave function theory. The TDOEP is free from the nonphysical asymptotic decay of the exchange potential of most conventional density functionals or from any other manifestations of the incomplete cancellation of the self-interaction energy. The systematic overestimation of the absolute values and dispersion of polarizabilities that plagues most conventional TDDFT cannot be seen in the TDOEP

Paramagnetic scattering cross-sections of Nd and Dy at neutron wavelength between 0.5 A0 - 4 A0

International Nuclear Information System (INIS)

Maayouf, R.M.A.; Abdelkawy, A.; Adib, M.; Hamouda, I.

1984-01-01

The paramagnetic scattering cross-sections of Nd and Dy are calculated, for neutron wavelengths between 0.5-4 A, theoretically and deduced from available experimental data. The theoretical calculations are carried out using magnetic form factors deduced from Hartree-Fock radial wave functions for the 4 f electrons. The resulting theoretical curves of the paragnetic scattering cross-sections are compared with those deduced from data obtained using the transmission measurements. Both theoretical and experimental values found to be consistant

Towards quantifying the role of exact exchange in the prediction hydrogen bond spin-spin coupling constants involving fluorine

Energy Technology Data Exchange (ETDEWEB)

San Fabián, J.; Omar, S.; García de la Vega, J. M., E-mail: garcia.delavega@uam.es [Departamento de Química Física Aplicada, Facultad de Ciencias, Universidad Autónoma de Madrid, Madrid (Spain)

2016-08-28

The effect of a fraction of Hartree-Fock exchange on the calculated spin-spin coupling constants involving fluorine through a hydrogen bond is analyzed in detail. Coupling constants calculated using wavefunction methods are revisited in order to get high-level calculations using the same basis set. Accurate MCSCF results are obtained using an additive approach. These constants and their contributions are used as a reference for density functional calculations. Within the density functional theory, the Hartree-Fock exchange functional is split in short- and long-range using a modified version of the Coulomb-attenuating method with the SLYP functional as well as with the original B3LYP. Results support the difficulties for calculating hydrogen bond coupling constants using density functional methods when fluorine nuclei are involved. Coupling constants are very sensitive to the Hartree-Fock exchange and it seems that, contrary to other properties, it is important to include this exchange for short-range interactions. Best functionals are tested in two different groups of complexes: those related with anionic clusters of type [F(HF){sub n}]{sup −} and those formed by difluoroacetylene and either one or two hydrogen fluoride molecules.

Density-Functional formalism

International Nuclear Information System (INIS)

Szasz, L.; Berrios-Pagan, I.; McGinn, G.

1975-01-01

A new Density-Functional formula is constructed for atoms. The kinetic energy of the electron is divided into two parts: the kinetic self-energy and the orthogonalization energy. Calculations were made for the total energies of neutral atoms, positive ions and for the He isoelectronic series. For neutral atoms the results match the Hartree-Fock energies within 1% for atoms with N 36 the results generally match the HF energies within 0.1%. For positive ions the results are fair; for the molecular applications a simplified model is developed in which the kinetic energy consists of the Weizsaecker term plus the Fermi energy reduced by a continuous function. (orig.) [de

Coulomb displacement energies in relativistic and non-relativistic self-consistent models

International Nuclear Information System (INIS)

Marcos, S.; Savushkin, L.N.; Giai, N. van.

1992-03-01

Coulomb displacement energies in mirror nuclei are comparatively analyzed in Dirac-Hartree and Skyrme-Hartree-Fock models. Using a non-linear effective Lagrangian fitted on ground state properties of finite nuclei, it is found that the predictions of relativistic models are lower than those of Hartree-Fock calculations with Skyrme force. The main sources of reduction are the kinetic energy and the Coulomb-nuclear interference potential. The discrepancy with the data is larger than in the Skyrme-Hartree-Fock case. (author) 24 refs., 3 tabs

Hole trapping at Al impurities in silica: A challenge for density functional theories

DEFF Research Database (Denmark)

Lægsgaard, Jesper; Stokbro, Kurt

2001-01-01

The atomic geometry and electronic structure around a neutral substitutional Al impurity in silica is investigated using either the unrestricted Hartree-Fock (UHF) approximation, or Beckes three-parameter hybrid functional (B3LYP). It is found that the B3LYP functional fails to describe...... the structural distortions around the Al impurity, while the UHF results are consistent with experimental information. We argue that the failure of the B3LYP functional is caused by the incomplete self-interaction cancellation usually present in density functional theories....

Some aspects of nuclear dynamics

International Nuclear Information System (INIS)

Gregoire, C.

1987-01-01

First the BBGKY hierarchy of equations is presented; the method developed here lies on a reduction procedure of a many body density distribution function. From the equations, Hartree and Hartree-Fock approximations are deduced, and time dependent Hartree-Fock equation. Then two derivations of a nuclear reaction kinetic equation are presented: the Woldmann-Snider equation and the Botermans-Malfliet equation. The Wigner transformation is used and the Landau-Vlasov equation is studied. (Or Vlasov-Uehling-Uhlenbeck or Boltzmann-Uehling-Uhlenbeck equation). Keypoints of approximate solutions are mentioned. Simulation calculations of phenomenological collisions are shown. Then dynamics of heavy ion reactions is studied from results presented

Covariant density functional theory: predictive power and first attempts of a microscopic derivation

Directory of Open Access Journals (Sweden)

Ring Peter

2018-01-01

Full Text Available We discuss systematic global investigations with modern covariant density functionals. The number of their phenomenological parameters can be reduced considerable by using microscopic input from ab-initio calculations in nuclear matter. The size of the tensor force is still an open problem. Therefore we use the first full relativistic Brueckner-Hartree-Fock calculations in finite nuclear systems in order to study properties of such functionals, which cannot be obtained from nuclear matter calculations.

Quadrupole collective correlations and termination of the superdeformed bands in mercury

International Nuclear Information System (INIS)

Bonche, P.; Heenen, P.H.; Krieger, S.J.; Weiss, M.S.; Meyer, J.

1990-03-01

Fully self-consistent Generator Coordinate Method calculations have been performed on a basis of quadrupole constrained Hartree-Fock plus BCS wave functions for the five even mercury isotopes 190-198 Hg. The GCM results support conclusions drawn from previous HF+BCS calculations. The predicted evolution of superdeformed band head (shape isomer) properties as a function of the neutron number is consistent with the data. Using calculated transition matrix elements, we evaluate in-band versus out-of-band quadrupole decay and explain the sudden termination of the superdeformed band

Application of relativistic distorted-wave method to electron-impact excitation of highly charged Fe XXIV ion embedded in weakly coupled plasmas

Science.gov (United States)

Chen, Zhanbin

2018-05-01

The process of excitation of highly charged Fe XXIV ion embedded in weakly coupled plasmas by electron impact is studied, together with the subsequent radiative decay. For the target structure, the calculation is performed using the multiconfiguration Dirac-Hartree-Fock method incorporating the Debye-Hückel potential for the electron-nucleus interaction. Fine-structure levels of the 1s22p and 1s2s2p configurations and the transition properties among these levels are presented over a wide range of screening parameters. For the collision dynamics, the distorted-wave method in the relativistic frame is adopted to include the effect of plasma background, in which the interparticle interactions in the system are described by screened interactions of the Debye-Hückel type. The continuum wave function of the projectile electron is obtained by solving the modified Dirac equations. The influence of plasma strength on the cross section, the linear polarization, and the angular distribution of x-ray photon emission are investigated in detail. Comparison of the present results with experimental data and other theoretical predictions, when available, is made.

Coherent density fluctuation model as a local-scale limit to ATDHF

International Nuclear Information System (INIS)

Antonov, A.N.; Petkov, I.Zh.; Stoitsov, M.V.

1985-04-01

The local scale transformation method is used for the construction of an Adiabatic Time-Dependent Hartree-Fock approach in terms of the local density distribution. The coherent density fluctuation relations of the model result in a particular case when the ''flucton'' local density is connected with the plane wave determinant model function be means of the local-scale coordinate transformation. The collective potential energy expression is obtained and its relation to the nuclear matter energy saturation curve is revealed. (author)

Atomic structure investigation of ionized krypton

International Nuclear Information System (INIS)

Kotze, P.B.

1981-12-01

The experimental lifetimes of ionized Krypton are discussed. Theoretical, the Coulomb approximation proves to be a reliable tool for the performance of calculations in Krypton II, where in general good agreement between experimental and theoretical lifetimes is reached, but its vulnerability is exposed in the case of Krypton III, where only results concerning levels with a 4p 3 ( 4 S 0 ) parent core can be obtained. Although the single configuration Hartree-Fock approximation turns out to be an adequate way of obtaining wave functions of excited states in Krypton III, cancellation effects resulting from configuration-interaction mixing, make the calculated transition probabilities in Krypton II less reliable. Previous work on configuration-interaction effects in the spectrum of Krypton II (El 76a, El 76b) reveals that good agreement between experimental and theoretical results can be obtained. A systematic theoretical analysis based on the multi-configurarion Hartree-Fock approximation to account for configuration-interaction effects should contribute a great deal to the existing knowledge of the energy spectra of ionized atoms

Transition mechanism of nuclear phase

International Nuclear Information System (INIS)

Kubo, T.; Sakata, F.; Marumori, T.; Iwasawa, K.; Hashimoto, Y.

1993-01-01

A general theory capable of exploring the microscopic structure of the time-dependent Hartree-Fock (TDHF) manifold is summarized. It is discussed that each stable fixed point in the TDHF-manifold represents a dynamical stable mean-field which is not reached by means of the conventional static Hartree-Fock (HF) or constrained Hartree-Fock (CHF) theories. A feasibility of the theory is shown by applying it to a simple model Hamiltonian. (orig.)

On the way to a microscopic derivation of covariant density functionals in nuclei

Science.gov (United States)

Ring, Peter

2018-02-01

Several methods are discussed to derive covariant density functionals from the microscopic input of bare nuclear forces. In a first step there are semi-microscopic functionals, which are fitted to ab-initio calculations of nuclear matter and depend in addition on very few phenomenological parameters. They are able to describe nuclear properties with the same precision as fully phenomenological functionals. In a second step we present first relativistic Brueckner-Hartree-Fock calculations in finite nuclei in order to study properties of such functionals, which cannot be obtained from nuclear matter calculations.

High energy QCD at NLO: from light-cone wave function to JIMWLK evolution

Energy Technology Data Exchange (ETDEWEB)

Lublinsky, Michael [Department of Physics, Ben-Gurion University of the Negev,Beer-Sheva 84105 (Israel); Physics Department, University of Connecticut,2152 Hillside Road, Storrs, CT 06269-3046 (United States); Mulian, Yair [Department of Physics, Ben-Gurion University of the Negev,Beer-Sheva 84105 (Israel)

2017-05-17

Soft components of the light cone wave-function of a fast moving projectile hadron is computed in perturbation theory to the third order in QCD coupling constant. At this order, the Fock space of the soft modes consists of one-gluon, two-gluon, and a quark-antiquark states. The hard component of the wave-function acts as a non-Abelian background field for the soft modes and is represented by a valence charge distribution that accounts for non-linear density effects in the projectile. When scattered off a dense target, the diagonal element of the S-matrix reveals the Hamiltonian of high energy evolution, the JIMWLK Hamiltonian. This way we provide a new direct derivation of the JIMWLK Hamiltonian at the Next-to-Leading Order.

Self-consistent green function calculations for isospin asymmetric nuclear matter

International Nuclear Information System (INIS)

Mansour, Hesham; Gad, Khalaf; Hassaneen, Khaled S.A.

2010-01-01

The one-body potentials for protons and neutrons are obtained from the self-consistent Green-function calculations of asymmetric nuclear matter, in particular their dependence on the degree of proton/neutron asymmetry. Results of the binding energy per nucleon as a function of the density and asymmetry parameter are presented for the self-consistent Green function approach using the CD-Bonn potential. For the sake of comparison, the same calculations are performed using the Brueckner-Hartree-Fock approximation. The contribution of the hole-hole terms leads to a repulsive contribution to the energy per nucleon which increases with the nuclear density. The incompressibility for asymmetric nuclear matter has been also investigated in the framework of the self-consistent Green-function approach using the CD-Bonn potential. The behavior of the incompressibility is studied for different values of the nuclear density and the neutron excess parameter. The nuclear symmetry potential at fixed nuclear density is also calculated and its value decreases with increasing the nucleon energy. In particular, the nuclear symmetry potential at saturation density changes from positive to negative values at nucleon kinetic energy of about 200 MeV. For the sake of comparison, the same calculations are performed using the Brueckner-Hartree-Fock approximation. The proton/neutron effective mass splitting in neutron-rich matter has been studied. The predicted isospin splitting of the proton/neutron effective mass splitting in neutron-rich matter is such that m n * ≥ m p * . (author)

Variational equations for the solution of the hartree-fock problem with angular momentum projection before the variation

International Nuclear Information System (INIS)

Schmid, K.W.; Gruemmer, F.

1979-01-01

A variational principle is used to determine the optimal angular momentum projected one determinant approach to the N-nucleon yrast-wave function for a given total spin value. The solution is given in terms of a set of coupled nonlinear equations. Besides an orthonormality constraint for the occupied orbits and a normalization conditions for the total wave function, this set consists out of a matrix equation taking care of the fact that the spin-projected wave function does not depend on the orientation of the intrinsic determinant it is based on, and a second subset of equations, which can be considered as a Thouless theorem for the spin-projected N-nucleon state, and desribes the diagonalization of the total Hamiltonian in the subspace of linear independent N-nucleon shell model configurations contained in the test-determinant. Furthermore, a numerical method for the solution of these equations is proposed and an extension of the theory for the description of excited bands is given. Finally, the consistency of the equations is checked by solving them for a simple example analytically. (orig.)

A Hartree–Fock study of the confined helium atom: Local and global basis set approaches

Energy Technology Data Exchange (ETDEWEB)

Young, Toby D., E-mail: tyoung@ippt.pan.pl [Zakład Metod Komputerowych, Instytut Podstawowych Prolemów Techniki Polskiej Akademia Nauk, ul. Pawińskiego 5b, 02-106 Warszawa (Poland); Vargas, Rubicelia [Universidad Autónoma Metropolitana Iztapalapa, División de Ciencias Básicas e Ingenierías, Departamento de Química, San Rafael Atlixco 186, Col. Vicentina, Iztapalapa, D.F. C.P. 09340, México (Mexico); Garza, Jorge, E-mail: jgo@xanum.uam.mx [Universidad Autónoma Metropolitana Iztapalapa, División de Ciencias Básicas e Ingenierías, Departamento de Química, San Rafael Atlixco 186, Col. Vicentina, Iztapalapa, D.F. C.P. 09340, México (Mexico)

2016-02-15

Two different basis set methods are used to calculate atomic energy within Hartree–Fock theory. The first is a local basis set approach using high-order real-space finite elements and the second is a global basis set approach using modified Slater-type orbitals. These two approaches are applied to the confined helium atom and are compared by calculating one- and two-electron contributions to the total energy. As a measure of the quality of the electron density, the cusp condition is analyzed. - Highlights: • Two different basis set methods for atomic Hartree–Fock theory. • Galerkin finite element method and modified Slater-type orbitals. • Confined atom model (helium) under small-to-extreme confinement radii. • Detailed analysis of the electron wave-function and the cusp condition.

Wigner’s phase-space function and atomic structure: II. Ground states for closed-shell atoms

DEFF Research Database (Denmark)

Springborg, Michael; Dahl, Jens Peder

1987-01-01

We present formulas for reduced Wigner phase-space functions for atoms, with an emphasis on the first-order spinless Wigner function. This function can be written as the sum of separate contributions from single orbitals (the natural orbitals). This allows a detailed study of the function. Here we...... display and analyze the function for the closed-shell atoms helium, beryllium, neon, argon, and zinc in the Hartree-Fock approximation. The quantum-mechanical exact results are compared with those obtained with the approximate Thomas-Fermi description of electron densities in phase space....

Communication: Orbital instabilities and triplet states from time-dependent density functional theory and long-range corrected functionals

Science.gov (United States)

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.

Gutzwiller variational wave function for a two-orbital Hubbard model on a square lattice

Energy Technology Data Exchange (ETDEWEB)

Muenster, Kevin Torben zu

2015-07-01

In this work, we formulated and applied the Gutzwiller variational many-body approach to multi-band Hubbard models. In chapter 1, we gave a short introduction to the problem and an outline of the scope of the work. In the chapter 2, we developed a complete, concise diagrammatic formalism for a perturbative evaluation of expectation values for Gutzwiller-correlated wave functions on finite lattices. The derivation of the diagrammatic expansion consists of three steps. In a first step, we introduced a one-to-one mapping between a sequence of fermion operators and their Hartree-Fock counterparts in order to eliminate all local contractions. We explicitly showed the consistency of the mapping. In a second step, we derived and applied the linked-cluster theorem. To this end, we expanded numerator and denominator in the Gutzwiller expectation value of one-site and two-site operators in terms of a perturbation series, and used Wick's theorem to express the coefficients in terms of diagrams. The introduction of the Hartree-Fock operators excludes all local contractions so that lines between identical lattice sites are zero by definition. The normal ordering of the operators and the sum over distinctive lattice sites permitted the introduction of Grassmann variables. For multi-band Gutzwiller wave functions, we had to introduce a formal representation of local operators in terms of an exponential series which led to a re-definition of the values of external and internal vertices. Then, the linked-cluster theorem applied, both for infinite and finite lattices, i.e., the unconnected diagrams in the numerator are canceled by the denominator. In this way, the nth-order in perturbation theory corresponds to summing all connected diagrams with n internal nodes. As a third and last step, we eliminated all internal nodes with two lines by fixing a subset of our variational parameters. We showed that, for our applications, this gauge fixing does not restrict the variational

Difficulties in applying pure Kohn-Sham density functional theory electronic structure methods to protein molecules

Science.gov (United States)

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.

Difficulties in applying pure Kohn-Sham density functional theory electronic structure methods to protein molecules

International Nuclear Information System (INIS)

Rudberg, Elias

2012-01-01

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. (fast track communication)

Time-dependent restricted-active-space self-consistent-field theory for laser-driven many-electron dynamics

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...

Radial behavior of the average local ionization energies of atoms

International Nuclear Information System (INIS)

Politzer, P.; Murray, J.S.; Grice, M.E.; Brinck, T.; Ranganathan, S.

1991-01-01

The radial behavior of the average local ionization energy bar I(r) has been investigated for the atoms He--Kr, using ab initio Hartree--Fock atomic wave functions. bar I(r) is found to decrease in a stepwise manner with the inflection points serving effectively to define boundaries between electronic shells. There is a good inverse correlation between polarizability and the ionization energy in the outermost region of the atom, suggesting that bar I(r) may be a meaningful measure of local polarizabilities in atoms and molecules

Two-photon excitation of argon

International Nuclear Information System (INIS)

Pindzola, P.S.; Payne, M.C.

1982-01-01

The authors calculate two photon excitation parameters for various excited states of argon assuming the absorption of near resonance broad-bandwidth laser radiation. Results are given for the case of two photons absorbed for the same laser beam as well as the case of absorbing photons of different frequency from each of two laser beams. The authors use multiconfiguration Hartree-Fock wave functions to evaluate the second-order sums over matrix elements. Various experimental laser schemes are suggested for the efficient excitation and subsequent ionization of argon

Approximate angular momentum projection from cranked intrinsic states

International Nuclear Information System (INIS)

Goodman, A.L.

1979-01-01

High-spin spectra are determined by approximately projecting states of good angular momentum from cranked Hartree-Fock-Bogoliubov (CHFB) wave functions. For each J the projected energy is E/sub PROJ/ approx. = E/sub CHFB/ - (ΔJ) 2 /2 J/sub CHFB/, where the moment of inertia J and the fluctuation ΔJ are spin dependent. For /sup 168,170/Yb and 174 Hf the projected J is less than the CHFB value for all J. Consequently approximate projection increases all yrast excitation energies for these nuclei

Open-system Kohn-Sham density functional theory.

Science.gov (United States)

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

Molecular dynamics of a proguanil derivative | Muhammad | Bayero ...

African Journals Online (AJOL)

... ab-initio Quantum chemical calculations at the Restricted Hatree-Fock (RHF) ... and 6-31++G basis sets were carried out for inclusion of electron correlation. ... The dipole moment of the Proguanil's derivative at both levels of theory is ... Keywords: Proguanil, Density Functional Theory, Restricted Hartree Fock, Gaussian ...

Microscopically-constrained Fock energy density functionals from chiral effective field theory. I. Two-nucleon interactions

International Nuclear Information System (INIS)

Gebremariam, B.; Bogner, S.K.; Duguet, T.

2011-01-01

The density matrix expansion (DME) of Negele and Vautherin is a convenient tool to map finite-range physics associated with vacuum two- and three-nucleon interactions into the form of a Skyrme-like energy density functional (EDF) with density-dependent couplings. In this work, we apply the improved formulation of the DME proposed recently in (arXiv:0910.4979) by Gebremariam et al. to the non-local Fock energy obtained from chiral effective field theory (EFT) two-nucleon (NN) interactions at next-to-next-to-leading-order (N 2 LO). The structure of the chiral interactions is such that each coupling in the DME Fock functional can be decomposed into a coupling constant arising from zero-range contact interactions and a coupling function of the density arising from the universal long-range pion exchanges. This motivates a new microscopically-guided Skyrme phenomenology where the density-dependent couplings associated with the underlying pion-exchange interactions are added to standard empirical Skyrme functionals, and the density-independent Skyrme parameters subsequently refit to data. A link to a downloadable Mathematica notebook containing the novel density-dependent couplings is provided.

Comparison of self-consistent calculations of the static polarizability of atoms and molecules

International Nuclear Information System (INIS)

Moullet, I.; Martins, J.L.

1990-01-01

The static dipole polarizabilities and other ground-state properties of H, H 2 , He, Na, and Na 2 are calculated using five different self-consistent schemes: Hartree--Fock, local spin density approximation, Hartree--Fock plus local density correlation, self-interaction-corrected local spin density approximation, and Hartree--Fock plus self-interaction-corrected local density correlation. The inclusion of the self-interaction corrected local spin density approximation in the Hartree--Fock method improves dramatically the calculated dissociation energies of molecules but has a small effect on the calculated polarizabilities. Correcting the local spin density calculations for self-interaction effects improves the calculated polarizability in the cases where the local spin density results are mediocre, and has only a small effect in the cases where the local spin density values are in reasonable agreement with experiment

Fully self-consistent GW calculations for molecules

DEFF Research Database (Denmark)

Rostgaard, Carsten; Jacobsen, Karsten Wedel; Thygesen, Kristian Sommer

2010-01-01

We calculate single-particle excitation energies for a series of 34 molecules using fully self-consistent GW, one-shot G0W0, Hartree-Fock (HF), and hybrid density-functional theory (DFT). All calculations are performed within the projector-augmented wave method using a basis set of Wannier...... functions augmented by numerical atomic orbitals. The GW self-energy is calculated on the real frequency axis including its full frequency dependence and off-diagonal matrix elements. The mean absolute error of the ionization potential (IP) with respect to experiment is found to be 4.4, 2.6, 0.8, 0.4, and 0...

Exact density functional and wave function embedding schemes based on orbital localization

International Nuclear Information System (INIS)

Hégely, Bence; Nagy, Péter R.; Kállay, Mihály; Ferenczy, György G.

2016-01-01

Exact schemes for the embedding of density functional theory (DFT) and wave function theory (WFT) methods into lower-level DFT or WFT approaches are introduced utilizing orbital localization. First, a simple modification of the projector-based embedding scheme of Manby and co-workers [J. Chem. Phys. 140, 18A507 (2014)] is proposed. We also use localized orbitals to partition the system, but instead of augmenting the Fock operator with a somewhat arbitrary level-shift projector we solve the Huzinaga-equation, which strictly enforces the Pauli exclusion principle. Second, the embedding of WFT methods in local correlation approaches is studied. Since the latter methods split up the system into local domains, very simple embedding theories can be defined if the domains of the active subsystem and the environment are treated at a different level. The considered embedding schemes are benchmarked for reaction energies and compared to quantum mechanics (QM)/molecular mechanics (MM) and vacuum embedding. We conclude that for DFT-in-DFT embedding, the Huzinaga-equation-based scheme is more efficient than the other approaches, but QM/MM or even simple vacuum embedding is still competitive in particular cases. Concerning the embedding of wave function methods, the clear winner is the embedding of WFT into low-level local correlation approaches, and WFT-in-DFT embedding can only be more advantageous if a non-hybrid density functional is employed.

Exact density functional and wave function embedding schemes based on orbital localization

Science.gov (United States)

Hégely, Bence; Nagy, Péter R.; Ferenczy, György G.; Kállay, Mihály

2016-08-01

Exact schemes for the embedding of density functional theory (DFT) and wave function theory (WFT) methods into lower-level DFT or WFT approaches are introduced utilizing orbital localization. First, a simple modification of the projector-based embedding scheme of Manby and co-workers [J. Chem. Phys. 140, 18A507 (2014)] is proposed. We also use localized orbitals to partition the system, but instead of augmenting the Fock operator with a somewhat arbitrary level-shift projector we solve the Huzinaga-equation, which strictly enforces the Pauli exclusion principle. Second, the embedding of WFT methods in local correlation approaches is studied. Since the latter methods split up the system into local domains, very simple embedding theories can be defined if the domains of the active subsystem and the environment are treated at a different level. The considered embedding schemes are benchmarked for reaction energies and compared to quantum mechanics (QM)/molecular mechanics (MM) and vacuum embedding. We conclude that for DFT-in-DFT embedding, the Huzinaga-equation-based scheme is more efficient than the other approaches, but QM/MM or even simple vacuum embedding is still competitive in particular cases. Concerning the embedding of wave function methods, the clear winner is the embedding of WFT into low-level local correlation approaches, and WFT-in-DFT embedding can only be more advantageous if a non-hybrid density functional is employed.

Exact density functional and wave function embedding schemes based on orbital localization

Energy Technology Data Exchange (ETDEWEB)

Hégely, Bence; Nagy, Péter R.; Kállay, Mihály, E-mail: kallay@mail.bme.hu [MTA-BME Lendület Quantum Chemistry Research Group, Department of Physical Chemistry and Materials Science, Budapest University of Technology and Economics, P.O. Box 91, H-1521 Budapest (Hungary); Ferenczy, György G. [Medicinal Chemistry Research Group, Research Centre for Natural Sciences, Hungarian Academy of Sciences, Magyar tudósok körútja 2, H-1117 Budapest (Hungary); Department of Biophysics and Radiation Biology, Semmelweis University, Tűzoltó u. 37-47, H-1094 Budapest (Hungary)

2016-08-14

Exact schemes for the embedding of density functional theory (DFT) and wave function theory (WFT) methods into lower-level DFT or WFT approaches are introduced utilizing orbital localization. First, a simple modification of the projector-based embedding scheme of Manby and co-workers [J. Chem. Phys. 140, 18A507 (2014)] is proposed. We also use localized orbitals to partition the system, but instead of augmenting the Fock operator with a somewhat arbitrary level-shift projector we solve the Huzinaga-equation, which strictly enforces the Pauli exclusion principle. Second, the embedding of WFT methods in local correlation approaches is studied. Since the latter methods split up the system into local domains, very simple embedding theories can be defined if the domains of the active subsystem and the environment are treated at a different level. The considered embedding schemes are benchmarked for reaction energies and compared to quantum mechanics (QM)/molecular mechanics (MM) and vacuum embedding. We conclude that for DFT-in-DFT embedding, the Huzinaga-equation-based scheme is more efficient than the other approaches, but QM/MM or even simple vacuum embedding is still competitive in particular cases. Concerning the embedding of wave function methods, the clear winner is the embedding of WFT into low-level local correlation approaches, and WFT-in-DFT embedding can only be more advantageous if a non-hybrid density functional is employed.

Angular momentum fuctuation energy in the cranking model

International Nuclear Information System (INIS)

Goodman, A.L.

1979-01-01

Angular momentum is approximately projected from Hartree-Fock-Bogoliubov cranked (HFBC) wave functions. At each J the projected energy is Esub(proj)approximately Esub(HFBC). The spin-dependent fluctuation ΔJ includes contributions from Jsub(y) and Jsub(z) as well as Jsub(x). There are no correlations in the three angular momentum components. Projected energies are calculated for 168 170 Yb and 174 Hf. When compared to experimental energies, the projected spectra are less compressed than the HFBC spectra. At low spins the projected and experimental energies are in good agreement. (Aut.)

Calculation of exchange constants in manganese ferrite (MnFe2O4)

International Nuclear Information System (INIS)

Zuo Xu; Barbiellini, Bernardo; Vittoria, Carmine

2004-01-01

The exchange constants and electronic structure of manganese ferrite (MnFe 2 O 4 ) were calculated using Becke's density functional. The total exchange energy consists of Hartree-Fock (HF) and Becke's density functional terms. We introduced one parameter w as the weight of HF's contribution. We also introduced a parameter α to scale the radial part of the 3d wave functions of Fe 3+ ions. By varying w and α the calculated exchange constants were quantitatively fitted to the experimental values of a spinel ferrite for the first time. Direct (d-d) and indirect (d-p-d) hopping are controlled by the parameters w and α

Tuning the effects of Landau level mixing on anisotropic transport in quantum Hall systems

International Nuclear Information System (INIS)

Smith, Peter M; Kennett, Malcolm P

2012-01-01

Electron-electron interactions in half-filled high Landau levels in two-dimensional electron gases in a strong perpendicular magnetic field can lead to states with anisotropic longitudinal resistance. This longitudinal resistance is generally believed to arise from broken rotational invariance, which is indicated by charge density wave order in Hartree-Fock calculations. We use the Hartree-Fock approximation to study the influence of externally tuned Landau level mixing on the formation of interaction-induced states that break rotational invariance in two-dimensional electron and hole systems. We focus on the situation when there are two non-interacting states in the vicinity of the Fermi level and construct a Landau theory to study coupled charge density wave order that can occur as interactions are tuned and the filling or mixing are varied. We consider numerically a specific example where mixing is tuned externally through Rashba spin-orbit coupling. We calculate the phase diagram and find the possibility of ordering involving coupled striped or triangular charge density waves in the two levels. Our results may be relevant to recent transport experiments on quantum Hall nematics in which Landau level mixing plays an important role. (paper)

On the XFEL Schrödinger Equation: Highly Oscillatory Magnetic Potentials and Time Averaging

KAUST Repository

Antonelli, Paolo

2014-01-14

We analyse a nonlinear Schrödinger equation for the time-evolution of the wave function of an electron beam, interacting selfconsistently through a Hartree-Fock nonlinearity and through the repulsive Coulomb interaction of an atomic nucleus. The electrons are supposed to move under the action of a time dependent, rapidly periodically oscillating electromagnetic potential. This can be considered a simplified effective single particle model for an X-ray free electron laser. We prove the existence and uniqueness for the Cauchy problem and the convergence of wave-functions to corresponding solutions of a Schrödinger equation with a time-averaged Coulomb potential in the high frequency limit for the oscillations of the electromagnetic potential. © 2014 Springer-Verlag Berlin Heidelberg.

A microscopic description of nuclear shapes

International Nuclear Information System (INIS)

Bonche, P.

1987-07-01

This talk describes recent three-dimensional self-consistent Hartree-Fock calculations. After an introduction providing the basic approximations and the different symmetries, we present an application to quadrupole deformation. We pursue with a study of octupole deformation properties of 222 Ra and 144 Ba nuclei for which states of good (positive and negative) parity are projected out. Finally we discuss an extension to the study of rotation and high-spin states with the cranked self-consistent Hartree-Fock method. As an example, the 24 Mg nucleus is studied as a function of angular momentum from ground state up to fission

Projected coupled cluster theory.

Science.gov (United States)

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.

Recent advances in density functional methods, pt. 1-2

CERN Document Server

Chong, Delano P

1995-01-01

Of all the different areas in computational chemistry, density functional theory (DFT) enjoys the most rapid development. Even at the level of the local density approximation (LDA), which is computationally less demanding, DFT can usually provide better answers than Hartree-Fock formalism for large systems such as clusters and solids. For atoms and molecules, the results from DFT often rival those obtained by ab initio quantum chemistry, partly because larger basis sets can be used. Such encouraging results have in turn stimulated workers to further investigate the formal theory as well as the

Fock model and Segal-Bargmann transform for minimal representations of Hermitian Lie groups

DEFF Research Database (Denmark)

Hilgert, Joachim; Kobayashi, Toshiyuki; Möllers, Jan

2012-01-01

For any Hermitian Lie group G of tube type we construct a Fock model of its minimal representation. The Fock space is defined on the minimal nilpotent K_C-orbit X in p_C and the L^2-inner product involves a K-Bessel function as density. Here K is a maximal compact subgroup of G, and g......_C=k_C+p_C is a complexified Cartan decomposition. In this realization the space of k-finite vectors consists of holomorphic polynomials on X. The reproducing kernel of the Fock space is calculated explicitly in terms of an I-Bessel function. We further find an explicit formula of a generalized Segal-Bargmann transform which...... intertwines the Schroedinger and Fock model. Its kernel involves the same I-Bessel function. Using the Segal--Bargmann transform we also determine the integral kernel of the unitary inversion operator in the Schroedinger model which is given by a J-Bessel function....

Actinide collisions for QED and superheavy elements with the time-dependent Hartree-Fock theory and the Balian-Vénéroni variational principle

Directory of Open Access Journals (Sweden)

Kedziora David J.

2011-10-01

Full Text Available Collisions of actinide nuclei form, during very short times of few zs (10−21 s, the heaviest ensembles of interacting nucleons available on Earth. Such collisions are used to produce super-strong electric fields by the huge number of interacting protons to test spontaneous positron-electron pair emission (vacuum decay predicted by the quantum electrodynamics (QED theory. Multi-nucleon transfer in actinide collisions could also be used as an alternative way to fusion in order to produce neutron-rich heavy and superheavy elements thanks to inverse quasifission mechanisms. Actinide collisions are studied in a dynamical quantum microscopic approach. The three-dimensional time-dependent Hartree-Fock (TDHF code tdhf3d is used with a full Skyrme energy density functional to investigate the time evolution of expectation values of one-body operators, such as fragment position and particle number. This code is also used to compute the dispersion of the particle numbers (e.g., widths of fragment mass and charge distributions from TDHF transfer probabilities, on the one hand, and using the BalianVeneroni variational principle, on the other hand. A first application to test QED is discussed. Collision times in 238U+238U are computed to determine the optimum energy for the observation of the vacuum decay. It is shown that the initial orientation strongly affects the collision times and reaction mechanism. The highest collision times predicted by TDHF in this reaction are of the order of ~ 4 zs at a center of mass energy of 1200 MeV. According to modern calculations based on the Dirac equation, the collision times at Ecm > 1 GeV are sufficient to allow spontaneous electron-positron pair emission from QED vacuum decay, in case of bare uranium ion collision. A second application of actinide collisions to produce neutron-rich transfermiums is discussed. A new inverse quasifission mechanism associated to a specific orientation of the nuclei is proposed to

Density functional theory study of vibrational spectra, and ...

Indian Academy of Sciences (India)

The FTIR and FT Raman spectra of dacarbazine were recorded in the regions 4000-400 and 3500-100 cm-1, respectively. The optimized geometry, wavenumber, polarizability and several thermodynamic properties of dacarbazine were studied using ab initio Hartree-Fock, MP2 and DFT methods. A complete vibrational ...

Dirac-Fock-Breit-Gaunt calculations for tungsten hexacarbonyl W(CO)6.

Science.gov (United States)

Malli, Gulzari L

2016-05-21

The first all-electron fully relativistic Dirac-Fock-Breit-Gaunt (DFBG), Dirac-Fock (DF), and nonrelativistic (NR) Hartree-Fock (HF) calculations are reported for octahedral (Oh) tungsten hexacarbonyl W(CO)6. Our DF and NR HF calculations predict atomization energy of 73.76 and 70.33 eV, respectively. The relativistic contribution of ∼3.4 eV to the atomization energy of W(CO)6 is fairly significant. The DF and NR energy for the reaction W + 6CO → W(CO)6 is calculated as -7.90 and -8.86 eV, respectively. The mean bond energy predicted by our NR and DF calculations is 142.5 kJ/mol and 177.5 kJ/mol, respectively, and our predicted DF mean bond energy is in excellent agreement with the experimental value of 179 kJ/mol quoted in the literature. The relativistic effects contribute ∼35 kJ/mol to the mean bond energy and the calculated BSSE is 1.6 kcal/mol, which indicates that the triple zeta basis set used here is fairly good. The mean bond energy and the atomization energy calculated in our DFBG SCF calculations, which include variationally both the relativistic and magnetic Breit effects, is 157.4 kJ/mol and 68.84 eV, respectively. The magnetic Breit effects lead to a decrease of ∼20 kJ/mol and ∼4.9 eV for the mean bond energy and atomization energy, respectively, for W(CO)6. Our calculated magnetic Breit interaction energy of -9.79 eV for the energy of reaction (ΔE) for W + 6CO → W(CO)6 is lower by ∼1.90 eV as compared to the corresponding DF value (ΔE) and contributes significantly to the ΔE. A detailed discussion is presented of electronic structure, bonding, and molecular energy levels at various levels of theory for W(CO)6.

Theoretical study of the properties of BH3NH3

International Nuclear Information System (INIS)

Binkley, J.S.; Thorne, L.R.

1983-01-01

Borane monoammoniate (BH 3 NH 3 ) has been studied using several ab initio electronic structure methods and Gaussian basis sets. Equilibrium geometries have been computed at the Hartree--Fock level and, using the electron-correlated Moller--Plesset perturbation method, carried out to third order (MP3) with double-zeta polarized quality basis sets. The computed MP3 geometry is in close agreement with recent microwave data; electron correlation is found to be necessary for a proper description of the B--N distance. Hartree--Fock dipole moments and harmonic vibrational frequencies are presented and discussed. Moller--Plesset perturbation theory carried out to fourth order with triple-zeta plus polarization basis sets is used to compute a B--N dissociation energy of 34.7 kcal mol -1 and a (Hartree--Fock zero-point corrected) rotational barrier of 2.065 kcal mol -1 , which is in excellent agreement with the experimental value. Analysis of the dissociation energy as a function of perturbation order indicates that terms involving triple and quadruple substitutions are required in the dissociation energy

Effective interaction for relativistic mean-field theories of nuclear structure

International Nuclear Information System (INIS)

Ai, H.B.; Celenza, L.S.; Harindranath, A.; Shakin, C.M.

1987-01-01

We construct an effective interaction, which when treated in a relativistic Hartree-Fock approximation, reproduces rather accurately the nucleon self-energy in nuclear matter and the Migdal parameters obtained via relativistic Brueckner-Hartree-Fock calculations. This effective interaction is constructed by adding Born terms, describing the exchange of pseudoparticles, to the Born terms of the Dirac-Hartree-Fock analysis. The pseudoparticles have relatively large masses and either real or imaginary coupling constants. (For example, exchange of a pseudo-sigma with an imaginary coupling constant has the effect of reducing the scalar attraction arising from sigma exchange while exchange of a pseudo-omega with an imaginary coupling constant has the effect of reducing the repulsion arising from omega exchange. The terms beyond the Born term in the case of pion exchange are well simulated by pseudo-sigma exchange with a real coupling constant.) The effective interaction constructed here may be used for calculations of the properties of finite nuclei in a relativistic Hartree-Fock approximation

Comparative studies of atomic independent-particle potentials

International Nuclear Information System (INIS)

Talman, J.D.; Ganas, P.S.; Green, A.E.S.

1979-01-01

A number of atomic properties are compared in various independent-particle models for atoms. The models studied are the Hartree-Fock method, a variationally optimized potential model, a parametrized analytic form of the same model, parametrized analytic models constructed to fit atomic energy levels, the so-called Hartree-Fock-Slater model, and the Xα model. The physical properties compared are single-particle energy levels, total energies, and dipole polarizabilities. The extent to which the virial theorem is satisfied in the different models is also considered. The atoms Be, Ne, Ar, Kr, and Xe and ions O v and Al iv hav been compared. The results show that the experimental properties can be well represented by several of the independent-particle models. Since it has been shown that the optimized potential models yield wavefunctions that are almost the same as Hartree-Fock wavefunctions, they provide a natural solution to the problem of extending the Hartree-Fock method to excited states

Comment on "Generalization of the Kohn-Sham system that can represent arbitrary one-electron density matrices"

Science.gov (United States)

Piris, Mario; Pernal, Katarzyna

2017-10-01

van Dam [Phys. Rev. A 93, 052512 (2016), 10.1103/PhysRevA.93.052512] claims that the one-particle reduced density matrix (1RDM) of an interacting system can be represented by means of a single-determinant wave function of fictitious noninteracting particles. van Dam [Phys. Rev. A 93, 052512 (2016), 10.1103/PhysRevA.93.052512] introduced orbitals within a mean-field framework that produce energy levels similar to Hartree-Fock orbital energies, therefore he also claims that conventional analyses based on Koopmans' theorem are possible in 1RDM functional theory. In this Comment, we demonstrate that both claims are unfounded.

Dynamic response function and large-amplitude dissipative collective motion

International Nuclear Information System (INIS)

Wu Xizhen; Zhuo Yizhong; Li Zhuxia; Sakata, Fumihiko.

1993-05-01

Aiming at exploring microscopic dynamics responsible for the dissipative large-amplitude collective motion, the dynamic response and correlation functions are introduced within the general theory of nuclear coupled-master equations. The theory is based on the microscopic theory of nuclear collective dynamics which has been developed within the time-dependent Hartree-Fock (TDHF) theory for disclosing complex structure of the TDHF-manifold. A systematic numerical method for calculating the dynamic response and correlation functions is proposed. By performing numerical calculation for a simple model Hamiltonian, it is pointed out that the dynamic response function gives an important information in understanding the large-amplitude dissipative collective motion which is described by an ensemble of trajectories within the TDHF-manifold. (author)

Theoretical hyperfine structures of 19F i and 17O i

Science.gov (United States)

Aourir, Nouria; Nemouchi, Messaoud; Godefroid, Michel; Jönsson, Per

2018-03-01

Multiconfiguration Hartree-Fock (MCHF) and multiconfiguration Dirac-Hartree-Fock (MCDHF) calculations are performed for the 2 p5P2o , 2 p4(3P ) 3 s 4P , 2 p4(3P ) 3 s 2P , and 2 p4(3P ) 3 p 4So states of 19F i to determine their hyperfine constants. Several computing strategies are considered to investigate electron correlation and relativistic effects. High-order correlation contributions are included in MCHF calculations based on single and double multireference expansions. The largest components of the single reference MCHF wave functions are selected to define the multireference (MR) sets. In this scheme, relativistic corrections are evaluated in the Breit-Pauli approximation. A similar strategy is used for the calculation of MCDHF relativistic wave functions and hyperfine parameters. While correlation and relativistic corrections are found to be rather small for the ground state, we highlight large relativistic effects on the hyperfine constant A3 /2 of 2 p4(3P ) 3 p 4So and, to a lesser extent, on A1 /2 of 2 p4(3P ) 3 s 4P . As expected for such a light system, electron correlation effects dominate over relativity in the calculation of the hyperfine interaction of all other levels considered. We also revisit the hyperfine constants of 2 p3(4S ) 3 s S5o and 2 p3(4S ) 3 p 5P in 17O using similar strategies. The results are found to be in excellent agreement with experiment.

Zero Field Splitting of the chalcogen diatomics using relativistic correlated wave-function methods

DEFF Research Database (Denmark)

Rota, Jean-Baptiste; Knecht, Stefan; Fleig, Timo

2011-01-01

The spectrum arising from the (π*)2 configuration of the chalcogen dimers, namely the X21, a2 and b0+ states, is calculated using Wave-Function Theory (WFT) based methods. Two-component (2c) and four-component (4c) MultiReference Configuration Interaction (MRCI) and Fock-Space Coupled Cluster (FSCC......) methods are used as well as two-step methods Spin-Orbit Complete Active Space Perturbation Theory at 2nd order (SO-CASPT2) and Spin-Orbit Difference Dedicated Configuration Interaction (SODDCI). The energy of the X21 state corresponds to the Zero-Field Splitting (ZFS) of the ground state spin triplet...

White noise calculus and Fock space

CERN Document Server

Obata, Nobuaki

1994-01-01

White Noise Calculus is a distribution theory on Gaussian space, proposed by T. Hida in 1975. This approach enables us to use pointwise defined creation and annihilation operators as well as the well-established theory of nuclear space.This self-contained monograph presents, for the first time, a systematic introduction to operator theory on fock space by means of white noise calculus. The goal is a comprehensive account of general expansion theory of Fock space operators and its applications. In particular,first order differential operators, Laplacians, rotation group, Fourier transform and their interrelations are discussed in detail w.r.t. harmonic analysis on Gaussian space. The mathematical formalism used here is based on distribution theory and functional analysis , prior knowledge of white noise calculus is not required.

Derivation of mean-field dynamics for fermions

International Nuclear Information System (INIS)

Petrat, Soeren

2014-01-01

the form vertical stroke x vertical stroke -s , with 0Hartree and Gross-Pitaevskii equations. Its application to fermions in this work is new. The method is based on a functional that ''counts the number of particles outside the condensate'', i.e., in the case of fermions, it measures those parts of the Schroedinger wave function that are not in the antisymmetric product of the Hartree states. We show that convergence of the functional to zero (which means that the mean-field equations approximate the dynamics well) is equivalent to convergence of the corresponding reduced one-particle density matrices in trace norm and in Hilbert-Schmidt norm. Finally, we show how also the recently treated semiclassical mean-field limits can be derived with this method.

Geometry and time scales of self-consistent orbits in a modified SU(2) model

International Nuclear Information System (INIS)

Jezek, D.M.; Hernandez, E.S.; Solari, H.G.

1986-01-01

We investigate the time-dependent Hartree-Fock flow pattern of a two-level many fermion system interacting via a two-body interaction which does not preserve the parity symmetry of standard SU(2) models. The geometrical features of the time-dependent Hartree-Fock energy surface are analyzed and a phase instability is clearly recognized. The time evolution of one-body observables along self-consistent and exact trajectories are examined together with the overlaps between both orbits. Typical time scales for the determinantal motion can be set and the validity of the time-dependent Hartree-Fock approach in the various regions of quasispin phase space is discussed

A spatially homogeneous and isotropic Einstein-Dirac cosmology

Science.gov (United States)

Finster, Felix; Hainzl, Christian

2011-04-01

We consider a spatially homogeneous and isotropic cosmological model where Dirac spinors are coupled to classical gravity. For the Dirac spinors we choose a Hartree-Fock ansatz where all one-particle wave functions are coherent and have the same momentum. If the scale function is large, the universe behaves like the classical Friedmann dust solution. If however the scale function is small, quantum effects lead to oscillations of the energy-momentum tensor. It is shown numerically and proven analytically that these quantum oscillations can prevent the formation of a big bang or big crunch singularity. The energy conditions are analyzed. We prove the existence of time-periodic solutions which go through an infinite number of expansion and contraction cycles.

Orbital momentum profiles and binding energy spectra for the complete valence shell of molecular fluorine

Energy Technology Data Exchange (ETDEWEB)

Zheng, Y.; Brion, C.E. [British Columbia Univ., Vancouver, BC (Canada). Dept. of Chemistry; Brunger, M.J.; Zhao, K.; Grisogono, A.M.; Braidwood, S.; Weigold, E. [Flinders Univ. of South Australia, Adelaide, SA (Australia). Electronic Structure of Materials Centre; Chakravorty, S.J.; Davidson, E.R. [Indiana Univ., Bloomington, IN (United States). Dept. of Chemistry; Sgamellotti, A. [Univ di Perugia (Italy). Dipartimento di Chimica; von Niessen, W. [Technische Univ. Braunschweig (Germany). Inst fuer Physikalische

1996-01-01

The first electronic structural study of the complete valence shell binding energy spectrum of molecular fluorine, encompassing both the outer and inner valence regions, is reported. These binding energy spectra as well as the individual orbital momentum profiles have been measured using an energy dispersive multichannel electron momentum spectrometer at a total energy of 1500 eV, with an energy resolution of 1.5 eV and a momentum resolution of 0.1 a.u. The measured binding energy spectra in the energy range of 14-60 eV are compared with the results of ADC(4) many-body Green`s function and also direct-Configuration Interaction (CI) and MRSD-CI calculations. The experimental orbital electron momentum profiles are compared with SCF theoretical profiles calculated using the target Hartree-Fock approximation with a range of basis sets and with Density Functional Theory predictions in the target Kohn-Sham approximation with non-local potentials. The truncated (aug-cc-pv5z) Dunning basis sets were used for the Density Functional Theory calculations which also include some treatment of correlation via the exchange and correlation potentials. Comparisons are also made with the full ion-neutral overlap amplitude calculated with MRSD-CI wave functions. Large, saturated basis sets (199-GTO) were employed for both the high level SCF near Hartree-Fock limit and MRSD-CI calculations to investigate the effects of electron correlation and relaxation. 66 refs., 9 tabs., 9 figs.

Orbital momentum profiles and binding energy spectra for the complete valence shell of molecular fluorine

International Nuclear Information System (INIS)

Zheng, Y.; Brion, C.E.; Brunger, M.J.; Zhao, K.; Grisogono, A.M.; Braidwood, S.; Weigold, E.; Chakravorty, S.J.; Davidson, E.R.; Sgamellotti, A.; von Niessen, W.

1996-01-01

The first electronic structural study of the complete valence shell binding energy spectrum of molecular fluorine, encompassing both the outer and inner valence regions, is reported. These binding energy spectra as well as the individual orbital momentum profiles have been measured using an energy dispersive multichannel electron momentum spectrometer at a total energy of 1500 eV, with an energy resolution of 1.5 eV and a momentum resolution of 0.1 a.u. The measured binding energy spectra in the energy range of 14-60 eV are compared with the results of ADC(4) many-body Green's function and also direct-Configuration Interaction (CI) and MRSD-CI calculations. The experimental orbital electron momentum profiles are compared with SCF theoretical profiles calculated using the target Hartree-Fock approximation with a range of basis sets and with Density Functional Theory predictions in the target Kohn-Sham approximation with non-local potentials. The truncated (aug-cc-pv5z) Dunning basis sets were used for the Density Functional Theory calculations which also include some treatment of correlation via the exchange and correlation potentials. Comparisons are also made with the full ion-neutral overlap amplitude calculated with MRSD-CI wave functions. Large, saturated basis sets (199-GTO) were employed for both the high level SCF near Hartree-Fock limit and MRSD-CI calculations to investigate the effects of electron correlation and relaxation. 66 refs., 9 tabs., 9 figs

IR, Raman and SERS studies of methyl salicylate

Science.gov (United States)

Varghese, Hema Tresa; Yohannan Panicker, C.; Philip, Daizy; Mannekutla, James R.; Inamdar, S. R.

2007-04-01

The IR and Raman spectra of methyl salicylate (MS) were recorded and analysed. Surface enhanced Raman scattering (SERS) spectrum was recorded in silver colloid. The vibrational wave numbers of the compound have been computed using the Hartree-Fock/6-31G * basis and compared with the experimental values. SERS studies suggest a flat orientation of the molecule at the metal surface.

Electron momentum spectroscopy of xenon: A detailed analysis

International Nuclear Information System (INIS)

Cook, J.P.D.; McCarthy, I.E.; Mitroy, J.; Weigold, E.

1986-01-01

Accurate measurements of the 1000-eV noncoplanar symmetric (e,2e) reaction on xenon are reported. Cross-section calculations are carried out with the use of both the plane-wave and distorted-wave impulse approximations. The distorted-wave impulse approximation accurately describes both the 5p -1 and 5s -1 angular correlations and their relative cross sections. It also describes accurately the 5p/sub 3/2/ -1 :5p/sub 1/2/ -1 branching ratios if Dirac-Fock target wave functions are used. The branching ratios show the inadequacy of Hartree-Fock wave functions for xenon. The plane-wave impulse-approximation overestimates the 5s -1 cross section relative to the 5p -1 and underestimates the cross section at large angles. The 5s -1 spectroscopic factors are assigned up to a separation energy of 45 eV, and the distorted-wave impulse-approximation calculation verifies that all the 5s -1 strength has been found. The spectroscopic factors for the 5s -1 manifold are obtained at 1000 and 1200 eV at a number of angles and are found to be independent of incident energy and ion recoil momentum. The spectroscopic factor for the lowest 5s -1 transition at 23.4 eV is 0.37 +- 0.01, whereas that for the ground-state 5p -1 transition is greater than or equal to 0.98

Orbital momentum distribution and binding energies for the complete valence shell of molecular bromine

International Nuclear Information System (INIS)

Frost, L.; Grisogono, A.M.; Weigold, E.

1987-08-01

The binding energy spectrum of Br 2 has been recorded in both the outer and inner valence regions using electron momentum spectroscopy. The measurements are compared with the results of several Green's function calculations using different approximations and based on both polarized and unpolarized wave functions. The inner valence region, observed for the first time, is found to exhibit complex structure that is shown to be due to many-body effects, thus indicating a breakdown of the simple MO picture for ionization in this region. Momentum distributions for the three outer valence orbitals are also measured and compared with spherically averaged calculations using the target Hartree-Fock and plane wave impulse approximations. The effect of polarization functions in the basis set is investigated. Orbital density maps in both momentum and position space have been calculated and compared with the experimental measurements

Communication: Evaluating non-empirical double hybrid functionals for spin-state energetics in transition-metal complexes

Science.gov (United States)

Wilbraham, Liam; Adamo, Carlo; Ciofini, Ilaria

2018-01-01

The computationally assisted, accelerated design of inorganic functional materials often relies on the ability of a given electronic structure method to return the correct electronic ground state of the material in question. Outlining difficulties with current density functionals and wave function-based approaches, we highlight why double hybrid density functionals represent promising candidates for this purpose. In turn, we show that PBE0-DH (and PBE-QIDH) offers a significant improvement over its hybrid parent functional PBE0 [as well as B3LYP* and coupled cluster singles and doubles with perturbative triples (CCSD(T))] when computing spin-state splitting energies, using high-level diffusion Monte Carlo calculations as a reference. We refer to the opposing influence of Hartree-Fock (HF) exchange and MP2, which permits higher levels of HF exchange and a concomitant reduction in electronic density error, as the reason for the improved performance of double-hybrid functionals relative to hybrid functionals. Additionally, using 16 transition metal (Fe and Co) complexes, we show that low-spin states are stabilised by increasing contributions from MP2 within the double hybrid formulation. Furthermore, this stabilisation effect is more prominent for high field strength ligands than low field strength ligands.

Potential harmonic expansion for atomic wave functions

International Nuclear Information System (INIS)

Fabre de la Ripelle, M.; Larsen, S.Y.

1991-01-01

One way to reduce the large degeneracy of the Hyperspherical Harmonic basis for solving few- and many-body bound state problems is to introduce an optimal basis truncation called the Potential Harmonic (PH) basis. Various PH truncation schemes are introduced, and their accuracies are evaluated in predicting the energies of the Helium and H - ground states , and the excited 2 1 S level of the Helium atom. It was found that the part of the PH basis that accounts for one-body correlations gives a better ground state energy for He than the Hartree-Fock approximation. When an orthogonal complement is introduced to the basis to account for e-e correlations, the error in the binding energy is found to be .00025 au and .00015 au for ground and excited helium, resp., and .00035 au for H - . Furthermore, the PH truncation is about 99.9% accurate in accounting for contributions coming from large values of the global angular momentum. This PH scheme is also much more accurate than previous versions based on the Faddeev equations. The present results indicate that the PH truncation can render the Hyperspherical Harmonic method useful for systems with N>3. (R.P.) 14 refs., 4 tabs

Effect of side chain length on the stability and structural properties of 3

African Journals Online (AJOL)

thiophene (DOOPT) and their dimers studied by Hartree-Fock (HF) and Density Functional Theory (DFT) methods. The DFT calculations suggest that dimers of the dialkoxyphenylthiophenes with longer side chains are thermodynamically more ...

Coulomb correlations in many-electron systems on the level of self-consistent fields

International Nuclear Information System (INIS)

Warken, M.

1991-06-01

It was the aim of this thesis to show means and ways, in order to regard Coulomb correlation already on the SCF level. As mean to facilitate this general averaged fields should serve. For this first in chapter I was shown, how by means of suitable gauge fixings terms into effective potentials of the Hartree-Fock or g-Hartree type are introduced, which permit an interpretation as correlation density or as effective coupling constant. The following considerations were exemplarily performed on the cases g-Hartree (in Coulomb gauge) and on f-Hartree-Fock. (orig./HSI) [de

Green's functions in quantum chemistry - I. The Σ perturbation method

International Nuclear Information System (INIS)

Sebastian, K.L.

1978-01-01

As an improvement over the Hartree-Fock approximation, a Green's Function method - the Σ perturbation method - is investigated for molecular calculations. The method is applied to the hydrogen molecule and to the π-electron system of ethylene under PPP approximation. It is found that when the algebraic approximation is used, the energy obtained is better than that of the HF approach, but is not as good as that of the configuration-interaction method. The main advantage of this procedure is that it is devoid of the most serious defect of HF method, viz. incorrect dissociation limits. (K.B.)

Self-consistent field with pseudowavefunctions

International Nuclear Information System (INIS)

Szasz, L.

1976-01-01

A computational method is given in which the energy of an atom is computed by using pseudowavefunctions only. The method centers on a model energy expression E/sub M/ which is similar to the Hartree--Fock energy expression, but contains only pseudowavefunctions. A theorem is proved according to which the Hartree--Fock orbitals can be transformed by a linear transformation into a set of uniquely defined pseudowavefunctions which have the property that, when substituted into E/sub M/, this quantity will closely approximate the Hartree--Fock energy E/sub F/. The new method is then formulated by identifying the total energy of an atom with the minimum of E/sub M/. Application of the energy minimum principle leads to a set of equations for the pseudowavefunctions which are similar to but simpler than the Hartree--Fock equations. These equations contain pseudopotentials for which explicit expressions are derived. The possibility of replacing these pseudopotentials by simpler model potentials is discussed, and the criteria for the selection of the model potential are outlined

Molecular bonding in SF6 measured by elastic electron scattering

International Nuclear Information System (INIS)

Miller, J.D.; Fink, M.

1992-01-01

Elastic differential cross-section measurements of gaseous SF 6 were made with 30 keV electrons in the range of 0.25 bohrs -1 ≤s≤10 bohrs -1 . Structural parameters derived in this study closely matched those found in an earlier total (elastic plus inelastic) scattering investigation. Multiple-scattering effects were incorporated in the structural refinement. The discrepancies between the independent atom model and the measured differential cross section reproduce earlier total scattering results for momentum transfers of greater than 5 bohrs -1 . By extending the measurements to smaller s values, a closer examination of a Hartree--Fock calculation for SF 6 was possible. It was found that the difference curve obtained from the Hartree--Fock calculation matched the experimental data in this region. A more quantitative analysis was performed using the analytic expressions of Bonham and Fink to compute moments of the molecular charge distribution from the differential cross-section data. Comparison of these results with similar fits to the Hartree--Fock calculation confirmed the good agreement between the Hartree--Fock calculation and the current elastic data

Inner-shell correlations and Sturm expansions in coupled perturbation calculations of atomic systems

International Nuclear Information System (INIS)

Sherstyuk, A.I.; Solov'eva, G.S.

1995-01-01

It is shown that virtual Hartree-Fock orbitals in Sturm-type expansions can be used to calculate the response of atomic systems to an external field within the framework of the coupled perturbation theory with allowance for correlation effects. The corrected electron-electron interaction in a system with field-distorted orbitals is considered by adding a nonlocal potential to a one-electron Hartree-Fock operator within each group of equivalent elections. The remaining correlation effects are calculated by solving a system of equations for corrections to the radial functions. The system is solved iteratively, with each subsequent iteration corresponding to a correction of an increasingly higher order in the electron--electron interaction. The explicit expression derived for the polarizability contains one-and two-particle radial integrals of the Sturm functions

Spin-orbit ZORA and four-component Dirac-Coulomb estimation of relativistic corrections to isotropic nuclear shieldings and chemical shifts of noble gas dimers

DEFF Research Database (Denmark)

Jankowska, Marzena; Kupka, Teobald; Stobiński, Leszek

2016-01-01

Hartree-Fock and density functional theory with the hybrid B3LYP and general gradient KT2 exchange-correlation functionals were used for non-relativistic and relativistic nuclear magnetic shielding calculations of helium, neon, argon, krypton and xenon dimers and free atoms. Relativistic...

Constrained Hartree-Fock and beyond

International Nuclear Information System (INIS)

Berger, J.F.; Girod, M.; Gogny, D.

1989-01-01

Completely microscopic descriptions of the fission phenomenon based on the nuclear mean field theory and its extensions are reviewed. The basic ideas underlying this kind of approach and the way one can set up a consistent microscopic dynamical model of the low energy fission process are presented. The main difficulties encountered in earlier calculations when trying to reproduce experimental fission barriers and to account for scission are recalled. We describe the method by which these difficulties have been overcome and discuss recent results. They concern a proposed interpretation for the scission mechanism and 'cold fission' events. Other issues like adiabaticity in the descent from the second saddle to scission and odd-even effects in cold fission are also discussed. (orig.)

On the role of anti-bound states in the RPA description of the giant monopole resonance

International Nuclear Information System (INIS)

Vertse, T.; Bang, J.

1989-01-01

The limit of the applicability of the resonant Random Phase Approximation (RPA) method is tested by calculating escape widths in the giant monopole resonance of 16 O and comparing them to the results of a time dependent Hartree-Fock calculation. Though the widths of the narrow s-wave component agree reasonably well, the broad p-wave component shows large disagreement, which cannot be cured by complementing the basis with anti-bound states in the RPA calculation. (author) 18 refs.; 3 tabs

Constraints on effective interactions imposed by antisymmetry and charge independence

Energy Technology Data Exchange (ETDEWEB)

Stringari, S [Trento Univ. (Italy). Dipartimento di Matematica e Fisica; Brink, D M [Oxford Univ. (UK). Dept. of Theoretical Physics

1978-07-24

Restrictions on the form of the energy functional following antisymmetry and charge independence have been investigated for a Hartree-Fock theory based on effective interactions. These restrictions impose severe constraints on density dependent effective interactions.

Mechanism of equalization of proton and neutron radii and the Coulomb anomaly

International Nuclear Information System (INIS)

Caurier, E.; Poves, A.; Zuker, A.

1980-01-01

It is shown that a one parameter modification of the effective forces allows to resolve the Coulomb energy anomalies in the Ca region within the framework of Hartree Fock (HF) and isospin projected Hartree Fock (IPHF) theories. A simple microscopic mechanism of equalization of neutron and proton radii is invoked to produce results consistent with available data

Ab initio calculations of the electronic and structural properties of beryllium-, magnesium- and calcium-nitrides

International Nuclear Information System (INIS)

Mokhtari, A.; Akbarzadeh, H.

2003-01-01

The electronic and structural properties of beryllium nitride (alpha and beta), magnesium- and calcium-nitrides were investigated using first principle full potential-linearized augmented plane wave method within density functional theory. We used Perdew and Wang-generalized gradient approximation, which is based on exchange correlation energy optimization, to calculate the total energy and the Engel-Vosko's GGA formalism, which optimize the corresponding potential, for band structure calculations. We also optimized internal parameters by relaxing the atomic positions in the force directions. Our results including lattice parameter, bulk modulus and it's pressure derivative, cohesive energy, band structure and density of states are compared with the experimental and other theoretical (Hartree-Fock approximation with a posteriori density functional correction) data

Investigation of electron momentum distributions for outer valence orbitals of trichlorofluoromethane by (e, 2e) electron momentum spectroscopy

International Nuclear Information System (INIS)

Zhou, L.X.; Shan, X.; Chen, X.J.; Yin, X.F.; Zhang, X.H.; Xu, C.K.; Wei, Z.; Xu, K.Z.

2006-01-01

The binding energy spectra and electron momentum distributions for the outer valence orbitals of trichlorofluoromethane (CFCl 3 ) have been measured by binary (e, 2e) electron momentum spectroscopy (EMS) at an impact energy of 1200 eV + binding energy. The experimental electron momentum profiles are compared with Hartree-Fock and density functional theory (DFT) calculations with different-sized basis sets. Generally, the DFT calculations employing B3LYP functional with large basis sets of AUG-cc-pVDZ and AUG-cc-pVTZ give better description of the experimental results. But for 3e orbital, all the theoretical calculations underestimate the experiment, which is probably due to the distorted-wave effect that often occurs in π*-like molecular orbital

Parsing polarization squeezing into Fock layers

DEFF Research Database (Denmark)

Mueller, Christian R.; Madsen, Lars Skovgaard; Klimov, Andrei B.

2016-01-01

photon number do the methods coincide; when the photon number is indefinite, we parse the state in Fock layers, finding that substantially higher squeezing can be observed in some of the single layers. By capitalizing on the properties of the Husimi Q function, we map this notion onto the Poincare space......, providing a full account of the measured squeezing....

Quasiparticle method in relativistic mean-field theories of nuclear structure

International Nuclear Information System (INIS)

Ai, H.

1988-01-01

In recent years, in order to understand the success of Dirac phenomenology, relativistic Brueckner-Hartree-Fock (RBHF) theory has been developed. This theory is a relativistic many-body theory of nuclear structure. Based upon the RBHF theory, which is characterized as having no free parameters other than those introduced in fitting free-space nucleon-nucleon scattering data, we construct an effective interaction. This interaction, when treated in a relativistic Hartree-Fock approximation, reproduces, rather accurately, the nucleon self-energy in nuclear matter, Migdal parameters obtained via relativistic Brueckner-Hartree-Fock calculations, and the saturation curves calculated with the full relativistic Brueckner-Hartree-Fock theory. This effective interaction is constructed by adding a number of pseudoparticles to the mesons used to construct one-boson-exchange (OBE) models of the nuclear force. The pseudoparticles have relatively large masses and either real or imaginary coupling constants. (For example, exchange of a pseudo-sigma with an imaginary coupling constant has the effect of reducing the scalar attraction arising from sigma exchange, while exchange of a pseudo-omega with an imaginary coupling constant has the effect of reducing the repulsion arising from omega exchange. The terms beyond the Born term in the case of pion exchange are well simulated by pseudo-sigma exchange with a real coupling constant.) The effective interaction constructed here may be used for calculations of the properties of finite nuclei in a relativistic Hartree-Fock approximation

Tensor decomposition in electronic structure calculations on 3D Cartesian grids

International Nuclear Information System (INIS)

Khoromskij, B.N.; Khoromskaia, V.; Chinnamsetty, S.R.; Flad, H.-J.

2009-01-01

In this paper, we investigate a novel approach based on the combination of Tucker-type and canonical tensor decomposition techniques for the efficient numerical approximation of functions and operators in electronic structure calculations. In particular, we study applicability of tensor approximations for the numerical solution of Hartree-Fock and Kohn-Sham equations on 3D Cartesian grids. We show that the orthogonal Tucker-type tensor approximation of electron density and Hartree potential of simple molecules leads to low tensor rank representations. This enables an efficient tensor-product convolution scheme for the computation of the Hartree potential using a collocation-type approximation via piecewise constant basis functions on a uniform nxnxn grid. Combined with the Richardson extrapolation, our approach exhibits O(h 3 ) convergence in the grid-size h=O(n -1 ). Moreover, this requires O(3rn+r 3 ) storage, where r denotes the Tucker rank of the electron density with r=O(logn), almost uniformly in n. For example, calculations of the Coulomb matrix and the Hartree-Fock energy for the CH 4 molecule, with a pseudopotential on the C atom, achieved accuracies of the order of 10 -6 hartree with a grid-size n of several hundreds. Since the tensor-product convolution in 3D is performed via 1D convolution transforms, our scheme markedly outperforms the 3D-FFT in both the computing time and storage requirements.

Extended screened exchange functional derived from transcorrelated density functional theory.

Science.gov (United States)

Umezawa, Naoto

2017-09-14

We propose a new formulation of the correlation energy functional derived from the transcorrelated method in use in density functional theory (TC-DFT). An effective Hamiltonian, H TC , is introduced by a similarity transformation of a many-body Hamiltonian, H, with respect to a complex function F: H TC =1FHF. It is proved that an expectation value of H TC for a normalized single Slater determinant, D n , corresponds to the total energy: E[n] = ⟨Ψ n |H|Ψ n ⟩/⟨Ψ n |Ψ n ⟩ = ⟨D n |H TC |D n ⟩ under the two assumptions: (1) The electron density nr associated with a trial wave function Ψ n = D n F is v-representable and (2) Ψ n and D n give rise to the same electron density nr. This formulation, therefore, provides an alternative expression of the total energy that is useful for the development of novel correlation energy functionals. By substituting a specific function for F, we successfully derived a model correlation energy functional, which resembles the functional form of the screened exchange method. The proposed functional, named the extended screened exchange (ESX) functional, is described within two-body integrals and is parametrized for a numerically exact correlation energy of the homogeneous electron gas. The ESX functional does not contain any ingredients of (semi-)local functionals and thus is totally free from self-interactions. The computational cost for solving the self-consistent-field equation is comparable to that of the Hartree-Fock method. We apply the ESX functional to electronic structure calculations for a solid silicon, H - ion, and small atoms. The results demonstrate that the TC-DFT formulation is promising for the systematic improvement of the correlation energy functional.

Localization of holes near charged defects in orbitally degenerate, doped Mott insulators

Science.gov (United States)

Avella, Adolfo; Oleś, Andrzej M.; Horsch, Peter

2018-05-01

We study the role of charged defects, disorder and electron-electron (e-e) interactions in a multiband model for t2g electrons in vanadium perovskites R1-xCaxVO3 (R = La,…,Y). By means of unrestricted Hartree-Fock calculations, we find that the atomic multiplet structure persists up to 50% Ca doping. Using the inverse participation number, we explore the degree of localization and its doping dependence for all electronic states. The observation of strongly localized wave functions is consistent with our conjecture that doped holes form spin-orbital polarons that are strongly bound to the charged Ca2+ defects. Interestingly, the long-range e-e interactions lead to a discontinuity in the wave function size across the chemical potential, where the electron removal states are more localized than the addition states.

Electron impact excitation of helium in Debye plasma

Energy Technology Data Exchange (ETDEWEB)

Diallo, S.; Gomis, L.; Faye, I. G.; Tall, M. S.; Diédhiou, I. [Département de Physique, Faculté des Sciences and Techniques, Université Cheikh Anta Diop, Dakar-Fann (Senegal); Diatta, C. S. [Institut International des Sciences et de Technologie, 28 Avenue des Ambassadeurs Dakar-Fann (Senegal); Zammit, M. [ARC Centre for Antimatter-Matter Studies, Curtin University, GPO Box U1987, Perth, Western Australia 6845 (Australia)

2015-03-15

The probability, differential, and integral scattering cross sections of the 1{sup 1}S→2{sup 1}S and 1{sup 1}S→2{sup 1}P transitions of helium have been calculated in the first Born approximation. The projectile-target interactions depending on the temperature and the density of plasma are described by the Debye-Hückel model. Wave functions of the target before and after collision were modeled by non orthogonal Hartree-Fock orbitals. The wave functions parameters are calculated with the Ritz variational method. We improve our unscreened first Born approximation integral cross sections by using the BE-scaled (B stands for binding energy and E excitation energy) method. The second Born approximation has also been used to calculate the excitation cross sections in Debye plasma. Our calculations are compared to other theoretical and experimental results where applicable.

Multiconfigurational Green's function approaches in quantum chemistry

International Nuclear Information System (INIS)

Yeager, D.L.

1984-01-01

The author discusses multiconfigurational Green's function techniques and generalizations. In particular he is interested in developing and applying these techniques for isolated atoms and small molecules. Furthermore, he develops formalisms that are fairly clear, accurate, and capable of being applied to open-shell and highly-correlated systems as well as to closed-shell systems with little electronic correlation. The two kinds of Green's functions that this article discusses are the single-particle Green's function and the retarded two-time Green's function in the energy representation. The poles of the former give the ionization potentials and electron affinities while the poles of the latter give the excitation energies. The multiconfigurational approximations are known as the multiconfigurational electron propagator (MCEP) and the multiconfigurational time-dependent Hartree-Fock (MCTDHF) (also known as the multiconfigurational random phase approximation (MCRPA) or the multiconfigurational linear response), respectively. 44 references

Quadratically convergent MCSCF scheme using Fock operators

International Nuclear Information System (INIS)

Das, G.

1981-01-01

A quadratically convergent formulation of the MCSCF method using Fock operators is presented. Among its advantages the present formulation is quadratically convergent unlike the earlier ones based on Fock operators. In contrast to other quadratically convergent schemes as well as the one based on generalized Brillouin's theorem, this method leads easily to a hybrid scheme where the weakly coupled orbitals (such as the core) are handled purely by Fock equations, while the rest of the orbitals are treated by a quadratically convergent approach with a truncated virtual space obtained by the use of the corresponding Fock equations

Covariant boost and structure functions of baryons in Gross-Neveu models

International Nuclear Information System (INIS)

Brendel, Wieland; Thies, Michael

2010-01-01

Baryons in the large N limit of two-dimensional Gross-Neveu models are reconsidered. The time-dependent Dirac-Hartree-Fock approach is used to boost a baryon to any inertial frame and shown to yield the covariant energy-momentum relation. Momentum distributions are computed exactly in arbitrary frames and used to interpolate between the rest frame and the infinite momentum frame, where they are related to structure functions. Effects from the Dirac sea depend sensitively on the occupation fraction of the valence level and the bare fermion mass and do not vanish at infinite momentum. In the case of the kink baryon, they even lead to divergent quark and antiquark structure functions at x=0.

Green's functions in quantum chemistry II - Improving the Σ perturbation approach

International Nuclear Information System (INIS)

Sebastian, K.L.; Narayanan, P.; Rama Varma, K.T.

1978-01-01

Two methods, which are expected to lead to results better than those of the Σ perturbation approach given earlier are investigated. Within the algebraic approximation, the methods are applied to the hydrogen molecule and to ethylene in the Pariser-Parr-Pople (PPP) approximation. Both the methods are seen to suffer from the defect of not conserving the number of particles in the system. The methods are (a) the use of a partitioning other than Hartree-Fock. Due to the non-conservation of particle number, the method does not seem to be suited for the calculation of the ground state energy, but it gives good results for ionisation potentials. The investigation reveals that the only partitioning which conserves the number of particles is the Hartree-Fock partitioning (b) the renormalised Σ perturbation method, suggested by Csnak and others. For ethylene in the PPP approximation, the method does conserve the number of particles (but not in general). However, the energy obtained is not as good as that in the Σ perturbation method. This method therefore seems to be of limited applicability in molecular calculations. (author)

Dielectronic recombination cross sections for H-like ions

International Nuclear Information System (INIS)

Pindzola, M.S.; Badnell, N.R.; Griffin, D.C.

1990-01-01

Dielectronic recombination cross sections for several H-like atomic ions are calculated in an isolated-resonance, distorted-wave approximation. Fine-structure and configuration-interaction effects are examined in detail for the O 7+ cross section. Hartree-Fock, intermediate-coupled, multiconfiguration dielectronic recombination cross sections for O 7+ are then compared with the recent experimental measurements obtained with the Test Storage Ring in Heidelberg. The cross-section spectra line up well in energy and the shape of the main resonance structures are comparable. The experimental integrated cross sections differ by up to 20% from theory, but this may be due in part to uncertainties in the electron distribution function

On-line system for investigation of atomic structure

International Nuclear Information System (INIS)

Amus'ya, M.Ya.; Chernysheva, L.V.

1983-01-01

A description of the on-line ATOM system is presented that enables to investigate the structure of atomic electron shells and their interactions with different scattering particles-electrons, positronse photons, mesons - with the use of computerized numerical solutions. The problem is stated along with mathematical description of atomic properties including theoretical and numerical models for each investigated physical process. The ATOM system structure is considered. The Hartree-Fock method is used to determine the wave functions of the ground and excited atomic states. The programs are written in the ALGOL langauge. Different atomic characteristics were possible to be calculated for the first time with an accuracy exceeding an experimental one

Sampling procedures using optical-data and partial wave cross sections in a Monte Carlo code for simulating kilovolt electron and positron transport in solids

International Nuclear Information System (INIS)

Fernandez-Varea, J.M.; Salvat, F.; Liljequist, D.

1994-09-01

The details of a Monte Carlo code for computing the penetration and energy loss of electrons and positrons in solids are described. The code, intended for electrons and positrons with energies from ∼ 100 eV to ∼ 100 keV, is based on the simulation of individual elastic and inelastic collisions. Elastic collisions are simulated using differential cross sections computed by the relativistic partial wave method applied to a muffin-tin Dirac-Hartree-Fock-Slater potential. Inelastic collisions are simulated by means of a model based on optical and photoelectric data, which are extended to the non-zero momentum transfer region by means of somewhat different algorithms for valence electron excitations and inner-shell excitations. This report focuses on the description of detailed formulae and sampling methods. 10 refs, 3 figs, 8 tabs

Functional integral representation of the nuclear many-body grand partition function

International Nuclear Information System (INIS)

Kerman, A.K.; Troudet, T.

1984-01-01

A local functional integral formulation of the nuclear many-body problem is proposed which is a generalization of the method previously developed. Its most interesting feature is that it allows an expansion of the many-body evolution operator around any arbitrary mean-field which takes into account the pairing correlations between the nucleons. This is explicitly illustrated for the nuclear many-body grand partition function for which special attention is paid to the static temperature-dependent Hartree-Fock-Bogolyubov (H.F.B.) approximation. Indeed, the temperature-dependent H.F.B. configuration appears to be the optimal choice from a variational point of view among all the possible independent quasi-particle motion approximations. An analytic approximation of the energy level density rho (E,A) is given using explicitly the arbitrariness in the choice of the mean-field and a possible numerical application is proposed. Finally, a new compact formulation of our functional integral that might be useful for future Monte Carlo calculations is proposed

Self-consistent description of the SHFB equations for 112Sn

Science.gov (United States)

Ghafouri, M.; Sadeghi, H.; Torkiha, M.

2018-03-01

The Hartree-Fock (HF) method is an excellent approximation of the closed shell magic nuclei. Pair correlation is essential for the description of open shell nuclei and has been derived for even-even, odd-odd and even-odd nuclei. These effects are reported by Hartree-Fock with BCS (HFBCS) or Hartree-Fock-Bogolyubov (HFB). These issues have been investigated, especially in the nuclear charts, and such studies have been compared with the observed information. We compute observations such as total binding energy, charge radius, densities, separation energies, pairing gaps and potential energy surfaces for neutrons and protons, and compare them with experimental data and the result of the spherical codes. In spherical even-even neutron-rich nuclei are considered in the Skyrme-Hartree-Fock-Bogolyubov (SHFB) method with density-dependent pairing interaction. Zero-range density-dependent interactions is used in the pairing channel. We solve SHF or SHFB equations in the spatial coordinates with spherical symmetry for tin isotopes such as 112Sn. The numerical accuracy of solving equations in the coordinate space is much greater than the fundamental extensions, which yields almost precise results.

Theoretical investigation of pressure-induced structural transitions in americium using GGA+U and hybrid density functional theory methods

DEFF Research Database (Denmark)

Verma, Ashok K.; Modak, P.; Sharma, Surinder M.

2013-01-01

First-principles calculations have been performed for americium (Am) metal using the generalized gradient approximation + orbital-dependent onsite Coulomb repulsion via Hubbard interaction (GGA+U) and hybrid density functional theory (HYB-DFT) methods to investigate various ground state properties......-I to Am-II transition. Good agreement was found between calculated and experimental equations of states for all phases, but the first three phases need larger U (α) parameters (where α represents the fraction of Hartree-Fock exchange energy replacing the DFT exchange energy) than the fourth phase in order...

Coupled state analysis of electron excitations in asymmetric collision systems

International Nuclear Information System (INIS)

Mehler, G.; Reus, T. de; Mueller, U.; Reinhardt, J.; Mueller, B.; Greiner, W.; Soff, G.

1985-01-01

A coupled channel formalism is presented, using relativistic basis states of the target atom. Screening effects are incorporated by means of an effective potential of Hartree-Fock-Slater type. Relativistic wave packets are employed for the description of the continuum. The impact parameter dependence of the K-hole production in p-Ag collisions is calculated, including quadrupole contributions of the projectile Coulomb potential. The results are compared with experimental data. (orig.)

Stochastic TDHF and the Boltzman-Langevin equation

International Nuclear Information System (INIS)

Suraud, E.; Reinhard, P.G.

1991-01-01

Outgoing from a time-dependent theory of correlations, we present a stochastic differential equation for the propagation of ensembles of Slater determinants, called Stochastic Time-Dependent Hartree-Fock (Stochastic TDHF). These ensembles are allowed to develop large fluctuations in the Hartree-Fock mean fields. An alternative stochastic differential equation, the Boltzmann-Langevin equation, can be derived from Stochastic TDHF by averaging over subensembles with small fluctuations

effect of side chain length on the stability and structural properties of 3

African Journals Online (AJOL)

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We report on the effect of the alkoxy chain length on the thermodynamic ... studied by Hartree-Fock (HF) and Density Functional Theory (DFT) methods. ..... with longer alkoxy substituents on the phenyl ring have lesser value of change in Gibbs ...

Superintegrability of the Fock-Darwin system

Science.gov (United States)

Drigho-Filho, E.; Kuru, Ş.; Negro, J.; Nieto, L. M.

2017-08-01

The Fock-Darwin system is analyzed from the point of view of its symmetry properties in the quantum and classical frameworks. The quantum Fock-Darwin system is known to have two sets of ladder operators, a fact which guarantees its solvability. We show that for rational values of the quotient of two relevant frequencies, this system is superintegrable, the quantum symmetries being responsible for the degeneracy of the energy levels. These symmetries are of higher order and close a polynomial algebra. In the classical case, the ladder operators are replaced by ladder functions and the symmetries by constants of motion. We also prove that the rational classical system is superintegrable and its trajectories are closed. The constants of motion are also generators of symmetry transformations in the phase space that have been integrated for some special cases. These transformations connect different trajectories with the same energy. The coherent states of the quantum superintegrable system are found and they reproduce the closed trajectories of the classical one.

Calculation of wave-functions with frozen orbitals in mixed quantum mechanics/molecular mechanics methods. II. Application of the local basis equation.

Science.gov (United States)

Ferenczy, György G

2013-04-05

The application of the local basis equation (Ferenczy and Adams, J. Chem. Phys. 2009, 130, 134108) in mixed quantum mechanics/molecular mechanics (QM/MM) and quantum mechanics/quantum mechanics (QM/QM) methods is investigated. This equation is suitable to derive local basis nonorthogonal orbitals that minimize the energy of the system and it exhibits good convergence properties in a self-consistent field solution. These features make the equation appropriate to be used in mixed QM/MM and QM/QM methods to optimize orbitals in the field of frozen localized orbitals connecting the subsystems. Calculations performed for several properties in divers systems show that the method is robust with various choices of the frozen orbitals and frontier atom properties. With appropriate basis set assignment, it gives results equivalent with those of a related approach [G. G. Ferenczy previous paper in this issue] using the Huzinaga equation. Thus, the local basis equation can be used in mixed QM/MM methods with small size quantum subsystems to calculate properties in good agreement with reference Hartree-Fock-Roothaan results. It is shown that bond charges are not necessary when the local basis equation is applied, although they are required for the self-consistent field solution of the Huzinaga equation based method. Conversely, the deformation of the wave-function near to the boundary is observed without bond charges and this has a significant effect on deprotonation energies but a less pronounced effect when the total charge of the system is conserved. The local basis equation can also be used to define a two layer quantum system with nonorthogonal localized orbitals surrounding the central delocalized quantum subsystem. Copyright © 2013 Wiley Periodicals, Inc.

Hartree-Fock and density functional theory study of alpha-cyclodextrin conformers.

Science.gov (United States)

Jiménez, Verónica; Alderete, Joel B

2008-01-31

Herein, we report the geometry optimization of four conformers of alpha-cyclodextrin (alpha-CD) by means of PM3, HF/STO-3G, HF/3-21G, HF/6-31G(d), B3LYP/6-31G(d), and X3LYP/6-31G(d) calculations. The analysis of several geometrical parameters indicates that all conformers possess bond lengths, angles, and dihedrals that agree fairly well with the crystalline structure of alpha-CD. However, only three of them (1-3) resemble the polar character of CDs and show intramolecular hydrogen-bonding patterns that agree with experimental NMR data. Among them, conformer 3 appears to be the most stable species both in the gas phase and in solution; therefore, it is expected to be the most suitable representative structure for alpha-CD conformation. The purpose of selecting such a species is to identify an appropriate structure to be employed as a starting point for reliable computational studies on complexation phenomena. Our results indicate that the choice of a particular alpha-CD conformer should affect the results of ab initio computational studies on the inclusion complexation with this cyclodextrin since both the direction and the magnitude of the dipole moment depend strongly on the conformation of alpha-CD.

Theoretical calculations of electron-impact and radiative processes in atoms

International Nuclear Information System (INIS)

Pindzola, M.S.

1975-01-01

Electron-impact and radiative processes in atoms are investigated with particular attention paid to the effects of electron correlations. Using the optical potential method, the cross section for the elastic scattering of electrons by the neutral argon atom is calculated from 0 to 300 eV. Corrections to the Hartree--Fock cross section are obtained from a many-particle perturbation expansion. The effects of electron correlations are found to be quite significant at low energy. The optical potential results are compared with a polarized orbital calculation, the Born approximation and experiment. The 2s and 2p excitation cross sections for electron scattering on hydrogen are calculated by two similar methods. The distorted wave method is applied and the effect of calculating the outgoing scattered electron in the potential of the initial or final state is investigated. The imaginary part of the optical potential is also calculated in lowest order by the use of many-body diagrams. The subshell photoionization cross sections in argon are calculated using the acceleration, length and velocity forms of the dipole operator. First order electron correlation corrections to the Hartree--Fock approximation are obtained through the use of many-body perturbation theory. Also investigated is the two photon ionization cross section for the neutral argon atom. A double perturbation expansion in the Coulomb correlations and the atom-radiation field interaction is made. Contributions from intermediate states are obtained by direct summation over Hartree--Fock bound and continuum single particle states. The effects of electron correlations and photon radiative corrections are investigated

Modified Fourth-Order Kinetic Energy Gradient Expansion with Hartree Potential-Dependent Coefficients.

Science.gov (United States)

Constantin, Lucian A; Fabiano, Eduardo; Della Sala, Fabio

2017-09-12

Using the semiclassical neutral atom theory, we developed a modified fourth-order kinetic energy (KE) gradient expansion (GE4m) that keeps unchanged all the linear-response terms of the uniform electron gas and gives a significant improvement with respect to the known semilocal functionals for both large atoms and jellium surfaces. On the other hand, GE4m is not accurate for light atoms; thus, we modified the GE4m coefficients making them dependent on a novel ingredient, the reduced Hartree potential, recently introduced in the Journal of Chemical Physics 2016, 145, 084110, in the context of exchange functionals. The resulting KE gradient expansion functional, named uGE4m, belongs to the novel class of u-meta-generalized-gradient-approximations (uMGGA) whose members depend on the conventional ingredients (i.e., the reduced gradient and Laplacian of the density) as well as on the reduced Hartree potential. To test uGE4m, we defined an appropriate benchmark (including total KE and KE differences for atoms, molecules and jellium clusters) for gradient expansion functionals, that is, including only those systems which are mainly described by a slowly varying density regime. While most of the GGA and meta-GGA KE functionals (we tested 18 of them) are accurate for some properties and inaccurate for others, uGE4m shows a consistently good performance for all the properties considered. This represents a qualitative boost in the KE functional development and highlights the importance of the reduced Hartree potential for the construction of next-generation KE functionals.

Electronic structure investigations of 4-aminophthal hydrazide by UV-visible, NMR spectral studies and HOMO-LUMO analysis by ab initio and DFT calculations.

Science.gov (United States)

Sambathkumar, K; Jeyavijayan, S; Arivazhagan, M

2015-08-05

Combined experimental and theoretical studies were conducted on the molecular structure and vibrational spectra of 4-AminoPhthalhydrazide (APH). The FT-IR and FT-Raman spectra of APH were recorded in the solid phase. The molecular geometry and vibrational frequencies of APH in the ground state have been calculated by using the ab initio HF (Hartree-Fock) and density functional methods (B3LYP) invoking 6-311+G(d,p) basis set. The optimized geometric bond lengths and bond angles obtained by HF and B3LYP method show best agreement with the experimental values. Comparison of the observed fundamental vibrational frequencies of APH with calculated results by HF and density functional methods indicates that B3LYP is superior to the scaled Hartree-Fock approach for molecular vibrational problems. The difference between the observed and scaled wave number values of most of the fundamentals is very small. A detailed interpretation of the NMR spectra of APH was also reported. The theoretical spectrograms for infrared and Raman spectra of the title molecule have been constructed. UV-vis spectrum of the compound was recorded and the electronic properties, such as HOMO and LUMO energies, were performed by time dependent density functional theory (TD-DFT) approach. Finally the calculations results were applied to simulated infrared and Raman spectra of the title compound which show good agreement with observed spectra. And the temperature dependence of the thermodynamic properties of constant pressure (Cp), entropy (S) and enthalpy change (ΔH0→T) for APH were also determined. Copyright © 2015 Elsevier B.V. All rights reserved.

Quantum chemical approach for positron annihilation spectra of atoms and molecules beyond plane-wave approximation

Science.gov (United States)

Ikabata, Yasuhiro; Aiba, Risa; Iwanade, Toru; Nishizawa, Hiroaki; Wang, Feng; Nakai, Hiromi

2018-05-01

We report theoretical calculations of positron-electron annihilation spectra of noble gas atoms and small molecules using the nuclear orbital plus molecular orbital method. Instead of a nuclear wavefunction, the positronic wavefunction is obtained as the solution of the coupled Hartree-Fock or Kohn-Sham equation for a positron and the electrons. The molecular field is included in the positronic Fock operator, which allows an appropriate treatment of the positron-molecule repulsion. The present treatment succeeds in reproducing the Doppler shift, i.e., full width at half maximum (FWHM) of experimentally measured annihilation (γ-ray) spectra for molecules with a mean absolute error less than 10%. The numerical results indicate that the interpretation of the FWHM in terms of a specific molecular orbital is not appropriate.

Ab initio calculations of the electronic and structural properties of beryllium-, magnesium- and calcium-nitrides

Energy Technology Data Exchange (ETDEWEB)

Mokhtari, A.; Akbarzadeh, H

2003-09-01

The electronic and structural properties of beryllium nitride (alpha and beta), magnesium- and calcium-nitrides were investigated using first principle full potential-linearized augmented plane wave method within density functional theory. We used Perdew and Wang-generalized gradient approximation, which is based on exchange correlation energy optimization, to calculate the total energy and the Engel-Vosko's GGA formalism, which optimize the corresponding potential, for band structure calculations. We also optimized internal parameters by relaxing the atomic positions in the force directions. Our results including lattice parameter, bulk modulus and it's pressure derivative, cohesive energy, band structure and density of states are compared with the experimental and other theoretical (Hartree-Fock approximation with a posteriori density functional correction) data.

Theoretical analysis for the specific heat and thermal parameters of solid C60

Science.gov (United States)

Soto, J. R.; Calles, A.; Castro, J. J.

1997-08-01

We present the results of a theoretical analysis for the thermal parameters and phonon contribution to the specific heat in solid C60. The phonon contribution to the specific heat is calculated through the solution of the corresponding dynamical matrix, for different points in the Brillouin zone, and the construccion of the partial and generalized phonon density of states. The force constants are obtained from a first principle calculation, using a SCF Hartree-Fock wave function from the Gaussian 92 program. The thermal parameters reported are the effective temperatures and vibrational amplitudes as a function of temperature. Using this model we present a parametization scheme in order to reproduce the general behaviour of the experimental specific heat for these materials.

Extended Møller-Plesset perturbation theory for dynamical and static correlations

International Nuclear Information System (INIS)

Tsuchimochi, Takashi; Van Voorhis, Troy

2014-01-01

We present a novel method that appropriately handles both dynamical and static electron correlations in a balanced manner, using a perturbation theory on a spin-extended Hartree-Fock (EHF) wave function reference. While EHF is a suitable candidate for degenerate systems where static correlation is ubiquitous, it is known that most of dynamical correlation is neglected in EHF. In this work, we derive a perturbative correction to a fully spin-projected self-consistent wave function based on second-order Møller-Plesset perturbation theory (MP2). The proposed method efficiently captures the ability of EHF to describe static correlation in degeneracy, combined with MP2's ability to treat dynamical correlation effects. We demonstrate drastic improvements on molecular ground state and excited state potential energy curves and singlet-triplet splitting energies over both EHF and MP2 with similar computational effort to the latter

Fission of heavy nuclei: microscopic study of fission barriers and fragments angular momentum

International Nuclear Information System (INIS)

Bonneau, L.

2003-11-01

A lot of experimental data on nuclear fission has been being collected for the last 65 years, allowing theoreticians to confront their models with reality. The first part of this work is dedicated to the computation of fission barriers. We have extended the HF + BCS (Hartree Fock + Bandeen-Cooper-Schrieffer) method in order to include a new set of polynomials on which wave functions can be broken to, more accurately than on Hermite's polynomials in the 2 fragment configuration. The fission barriers of 26 heavy nuclei from Thorium-230 to Nobelium-256 have been assessed and compared to experimental data, it appears that differences are no greater than 1 MeV. We have discovered a neat correlation between the variation of the experimental fission lifetimes of even Fermium isotopes and the computed heights of second barriers. Moreover our model reproduces the hyper-deformed well of Thorium-230 with a good agreement on the well depth. The second part deals with the scission region. We have performed Hartree-Fock calculations in order to explore different ways of fragmentation. We have shown that the harmonic oscillator gives a valid description of such ways. In order to compute the mean value of J 2 in the fragments we have been driven to propose an adequate definition of that quantity consistent with the non-locality property of the J 2 operator. (A.C.)

Fission of heavy nuclei: microscopic study of fission barriers and fragments angular momentum; Fission des noyaux lourds: etude microscopique des barrieres de fission et du moment angulaire des fragments

Energy Technology Data Exchange (ETDEWEB)

Bonneau, L

2003-11-01

A lot of experimental data on nuclear fission has been being collected for the last 65 years, allowing theoreticians to confront their models with reality. The first part of this work is dedicated to the computation of fission barriers. We have extended the HF + BCS (Hartree Fock + Bandeen-Cooper-Schrieffer) method in order to include a new set of polynomials on which wave functions can be broken to, more accurately than on Hermite's polynomials in the 2 fragment configuration. The fission barriers of 26 heavy nuclei from Thorium-230 to Nobelium-256 have been assessed and compared to experimental data, it appears that differences are no greater than 1 MeV. We have discovered a neat correlation between the variation of the experimental fission lifetimes of even Fermium isotopes and the computed heights of second barriers. Moreover our model reproduces the hyper-deformed well of Thorium-230 with a good agreement on the well depth. The second part deals with the scission region. We have performed Hartree-Fock calculations in order to explore different ways of fragmentation. We have shown that the harmonic oscillator gives a valid description of such ways. In order to compute the mean value of J{sup 2} in the fragments we have been driven to propose an adequate definition of that quantity consistent with the non-locality property of the J{sup 2} operator. (A.C.)

Quasihomogeneous function method and Fock's problem

International Nuclear Information System (INIS)

Smyshlyaev, V.P.

1987-01-01

The diffraction of a high-frequency wave by a smooth convex body near the tangency point of the limiting ray to the surface is restated as the scattering problem for the Schrodinger equation with a linear potential on a half-axis. Various prior estimates for the scattering problem are used in order to prove existence, uniqueness, and smoothness theorems. The corresponding solution satisfies the principle of limiting absorption. The formal solution of the corresponding Schrodinger equation in the form of quasihomogeneous functions is essentially used in their constructions

Symmetry-projected variational approach to the one-dimensional Hubbard model

International Nuclear Information System (INIS)

Schmid, K.W.; Dahm, T.; Margueron, J.; Muether, H.

2005-01-01

We apply a variational method devised for the nuclear many-body problem to the one-dimensional Hubbard model with nearest neighbor hopping and periodic boundary conditions. The test wave function consist for each state out of a single Hartree-Fock determinant mixing all the sites (or momenta) as well as the spin projections of the electrons. Total spin and linear momentum are restored by projection methods before the variation. It is demonstrated that this approach reproduces the results of exact diagonalizations for half-filled N=12 and N=14 lattices not only for the energies and occupation numbers of the ground but also of the lowest excited states rather well. Furthermore, a system of ten electrons in an N=12 lattice is investigated and, finally, an N=30 lattice is studied. In addition to energies and occupation numbers we present the spectral functions computed with the help of the symmetry-projected wave functions as well

A Floquet-Green's function approach to mesoscopic transport under ac bias

International Nuclear Information System (INIS)

Wu, B H; Cao, J C

2008-01-01

The current response of a mesoscopic system under a periodic ac bias is investigated by combining the Floquet theorem and the nonequilibrium Green's function method. The band structure of the lead under ac bias is fully taken into account by using appropriate self-energies in an enlarged Floquet space. Both the retarded and lesser Green's functions are obtained in the Floquet basis to account for the interference and interaction effects. In addition to the external ac bias, the time-varying Coulomb interaction, which is treated at the self-consistent Hartree-Fock level, provides another internal ac field. The numerical results show that the time-varying Coulomb field yields decoherence and reduces the ringing behavior of the current response to a harmonic bias

Correlations and fluctuations in static and dynamic mean-field approaches

International Nuclear Information System (INIS)

Balian, R.; Veneroni, M.

1991-01-01

Let the state of a many-body system at an initial time be specified, completely or partly; find the expectation values, correlations and fluctuations of single-particle observables at a later time. The characteristic function of these observables is optimized within a general variational scheme. The expansion of the optimal characteristic function provides the same results as the conventional mean-field approaches for the thermodynamic potentials and the expectation values: for fermions the best initial state is then the Hartree-Fock (HF) solution and the evolution is described by the time-dependent Hartree-Fock (TDHF) equation. Two special cases are investigated as preliminary steps. The first case deals with the evaluation of correlations for static problems, where the initial and final times coincide. In the second special case, the exact initial state is assumed to be an independent-particle one. (K.A.) 23 refs.; 1 fig

Thermal effects in gravitational Hartree systems

Energy Technology Data Exchange (ETDEWEB)

Aki, Gonca L. [Weierstrass-Institut fuer Angewandte Analysis und Stochastik (WIAS) im Forschungsverbund Berlin e.V. (Germany); Dolbeault, Jean [Paris-Dauphine Univ. (FR). Ceremade (UMR CNRS 7534); Sparber, Christof [Illinois Univ., Chicago, IL (United States). Dept. of Mathematics, Statistics, and Computer Science

2010-07-01

We consider the non-relativistic Hartree model in the gravitational case, i.e. with attractive Coulomb-Newton interaction. For a given mass M>0, we construct stationary states with non-zero temperature T by minimizing the corresponding free energy functional. It is proved that minimizers exist if and only if the temperature of the system is below a certain threshold T*>0 (possibly infinite), which itself depends on the specific choice of the entropy functional. We also investigate whether the corresponding minimizers are mixed or pure quantum states and characterize a critical temperature T{sub c} element of (0,T*) above which mixed states appear. (orig.)

Thermal Effects in Gravitational Hartree Systems

KAUST Repository

Aki, Gonca L.

2011-04-06

We consider the non-relativistic Hartree model in the gravitational case, i. e. with attractive Coulomb-Newton interaction. For a given mass M > 0, we construct stationary states with non-zero temperature T by minimizing the corresponding free energy functional. It is proved that minimizers exist if and only if the temperature of the system is below a certain threshold T* > 0 (possibly infinite), which itself depends on the specific choice of the entropy functional. We also investigate whether the corresponding minimizers are mixed or pure quantum states and characterize a critical temperature Tc ∈ (0,T*) above which mixed states appear. © 2011 Springer Basel AG.

Thermal Effects in Gravitational Hartree Systems

KAUST Repository

Aki, Gonca L.; Dolbeault, Jean; Sparber, Christof

2011-01-01

We consider the non-relativistic Hartree model in the gravitational case, i. e. with attractive Coulomb-Newton interaction. For a given mass M > 0, we construct stationary states with non-zero temperature T by minimizing the corresponding free energy functional. It is proved that minimizers exist if and only if the temperature of the system is below a certain threshold T* > 0 (possibly infinite), which itself depends on the specific choice of the entropy functional. We also investigate whether the corresponding minimizers are mixed or pure quantum states and characterize a critical temperature Tc ∈ (0,T*) above which mixed states appear. © 2011 Springer Basel AG.

The problem of the universal density functional and the density matrix functional theory

International Nuclear Information System (INIS)

Bobrov, V. B.; Trigger, S. A.

2013-01-01

The analysis in this paper shows that the Hohenberg-Kohn theorem is the constellation of two statements: (i) the mathematically rigorous Hohenberg-Kohn lemma, which demonstrates that the same ground-state density cannot correspond to two different potentials of an external field, and (ii) the hypothesis of the existence of the universal density functional. Based on the obtained explicit expression for the nonrel-ativistic particle energy in a local external field, we prove that the energy of the system of more than two non-interacting electrons cannot be a functional of the inhomogeneous density. This result is generalized to the system of interacting electrons. It means that the Hohenberg-Kohn lemma cannot provide justification of the universal density functional for fermions. At the same time, statements of the density functional theory remain valid when considering any number of noninteracting ground-state bosons due to the Bose condensation effect. In the framework of the density matrix functional theory, the hypothesis of the existence of the universal density matrix functional corresponds to the cases of noninteracting particles and to interaction in the Hartree-Fock approximation.

Photon wave function

OpenAIRE

Bialynicki-Birula, Iwo

2005-01-01

Photon wave function is a controversial concept. Controversies stem from the fact that photon wave functions can not have all the properties of the Schroedinger wave functions of nonrelativistic wave mechanics. Insistence on those properties that, owing to peculiarities of photon dynamics, cannot be rendered, led some physicists to the extreme opinion that the photon wave function does not exist. I reject such a fundamentalist point of view in favor of a more pragmatic approach. In my view, t...

Study of Atoms and Molecules with Auxiliary-Field Quantum Monte Carlo

Science.gov (United States)

Purwanto, Wirawan; Suewattana, Malliga; Krakauer, Henry; Zhang, Shiwei; Walter, Eric J.

2006-03-01

We study the ground-state properties of second-row atoms and molecules using the phaseless auxiliary-field quantum Monte Carlo (AF QMC) method. This method projects the many-body ground state from a trial wave function by means of random walks in the Slater-determinant space. We use a single Slater-determinant trial wave function obtained from density-functional theory (DFT) or Hartree-Fock (HF) calculations. The calculations were done with a plane-wave basis and supercells with periodic boundary condition. We investigate the finite-size effects and the accuracy of pseudopotentials within DFT, HF, and AF QMC frameworks. Pseudopotentials generated from both LDA (OPIUM) and HF are employed. We find that the many-body QMC calculations show a greater sensitivity to the accuracy of the pseudopotentials. With reliable pseudopotentials, the ionization potentials and dissociation energies obtained using AF QMC are in excellent agreement with the experimental results. S. Zhang and H. Krakauer, Phys. Rev. Lett. 90, 136401 (2003) http://opium.sourceforge.net I. Ovcharenko, A. Aspuru-Guzik, and W. A. Lester, J. Chem. Phys. 114, 7790 (2001)

A J matrix engine for density functional theory calculations

International Nuclear Information System (INIS)

White, C.A.; Head-Gordon, M.

1996-01-01

We introduce a new method for the formation of the J matrix (Coulomb interaction matrix) within a basis of Cartesian Gaussian functions, as needed in density functional theory and Hartree endash Fock calculations. By summing the density matrix into the underlying Gaussian integral formulas, we have developed a J matrix open-quote open-quote engine close-quote close-quote which forms the exact J matrix without explicitly forming the full set of two electron integral intermediates. Several precomputable quantities have been identified, substantially reducing the number of floating point operations and memory accesses needed in a J matrix calculation. Initial timings indicate a speedup of greater than four times for the (pp parallel pp) class of integrals with speedups increasing to over ten times for (ff parallel ff) integrals. copyright 1996 American Institute of Physics

Covariant density functional theory: The role of the pion

International Nuclear Information System (INIS)

Lalazissis, G. A.; Karatzikos, S.; Serra, M.; Otsuka, T.; Ring, P.

2009-01-01

We investigate the role of the pion in covariant density functional theory. Starting from conventional relativistic mean field (RMF) theory with a nonlinear coupling of the σ meson and without exchange terms we add pions with a pseudovector coupling to the nucleons in relativistic Hartree-Fock approximation. In order to take into account the change of the pion field in the nuclear medium the effective coupling constant of the pion is treated as a free parameter. It is found that the inclusion of the pion to this sort of density functionals does not destroy the overall description of the bulk properties by RMF. On the other hand, the noncentral contribution of the pion (tensor coupling) does have effects on single particle energies and on binding energies of certain nuclei.

A unique Fock quantization for fields in non-stationary spacetimes

International Nuclear Information System (INIS)

Cortez, Jerónimo; Marugán, Guillermo A. Mena; Olmedo, Javier; Velhinho, José M.

2010-01-01

In curved spacetimes, the lack of criteria for the construction of a unique quantization is a fundamental problem undermining the significance of the predictions of quantum field theory. Inequivalent quantizations lead to different physics. Recently, however, some uniqueness results have been obtained for fields in non-stationary settings. In particular, for vacua that are invariant under the background symmetries, a unitary implementation of the classical evolution suffices to pick up a unique Fock quantization in the case of Klein-Gordon fields with time-dependent mass, propagating in a static spacetime whose spatial sections are three-spheres. In fact, the field equation can be reinterpreted as describing the propagation in a Friedmann-Robertson-Walker spacetime after a suitable scaling of the field by a function of time. For this class of fields, we prove here an even stronger result about the Fock quantization: the uniqueness persists when one allows for linear time-dependent transformations of the field in order to account for a scaling by background functions. In total, paying attention to the dynamics, there exists a preferred choice of quantum field, and only one SO(4)-invariant Fock representation for it that respects the standard probabilistic interpretation along the evolution. The result has relevant implications e.g. in cosmology

Ab initio calculations and modelling of atomic cluster structure

DEFF Research Database (Denmark)

Solov'yov, Ilia; Lyalin, Andrey G.; Solov'yov, Andrey V.

2004-01-01

The optimized structure and electronic properties of small sodium and magnesium clusters have been investigated using it ab initio theoretical methods based on density-functional theory and post-Hartree-Fock many-body perturbation theory accounting for all electrons in the system. A new theoretical...

68 - 75 Galadanchi et al.c

African Journals Online (AJOL)

User

Restricted HartreeFock (RHF) and Density Functional Theory (DFT) studies were carried out on the organic semi ... arrays), organic light emitting diodes (OLEDs), solar cells and low-cost devices (Kitamura,Arakawa, 2008;. Hwan et al.2004; Byoungnan,2008). Organic semiconductors are materials with semiconducting.

Reaction Kinetics of Acetone Peroxide Formation and Structure Investigations Using Raman Spectroscopy and X-ray Diffraction

DEFF Research Database (Denmark)

Jensen, Lars; Mortensen, Peter Mølgaard; Trane, Rasmus

2009-01-01

functional theory (DFT)/Hartree-Fock approach. It was not possible from this to assess with certainty which intermediate products formed most extensively in an acetone/hydrogen peroxide mixture. However, it was concluded that the most likely reaction mixture is a mixture of the different intermediate...

Renormalization of Molecular Quasiparticle Levels at Metal-Molecule Interfaces: Trends across Binding Regimes

DEFF Research Database (Denmark)

Thygesen, Kristian Sommer; Rubio, Angel

2009-01-01

a microscopic model of the metal-molecule interface, we illustrate the basic features of this renormalization mechanism through systematic GW, Hartree-Fock, and Kohn-Sham calculations for the molecular energy levels as function of the model parameters. We identify two different polarization mechanisms: (i...

A Sparse Self-Consistent Field Algorithm and Its Parallel Implementation: Application to Density-Functional-Based Tight Binding.

Science.gov (United States)

Scemama, Anthony; Renon, Nicolas; Rapacioli, Mathias

2014-06-10

We present an algorithm and its parallel implementation for solving a self-consistent problem as encountered in Hartree-Fock or density functional theory. The algorithm takes advantage of the sparsity of matrices through the use of local molecular orbitals. The implementation allows one to exploit efficiently modern symmetric multiprocessing (SMP) computer architectures. As a first application, the algorithm is used within the density-functional-based tight binding method, for which most of the computational time is spent in the linear algebra routines (diagonalization of the Fock/Kohn-Sham matrix). We show that with this algorithm (i) single point calculations on very large systems (millions of atoms) can be performed on large SMP machines, (ii) calculations involving intermediate size systems (1000-100 000 atoms) are also strongly accelerated and can run efficiently on standard servers, and (iii) the error on the total energy due to the use of a cutoff in the molecular orbital coefficients can be controlled such that it remains smaller than the SCF convergence criterion.

Modern physics for scientists and engineers

CERN Document Server

Morrison, John C

2015-01-01

The second edition of Modern Physics for Scientists and Engineers is intended for a first course in modern physics. Beginning with a brief and focused account of the historical events leading to the formulation of modern quantum theory, later chapters delve into the underlying physics. Streamlined content, chapters on semiconductors, Dirac equation and quantum field theory, as well as a robust pedagogy and ancillary package, including an accompanying website with computer applets, assist students in learning the essential material. The applets provide a realistic description of the energy levels and wave functions of electrons in atoms and crystals. The Hartree-Fock and ABINIT applets are valuable tools for studying the properties of atoms and semiconductors.

Use of results from microscopic methods in optical model calculations

International Nuclear Information System (INIS)

Lagrange, C.

1985-11-01

A concept of vectorization for coupled-channel programs based upon conventional methods is first presented. This has been implanted in our program for its use on the CRAY-1 computer. In a second part we investigate the capabilities of a semi-microscopic optical model involving fewer adjustable parameters than phenomenological ones. The two main ingredients of our calculations are, for spherical or well-deformed nuclei, the microscopic optical-model calculations of Jeukenne, Lejeune and Mahaux and nuclear densities from Hartree-Fock-Bogoliubov calculations using the density-dependent force D1. For transitional nuclei deformation-dependent nuclear structure wave functions are employed to weigh the scattering potentials for different shapes and channels [fr

Dynamic polarizability of a complex atom in strong laser fields

International Nuclear Information System (INIS)

Rapoport, L.P.; Klinskikh, A.F.; Mordvinov, V.V.

1997-01-01

An asymptotic expansion of the dynamic polarizability of a complex atom in a strong circularly polarized light field is found for the case of high frequencies. The self-consistent approximation of the Hartree-Fock type for the ''atom+field'' system is developed, within the framework of which a numerical calculation of the dynamic polarizability of Ne, Kr, and Ar atoms in a strong radiation field is performed. The strong field effect is shown to manifest itself not only in a change of the energy spectrum and the character of behavior of the wave functions of atomic electrons, but also in a modification of the one-electron self-consistent potential for the atom in the field

Balancing Exchange Mixing in Density-Functional Approximations for Iron Porphyrin.

Science.gov (United States)

Berryman, Victoria E J; Boyd, Russell J; Johnson, Erin R

2015-07-14

Predicting the correct ground-state multiplicity for iron(II) porphyrin, a high-spin quintet, remains a significant challenge for electronic-structure methods, including commonly employed density functionals. An even greater challenge for these methods is correctly predicting favorable binding of O2 to iron(II) porphyrin, due to the open-shell singlet character of the adduct. In this work, the performance of a modest set of contemporary density-functional approximations is assessed and the results interpreted using Bader delocalization indices. It is found that inclusion of greater proportions of Hartree-Fock exchange, in hybrid or range-separated hybrid functionals, has opposing effects; it improves the ability of the functional to identify the ground state but is detrimental to predicting favorable dioxygen binding. Because of the uncomplementary nature of these properties, accurate prediction of both the relative spin-state energies and the O2 binding enthalpy eludes conventional density-functional approximations.

Interacting fermions and bosons with definite total momentum

International Nuclear Information System (INIS)

Alon, Ofir E.; Streltsov, Alexej I.; Cederbaum, Lorenz S.

2005-01-01

Any exact eigenstate with a definite momentum of a many-body Hamiltonian can be written as an integral over a symmetry-broken function Φ. For two particles, we exactly express Φ in terms of (single-particle) orbitals for all energy levels and any interparticle interaction. Especially for the ground state, Φ is given by the simple Hartree-Fock and Hartree Ansaetze for fermions and bosons, respectively. Implications for several and many particles as well as a numerical example for interacting bosons are provided

KIDS Nuclear Energy Density Functional: 1st Application in Nuclei

Science.gov (United States)

Gil, Hana; Papakonstantinou, Panagiota; Hyun, Chang Ho; Oh, Yongseok

We apply the KIDS (Korea: IBS-Daegu-Sungkyunkwan) nuclear energy density functional model, which is based on the Fermi momentum expansion, to the study of properties of lj-closed nuclei. The parameters of the model are determined by the nuclear properties at the saturation density and theoretical calculations on pure neutron matter. For applying the model to the study of nuclei, we rely on the Skyrme force model, where the Skyrme force parameters are determined through the KIDS energy density functional. Solving Hartree-Fock equations, we obtain the energies per particle and charge radii of closed magic nuclei, namely, 16O, 28O, 40Ca, 48Ca, 60Ca, 90Zr, 132Sn, and 208Pb. The results are compared with the observed data and further improvement of the model is shortly mentioned.

Global hybrids from the semiclassical atom theory satisfying the local density linear response.

Science.gov (United States)

Fabiano, Eduardo; Constantin, Lucian A; Cortona, Pietro; Della Sala, Fabio

2015-01-13

We propose global hybrid approximations of the exchange-correlation (XC) energy functional which reproduce well the modified fourth-order gradient expansion of the exchange energy in the semiclassical limit of many-electron neutral atoms and recover the full local density approximation (LDA) linear response. These XC functionals represent the hybrid versions of the APBE functional [Phys. Rev. Lett. 2011, 106, 186406] yet employing an additional correlation functional which uses the localization concept of the correlation energy density to improve the compatibility with the Hartree-Fock exchange as well as the coupling-constant-resolved XC potential energy. Broad energetic and structural testing, including thermochemistry and geometry, transition metal complexes, noncovalent interactions, gold clusters and small gold-molecule interfaces, as well as an analysis of the hybrid parameters, show that our construction is quite robust. In particular, our testing shows that the resulting hybrid, including 20% of Hartree-Fock exchange and named hAPBE, performs remarkably well for a broad palette of systems and properties, being generally better than popular hybrids (PBE0 and B3LYP). Semiempirical dispersion corrections are also provided.

Spatial dependence of pair correlations (nuclear scissors)

International Nuclear Information System (INIS)

Bal'butsev, E.B.; Malov, L.A.

2009-01-01

The solution of time-dependent Hartree-Fock-Bogolyubov equations by the Wigner function moments method leads to the appearance of low-lying modes whose description requires accurate knowledge of the anomalous density matrix. It is shown that calculations with the Woods-Saxon potential satisfy this requirement

Simulations and analysis of the Raman scattering and differential Raman scattering/Raman optical activity (ROA) spectra of amino acids, peptides and proteins in aqueous solution

DEFF Research Database (Denmark)

Jalkanen, Karl J.; Nieminen, R. M.; Bohr, Jakob

2000-01-01

The Raman and Raman optical activity (ROA) spectra of amino acids and small peptides in aqueous solution have been simulated by density functional theory and restricted Hartree/Fock methods. The treatment of the aqueous environment in treated in two ways. The water molecules in the first hydratio...

Polarizable Density Embedding Coupled Cluster Method

DEFF Research Database (Denmark)

Hršak, Dalibor; Olsen, Jógvan Magnus Haugaard; Kongsted, Jacob

2018-01-01

by an embedding potential consisting of a set of fragment densities obtained from calculations on isolated fragments with a quantum-chemistry method such as Hartree-Fock (HF) or Kohn-Sham density functional theory (KS-DFT) and dressed with a set of atom-centered anisotropic dipole-dipole polarizabilities...

Λ hypernuclei in the Skyrme-Hartree-Fock treatment with G-matrix motivated interactions

International Nuclear Information System (INIS)

Lanskoy, D.E.; Yamamoto, Y.

1997-01-01

Skyrme-like hyperon-nucleon potentials are derived from G-matrix calculations and shown to reproduce well the Λ single-particle spectra of hypernuclei measured in BNL and KEK. Fit of the spectra can restrict p-wave ΛN interaction, radii of Λ orbits in hypernuclear ground states, Λ well depth and effective mass in nuclear matter rather tightly. Implications of ΛN spin-orbit force to the spectra are considered. (author)

Positive semidefinite tensor factorizations of the two-electron integral matrix for low-scaling ab initio electronic structure.

Science.gov (United States)

Hoy, Erik P; Mazziotti, David A

2015-08-14

Tensor factorization of the 2-electron integral matrix is a well-known technique for reducing the computational scaling of ab initio electronic structure methods toward that of Hartree-Fock and density functional theories. The simplest factorization that maintains the positive semidefinite character of the 2-electron integral matrix is the Cholesky factorization. In this paper, we introduce a family of positive semidefinite factorizations that generalize the Cholesky factorization. Using an implementation of the factorization within the parametric 2-RDM method [D. A. Mazziotti, Phys. Rev. Lett. 101, 253002 (2008)], we study several inorganic molecules, alkane chains, and potential energy curves and find that this generalized factorization retains the accuracy and size extensivity of the Cholesky factorization, even in the presence of multi-reference correlation. The generalized family of positive semidefinite factorizations has potential applications to low-scaling ab initio electronic structure methods that treat electron correlation with a computational cost approaching that of the Hartree-Fock method or density functional theory.

Positive semidefinite tensor factorizations of the two-electron integral matrix for low-scaling ab initio electronic structure

Energy Technology Data Exchange (ETDEWEB)

Hoy, Erik P.; Mazziotti, David A., E-mail: damazz@uchicago.edu [Department of Chemistry and The James Franck Institute, The University of Chicago, Chicago, Illinois 60637 (United States)

2015-08-14

Tensor factorization of the 2-electron integral matrix is a well-known technique for reducing the computational scaling of ab initio electronic structure methods toward that of Hartree-Fock and density functional theories. The simplest factorization that maintains the positive semidefinite character of the 2-electron integral matrix is the Cholesky factorization. In this paper, we introduce a family of positive semidefinite factorizations that generalize the Cholesky factorization. Using an implementation of the factorization within the parametric 2-RDM method [D. A. Mazziotti, Phys. Rev. Lett. 101, 253002 (2008)], we study several inorganic molecules, alkane chains, and potential energy curves and find that this generalized factorization retains the accuracy and size extensivity of the Cholesky factorization, even in the presence of multi-reference correlation. The generalized family of positive semidefinite factorizations has potential applications to low-scaling ab initio electronic structure methods that treat electron correlation with a computational cost approaching that of the Hartree-Fock method or density functional theory.

Large scale nuclear structure studies

International Nuclear Information System (INIS)

Faessler, A.

1985-01-01

Results of large scale nuclear structure studies are reported. The starting point is the Hartree-Fock-Bogoliubov solution with angular momentum and proton and neutron number projection after variation. This model for number and spin projected two-quasiparticle excitations with realistic forces yields in sd-shell nuclei similar good results as the 'exact' shell-model calculations. Here the authors present results for a pf-shell nucleus 46 Ti and results for the A=130 mass region where they studied 58 different nuclei with the same single-particle energies and the same effective force derived from a meson exchange potential. They carried out a Hartree-Fock-Bogoliubov variation after mean field projection in realistic model spaces. In this way, they determine for each yrast state the optimal mean Hartree-Fock-Bogoliubov field. They apply this method to 130 Ce and 128 Ba using the same effective nucleon-nucleon interaction. (Auth.)

Well-posedness for Semi-relativistic Hartree Equations of Critical Type

International Nuclear Information System (INIS)

Lenzmann, Enno

2007-01-01

We prove local and global well-posedness for semi-relativistic, nonlinear Schroedinger equations with initial data in H s (R 3 ). Here F(u) is a critical Hartree nonlinearity that corresponds to Coulomb or Yukawa type self-interactions. For focusing F(u), which arise in the quantum theory of boson stars, we derive global-in-time existence for small initial data, where the smallness condition is expressed in terms of the L 2 -norm of solitary wave ground states. Our proof of well-posedness does not rely on Strichartz type estimates. As a major benefit from this, our method enables us to consider external potentials of a quite general class

Gauge-invariant variational methods for Hamiltonian lattice gauge theories

International Nuclear Information System (INIS)

Horn, D.; Weinstein, M.

1982-01-01

This paper develops variational methods for calculating the ground-state and excited-state spectrum of Hamiltonian lattice gauge theories defined in the A 0 = 0 gauge. The scheme introduced in this paper has the advantage of allowing one to convert more familiar tools such as mean-field, Hartree-Fock, and real-space renormalization-group approximation, which are by their very nature gauge-noninvariant methods, into fully gauge-invariant techniques. We show that these methods apply in the same way to both Abelian and non-Abelian theories, and that they are at least powerful enough to describe correctly the physics of periodic quantum electrodynamics (PQED) in (2+1) and (3+1) space-time dimensions. This paper formulates the problem for both Abelian and non-Abelian theories and shows how to reduce the Rayleigh-Ritz problem to that of computing the partition function of a classical spin system. We discuss the evaluation of the effective spin problem which one derives the PQED and then discuss ways of carrying out the evaluation of the partition function for the system equivalent to a non-Abelian theory. The explicit form of the effective partition function for the non-Abelian theory is derived, but because the evaluation of this function is considerably more complicated than the one derived in the Abelian theory no explicit evaluation of this function is presented. However, by comparing the gauge-projected Hartree-Fock wave function for PQED with that of the pure SU(2) gauge theory, we are able to show that extremely interesting differences emerge between these theories even at this simple level. We close with a discussion of fermions and a discussion of how one can extend these ideas to allow the computation of the glueball and hadron spectrum

Energy level alignment and quantum conductance of functionalized metal-molecule junctions

DEFF Research Database (Denmark)

Jin, Chengjun; Strange, Mikkel; Markussen, Troels

2013-01-01

We study the effect of functional groups (CH3*4, OCH3, CH3, Cl, CN, F*4) on the electronic transport properties of 1,4-benzenediamine molecular junctions using the non-equilibrium Green function method. Exchange and correlation effects are included at various levels of theory, namely density...... functional theory (DFT), energy level-corrected DFT (DFT+Σ), Hartree-Fock and the many-body GW approximation. All methods reproduce the expected trends for the energy of the frontier orbitals according to the electron donating or withdrawing character of the substituent group. However, only the GW method...... predicts the correct ordering of the conductance amongst the molecules. The absolute GW (DFT) conductance is within a factor of two (three) of the experimental values. Correcting the DFT orbital energies by a simple physically motivated scissors operator, Σ, can bring the DFT conductances close...

Semiclassical description of hot nuclear systems

International Nuclear Information System (INIS)

Brack, M.

1984-01-01

We present semiclassical density variational calculations for highly excited nuclear systems. We employ the newly derived functionals tau[rho] and sigma[rho] of the extended Thomas-Fermi (ETF) model, generalized to finite temperatures. Excellent agreement is reached with Hartree-Fock (HF) results. We also calculated the fission barrier of 240 Pu as a function of the nuclear temperature

Deformation properties of osmium, platinum, mercury isotopes from self-consistent calculations: influence of the pairing treatment

International Nuclear Information System (INIS)

Sauvage-Letessier, J.; Quentin, P.; Flocard, H.

1981-01-01

The deformation properties of several isotopes of the elements Os, Pt and Hg have been computed by means of Hartree-Fock plus BCS calculations. The Hartree-Fock potential has been derived from the Skyrme interaction S III. Two approximations have been used for the treatment of pairing correlations: the constant (versus deformation) gap method and the constant (versus deformation) pairing matrix element method. A good agreement with experimental data is obtained for ground state deformation properties except for the exact location of the prolate-oblate transition as a function of the neutron number. For one nucleus 184 Hg, the pairing matrix elements have been calculated from the Gogny interaction D1, in order to study their single particle state- and deformation-dependence. From these results, the validity of the two approximations used for pairing correlations, is discussed

Explicit polarization (X-Pol) potential using ab initio molecular orbital theory and density functional theory.

Science.gov (United States)

Song, Lingchun; Han, Jaebeom; Lin, Yen-lin; Xie, Wangshen; Gao, Jiali

2009-10-29

The explicit polarization (X-Pol) method has been examined using ab initio molecular orbital theory and density functional theory. The X-Pol potential was designed to provide a novel theoretical framework for developing next-generation force fields for biomolecular simulations. Importantly, the X-Pol potential is a general method, which can be employed with any level of electronic structure theory. The present study illustrates the implementation of the X-Pol method using ab initio Hartree-Fock theory and hybrid density functional theory. The computational results are illustrated by considering a set of bimolecular complexes of small organic molecules and ions with water. The computed interaction energies and hydrogen bond geometries are in good accord with CCSD(T) calculations and B3LYP/aug-cc-pVDZ optimizations.

Double ionization of atoms by ion impact: two-step models

Energy Technology Data Exchange (ETDEWEB)

Fiori, Marcelo [Departamento de Fisica, Universidad Nacional de Salta, Salta (Argentina); Rocha, A B [Instituto de Quimica, Departamento de FIsico-Quimica, Universidade Federal do Rio de Janeiro, Rio de Janeiro, 21949-900, RJ (Brazil); Bielschowsky, C E [Instituto de Quimica, Departamento de FIsico-Quimica, Universidade Federal do Rio de Janeiro, Rio de Janeiro, 21949-900, RJ (Brazil); Jalbert, Ginette [Instituto de Fisica, Universidade Federal do Rio de Janeiro, Caixa Postal 68528, Rio de Janeiro, 21941-972, RJ (Brazil); Garibotti, C R [CONICET and Centro Atomico Bariloche, 8400 S. C. Bariloche, RIo Negro (Argentina)

2006-04-14

Total cross sections for the double ionization of He and Li atoms by the impact of H{sup +}, He{sup 2+} and Li{sup 3+} are calculated at intermediate and high energies within two-step models. The double ionization of He by the impact of other bare projectiles at a fixed energy is obtained as well. Single ionization probabilities are calculated within the continuum distorted wave -eikonal-initial-state (CDW-EIS) approximation. The required atomic bound and continuum wave functions are evaluated by numerically solving the atomic wave equation with an optimized potential model (OPM). Correlation between events is introduced by considering ion relaxation. The final state electronic correlation is considered by means of the so-called Gamow factor. We compare the transition probabilities resulting from our approach with those resulting from the use of a Rootham-Hartree-Fock initial state and a Coulomb continuum state with an effective charge. We find that the use of OPM waves gives a better agreement with the experimental results than with Coulomb waves.

Hierarchical wave functions revisited

International Nuclear Information System (INIS)

Li Dingping.

1997-11-01

We study the hierarchical wave functions on a sphere and on a torus. We simplify some wave functions on a sphere or a torus using the analytic properties of wave functions. The open question, the construction of the wave function for quasi electron excitation on a torus, is also solved in this paper. (author)

Analytic calculations of hyper-Raman spectra from density functional theory hyperpolarizability gradients

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.

Angular-momentum-projected cranked HFB approach to the study of nuclear rotations

International Nuclear Information System (INIS)

Wuest, E.; Ansari, A.; Mosel, U.

1985-01-01

Employing a pairing-plus-quadrupole interaction hamiltonian and projecting out good angular momentum states from the cranked Hartree-Fock-Bogoliubov (CHFB) intrinsic wave functions the yrast spectra of 158 Dy and 168 Yb are calculated up to moderately high spins (Isub(max)=16) as to include the backbending region. Then the variation of pairing correlation, g-factor and rotational alignment of neutron spin as a function of total angular momentum is studied. The effect of particle number projection on the spin-projected CHFB wave functions is also investigated and is found to be unimportant for the calculation of g-factors. On the other hand, corrections of the excitation energies for number fluctuations in the CHFB wave functions are essential. Furthermore, looking at the distribution of the total projection quantum number K in various cranking wave functions we are able to throw some light on the Knot=0 nature of the aligned s-band. A variation-after-spin projection calculation strictly for the axial shape, without cranking, is also carried out for both the nuclei considered here. In the low-spin region this numerically 'cheaper' scheme produces energy spectra similar to that of the CHFB method, and may thus be used to readjust the interaction parameters. (orig.)

Fission of heavy nuclei: microscopic study of fission barriers and fragments angular momentum; Fission des noyaux lourds: etude microscopique des barrieres de fission et du moment angulaire des fragments

Energy Technology Data Exchange (ETDEWEB)

Bonneau, L

2003-11-01

A lot of experimental data on nuclear fission has been being collected for the last 65 years, allowing theoreticians to confront their models with reality. The first part of this work is dedicated to the computation of fission barriers. We have extended the HF + BCS (Hartree Fock + Bandeen-Cooper-Schrieffer) method in order to include a new set of polynomials on which wave functions can be broken to, more accurately than on Hermite's polynomials in the 2 fragment configuration. The fission barriers of 26 heavy nuclei from Thorium-230 to Nobelium-256 have been assessed and compared to experimental data, it appears that differences are no greater than 1 MeV. We have discovered a neat correlation between the variation of the experimental fission lifetimes of even Fermium isotopes and the computed heights of second barriers. Moreover our model reproduces the hyper-deformed well of Thorium-230 with a good agreement on the well depth. The second part deals with the scission region. We have performed Hartree-Fock calculations in order to explore different ways of fragmentation. We have shown that the harmonic oscillator gives a valid description of such ways. In order to compute the mean value of J{sup 2} in the fragments we have been driven to propose an adequate definition of that quantity consistent with the non-locality property of the J{sup 2} operator. (A.C.)

Lower bounds for the ground states of He-isoelectronic series

International Nuclear Information System (INIS)

Fraga, Serafin

1981-01-01

A formulation, based on the concept of null local kinetic energy regions, has been developed for the determination of lower bounds for the ground state of a two-electron atom. Numerical results, obtained from Hartree-Fock functions, are presented for the elements He through Kr of the two-electron series

Self-consistent hybrid functionals for solids: a fully-automated implementation

Science.gov (United States)

Erba, A.

2017-08-01

A fully-automated algorithm for the determination of the system-specific optimal fraction of exact exchange in self-consistent hybrid functionals of the density-functional-theory is illustrated, as implemented into the public Crystal program. The exchange fraction of this new class of functionals is self-consistently updated proportionally to the inverse of the dielectric response of the system within an iterative procedure (Skone et al 2014 Phys. Rev. B 89, 195112). Each iteration of the present scheme, in turn, implies convergence of a self-consistent-field (SCF) and a coupled-perturbed-Hartree-Fock/Kohn-Sham (CPHF/KS) procedure. The present implementation, beside improving the user-friendliness of self-consistent hybrids, exploits the unperturbed and electric-field perturbed density matrices from previous iterations as guesses for subsequent SCF and CPHF/KS iterations, which is documented to reduce the overall computational cost of the whole process by a factor of 2.

Orbital stability of standing waves of a class of fractional Schrödinger equations with Hartree-type nonlinearity

KAUST Repository

Cho, Yonggeun; Fall, Mouhamed M.; Hajaiej, Hichem; Markowich, Peter A.; Trabelsi, Saber

2016-01-01

This paper is devoted to the mathematical analysis of a class of nonlinear fractional Schrödinger equations with a general Hartree-type integrand. We show the well-posedness of the associated Cauchy problem and prove the existence and stability

Effects of pairing correlation on low-lying quasi-particle resonance in neutron drip-line nuclei

OpenAIRE

Kobayashi, Yoshihiko; Matsuo, Masayuki

2015-01-01

We discuss effects of pairing correlation on quasi-particle resonance. We analyze in detail how the width of low-lying quasi-particle resonance is governed by the pairing correlation in the neutron drip-line nuclei. We consider the 46Si + n system to discuss low-lying p wave quasi-particle resonance. Solving the Hartree-Fock-Bogoliubov equation in the coordinate space with scattering boundary condition, we calculate the phase shift, the elastic cross section, the resonance width and the reson...

A theoretical study on the photoionization of the valence orbitals of phosphine

Directory of Open Access Journals (Sweden)

Nascimento Edmar M.

2006-01-01

Full Text Available We report a theoretical study on the photoionization of phosphine in the static-exchange level and frozen core approximation, using the method of continued fractions. The main subject of the present study is to investigate in which extent the Hartree-Fock description of the target applied to molecular photoionization is valid. Also, the role played by multichannel coupling is analysed. Our study shows that single-channel Hartree-Fock calculations can provide reliable results except for photon energies near the photoionization threshold.

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

Quadrupole moments as measures of electron correlation in two-electron atoms

International Nuclear Information System (INIS)

Ceraulo, S.C.; Berry, R.S.

1991-01-01

We have calculated quadrupole moments, Q zz , of helium in several of its doubly excited states and in two of its singly excited Rydberg states, and of the alkaline-earth atoms Be, Mg, Ca, Sr, and Ba in their ground and low-lying excited states. The calculations use well-converged, frozen-core configuration-interaction (CI) wave functions and, for interpretive purposes, Hartree-Fock (HF) atomic wave functions and single-term, optimized, molecular rotor-vibrator (RV) wave functions. The quadrupole moments calculated using RV wave functions serve as a test of the validity of the correlated, moleculelike model, which has been used to describe the effects of electron correlation in these two-electron and pseudo-two-electron atoms. Likewise, the quadrupole moments calculated with HF wave functions test the validity of the independent-particle model. In addition to their predictive use and their application to testing simple models, the quadrupole moments calculated with CI wave functions reveal previously unavailable information about the electronic structure of these atoms. Experimental methods by which these quadrupole moments might be measured are also discussed. The quadrupole moments computed from CI wave functions are presented as predictions; measurements of Q zz have been made for only two singly excited Rydberg states of He, and a value of Q zz has been computed previously for only one of the states reported here. We present these results in the hope of stimulating others to measure some of these quadrupole moments

Relativistic Dirac-Fock and many-body perturbation calculations on He, He-like ions, Ne, and Ar

International Nuclear Information System (INIS)

Ishikawa, Y.

1990-01-01

Relativistic Dirac-Fock and diagrammatic many-body perturbation-theory calculations have been performed on He, several He-like ions, Ne, and Ar. The no-pair Dirac-Coulomb Hamiltonian is taken as the starting point. A solution of the Dirac-Fock equations is obtained by analytic expansion in basis sets of Gaussian-type functions. Many-body perturbation improvements of Coulomb correlation are done to third order

Picture change error in quasirelativistic electron/spin density, Laplacian and bond critical points

KAUST Repository

Bučinský , Luká š; Kucková , Lenka; Malček, Michal; Koží šek, Jozef; Biskupič, Stanislav; Jayatilaka, Dylan; Bü chel, Gabriel E.; Arion, Vladimir B.

2014-01-01

The change of picture of the quasirelativistic Hartree-Fock wave functions is considered for electron/spin densities, the negative Laplacian of electron density and the appropriate bond critical point characteristics from the Quantum Theory of Atoms In Molecules (QTAIM). [OsCl5(Hpz)]- and [RuCl5(NO)]2- transition metal complexes are considered. Both, scalar relativistic and spin-orbit effects have been accounted for using the Infinite Order Two Component (IOTC) Hamiltonian. Picture change error (PCE) correction in the electron and spin densities and the Laplacian of electron density are treated analytically. Generally, PCE is found significant only in the core region of the atoms for the electron/spin density as well as Laplacian.©2014 Elsevier B.V. All rights reserved.

Correlation Matrix Renormalization Theory: Improving Accuracy with Two-Electron Density-Matrix Sum Rules.

Science.gov (United States)

Liu, C; Liu, J; Yao, Y X; Wu, P; Wang, C Z; Ho, K M

2016-10-11

We recently proposed the correlation matrix renormalization (CMR) theory to treat the electronic correlation effects [Phys. Rev. B 2014, 89, 045131 and Sci. Rep. 2015, 5, 13478] in ground state total energy calculations of molecular systems using the Gutzwiller variational wave function (GWF). By adopting a number of approximations, the computational effort of the CMR can be reduced to a level similar to Hartree-Fock calculations. This paper reports our recent progress in minimizing the error originating from some of these approximations. We introduce a novel sum-rule correction to obtain a more accurate description of the intersite electron correlation effects in total energy calculations. Benchmark calculations are performed on a set of molecules to show the reasonable accuracy of the method.

Many-body effects in photoreactions of light nuclei below pion threshold

International Nuclear Information System (INIS)

Cavinato, M.; Marangoni, M.; Saruis, A.M.

1983-01-01

In the present paper it is discussed the reaction mechanism in photoabsorption of light nuclei below pion threshold in the frame of a self-consistent RPA theory with a Skyrme force. The role of both exchange currents in electromagnetic operators and two-body correlations in the nuclear wave function has been studied in the RPA formalism. Exchange currents in RPA calculations are related to the effective mass in the Hartree-Fock field. Comparison is made between the RPA formalism and the Gari and Hebach theory. The relative contribution of exchange currents and nuclear correlations to the photoreaction of 16 O is evaluated from proton threshold up to 80 MeV. E1 and E2 multipoles are included in the calculation

Superconductivity of the two-dimensional Penson-Kolb model

International Nuclear Information System (INIS)

Czart, W.R.; Robaszkiewicz, S.

2001-01-01

Two-dimensional (d = 2) Penson-Kolb model, i.e. the tight-binding model with the pair-hopping (intersite charge exchange) interaction, is considered and the effects of phase fluctuations on the s-wave superconductivity of this system are discussed within Kosterlitz-Thouless scenario. The London penetration depth λ at T = 0, the Kosterlitz Thouless critical temperature T c , and the Hartree-Fock approximation critical temperature T p are determined as a function of particle concentration and interaction. The Uemura type plots (T c vs. λ -2 (0)) are derived. Beyond weak coupling and for low concentrations they show the existence of universal scaling: T c ∼ 1/λ 2 (0), as it previously found for the attractive Hubbard model and for the models intersite electron pairing. (author)

Filling of double vacancy in the K atomic shell with emission of one single photon

International Nuclear Information System (INIS)

Jalbert, G.

1978-12-01

A method was developed to calculate the transition rate for two-electron one-photon K(sub αα) transition (2s 2p → 1s 2 ). The method was tested for Ni with two K-shell vacancies in the initial state. The (sub αα) rate is calculated within the framework of a single system formed by the atom and the radiation. The transition is originated in the interactiion between the parts of that system. In the dipole approximation, the transition rate is obtained from the second order term of the time dependente perturbation theory. Hartree-Fock-Slater wave functions were used in the calculations for Ni. The results are compared with the available theoretical and experimental information. (Author) [pt

Picture change error in quasirelativistic electron/spin density, Laplacian and bond critical points

KAUST Repository

Bučinský, Lukáš

2014-06-01

The change of picture of the quasirelativistic Hartree-Fock wave functions is considered for electron/spin densities, the negative Laplacian of electron density and the appropriate bond critical point characteristics from the Quantum Theory of Atoms In Molecules (QTAIM). [OsCl5(Hpz)]- and [RuCl5(NO)]2- transition metal complexes are considered. Both, scalar relativistic and spin-orbit effects have been accounted for using the Infinite Order Two Component (IOTC) Hamiltonian. Picture change error (PCE) correction in the electron and spin densities and the Laplacian of electron density are treated analytically. Generally, PCE is found significant only in the core region of the atoms for the electron/spin density as well as Laplacian.©2014 Elsevier B.V. All rights reserved.

The Mehler-Fock transform of general order and arbitrary index and its inversion

Directory of Open Access Journals (Sweden)

Cyril Nasim

1984-01-01

Full Text Available An integral transform involving the associated Legendre function of zero order, P−12+iτ(x, x∈[1,∞, as the kernel (considered as a function of τ, is called Mehler-Fock transform. Some generalizations, involving the function P−12+iτμ(x, where the order μ is an arbitrary complex number, including the case when μ=0,1,2,… have been known for some time. In this present note, we define a general Mehler-Fock transform involving, as the kernel, the Legendre function P−12+tμ(x, of general order μ and an arbitrary index −12+t, t=σ+iτ, −∞<τ<∞. Then we develop a symmetric inversion formulae for these transforms. Many well-known results are derived as special cases of this general form. These transforms are widely used for solving many axisymmetric potential problems.

Development of New Open-Shell Perturbation and Coupled-Cluster Theories Based on Symmetric Spin Orbitals

Science.gov (United States)

Lee, Timothy J.; Arnold, James O. (Technical Monitor)

1994-01-01

A new spin orbital basis is employed in the development of efficient open-shell coupled-cluster and perturbation theories that are based on a restricted Hartree-Fock (RHF) reference function. The spin orbital basis differs from the standard one in the spin functions that are associated with the singly occupied spatial orbital. The occupied orbital (in the spin orbital basis) is assigned the delta(+) = 1/square root of 2(alpha+Beta) spin function while the unoccupied orbital is assigned the delta(-) = 1/square root of 2(alpha-Beta) spin function. The doubly occupied and unoccupied orbitals (in the reference function) are assigned the standard alpha and Beta spin functions. The coupled-cluster and perturbation theory wave functions based on this set of "symmetric spin orbitals" exhibit much more symmetry than those based on the standard spin orbital basis. This, together with interacting space arguments, leads to a dramatic reduction in the computational cost for both coupled-cluster and perturbation theory. Additionally, perturbation theory based on "symmetric spin orbitals" obeys Brillouin's theorem provided that spin and spatial excitations are both considered. Other properties of the coupled-cluster and perturbation theory wave functions and models will be discussed.

Double- and triple-differential cross sections for electron-impact ionization of helium

International Nuclear Information System (INIS)

Biswas, R.; Sinha, C.

1995-01-01

Triple- (TDCS) and double- (DDCS) differential cross sections have been calculated for single ionization in electron-helium collisions for asymmetric geometry at intermediate and medium high energies. The TDCS and DDCS results have been presented for different kinematical situations and have been compared with the corresponding experiments. In the present prescription, the final-state wave function involves the correlation between the two continuum electrons and satisfies the three-body asymptotic boundary condition (for asymmetric geometry), which is an important criterion for reliable ionization cross sections. The sensitivity of the ionization cross sections (particularly of the TDCS) with respect to the choice of the bound-state wave function of the He atom has also been studied, using two different forms of wave function of the He atom. The binary-to-recoil peak intensity ratio against momentum transfer in TDCS is found to be in closer agreement with the experiment for the simple Hylleraas wave function than for the Hartree-Fock wave function. The DDCS results are found to be in good agreement with the experimental data of Mueller-Fiedler et al. [J. Phys. B 19, 1211 (1986)] for lower ejected energy (E 2 ), while for higher E 2 the results are closer to the measurements of Shyn et al. [Phys. Rev. A 19, 557 (1979)] and Avaldi et al. [Nuovo Cimento D 9, 97 (1987)

Zn Coordination Chemistry:  Development of Benchmark Suites for Geometries, Dipole Moments, and Bond Dissociation Energies and Their Use To Test and Validate Density Functionals and Molecular Orbital Theory.

Science.gov (United States)

Amin, Elizabeth A; Truhlar, Donald G

2008-01-01

We present nonrelativistic and relativistic benchmark databases (obtained by coupled cluster calculations) of 10 Zn-ligand bond distances, 8 dipole moments, and 12 bond dissociation energies in Zn coordination compounds with O, S, NH3, H2O, OH, SCH3, and H ligands. These are used to test the predictions of 39 density functionals, Hartree-Fock theory, and seven more approximate molecular orbital theories. In the nonrelativisitic case, the M05-2X, B97-2, and mPW1PW functionals emerge as the most accurate ones for this test data, with unitless balanced mean unsigned errors (BMUEs) of 0.33, 0.38, and 0.43, respectively. The best local functionals (i.e., functionals with no Hartree-Fock exchange) are M06-L and τ-HCTH with BMUEs of 0.54 and 0.60, respectively. The popular B3LYP functional has a BMUE of 0.51, only slightly better than the value of 0.54 for the best local functional, which is less expensive. Hartree-Fock theory itself has a BMUE of 1.22. The M05-2X functional has a mean unsigned error of 0.008 Å for bond lengths, 0.19 D for dipole moments, and 4.30 kcal/mol for bond energies. The X3LYP functional has a smaller mean unsigned error (0.007 Å) for bond lengths but has mean unsigned errors of 0.43 D for dipole moments and 5.6 kcal/mol for bond energies. The M06-2X functional has a smaller mean unsigned error (3.3 kcal/mol) for bond energies but has mean unsigned errors of 0.017 Å for bond lengths and 0.37 D for dipole moments. The best of the semiempirical molecular orbital theories are PM3 and PM6, with BMUEs of 1.96 and 2.02, respectively. The ten most accurate functionals from the nonrelativistic benchmark analysis are then tested in relativistic calculations against new benchmarks obtained with coupled-cluster calculations and a relativistic effective core potential, resulting in M05-2X (BMUE = 0.895), PW6B95 (BMUE = 0.90), and B97-2 (BMUE = 0.93) as the top three functionals. We find significant relativistic effects (∼0.01 Å in bond lengths, ∼0

Knock-on type exchange and the density dependence of an effective interaction

International Nuclear Information System (INIS)

Jeukenne, J.P.; Mahaux, C.

1981-01-01

We investigate the origin of the density-dependence of the strength of an effective interaction previously derived from a Brueckner-Hartree-Fock calculation of the optical-model potential in nuclear matter. From the analysis of a model based on the Hartree-Fock approximation and on a Yukawa interaction with a Majorana exchange component, we study to what extent this dependence derives from the momentum-dependence of the exchange contribution of the knock-on type. The model is also used to discuss zero-range pseudopotential methods for including this knock-on contribution. (orig.)

Electric dipole transitions for four-times ionized cerium (Ce V)

Energy Technology Data Exchange (ETDEWEB)

Usta, Betül Karaçoban, E-mail: bkaracoban@sakarya.edu.tr; Akgün, Elif, E-mail: elif.akgun@ogr.sakarya.edu.tr; Alparslan, Büşra, E-mail: busra.alparslan1@ogr.sakarya.edu.tr [Physics Department, Sakarya University, 54187, Sakarya (Turkey)

2016-03-25

We have calculated the transition parameters, such as wavelengths, oscillator strengths, and transition probabilities (or rates), for the electric dipole (E1) transitions in four-times ionized cerium (Ce V, Z = 58) by using the multiconfiguration Hartree-Fock method within the framework of Breit-Pauli (MCHF+BP) relativistic corrections and the relativistic Hartree-Fock (HFR) method. The obtained results have been compared with other works available in literature. A discussion of these calculations for Ce V in this study has also been in view of the MCHF+BP and HFR methods.

Projected quasiparticle theory for molecular electronic structure

Science.gov (United States)

Scuseria, Gustavo E.; Jiménez-Hoyos, Carlos A.; Henderson, Thomas M.; Samanta, Kousik; Ellis, Jason K.

2011-09-01

We derive and implement symmetry-projected Hartree-Fock-Bogoliubov (HFB) equations and apply them to the molecular electronic structure problem. All symmetries (particle number, spin, spatial, and complex conjugation) are deliberately broken and restored in a self-consistent variation-after-projection approach. We show that the resulting method yields a comprehensive black-box treatment of static correlations with effective one-electron (mean-field) computational cost. The ensuing wave function is of multireference character and permeates the entire Hilbert space of the problem. The energy expression is different from regular HFB theory but remains a functional of an independent quasiparticle density matrix. All reduced density matrices are expressible as an integration of transition density matrices over a gauge grid. We present several proof-of-principle examples demonstrating the compelling power of projected quasiparticle theory for quantum chemistry.

RHF and DFT study of the optimized molecular structure and atomic ...

African Journals Online (AJOL)

Restricted HartreeFock (RHF) and Density Functional Theory (DFT) studies were carried out on the organic semi conductor material Pentacene. 6-31G and 6-31G* basis sets were used to optimize the molecule and compute the charge distribution at both levels of theory. The results show that the Carbon-Hydrogen bonds in ...

The Hondo 15 program for calculation of molecule electronic structure: its adaptation to Cyber 170/750 system of IEAv and use manual

International Nuclear Information System (INIS)

Rosato, A.; Pinheiro, A.M.B.S.; Ornellas, F.R.; Roberto Neto, O.

1985-01-01

The HONDO/5 program, herein described, performs a Hartree-Fock-Roothaan type calculation in molecules employing Gaussian type functions in the expansion of the molecular orbitals. After a brief exposition of the method upon which the theory is based, a new manual is presented in a more detailed version than the original one. (Author) [pt

Theoretical Studies Of Molecular Structure And Vibrational Spectra Of 5-Aminolevulinic Acid Hexyl Ester

International Nuclear Information System (INIS)

Comert, H.

2010-01-01

The molecular geometry and vibrational frequencies of The 5-Aminolevulinic acid's hexyl ester (ALA-H) in the ground state have been calculated using Hartree-Fock (HF) and Density functional method (B3LYP) with 6-31++G(d) basis set. The calculated vibrational spectra and geometric parameters of title compound were compered with experimental ones.

Quantum stochastic calculus in Fock space: A review

International Nuclear Information System (INIS)

Hudson, R.L.

1986-01-01

This paper presents a survey of the recently developed theory of quantum stochastic calculus in Boson Fock space, together with its applications. The work focuses on a non-commutative generalization of the classical Ito stochastic calculus of Brownian motion, which exploits to the full the Wiener-Segal duality transformation identifying the L 2 space of Wiener measure with a Boson Fock space. This Fock space emerges as the natural home of not only Brownian motion but also classical Poisson processes, and even of Fermionic processes of the type developed by Barnett et al. The principle physical application of the theory to the construction and characterization of unitary dilations of quantum dynamical semigroups is also described

Chemical bond as a test of density-gradient expansions for kinetic and exchange energies

International Nuclear Information System (INIS)

Perdew, J.P.; Levy, M.; Painter, G.S.; Wei, S.; Lagowski, J.B.

1988-01-01

Errors in kinetic and exchange contributions to the molecular bonding energy are assessed for approximate density functionals by reference to near-exact Hartree-Fock values. From the molecular calculations of Allan et al. and of Lee and Ghosh, it is demonstrated that the density-gradient expansion does not accurately describe the noninteracting kinetic contribution to the bonding energy, even when this expansion is carried to fourth order and applied in its spin-density-functional form to accurate Hartree-Fock densities. In a related study, it is demonstrated that the overbinding of molecules such as N 2 and F 2 , which occurs in the local-spin-density (LSD) approximation for the exchange-correlation energy, is not attributable to errors in the self-consistent LSD densities. Contrary to expectations based upon the Gunnarsson-Jones nodality argument, it is found that the LSD approximation for the exchange energy can seriously overbind a molecule even when bonding does not create additional nodes in the occupied valence orbitals. LSD and exact values for the exchange contribution to the bonding energy are displayed and discussed for several molecules

Physics in Screening Environments

Science.gov (United States)

Certik, Ondrej

In the current study, we investigated atoms in screening environments like plasmas. It is common practice to extract physical data, such as temperature and electron densities, from plasma experiments. We present results that address inherent computational difficulties that arise when the screening approach is extended to include the interaction between the atomic electrons. We show that there may arise an ambiguity in the interpretation of physical properties, such as temperature and charge density, from experimental data due to the opposing effects of electron-nucleus screening and electron-electron screening. The focus of the work, however, is on the resolution of inherent computational challenges that appear in the computation of two-particle matrix elements. Those enter already at the Hartree-Fock level. Furthermore, as examples of post Hartree-Fock calculations, we show second-order Green's function results and many body perturbation theory results of second order. A self-contained derivation of all necessary equations has been included. The accuracy of the implementation of the method is established by comparing standard unscreened results for various atoms and molecules against literature for Hartree-Fock as well as Green's function and many body perturbation theory. The main results of the thesis are presented in the chapter called Screened Results, where the behavior of several atomic systems depending on electron-electron and electron-nucleus Debye screening was studied. The computer code that we have developed has been made available for anybody to use. Finally, we present and discuss results obtained for screened interactions. We also examine thoroughly the computational details of the calculations and particular implementations of the method.

Derivation of equation of quasipotential type using the method of Fock-- Podolsky

Energy Technology Data Exchange (ETDEWEB)

Blokhintsev, D I; Rizov, V A; Todorov, I T

1975-12-31

A quasipotential equation is derived for the relativistic Coulomb problem from the equations of motion of quantum electrodynamics using the method of Fock-- Podolsky (Tamm-Dancoff). Relation with an inhomogeneous equation for the 4-point retarded function is exhibited. (auth)

Fourth-order terms in the diagrammatic perturbation expansion for the electronic energy of atoms and molecules

International Nuclear Information System (INIS)

Wilson, S.; Silver, D.M.

1979-01-01

Third-order diagrammatic perturbation theory provides a simple and accurate description of the electronic structure of atoms and molecules beyond that afforded by independent electron models. The largest corrections to such treatments, the fourth-order terms, are presented and discussed. All of the diagrams, which arise when the closed-shell Hartree--Fock function is utilized as a reference function, are given through fourth order. 18 references