Relativistic Brueckner-Hartree-Fock theory for finite nuclei
Shen, Shihang; Liang, Haozhao; Meng, Jie; Ring, Peter; Zhang, Shuangquan
2016-01-01
Starting with a bare nucleon-nucleon interaction, for the first time the full relativistic Brueckner-Hartree-Fock equations are solved for finite nuclei in a Dirac-Woods-Saxon basis. No free parameters are introduced to calculate the ground-state properties of finite nuclei. The nucleus $^{16}$O is investigated as an example. The resulting ground-state properties, such as binding energy and charge radius, are considerably improved as compared with the non-relativistic Brueckner-Hartree-Fock results and much closer to the experimental data. This opens the door for \\emph{ab initio} covariant investigations of heavy nuclei.
Relativistic Hartree-Fock-Bogoliubov model for deformed nuclei
Ebran, J -P; Arteaga, D Pena; Vretenar, D
2010-01-01
The Relativistic Hartree-Fock-Bogoliubov model for axially deformed nuclei (RHFBz) is introduced. The model is based on an effective Lagrangian with density-dependent meson-nucleon couplings in the particle-hole channel, and the pairing part of the Gogny force is used in the pairing channel. The RHFBz quasiparticle equations are solved by expansion in the basis of a deformed harmonic oscillator. Illustrative RHFBz calculations are performed for Carbon, Neon and Magnesium isotopes. The effect of the explicitly including the pion field is investigated for binding energies, deformation parameters, and charge radii.
RONG; Jian; MA; Zhongyu
2004-01-01
The relativistic microscopic optical potential in the asymmetric nuclear matter is studied in the framework of the Dirac Brueckner-Hartree-Fock method. A new decomposition of the Dirac structure of the nuclear self-energy in nuclear matter is adopted. The self-energy of a nucleon with E＞ 0 in nuclear matter is calculated with the G matrix in the Hartree-Fock approach. The optical potential of a nucleon in the nuclear medium is identified with the nucleon self-energy. The energy and asymmetric parameter dependence of the relativistic optical potentials for proton and neutron are discussed. The resulting Schroedinger equivalent potentials have reasonable behaviors of the energy dependence. The asymmetric parameter dependence of relativistic optical potentials and Schroedinger potentials are emphasized.
Momentum distribution of relativistic nuclei with Hartree-Fock mesonic correlations
Amaro, J.E. [Departamento de Fisica Moderna, Universidad de Granada, E-18071 Granada (Spain); Barbaro, M.B. [Dipartimento di Fisica Teorica, Universita di Torino and INFN, Sezione di Torino, Via P. Giuria 1, 10125 Torino (Italy); Departamento de Fisica Atomica, Molecular y Nuclear Universidad de Sevilla, Apdo. 1065, E-41080 Sevilla (Spain); Caballero, J.A. [Departamento de Fisica Atomica, Molecular y Nuclear Universidad de Sevilla, Apdo. 1065, E-41080 Sevilla (Spain); Donnelly, T.W. [Center for Theoretical Physics, Laboratory for Nuclear Science and Department of Physics Massachusetts Institute of Technology, Cambridge, MA 02139 (United States); Molinari, A. [Dipartimento di Fisica Teorica, Universita di Torino and INFN, Sezione di Torino, Via P. Giuria 1, 10125 Torino (Italy)
2002-12-01
The impact of Hartree-Fock correlations on the nuclear momentum distribution is studied in a fully relativistic one-boson-exchange model. Hartree-Fock equations are exactly solved to first order in the coupling constants. The renormalization of the Dirac spinors in the medium is shown to affect the momentum distribution, as opposed to what happens in the non-relativistic case. The unitarity of the model is shown to be preserved by the present renormalization procedure. (orig.)
Excess Charge for Pseudo-relativistic Atoms in Hartree-Fock Theory
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....
Excess Charge for Pseudo-relativistic Atoms in Hartree-Fock Theory
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....
Bouazza, Safa; Palmeri, Patrick; Quinet, Pascal
2017-09-01
We present a semi-empirical determination of Mo II radiative parameters in a wide wavelength range 1716-8789 Å. Our fitting procedure to experimental oscillator strengths available in the literature permits us to provide reliable values for a large number of Mo II lines, predicting previously unmeasured oscillator strengths of lines involving 4d45p and 4d35s5p odd-parity configurations. The extracted transition radial integral values are compared with ab-initio calculations: on average they are 0.88 times the values obtained with the basic pseudo-relativistic Hartree Fock method and they agree well when core polarization effects are included. When making a survey of our present and previous studies and including also those given in the literature we observe as general trends a decreasing of transition radial integral values with filling nd shells of the same principal quantum numbers for ndk(n + 1)s → ndk(n + 1)p transitions.
A New Decomposition Approach of Dirac Brueckner Hartree-Fock G Matrix for Asymmetric Nuclear Matter
刘玲; 马中玉
2002-01-01
Asymmetric nuclear matter is investigated by the Dirac Brueckner Hartree-Fock (DBHF) approach with a new decomposition of the Dirac structure of nucleon self-energy from the G matrix. It is found that the isospin dependence of the scalar and vector potentials is relatively weak, although both potentials for neutron (proton)become deep (shallow) in the neutron-rich nuclear matter. The results in asymmetric nuclear matter are rather different from those obtained by a simple method, where the nucleon self-energy is deduced from the single-particle energy. The nuclear binding energy as a function of the asymmetry parameter fulfils the empirical parabolic law up to very extreme isospin asymmetric nuclear matter in the DBHF approach. The behaviour of the density dependence of the asymmetry energy is different from that obtained by non-relativistic approaches, although both give similar asymmetry energy at the nuclear saturation density.
Nuclear relativistic Hartree-Fock calculations including pions interacting with a scalar field
Marcos, S.; Lopez-Quelle, M.; Niembro, R.; Savushkin, L. N. [Departamento de Fisica Moderna, Universidad de Cantabria, Santander (Spain); Departamento de Fisica Aplicada, Universidad de Cantabria, Santander (Spain); Departamento de Fisica Moderna, Universidad de Cantabria, Santander (Spain); Department of Physics, St. Petersburg University for Telecommunications, St. Petersburg (Russian Federation)
2012-10-20
The effect of pions on the nuclear shell structure is analyzed in a relativistic Hartree-Fock approximation (RHFA). The Lagrangian includes, in particular, a mixture of {pi}N pseudoscalar (PS) and pseudovector (PV) couplings, self-interactions of the scalar field {sigma} and a {sigma} - {pi} interaction that dresses pions with an effective mass (m*{sub {pi}}). It is found that an increase of m*{sub {pi}} strongly reduces the unrealistic effect of pions, keeping roughly unchanged their contribution to the total binding energy.
Hu, Jinniu; Shen, Hong
2016-01-01
We study the properties of nuclear matter with lattice nucleon-nucleon ($NN$) potential in the relativistic Brueckner-Hartree-Fock (RBHF) theory. To use this potential in such a microscopic many-body theory, we firstly have to construct a one-boson-exchange potential (OBEP) based on the latest lattice $NN$ potential. Three mesons, pion, $\\sigma$ meson, and $\\omega$ meson, are considered. Their coupling constants and cut-off momenta are determined by fitting the on-shell behaviors and phase shifts of the lattice force, respectively. Therefore, we obtain two parameter sets of the OBEP potential (named as LOBEP1 and LOBEP2) with these two fitting ways. We calculate the properties of symmetric and pure neutron matter with LOBEP1 and LOBEP2. In non-relativistic Brueckner-Hartree-Fock case, the binding energies of symmetric nuclear matter are around $-3$ and $-5$ MeV at saturation densities, while it becomes $-8$ and $-12$ MeV in relativistic framework with $^1S_0,~^3S_1,$ and $^3D_1$ channels using our two paramet...
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)
Pion tensor force and nuclear binding energy in the relativistic Hartree-Fock formalism
Marcos, S.; López-Quelle, M.; Niembro, R.; Savushkin, L. N.
2014-03-01
The binding energies of several isotopic families are studied within the relativistic Hartree-Fock approximation with the pseudovector coupling for the πN vertex, to find out a suitable strength for the effective pion tensor force (EPTF). An approximation for determining separately the contributions of the central and tensor forces generated by pion is considered. The results for heavy nuclei indicate that a realistic strength for the EPTF is smaller than a half of that appearing in the OPEP. This conclusion also applies to the results for the single-particle energies. Besides, it has been found that there is a genuine relativistic contribution of the EPTF in nuclear matter which is small but significant.
Pseudospin symmetry in finite nuclei within the relativistic Hartree-Fock framework
Lopez-Quelle, M [Departamento de Fisica Aplicada, Universidad de Cantabria, E-39005 Santander (Spain); Savushkin, L N [Department of Physics, St Petersburg University for Telecommunications, 191186 St Petersburg (Russian Federation); Marcos, S [Departamento de Fisica Moderna, Universidad de Cantabria, E-39005 Santander (Spain); Niembro, R [Departamento de Fisica Moderna, Universidad de Cantabria, E-39005 Santander (Spain)
2005-10-01
In the present work, we analyse the behaviour of the pseudospin symmetry (PSS) in heavy nuclei ({sup 208}Pb) in the framework of the relativistic Hartree-Fock approximation (RHFA). The quasidegeneracy of the pseudospin partners and the similarity of the small F components of their respective Dirac spinors have a somewhat lower degree of accuracy than in the relativistic mean field approximation (RMFA). Both properties improve when the number of nodes of the small component increases, as happens in the RMFA. The behaviour of the single-particle potentials appearing in the Dirac equation of the pseudospin partners is analysed. There is no dominance of the pseudocentrifugal barrier (PCB) compared to the pseudospin-orbit potential (PSOP). In the RHFA, the PSS is an approximately satisfied symmetry in nuclei and its dynamical character is reinforced with respect to the RMFA.
Complete equation of state for neutron stars using the relativistic Hartree-Fock approximation
Miyatsu, Tsuyoshi; Cheoun, Myung-Ki [Department of Physics, Soongsil University, Seoul 156-743 (Korea, Republic of); Yamamuro, Sachiko; Nakazato, Ken' ichiro [Department of Physics, Faculty of Science and Technology, Tokyo University of Science (TUS), Noda 278-8510 (Japan)
2014-05-02
We construct the equation of state in a wide-density range for neutron stars within relativistic Hartree-Fock approximation. The properties of uniform and nonuniform nuclear matter are studied consistently. The tensor couplings of vector mesons to baryons due to exchange contributions (Fock terms) are included, and the change of baryon internal structure in matter is also taken into account using the quark-meson coupling model. The Thomas-Fermi calculation is adopted to describe nonuniform matter, where the lattice of nuclei and the neutron drip out of nuclei are considered. Even if hyperons exist in the core of a neutron star, we obtain the maximum neutron-star mass of 1.95M{sub ⊙}, which is consistent with the recently observed massive pulsar, PSR J1614-2230. In addition, the strange vector (φ) meson also plays a important role in supporting a massive neutron star.
Pairing phase transition: A Finite-Temperature Relativistic Hartree-Fock-Bogoliubov study
Li, Jia Jie; Long, Wen Hui; Van Giai, Nguyen
2015-01-01
Background: The relativistic Hartree-Fock-Bogoliubov (RHFB) theory has recently been developed and it provides a unified and highly predictive description of both nuclear mean field and pairing correlations. Ground state properties of finite nuclei can accurately be reproduced without neglecting exchange (Fock) contributions. Purpose: Finite-temperature RHFB (FT-RHFB) theory has not yet been developed, leaving yet unknown its predictions for phase transitions and thermal excitations in both stable and weakly bound nuclei. Method: FT-RHFB equations are solved in a Dirac Woods-Saxon (DWS) basis considering two kinds of pairing interactions: finite or zero range. Such a model is appropriate for describing stable as well as loosely bound nuclei since the basis states have correct asymptotic behaviour for large spatial distributions. Results: Systematic FT-RH(F)B calculations are performed for several semi-magic isotopic/isotonic chains comparing the predictions of a large number of Lagrangians, among which are PK...
Δ (1232 ) effects in density-dependent relativistic Hartree-Fock theory and neutron stars
Zhu, Zhen-Yu; Li, Ang; Hu, Jin-Niu; Sagawa, Hiroyuki
2016-10-01
The density-dependent relativistic Hartree-Fock (DDRHF) theory is extended to include Δ isobars for the study of dense nuclear matter and neutron stars. To this end, we solve the Rarita-Schwinger equation for spin-3/2 particle. Both the direct and exchange terms of the Δ isobars' self-energies are evaluated in detail. In comparison with the relativistic mean field theory (Hartree approximation), a weaker parameter dependence is found for DDRHF. An early appearance of Δ isobars is recognized at ρB˜0.28 fm-3, comparable with that of hyperons. Also, we find that the Δ isobars' softening of the equation of state is mainly due to the reduced Fock contributions from the coupling of the isoscalar mesons, while the pion contributions are negligibly small. We finally conclude that with typical parameter sets, neutron stars with Δ isobars in their interiors could be as heavy as the two massive pulsars whose masses are precisely measured, with slightly smaller radii than normal neutron stars.
$\\Delta$ (1232) effects in density-dependent relativistic Hartree-Fock theory and neutron stars
Zhu, Zhen-Yu; Hu, Jin-Niu; Sagawa, Hiroyuki
2016-01-01
The density-dependent relativistic Hartree-Fock (DDRHF) theory is extended to include $\\Delta$-isobars for the study of dense nuclear matter and neutron stars. To this end, we solve the Rarita-Schwinger equation for spin-3/2 particle. Both the direct and exchange terms of the $\\Delta$-isobars' self-energies are evaluated in details. In comparison with the relativistic mean field theory (Hartree approximation), a weaker parameter dependence is found for DDRHF. An early appearance of $\\Delta$-isobars is recognized at $\\rho_B\\sim0.27$fm$^{-3}$, comparable with that of hyperons. Also, we find that the $\\Delta$-isobars' softening of the equation of state is found to be mainly due to the reduced Fock contributions from the coupling of the isoscalar mesons, while the pion contributions are found negligibly small. We finally conclude that with typical parameter sets, neutron stars with $\\Delta$-isobars in their interiors could be as heavy as the two massive pulsars whose masses are precisely measured, with slightly s...
Ebran, J-P [CEA/DAM/DIF, F-91297 Arpajon (France); Khan, E; Arteaga, D Pena [Institut de Physique Nucleaire, University Paris-Sud, IN2P3-CNRS, F-91406 Orsay Cedex (France); Vretenar, D, E-mail: jean-paul.ebran@cea.fr [Physics Department, Faculty of Science, University of Zagreb, 10000 Zagreb (Croatia)
2011-09-16
The Relativistic Hartree-Fock-Bogoliubov model for axially deformed nuclei (RHFBz) is presented. The model involves a phenomenological Lagrangian with density-dependent meson-nucleon couplings in the particle-hole channel and the central part of the Gogny force in the particle-particle channel. The RHFBz equations are solved by expansion in the basis of a deformed harmonic oscillator. Illustrative RHFBz calculations are performed for Neon isotopes.
Xu, Ruirui; Ma, Zhongyu; Zhang, Yue; Tian, Yuan; van Dalen, E. N. E.; Müther, H.
2016-09-01
Background: For the study of exotic nuclei it is important to have an optical model potential that is reliable not only for stable nuclei but can also be extrapolated to nuclear systems with exotic numbers of protons and neutrons. An efficient way to obtain such a potential is to develop a microscopic optical potential (MOP) based on a fundamental theory with a minimal number of free parameters, which are adjusted to describe stable nuclei all over the nuclide chart. Purpose: The choice adopted in the present work is to develop the MOP within a relativistic scheme which provides a natural and consistent relation between the spin-orbit part and the central part of the potential. The Dirac-Brueckner-Hartree-Fock (DBHF) approach provides such a microscopic relativistic scheme, which is based on a realistic nucleon-nucleon interaction and reproduces the saturation properties of symmetric nuclear matter without any adjustable parameter. Its solution using the projection technique within the subtracted T -matrix representation provides a reliable extension to asymmetric nuclear matter, which is important to describe the features of isospin asymmetric nuclei. The present work performs a global analysis of the isospin dependent nucleon-nucleus MOP based on the DBHF calculation in symmetric and asymmetric nuclear matter. Methods: The DBHF approach is used to evaluate the relativistic structure of the nucleon self-energies in nuclear matter at various densities and asymmetries. The Schrödinger equivalent potentials of finite nuclei are derived from these Dirac components by a local density approximation (LDA). The density distributions of finite nuclei are taken from the Hartree-Fock-Bogoliubov approach with Gogny D1S force. An improved LDA approach (ILDA) is employed to get a better prediction of the scattering observables. A χ2 assessment system based on the global simulated annealing algorithm is developed to optimize the very few free components in this study. Results
Hassaneen, Khaled; Mansour, Hesham
2017-02-01
The single-particle potentials and other properties at absolute zero temperature in isospin asymmetric nuclear matter are investigated in the frame of an extended Brueckner theory. Also thermal quantities are calculated in asymmetric nuclear matter using CD-Bonn potential and the Urbana three-body forces (3BF). Also, the effects of the hole-hole contributions are investigated within the self-consistent Greens function approach. The inclusion of 3BF or the hole-hole contributions improves the predicted saturation property of symmetric nuclear matter within the Brueckner-Hartree-Fock approach and it leads to a significant stiffening of the density dependence of symmetry energy at high densities but the exact saturation point is not reproduced. This is of great importance in astrophysical calculation. A phenomenological term simulating the three-body interaction is introduced to assure the empirical saturation property. The hot properties of asymmetric nuclear matter such as the internal energy and the pressure are analyzed using T2-approximation method at low temperatures.
New Multithreaded Hybrid CPU/GPU Approach to Hartree-Fock.
Asadchev, Andrey; Gordon, Mark S
2012-11-13
In this article, a new multithreaded Hartree-Fock CPU/GPU method is presented which utilizes automatically generated code and modern C++ techniques to achieve a significant improvement in memory usage and computer time. In particular, the newly implemented Rys Quadrature and Fock Matrix algorithms, implemented as a stand-alone C++ library, with C and Fortran bindings, provides up to 40% improvement over the traditional Fortran Rys Quadrature. The C++ GPU HF code provides approximately a factor of 17.5 improvement over the corresponding C++ CPU code.
Marcos, S [Departamento de FIsica Moderna, Universidad de Cantabria, E-39005 Santander (Spain); Savushkin, L N [Department of Physics, St Petersburg University for Telecommunications, 191065 St Petersburg (Russian Federation); Fomenko, V N [Department of Mathematics, St Petersburg University for Railway Engineering, 190031 St Petersburg (Russian Federation); Lopez-Quelle, M [Departamento de FIsica Aplicada, Universidad de Cantabria, E-39005 Santander (Spain); Niembro, R [Departamento de FIsica Moderna, Universidad de Cantabria, E-39005 Santander (Spain)
2004-06-01
An exact method is suggested to treat the nonlinear self-interactions (NLSI) in the relativistic Hartree-Fock (RHF) approach for nuclear systems. We consider here the NLSI constructed from the relativistic scalar nucleon densities including products of six and eight fermion fields. This type of NLSI corresponds to the zero-range limit of the standard cubic and quartic self-interactions of the scalar field. The method to treat the NLSI uses the Fierz transformation, which enables one to express the exchange (Fock) components in terms of the direct (Hartree) ones. The method is applied to nuclear matter and finite nuclei. It is shown that, in the RHF formalism, the NLSI, which are explicitly isovector-independent, generate scalar, vector and tensor nucleon self-energies with a strong isovector dependence. This strong isovector structure of the self-energies is due to the exchange terms of the RHF method. Calculations are carried out with a parametrization containing five free parameters. The model allows a description of both types of systems compatible with experimental data.
Jiménez-Hoyos, Carlos A; Scuseria, Gustavo E
2013-01-01
Recent work from our research group has demonstrated that symmetry-projected Hartree--Fock (HF) methods provide a compact representation of molecular ground state wavefunctions based on a superposition of non-orthogonal Slater determinants. The symmetry-projected ansatz can account for static correlations in a computationally efficient way. Here we present a variational extension of this methodology applicable to excited states of the same symmetry as the ground state. Benchmark calculations on the C$_2$ dimer with a modest basis set, which allows comparison with full configuration interaction results, indicate that this extension provides a high quality description of the low-lying spectrum for the entire dissociation profile. We apply the same methodology to obtain the full low-lying vertical excitation spectrum of formaldehyde, in good agreement with available theoretical and experimental data, as well as to a challenging model $C_{2v}$ insertion pathway for BeH$_2$. The variational excited state methodolo...
Time-Dependent Hartree-Fock Approach to Nuclear Pasta at Finite Temperature
Schuetrumpf, Bastian; Iida, Kei; Maruhn, Joachim; Mecke, Klaus; Reinhard, Paul-Gerhard
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 $\\alpha$ 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.
Spiral magnetic phases on the Kondo Lattice Model: A Hartree-Fock approach
Costa, N. C.; Lima, J. P.; dos Santos, Raimundo R.
2017-02-01
We study the Kondo Lattice Model (KLM) on a square lattice through a Hartree-Fock approximation in which the local spins are treated semi-classically, in the sense that their average values are modulated by a magnetic wavevector Q while they couple with the conduction electrons through fermion operators. In this way, we obtain a ground state phase diagram in which spiral magnetic phases (in which the wavevector depends on the coupling constants and on the density) interpolate between the low-density ferromagnetic phase and the antiferromagnetic phase at half filling; within small regions of the phase diagram commensurate magnetic phases can coexist with Kondo screening. We have also obtained 'Doniach-like' diagrams, showing the effect of temperature on the ground state phases, and established that for some ranges of the model parameters (the exchange coupling and conduction electron density) the magnetic wavevector changes with temperature, either continuously or abruptly (e.g., from spiral to ferromagnetic).
Nuclear Pasta at Finite Temperature with the Time-Dependent Hartree-Fock Approach
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.
He, Liming; Zhu, Yunxia; Zhang, Meng; Tu, Yaoquan
2011-11-01
We present a new second-order representation of the relativistic Hartree-Fock equation, which can be solved by the standard Hartree-Fock technique. An alternative reduction for the magnetic part of the Breit interaction is presented in an explicit expression. A corresponding program has been developed, which improves significantly the scaled linear mesh introduced by Herman and Skillman. The structures for a number of atoms and ions are calculated and the agreement of our results with those published is excellent. We evaluate the fine-structure intervals of nd(n = 3-40) Rydberg series for sodium. The inverted fine-structure splitting values are obtained directly as the differences of eigenvalues obtained from a self-consistent field procedure. Taking into account the Gaunt effect enables the accuracy of the calculation to be substantially improved. The complete treatments reproduce very well the inverted fine structures along the Rydberg series and the relative difference between the present results and the experiments does not exceed 4.4%.
Brorsen, Kurt R.; Sirjoosingh, Andrew; Pak, Michael V.; Hammes-Schiffer, Sharon
2015-06-01
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.
Augspurger, Joseph D.; Dykstra, Clifford E.
1993-08-01
Molecular Sternheimer shielding constants, γ, the proportionality constants relating the electric field gradient at a quadrupolar nucleus to an external electric field gradient are usually introduced phenomenologically. In this report, we take a comprehensive view of the sensitivity of the electric field gradient at a nucleus to arbitrary external electrical potentials and we show how the response can be obtained from analytically determined properties via derivative Hartree-Fock theory. From application of this ab initio technique, values have been obtained for the first and second order changes in nuclear quadrupole coupling with respect to external fields and field gradients, as well as nearby ideal multipole moments, for HCN and HCl. These values have been used to evaluate the change in the nuclear quadrupole coupling for several weakly bound complexes and to provide a nonempirical approach to relative effects on Sternheimer shielding. In weak molecular complexes, the effect of uniform fields can be as sizable as the effect of external field gradients in the overall change in nuclear quadrupole coupling, and so the underlying issue of convergence of multipolar expansions is considered over a range of geometries. This is important for structural interpretations of both nuclear magnetic resonance (NMR) and microwave data, and a simple formula, representing a practical point of truncation, is presented for quadrupole coupling analysis.
Accurate Hartree-Fock energy of extended systems using large Gaussian basis sets
Paier, Joachim; Diaconu, Cristian V.; Scuseria, Gustavo E.; Guidon, Manuel; Vandevondele, Joost; Hutter, Jürg
2009-11-01
Calculating highly accurate thermochemical properties of condensed matter via wave-function-based approaches (such as, e.g., Hartree-Fock or hybrid functionals) has recently attracted much interest. We here present two strategies providing accurate Hartree-Fock energies for solid LiH in a large Gaussian basis set and applying periodic boundary conditions. The total energies were obtained using two different approaches, namely, a supercell evaluation of Hartree-Fock exchange using a truncated Coulomb operator and an extrapolation toward the full-range Hartree-Fock limit of a Padé fit to a series of short-range screened Hartree-Fock calculations. These two techniques agreed to significant precision. We also present the Hartree-Fock cohesive energy of LiH (converged to within sub-millielectron volt) at the experimental equilibrium volume as well as the Hartree-Fock equilibrium lattice constant and bulk modulus.
Y. Sajeev
2015-08-01
Full Text Available The equation-of-motion coupled cluster (EOMCC method based on the excited state Hartree-Fock (ESHF solutions is shown to be appropriate for computing the entire ground state potential energy curves of strongly correlated higher-order bonds. The new approach is best illustrated for the homolytic dissociation of higher-order bonds in molecules. The required multireference character of the true ground state wavefunction is introduced through the linear excitation operator of the EOMCC method. Even at the singles and doubles level of cluster excitation truncation, the nonparallelity error of the ground state potential energy curve from the ESHF based EOMCC method is small.
Zhang, Ying; Meng, Jie
2010-01-01
The neutron pair correlation in nuclei near the neutron drip-line is investigated using the selfconsistent continuum Skyrme-Hartree-Fock-Bogoliubov theory formulated with the coordinate-space Green's function technique. Numerical analysis is performed for even-even N = 86 isotones in the Mo-Sn region, where the 3p3/2 and 3p1/2 orbits lying near the Fermi energy are either weakly bound or unbound. The quasiparticle states originating from the l = 1 orbits form resonances with large widths, which are due to the low barrier height and the strong continuum coupling caused by the pair potential. Analyzing in detail the pairing properties and roles of the quasiparticle resonances, we found that the l = 1 broad quasiparticle resonances persist to feel the pair potential and contribute to the pair correlation even when their widths are comparable with the resonance energy.
Constrained Hartree-Fock and quasi-spin projection
Cambiaggio, M. C.; Plastino, A.; Szybisz, L.
1980-08-01
The constrained Hartree-Fock approach of Elliott and Evans is studied in detail with reference to two quasi-spin models, and their predictions compared with those arising from a projection method. It is found that the new approach works fairly well, although limitations to its applicability are encountered.
de Lara-Castells, María Pilar; Mitrushchenkov, Alexander O.; Stoll, Hermann
2015-09-01
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 Ag2/graphene interaction. It extends the dispersionless density functional theory developed by Pernal et al. [Phys. Rev. Lett. 103, 263201 (2009)] by including periodic boundary conditions while the dispersion is parametrized via the method of increments [H. Stoll, J. Chem. Phys. 97, 8449 (1992)]. Starting with the elementary cluster unit of the target surface (benzene), continuing through the realistic cluster model (coronene), and ending with the periodic model of the extended system, modern ab initio methodologies for intermolecular interactions as well as state-of-the-art van der Waals-corrected density functional-based approaches are put together both to assess the accuracy of the composite scheme and to better characterize the Ag2/graphene interaction. The present work illustrates how the combination of DFT and post-HF perspectives may be efficient to design simple and reliable ab initio-based schemes in extended systems for surface science applications.
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.
Nakajima, Yuya; Seino, Junji; Nakai, Hiromi
2016-05-10
An analytical energy gradient for the spin-dependent general Hartree-Fock method based on the infinite-order Douglas-Kroll-Hess (IODKH) method was developed. To treat realistic systems, the local unitary transformation (LUT) scheme was employed both in energy and energy gradient calculations. The present energy gradient method was numerically assessed to investigate the accuracy in several diatomic molecules containing fifth- and sixth-period elements and to examine the efficiency in one-, two-, and three-dimensional silver clusters. To arrive at a practical calculation, we also determined the geometrical parameters of fac-tris(2-phenylpyridine)iridium and investigated the efficiency. The numerical results confirmed that the present method describes a highly accurate relativistic effect with high efficiency. The present method can be a powerful scheme for determining geometries of large molecules, including heavy-element atoms.
Lewin, Mathieu
2011-01-01
In a recent paper published in Nonlinear Analysis: Theory, Methods & Applications, C. Argaez and M. Melgaard studied excited states for pseudo-relativistic multi-configuration methods. Their paper follows a previous work of mine in the non-relativistic case (Arch. Rat. Mech. Anal., 171, 2004). The main results of the paper of C. Argaez and M. Melgaard are correct, but the proofs are both wrong and incomplete.
Norman, Patrick; Schimmelpfennig, Bernd; Ruud, Kenneth;
2002-01-01
A systematic investigation of a hierarchy of methods for including relativistic effects in the calculation of linear and nonlinear optical properties was carried out. The simple ECP method and the more involved spin-averaged Douglas-Kroll approximation were compared to benchmark results obtained ...
Veeraraghavan, Srikant; Mazziotti, David A
2014-03-28
We present a density matrix approach for computing global solutions of restricted open-shell Hartree-Fock theory, based on semidefinite programming (SDP), that gives upper and lower bounds on the Hartree-Fock energy of quantum systems. While wave function approaches to Hartree-Fock theory yield an upper bound to the Hartree-Fock energy, we derive a semidefinite relaxation of Hartree-Fock theory that yields a rigorous lower bound on the Hartree-Fock energy. We also develop an upper-bound algorithm in which Hartree-Fock theory is cast as a SDP with a nonconvex constraint on the rank of the matrix variable. Equality of the upper- and lower-bound energies guarantees that the computed solution is the globally optimal solution of Hartree-Fock theory. The work extends a previously presented method for closed-shell systems [S. Veeraraghavan and D. A. Mazziotti, Phys. Rev. A 89, 010502-R (2014)]. For strongly correlated systems the SDP approach provides an alternative to the locally optimized Hartree-Fock energies and densities with a certificate of global optimality. Applications are made to the potential energy curves of C2, CN, Cr2, and NO2.
Veeraraghavan, Srikant; 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)
2014-03-28
We present a density matrix approach for computing global solutions of restricted open-shell Hartree-Fock theory, based on semidefinite programming (SDP), that gives upper and lower bounds on the Hartree-Fock energy of quantum systems. While wave function approaches to Hartree-Fock theory yield an upper bound to the Hartree-Fock energy, we derive a semidefinite relaxation of Hartree-Fock theory that yields a rigorous lower bound on the Hartree-Fock energy. We also develop an upper-bound algorithm in which Hartree-Fock theory is cast as a SDP with a nonconvex constraint on the rank of the matrix variable. Equality of the upper- and lower-bound energies guarantees that the computed solution is the globally optimal solution of Hartree-Fock theory. The work extends a previously presented method for closed-shell systems [S. Veeraraghavan and D. A. Mazziotti, Phys. Rev. A 89, 010502–R (2014)]. For strongly correlated systems the SDP approach provides an alternative to the locally optimized Hartree-Fock energies and densities with a certificate of global optimality. Applications are made to the potential energy curves of C{sub 2}, CN, Cr {sub 2}, and NO {sub 2}.
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.
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.
Rodriguez-Bautista, Mariano; Díaz-García, Cecilia; Navarrete-López, Alejandra M.; Vargas, Rubicelia; Garza, Jorge
2015-07-01
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.
Misfits in Skyrme-Hartree-Fock
Erler, J; Reinhard, P -G
2010-01-01
We address very briefly five critical points in the context of the Skyrme-Hartree-Fock (SHF) scheme: 1) the impossibility to consider it as an interaction, 2) a possible inconsistency of correlation corrections as, e.g., the center-of-mass correction, 3) problems to describe the giant dipole resonance (GDR) simultaneously in light and heavy nuclei, 4) deficiencies in the extrapolation of binding energies to super-heavy elements (SHE), and 5) a yet inappropriate trend in fission life-times when going to the heaviest SHE. While the first two points have more a formal bias, the other three points have practical implications and wait for solution.
Umar, A. S.; Oberacker, V. E.; Simenel, C.
2016-08-01
Background: Synthesis of superheavy elements (SHEs) with fusion-evaporation reactions is strongly hindered by the quasifission (QF) mechanism which prevents the formation of an equilibrated compound nucleus and which depends on the structure of the reactants. New SHEs have been recently produced with doubly-magic 48Ca beams. However, SHE synthesis experiments with single-magic 50Ti beams have so far been unsuccessful. Purpose: In connection with experimental searches for Z =117 ,119 superheavy elements, we perform a theoretical study of fusion and quasifission mechanisms in 48Ca,50Ti+249Bk reactions in order to investigate possible differences in reaction mechanisms induced by these two projectiles. Methods: The collision dynamics and the outcome of the reactions are studied using unrestricted time-dependent Hartree-Fock (TDHF) calculations as well as the density-constrained TDHF method to extract the nucleus-nucleus potentials and the excitation energy in each fragment. Results: Nucleus-nucleus potentials, nuclear contact times, masses and charges of the fragments, as well as their kinetic and excitation energies strongly depend on the orientation of the prolate 249Bk nucleus. Long contact times associated with fusion are observed in collisions of both projectiles with the side of the 249Bk nucleus, but not on collisions with its tip. The energy and impact parameter dependencies of the fragment properties, as well as their mass-angle and mass-total kinetic energy correlations are investigated. Conclusions: Entrance channel reaction dynamics are similar with both 48Ca and 50Ti projectiles. Both are expected to lead to the formation of a compound nucleus by fusion if they have enough energy to get in contact with the side of the 249Bk target.
Computational Nuclear Physics and Post Hartree-Fock Methods
Lietz, Justin; Jansen, Gustav R; Hagen, Gaute; Hjorth-Jensen, Morten
2016-01-01
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.
Robust Periodic Hartree-Fock Exchange for Large-Scale Simulations Using Gaussian Basis Sets.
Guidon, Manuel; Hutter, Jürg; VandeVondele, Joost
2009-11-10
Hartree-Fock exchange with a truncated Coulomb operator has recently been discussed in the context of periodic plane-waves calculations [Spencer, J.; Alavi, A. Phys. Rev. B: Solid State, 2008, 77, 193110]. In this work, this approach is extended to Gaussian basis sets, leading to a stable and accurate procedure for evaluating Hartree-Fock exchange at the Γ-point. Furthermore, it has been found that standard hybrid functionals can be transformed into short-range functionals without loss of accuracy. The well-defined short-range nature of the truncated exchange operator can naturally be exploited in integral screening procedures and makes this approach interesting for both condensed phase and gas phase systems. The presented Hartree-Fock implementation is massively parallel and scales up to ten thousands of cores. This makes it feasible to perform highly accurate calculations on systems containing thousands of atoms or ten thousands of basis functions. The applicability of this scheme is demonstrated by calculating the cohesive energy of a LiH crystal close to the Hartree-Fock basis set limit and by performing an electronic structure calculation of a complete protein (rubredoxin) in solution with a large and flexible basis set.
The Gogny-Hartree-Fock-Bogoliubov nuclear-mass model
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.)
GUO Lu; ZHAO En-Guang; SAKATA Fumihiko
2003-01-01
Ground-state.properties of C, O, and Ne isotopes are described in the framework of Hartree-FockBogoliubov theory with density-dependent finite-range Gogny interaction D1S. We include all the contributions to the Hartree-Fock and pairing field arising from Gogny and Coulomb interaction as well as the center of mass correction in the numerical calculations. These ground-state properties of C, O, and Ne isotopes are compared with available experimental results, Hartree-Fock plus BCS, shell model and relativistic Hartree-Bogoliubov calculations. The agreement between experiments and our theoretical results is pretty well. The predicted drip-line is dependent strongly on the model and effective interaction due to their sensitivity to various theoretical details. The calculations predict no evidence for halo structure predicted for C, O, and Ne isotopes in a previous RHB study.
GUOLu; ZHAOEn-Guang; SAKATAFumihiko
2003-01-01
Ground-state properties of C, O, and Ne isotopes are described in the framework of Hartree-Fock-Bogoliubov theory with density-dependent finite-range Gogny interaction D1S. We include all the contributions to the Hartree-Fock and pairing feld arising from Gogny and Coulomb interaction as well as the center of mass correction in the numerical calcu/ations. These ground-state properties of C, O, and Ne isotopes are compared with available experimental results, Hartree-Fock plus BCS, shell model and relativistic Hartree--Bogoliubov calculations. The agreement between experiments and our theoretical results is pretty well. The predicted drip-line is dependent strongly on the model and effective interaction due to their sensitivity to various theoretical details. The calculations predict no evidence for halo structure predicted for C,O, and Ne isotopes in a previous RHB study.
Koopmans' theorem in statistical Hartree-Fock theory
Pain, Jean-Christophe
2011-01-01
In this short paper, the validity of Koopmans' theorem in the Hartree-Fock theory at non-zero temperature (Hartree-Fock statistical theory) is investigated. It is shown that Koopmans' theorem does not apply in the grand-canonical ensemble, due to a missing contribution to the energy proportional to the interaction between two electrons belonging to the same orbital. Hartree-Fock statistical theory has also been applied in the canonical ensemble [Blenski et al., Phys. Rev. E 55, R4889 (1997)] for the purpose of photo-absorption calculations. In that case, the Hartree-Fock self-consistent-field equations are derived in the super-configuration approximation. It is shown that Koopmans' theorem does not hold in the canonical ensemble, but that a restricted version of the theorem can be obtained, by assuming that a particular quantity multiplying the interaction matrix element in the expression of the energy does not change during the removal of an electron.
A Hartree-Fock-Bogoliubov mass formula
Samyn, M; Heenen, P H; Pearson, J M; Tondeur, F
2002-01-01
In order to have more reliable predictions of nuclear masses at the neutron drip line, we here go beyond the recent mass formula HFBCS-1 and present a new mass formula, HFB-1, based on the Hartree-Fock-Bogoliubov method. As with the HFBCS-1 mass formula, we use a 10-parameter Skyrme force along with a 4-parameter delta-function pairing force and a 2-parameter phenomenological Wigner term. However, with the original HFBCS-1 Skyrme force (MSk7), the rms error becomes unacceptably large and a new force fit is required. With the isoscalar and isovector effective masses constrained to be equal, the remaining 15 degrees of freedom are fitted to the masses of all the 1754 measured nuclei with A>=16, |N-Z|>2 given in the 1995 Audi-Wapstra compilation. The rms error with respect to the masses of all the 1888 measured nuclei with Z,N>=8 is 0.764 MeV. A complete mass table, HFB-1 (available on the Web), has been constructed, giving all nuclei lying between the two drip lines over the range Z,N>=8 and Z<=120. A compar...
A collisional extension of time-dependent Hartree-Fock
Lacombe, L.; Reinhard, P.-G.; Dinh, P. M.; Suraud, E.
2016-12-01
We propose a collisional extension of time-dependent mean-field theories on the basis of a recently proposed stochastic extension of mean-field dynamics (stochastic time-dependent Hartree-Fock, STDHF). The latter theory is unfortunately too involved to envision practical applications in realistic systems in the near future and is thus bound to model systems. It is also hard to explore moderate to low energies with STDHF, because of vanishing transition probabilities that are impossible to sample properly. For such moderately excited situations covering small fluctuations, we compactify sampling by employing the same average mean field for all STDHF trajectories. The new approach, coined average STDHF (ASTDHF), ignores the fluctuations of the mean field but still accounts correctly for the collisional correlations responsible for dissipative features on top of mean-field dynamics. We detail the main features of the new approach in relation to existing equations, in particular quantum kinetic theories. The new theory is directly connected to STDHF, both formally and practically. We thus discuss in detail how the two approaches are related to each other. We apply the new scheme to illustrative examples taking as benchmark STDHF dynamics in 1D. ASTDHF provides results that are in remarkable agreement with the more elaborate STDHF. It makes it a promising approach to deal with dissipative dynamics in finite quantum systems, because of its moderate cost allowing applications in realistic systems and the possibility of exploring any excitation energy range where collisional correlations are expected to play a role.
Hartree-Fock and Random Phase Approximation theories in a many-fermion solvable model
Co', Giampaolo
2016-01-01
We present an ideal system of interacting fermions where the solutions of the many-body Schroedinger equation can be obtained without making approximations. These exact solutions are used to test the validity of two many-body effective approaches, the Hartree-Fock and the Random Phase Approximation theories. The description of the ground state done by the effective theories improves with increasing number of particles.
Fission dynamics within time-dependent Hartree-Fock: boost-induced fission
Goddard, P M; Rios, A
2015-01-01
Background: Nuclear fission is a complex large-amplitude collective decay mode in heavy nuclei. Microscopic density functional studies of fission have previously concentrated on adiabatic approaches based on constrained static calculations ignoring dynamical excitations of the fissioning nucleus, and the daughter products. Purpose: To explore the ability of dynamic mean-field methods to describe induced fission processes, using quadrupole boosts in the nuclide $^{240}$Pu as an example. Methods: Quadrupole constrained Hartree-Fock calculations are used to create a potential energy surface. An isomeric state and a state beyond the second barrier peak are excited by means of instantaneous as well as temporally extended gauge boosts with quadrupole shapes. The subsequent deexcitation is studied in a time-dependent Hartree-Fock simulation, with emphasis on fissioned final states. The corresponding fission fragment mass numbers are studied. Results: In general, the energy deposited by the quadrupole boost is quickl...
Fission dynamics within time-dependent Hartree-Fock: deformation-induced fission
Goddard, P M; Rios, A
2015-01-01
Background: Nuclear fission is a complex large-amplitude collective decay mode in heavy nuclei. Microscopic density functional studies of fission have previously concentrated on adiabatic approaches based on constrained static calculations ignoring dynamical excitations of the fissioning nucleus, and the daughter products. Purpose: To explore the ability of dynamic mean-field methods to describe fast fission processes beyond the fission barrier, using the nuclide $^{240}$Pu as an example. Methods: Time-dependent Hartree-Fock calculations based on the Skyrme interaction are used to calculate non-adiabatic fission paths, beginning from static constrained Hartree-Fock calculations. The properties of the dynamic states are interpreted in terms of the nature of their collective motion. Fission product properties are compared to data. Results: Parent nuclei constrained to begin dynamic evolution with a deformation less than the fission barrier exhibit giant-resonance-type behaviour. Those beginning just beyond the ...
Can X-ray constrained Hartree-Fock wavefunctions retrieve electron correlation?
Genoni, Alessandro; Dos Santos, Leonardo H R; Meyer, Benjamin; Macchi, Piero
2017-03-01
The X-ray constrained wavefunction (XC-WF) method proposed by Jayatilaka [Jayatilaka & Grimwood (2001) ▸, Acta Cryst. A57, 76-86] has attracted much attention because it represents a possible third way of theoretically studying the electronic structure of atoms and molecules, combining features of the more popular wavefunction- and DFT-based approaches. In its original formulation, the XC-WF technique extracts statistically plausible wavefunctions from experimental X-ray diffraction data of molecular crystals. A weight is used to constrain the pure Hartree-Fock solution to the observed X-ray structure factors. Despite the wavefunction being a single Slater determinant, it is generally assumed that its flexibility could guarantee the capture, better than any other experimental model, of electron correlation effects, absent in the Hartree-Fock Hamiltonian but present in the structure factors measured experimentally. However, although the approach has been known for long time, careful testing of this fundamental hypothesis is still missing. Since a formal demonstration is impossible, the validation can only be done heuristically and, to accomplish this task, X-ray constrained Hartree-Fock calculations have been performed using structure factor amplitudes computed at a very high correlation level (coupled cluster) for selected molecules in isolation, in order to avoid the perturbations due to intermolecular interactions. The results show that a single-determinant XC-WF is able to capture the electron correlation effects only partially. The largest amount of electron correlation is extracted when: (i) a large external weight is used (much larger than what has normally been used in XC-WF calculations using experimental data); and (ii) the high-order reflections, which carry less information on the electron correlation, are down-weighted (or even excluded), otherwise they would bias the fitting towards the unconstrained Hartree-Fock wavefunction.
Quiney, HM; Glushkov, VN; Wilson, S
2002-01-01
Using basis sets of distributed s-type Gaussian functions with positions and exponents optimized so as to support Hartree-Fock total energies with an accuracy approaching the sub-muHartree level, Dirac-Hartree-Fock-Coulomb calculations are reported for the ground states of the H-2, LiH, and BH molec
Knippenberg, Stefan; Gieseking, Rebecca L; Rehn, Dirk R; Mukhopadhyay, Sukrit; Dreuw, Andreas; Brédas, Jean-Luc
2016-11-08
Third-order nonlinear optical (NLO) properties of polymethine dyes have been widely studied for applications such as all-optical switching. However, the limited accuracy of the current computational methodologies has prevented a comprehensive understanding of the nature of the lowest excited states and their influence on the molecular optical and NLO properties. Here, attention is paid to the lowest excited-state energies and their energetic ratio, as these characteristics impact the figure-of-merit for all-optical switching. For a series of model polymethines, we compare several algebraic diagrammatic construction (ADC) schemes for the polarization propagator with approximate second-order coupled cluster (CC2) theory, the widely used INDO/MRDCI approach and the symmetry-adapted cluster configuration interaction (SAC-CI) algorithm incorporating singles and doubles linked excitation operators (SAC-CI SD-R). We focus in particular on the ground-to-excited state transition dipole moments and the corresponding state dipole moments, since these quantities are found to be of utmost importance for an effective description of the third-order polarizability γ and two-photon absorption spectra. A sum-overstates expression has been used, which is found to quickly converge. While ADC(3/2) has been found to be the most appropriate method to calculate these properties, CC2 performs poorly.
Fractional Electron Loss in Approximate DFT and Hartree-Fock Theory.
Peach, Michael J G; Teale, Andrew M; Helgaker, Trygve; Tozer, David J
2015-11-10
Plots of electronic energy vs electron number, determined using approximate density functional theory (DFT) and Hartree-Fock theory, are typically piecewise convex and piecewise concave, respectively. The curves also commonly exhibit a minimum and maximum, respectively, in the neutral → anion segment, which lead to positive DFT anion HOMO energies and positive Hartree-Fock neutral LUMO energies. These minima/maxima are a consequence of using basis sets that are local to the system, preventing fractional electron loss. Ground-state curves are presented that illustrate the idealized behavior that would occur if the basis set were to be modified to enable fractional electron loss without changing the description in the vicinity of the system. The key feature is that the energy cannot increase when the electron number increases, so the slope cannot be anywhere positive, meaning frontier orbital energies cannot be positive. For the convex (DFT) case, the idealized curve is flat beyond a critical electron number such that any additional fraction of an electron added to the system is unbound. The anion HOMO energy is zero. For the concave (Hartree-Fock) case, the idealized curve is flat up to some critical electron number, beyond which it curves down to the anion energy. A minimum fraction of an electron is required before any binding occurs, but beyond that, the full fraction abruptly binds. The neutral LUMO energy is zero. Approximate DFT and Hartree-Fock results are presented for the F → F(-) segment, and results approaching the idealized behavior are recovered for highly diffuse basis sets. It is noted that if a DFT calculation using a highly diffuse basis set yields a negative LUMO energy then a fraction of an electron must bind and the electron affinity must be positive, irrespective of whether an electron binds experimentally. This is illustrated by calculations on Ne → Ne(-).
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
Qualitative breakdown of the unrestricted Hartree-Fock energy
Mori-Sánchez, Paula, E-mail: paula.mori@uam.es [Departamento de Química and Instituto de Física de la Materia Condensada (IFIMAC), Universidad Autónoma de Madrid, 28049 Madrid (Spain); Cohen, Aron J., E-mail: ajc54@cam.ac.uk [Department of Chemistry, Lensfield Road, University of Cambridge, Cambridge CB2 1EW (United Kingdom)
2014-10-28
The stretching of closed-shell molecules is a qualitative problem for restricted Hartree-Fock that is usually circumvented by the use of unrestricted Hartree-Fock (UHF). UHF is well known to break the spin symmetry at the Coulson-Fischer point, leading to a discontinuous derivative in the potential energy surface and incorrect spin density. However, this is generally not considered as a major drawback. In this work, we present a set of two electron molecules which magnify the problem of symmetry breaking and lead to drastically incorrect potential energy surfaces with UHF. These molecules also fail with unrestricted density-functional calculations where a functional such as B3LYP gives both symmetry breaking and an unphysically low energy due to the delocalization error. The implications for density functional theory are also discussed.
Particle unstable nuclei in the Hartree-Fock theory
Kruppa, A.T. [Magyar Tudomanyos Akademia, Debrecen (Hungary). Atommag Kutato Intezete; Heenen, P.H. [Brussels Univ. (Belgium). Service de Physique Nucleaire Theorique; Flocard, H. [Paris-11 Univ., 91 - Orsay (France). Inst. de Physique Nucleaire; Liotta, R.J. [Manne Siegbahn Inst. of Physics, Stockholm (Sweden)
1997-12-31
Ground state energies and decay widths of particle unstable nuclei are calculated within the Hartree-Fock approximation by performing a complex scaling of the many-body Hamiltonian. Through this transformation, the wave functions of the resonant state become square integrable. The method is implemented with Skyrme effective interactions. Several Skyrme parametrizations are tested on four unstable nuclei: {sup 10}He, {sup 12}O, {sup 26}O and {sup 28}O. (author). 24 refs.
Tensor numerical methods in quantum chemistry: from Hartree-Fock to excitation energies.
Khoromskaia, Venera; Khoromskij, Boris N
2015-12-21
We resume the recent successes of the grid-based tensor numerical methods and discuss their prospects in real-space electronic structure calculations. These methods, based on the low-rank representation of the multidimensional functions and integral operators, first appeared as an accurate tensor calculus for the 3D Hartree potential using 1D complexity operations, and have evolved to entirely grid-based tensor-structured 3D Hartree-Fock eigenvalue solver. It benefits from tensor calculation of the core Hamiltonian and two-electron integrals (TEI) in O(n log n) complexity using the rank-structured approximation of basis functions, electron densities and convolution integral operators all represented on 3D n × n × n Cartesian grids. The algorithm for calculating TEI tensor in a form of the Cholesky decomposition is based on multiple factorizations using algebraic 1D "density fitting" scheme, which yield an almost irreducible number of product basis functions involved in the 3D convolution integrals, depending on a threshold ε > 0. The basis functions are not restricted to separable Gaussians, since the analytical integration is substituted by high-precision tensor-structured numerical quadratures. The tensor approaches to post-Hartree-Fock calculations for the MP2 energy correction and for the Bethe-Salpeter excitation energies, based on using low-rank factorizations and the reduced basis method, were recently introduced. Another direction is towards the tensor-based Hartree-Fock numerical scheme for finite lattices, where one of the numerical challenges is the summation of electrostatic potentials of a large number of nuclei. The 3D grid-based tensor method for calculation of a potential sum on a L × L × L lattice manifests the linear in L computational work, O(L), instead of the usual O(L(3) log L) scaling by the Ewald-type approaches.
Bassem, Y El
2016-01-01
In a previous work [Int. J. Mod. Phys. E 24, 1550073 (2015)], hereafter referred as paper I, we have investigated the ground-state properties of Nd, Ce and Sm isotopes within Hartree-Fock-Bogoliubov method with SLy5 skyrme force in which the pairing strength has been generalized with a new proposed formula. However, that formula is more appropriate for the region of Nd. In this work, we have studied the ground-state properties of both even-even and odd Mo and Ru isotopes. For this, we have used Hartree- Fock-Bogoliubov method with SLy4 skyrme force, and a new formula of the pairing strength which is more accurate for this region of nuclei. The results have been compared with available experimental data, the results of Hartree-Fock-Bogoliubov calculations based on the D1S Gogny effective nucleon-nucleon interaction and predictions of some nuclear models such as Finite Range Droplet Model (FRDM) and Relativistic Mean Field (RMF) theory.
Potential Energy Surface in Hartree-Fock Theory:Adiabatic or Configuration-Constrained?
GUO Lu; Sakata Fumihiko; ZHAO En-Guang
2004-01-01
Validity of adiabatic assumption is discussed within the constrained Hartree-Fock theory for self-conjugate nucleus 72Kr. It is shown that the adiabatic assumption does not provide a correct description for the nature of nucleus when a configuration change is involved. The excited Hartree-Fock states and the continuously-connected constrained Hartree-Fock states are given for the first time by applying the configuration dictated constrained Hartree-Fock theory with Gogny force. The importance of self-consistency between the mean-field and the single particle wave functions is emphasized even when a small number of nucleons are involved in the configuration change.
Properties of the periodic Hartree-Fock minimizer
Ghimenti, Marco
2008-01-01
We study the periodic Hartree-Fock model used for the description of electrons in a crystal. The existence of a minimizer was previously shown by Catto, Le Bris and Lions (Ann. Inst. H. Poincare Anal. Non Lineaire} 18 (2001), no.6, 687--760). We prove in this paper that any minimizer is necessarily a projector and that it solves a certain nonlinear equation, similarly to the atomic case. In particular we show that the Fermi level is either empty or totally filled.
Ground state properties of graphene in Hartree-Fock theory
Hainzl, Christian; Sparber, Christof
2012-01-01
We study the Hartree-Fock approximation of graphene in infinite volume, with instantaneous Coulomb interactions. First we construct its translation-invariant ground state and we recover the well-known fact that, due to the exchange term, the effective Fermi velocity is logarithmically divergent at zero momentum. In a second step we prove the existence of a ground state in the presence of local defects and we discuss some properties of the linear response to an external electric field. All our results are non perturbative.
A divide and conquer real space finite-element Hartree-Fock method
Alizadegan, R.; Hsia, K. J.; Martinez, T. J.
2010-01-01
Since the seminal contribution of Roothaan, quantum chemistry methods are traditionally expressed using finite basis sets comprised of smooth and continuous functions (atom-centered Gaussians) to describe the electronic degrees of freedom. Although this approach proved quite powerful, it is not well suited for large basis sets because of linear dependence problems and ill conditioning of the required matrices. The finite element method (FEM), on the other hand, is a powerful numerical method whose convergence is also guaranteed by variational principles and can be achieved systematically by increasing the number of degrees of freedom and/or the polynomial order of the shape functions. Here we apply the real-space FEM to Hartree-Fock calculations in three dimensions. The method produces sparse, banded Hermitian matrices while allowing for variable spatial resolution. This local-basis approach to electronic structure theory allows for systematic convergence and promises to provide an accurate and efficient way toward the full ab initio analysis of materials at larger scales. We introduce a new acceleration technique for evaluating the exchange contribution within FEM and explore the accuracy and robustness of the method for some selected test atoms and molecules. Furthermore, we applied a divide-and-conquer (DC) method to the finite-element Hartree-Fock ab initio electronic-structure calculations in three dimensions. This DC approach leads to facile parallelization and should enable reduced scaling for large systems.
Bouguettoucha, A.
1996-06-14
A possible effects of the C{sub 4}-symmetry in the superdeformed nuclei of the A {approx}150 mass range has been studied microscopically using cranking Strutinsky method with the deformed Woods-Saxon potential and the Hartree-Fock approach with the Skyrme interaction. If the existence of such a symmetry is judged by the moments Q{sub 44}, the results of the calculation indicate a very weak effect of this kind. Four new superdeformed bands in the {sup 148}Gd nucleus have been studied in reaction to the recent experimental observations (Eurogam Phase 2): a backbending has been tentatively observed at very high rotational frequency in the third excited band. One of the other bands exhibits a J{sup (2)} moment very similar to that of the yrast band in {sup 152}Dy, and this is the first example of identical bands which differ by four mass units. Calculations with the methods mentioned above have been used to analyse the band structure in terms of the nucleonic configurations. Calculation have been performed for some nuclear configurations predicted to involve the exotic octupole deformations (Y{sub 30-}`pear shapes`; Y{sub 31-}`banana mode`; Y{sub 32-}`T{sub d}-symmetry` and Y{sub 33-}`C{sub 3}-symmetry`). While the previous calculations based on the Strutinsky method could not treat the coupling between those modes, the Hartree-Fock approach allows to see for the first time in which propositions the various modes couple. (author). 116 refs.
Hellweg, Arnim
2016-01-01
Hartree--Fock theory is one of the most ancient methods of computational chemistry, but up to the present day quantum chemical calculations on Hartree--Fock level or with hybrid density functional theory can be excessively time consuming. We compare three currently available techniques to reduce the computational demands of such calculations in terms of timing and accuracy.
On Blowup for time-dependent generalized Hartree-Fock equations
Hainzl, Christian; Lewin, Mathieu; Schlein, Benjamin
2009-01-01
We prove finite-time blowup for spherically symmetric and negative energy solutions of Hartree-Fock and Hartree-Fock-Bogoliubov type equations, which describe the evolution of attractive fermionic systems (e. g. white dwarfs). Our main results are twofold: First, we extend the recent blowup result of [Hainzl and Schlein, Comm. Math. Phys. \\textbf{287} (2009), 705--714] to Hartree-Fock equations with infinite rank solutions and a general class of Newtonian type interactions. Second, we show the existence of finite-time blowup for spherically symmetric solutions of a Hartree-Fock-Bogoliubov model, where an angular momentum cutoff is introduced. We also explain the key difficulties encountered in the full Hartree-Fock-Bogoliubov theory.
Error estimates for the Skyrme-Hartree-Fock model
Erler, J
2014-01-01
There are many complementing strategies to estimate the extrapolation errors of a model which was calibrated in least-squares fits. We consider the Skyrme-Hartree-Fock model for nuclear structure and dynamics and exemplify the following five strategies: uncertainties from statistical analysis, covariances between observables, trends of residuals, variation of fit data, dedicated variation of model parameters. This gives useful insight into the impact of the key fit data as they are: binding energies, charge r.m.s. radii, and charge formfactor. Amongst others, we check in particular the predictive value for observables in the stable nucleus $^{208}$Pb, the super-heavy element $^{266}$Hs, $r$-process nuclei, and neutron stars.
Semiempirical Hartree-Fock calculations for $KNbO_{3}$
Eglitis, R I; Borstel, G
1996-01-01
In applying the semiempirical intermediate neglect of differential overlap (INDO) method based on the Hartree-Fock formalism to a cubic perovskite-based ferroelectric material KNbO3, it was demonstrated that the accuracy of the method is sufficient for adequately describing the small energy differences related to the ferroelectric instability. The choice of INDO parameters has been done for a system containing Nb. Based on the parametrization proposed, the electronic structure, equilibrium ground state structure of the orthorhombic and rhombohedral phases, and Gamma-TO phonon frequencies in cubic and rhombohedral phases of KNbO3 were calculated and found to be in good agreement with the experimental data and with the first-principles calculations available.
Using Hartree-Fock pseudopotentials in GW calculations
Hamann, D. R.; Vanderbilt, David
2010-03-01
The issue of including shallow ``semi-core'' states as valence has recently resurfaced in the context of self-consistent GW calculations.footnotetextF. Bruneval et al., Phys. Rev. Lett. 97, 267601 (2006). Supposing that semi-core-valence exchange is the dominant process necessitating the inclusion of semi-cores, we have investigated whether the use Hartree-Fock pseudopotentialsfootnotetextW. A. Al-Saidi, E. J. Walter, and A. M. Rappe, Phys. Rev. B 77, 075122 (2008). instead of density-functional psp's might obviate the need for semi-cores. The answers to this question appear to be ``yes'' for the case of CuCl (filled d shell), and ``semi-cores don't matter anyway'' for ScN (empty d shell). Opportunity permitting, additional examples will be discussed.
Correlated Electron Calculations with Hartree-Fock Scaling
Gebauer, Ralph; Car, Roberto
2013-01-01
We introduce an energy functional for ground-state electronic structure calculations with fundamental variables the natural spin orbitals and their joint occupation probabilities in an implied many-body trial wave function. We use a controlled approximation for the two-particle density matrix that greatly extends the accuracy compared to current functionals of the one-particle density matrix only. Algebraic scaling of computational cost with electron number is achieved in general, and Hartree-Fock scaling in the seniority-zero version of the theory. We present results obtained with the latter version for saturated small molecular systems for which highly accurate quantum chemical computations are available for comparison. The results are variational, capturing most of the correlation energy from equilibrium to dissociation.
Self-consistent Hartree-Fock RPA calculations in 208Pb
Taqi, Ali H.; Ali, Mohammed S.
2017-07-01
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.
Hartree-Fock mean-field theory for trapped dirty bosons
Khellil, Tama; Pelster, Axel
2016-06-01
Here we work out in detail a non-perturbative approach to the dirty boson problem, which relies on the Hartree-Fock theory and the replica method. For a weakly interacting Bose gas within a trapped confinement and a delta-correlated disorder potential at finite temperature, we determine the underlying free energy. From it we determine via extremization self-consistency equations for the three components of the particle density, namely the condensate density, the thermal density, and the density of fragmented local Bose-Einstein condensates within the respective minima of the random potential landscape. Solving these self-consistency equations in one and three dimensions in two other publications has revealed how these three densities change for increasing disorder strength.
Phase structure of the massive chiral Gross-Neveu model from Hartree-Fock
Boehmer, Christian; Kraus, Sebastian; Thies, Michael
2008-01-01
The phase diagram of the massive chiral Gross-Neveu model (the massive Nambu-Jona-Lasinio model in 1+1 dimensions) is constructed. In the large N limit, the Hartree-Fock approach can be used. We find numerically a chiral crystal phase separated from a massive Fermi gas phase by a 1st order transition. Using perturbation theory, we also construct the critical sheet where the homogeneous phase becomes unstable in a 2nd order transition. A tricritical curve is located. The phase diagram is mapped out as a function of fermion mass, chemical potential and temperature and compared with the one of the discrete chiral Gross-Neveu model. As a by-product, we illustrate the crystal structure of matter at zero temperature for various densities and fermion masses.
Auxiliary Density Matrix Methods for Hartree-Fock Exchange Calculations.
Guidon, Manuel; Hutter, Jürg; VandeVondele, Joost
2010-08-10
The calculation of Hartree-Fock exchange (HFX) is computationally demanding for large systems described with high-quality basis sets. In this work, we show that excellent performance and good accuracy can nevertheless be obtained if an auxiliary density matrix is employed for the HFX calculation. Several schemes to derive an auxiliary density matrix from a high-quality density matrix are discussed. Key to the accuracy of the auxiliary density matrix methods (ADMM) is the use of a correction based on standard generalized gradient approximations for HFX. ADMM integrates seamlessly in existing HFX codes and, in particular, can be employed in linear scaling implementations. Demonstrating the performance of the method, the effect of HFX on the structure of liquid water is investigated in detail using Born-Oppenheimer molecular dynamics simulations (300 ps) of a system of 64 molecules. Representative for large systems are calculations on a solvated protein (Rubredoxin), for which ADMM outperforms the corresponding standard HFX implementation by approximately a factor 20.
Ground state properties of even-even and odd Nd,Ce and Sm isotopes in Hartree-Fock-Bogoliubov method
Bassem, Younes El
2015-01-01
In this work, we have studied ground-state properties of both even-even and odd Nd isotopes within Hartree-Fock-Bogoliubov method with SLy5 Skyrme force in which the pairing strength has been generalized with a new proposed formula. We calculated bind- ing energies, two-neutron separation energies, quadrupole deformation, charge, neutron and proton radii. Similar calculations have been carried out for Ce and Sm in order to verify the validity of our pairing strength formula. The results have been compared with available experimental data, the results of Hartree-Fock-Bogoliubov calculations based on the D1S Gogny effective nucleon-nucleon interaction and predictions of some nuclear models such as Finite Range Droplet Model (FRDM) and Relativistic Mean Field (RMF) theory.
Some Aspects of Nuclear Structure in Relativistic Approach
MAZhong-Yu; RONGJian; CAOLi-Gang; CHENBao-Qiu; LIULing
2004-01-01
The nucleon effective interaction in the nuclear medium is investigated in the framework of the DiracBrueckner-Hartree-Fock (DBHF) approach. A new decomposition of the Dirac structure of nucleon self-energy in the DBHF is adopted for asymmetric nuclear matter. The properties of finite nuclei are investigated with the nucleon effective interaction. The agreement with the experimental data is satisfactory. The relativistic microscopic optical potential in asymmetric nuclear matter is investigated in the DBHF approach. The proton scattering from nuclei is calculated and compared with the experimental data. A proper treatment of the resonant continuum for exotic nuclei is studied. The width effect of the resonant continuum on the pairing correlation is discussed. The quasiparticle relativistic random phase approximation based on the relativistic mean-field ground state in the response function formalism is also addressed.
CASTRO EUSTÁQUIO V. R. DE
2001-01-01
Full Text Available The generator coordinate Hartree-Fock method is used to generate adapted Gaussian basis sets for the atoms from Li (Z=3 through Xe (Z=54. In this method the Griffin-Hill-Wheeler-Hartree-Fock equations are integrated through the integral discretization technique. The wave functions generated in this work are compared with the widely used Roothaan-Hartree-Fock wave functions of Clementi and Roetti (1974, and with other basis sets reported in the literature. For all atoms studied, the errors in our total energy values relatively to the numerical Hartree-Fock limits are always less than 7.426 mhartree.
Buica, Gabriela; 10.1016/j.jqsrt.2007.05.004
2013-01-01
We theoretically study multiphoton ionization of Mg in the circularly as well as the linearly polarized laser fields. Specifically two-, three-, and four-photon ionization cross sections from the ground and first excited states are calculated as a function of photon energy. Calculations are performed using the frozen-core Hartree-Fock and also the model potential approaches and the results are compared. We find that the model potential approach provide results as good as or even slightly better than those by the frozen-core Hartree-Fock approach. We also report the relative ratios of the ionization cross sections by the circularly and linearly polarized laser fields as a function of photon energy, which exhibit clear effects of electron correlations.
Kambe, Takahide; Saito, Koichi
2016-01-01
As the interior density of a neutron star can become very high, it has been expected and discussed that quark matter may exist inside it. To describe the transition from hadron to quark phases (and vice versa), there are mainly two methods; one is the first-order phase transition, and the other is the crossover phenomenon. In the present study, using the flavor-SU (3) NJL model with the vector coupling interaction, we have calculated the equation of state for the quark phase at high density. Furthermore, for the hadron phase at low density, we have used two kinds of the equations of state; one is a relatively soft one by the QHD model, and the other is a stiff one calculated with relativistic Brueckner-Hartree-Fock approximation. Using those equations of state for the two phases, we have investigated the influence of various choices of parameters concerning the crossover region on the mass and radius of a neutron star.
Kupka, T.; Ruscic, B.; Botto, R. E.; Chemistry
2003-05-01
The nuclear shielding anisotropy and shielding tensor components calculated using the hybrid density functional B3PW91 are reported for a model set of compounds comprised of N{sub 2}, NH{sub 3}, CH{sub 4}, C{sub 2}H{sub 4}, HCN and CH{sub 3}CN. An estimation of density functional theory (DFT) and Hartree-Fock complete basis-set limit (CBS) parameters from a 2 (3) point exact fit vs. least-squares fit was obtained with the cc-pVxZ and aug-cc-pVxZ basis sets (x=D, T, Q, 5, 6). Both Hartree-Fock- and DFT-predicted CBS shielding anisotropies and shielding tensor components of the model molecules were in reasonable agreement with available experimental data. The utility of using a limited CBS approach for calculating accurate anisotropic shielding parameters of larger molecules as complementary methods to solid-state NMR is proposed.
Projected Hartree Fock Theory as a Polynomial Similarity Transformation Theory of Single Excitations
Qiu, Yiheng; Scuseria, Gustavo E
2016-01-01
Spin-projected Hartree-Fock is introduced as a particle-hole excitation ansatz over a symmetry-adapted reference determinant. Remarkably, this expansion has an analytic expression that we were able to decipher. While the form of the polynomial expansion is universal, the excitation amplitudes need to be optimized. This is equivalent to the optimization of orbitals in the conventional projected Hartree-Fock framework of non-orthogonal determinants. Using the inverse of the particle-hole expansion, we similarity transform the Hamiltonian in a coupled-cluster style theory. The left eigenvector of the non-hermitian Hamiltonian is constructed in a similar particle-hole expansion fashion, and we show that to numerically reproduce variational projected Hartree-Fock results, one needs as many pair excitations in the bra as the number of strongly correlated entangled pairs in the system. This single-excitation polynomial similarity transformation theory is an alternative to our recently presented double excitation the...
A finite-temperature Hartree-Fock code for shell-model Hamiltonians
Bertsch, G. F.; Mehlhaff, J. M.
2016-10-01
The codes HFgradZ.py and HFgradT.py find axially symmetric minima of a Hartree-Fock energy functional for a Hamiltonian supplied in a shell model basis. The functional to be minimized is the Hartree-Fock energy for zero-temperature properties or the Hartree-Fock grand potential for finite-temperature properties (thermal energy, entropy). The minimization may be subjected to additional constraints besides axial symmetry and nucleon numbers. A single-particle operator can be used to constrain the minimization by adding it to the single-particle Hamiltonian with a Lagrange multiplier. One can also constrain its expectation value in the zero-temperature code. Also the orbital filling can be constrained in the zero-temperature code, fixing the number of nucleons having given Kπ quantum numbers. This is particularly useful to resolve near-degeneracies among distinct minima.
Cheng, Lan, E-mail: chenglanster@gmail.com [Institute for Theoretical Chemistry, Department of Chemistry and Biochemistry, The University of Texas at Austin, Austin, Texas 78712 (United States); Stopkowicz, Stella, E-mail: stella.stopkowicz@kjemi.uio.no [Centre for Theoretical and Computational Chemistry, Department of Chemistry, University of Oslo, N-0315 Oslo (Norway); Gauss, Jürgen, E-mail: gauss@uni-mainz.de [Institut für Physikalische Chemie, Universität Mainz, D-55099 Mainz (Germany)
2013-12-07
A perturbative approach to compute second-order spin-orbit (SO) corrections to a spin-free Dirac-Coulomb Hartree-Fock (SFDC-HF) calculation is suggested. The proposed scheme treats the difference between the DC and SFDC Hamiltonian as perturbation and exploits analytic second-derivative techniques. In addition, a cost-effective scheme for incorporating relativistic effects in high-accuracy calculations is suggested consisting of a SFDC coupled-cluster treatment augmented by perturbative SO corrections obtained at the HF level. Benchmark calculations for the hydrogen halides HX, X = F-At as well as the coinage-metal fluorides CuF, AgF, and AuF demonstrate the accuracy of the proposed perturbative treatment of SO effects on energies and electrical properties in comparison with the more rigorous full DC treatment. Furthermore, we present, as an application of our scheme, results for the electrical properties of AuF and XeAuF.
Application of Fourth Order Vibrational Perturbation Theory with Analytic Hartree-Fock Force Fields
Gong, Justin Z.; Matthews, Devin A.; Stanton, John F.
2014-06-01
Fourth-Order Rayleigh-Schrodinger Perturbation Theory (VPT4) is applied to a series of small molecules. The quality of results have been shown to be heavily dependent on the quality of the quintic and sextic force constants used and that numerical sextic force constants converge poorly and are unreliable for VPT4. Using analytic Hartree-Fock force constants, it is shown that these analytic higher-order force constants are comparable to corresponding force constants from numerical calculations at a higher level of theory. Calculations show that analytic Hartree-Fock sextic force constants are reliable and can provide good results with Fourth-Order Rayleigh-Schrodinger Perturbation Theory.
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.
General technique for analytical derivatives of post-projected Hartree-Fock
Tsuchimochi, Takashi; Ten-no, Seiichiro
2017-02-01
In electronic structure theory, the availability of an analytical derivative is one of the desired features for a method to be useful in practical applications, as it allows for geometry optimization as well as computation of molecular properties. With the recent advances in the development of symmetry-projected Hartree-Fock (PHF) methods, we here aim at further extensions by devising the analytic gradients of post-PHF approaches with a special focus on spin-extended (spin-projected) configuration interaction with single and double substitutions (ECISD). Just like standard single-reference methods, the mean-field PHF part does not require the corresponding coupled-perturbed equation to be solved, while the correlation energy term needs the orbital relaxation effect to be accounted for, unless the underlying molecular orbitals are variationally optimized in the presence of the correlation energy. We present a general strategy for post-PHF analytical gradients, which closely parallels that for single-reference methods, yet addressing the major difference between them. The similarity between ECISD and multi-reference CI not only in the energy but also in the optimized geometry is clearly demonstrated by the numerical examples of ozone and cyclobutadiene.
Exploration of (super-)heavy elements using the Skyrme-Hartree-Fock model
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.)
Generalized Hartree-Fock-Bogoliubov description of the Fröhlich polaron
Kain, Ben; Ling, Hong Y.
2016-07-01
We adapt the generalized Hartree-Fock-Bogoliubov (HFB) method to an interacting many-phonon system free of impurities. The many-phonon system is obtained from applying the Lee-Low-Pine (LLP) transformation to the Fröhlich model which describes a mobile impurity coupled to noninteracting phonons. We specialize our general HFB description of the Fröhlich polaron to Bose polarons in quasi-one-dimensional cold-atom mixtures. The LLP-transformed many-phonon system distinguishes itself with an artificial phonon-phonon interaction which is very different from the usual two-body interaction. We use the quasi-one-dimensional model, which is free of an ultraviolet divergence that exists in higher dimensions, to better understand how this unique interaction affects polaron states and how the density and pair correlations inherent to the HFB method conspire to create a polaron ground state with an energy in good agreement with and far closer to the prediction from Feynman's variational path integral approach than mean-field theory where HFB correlations are absent.
Basis set effects on the Hartree-Fock description of confined many-electron atoms
Garza, Jorge; Hernández-Pérez, Julio M.; Ramírez, José-Zeferino; Vargas, Rubicelia
2012-01-01
In this work, the basis sets designed by Clementi, Bunge and Thakkar, for atomic systems, have been used to obtain the electronic structure of confined many-electron atoms by using Roothaan's approach in the Hartree-Fock context with a new code written in C, which uses the message-passing interface library. The confinement was imposed as Ludeña suggested to simulate walls with infinity potential. For closed-shell atoms, the Thakkar basis set functions give the best total energies (TE) as a function of the confinement radius, obtaining the following ordering: TE(Thakkar) Clementi). However, for few open-shell atoms this ordering is not preserved and a trend, for the basis sets, is not observed. Although there are differences between the TE predicted by these basis set functions, the corresponding pressures are similar to each other; it means that changes in the total energy are described almost in the same way by using any of these basis sets. By analysing the total energy as a function of the inverse of the volume we propose an equation of state; for regions of small volumes, this equation predicts that the pressure is inversely proportional to the square of the volume.
Brueckner-Hartree-Fock calculations for finite nuclei with renormalized realistic forces
Hu, B. S.; Xu, F. R.; Wu, Q.; Ma, Y. Z.; Sun, Z. H.
2017-03-01
One can adopt two-step G -matrix approximations for the Brueckner-Hartree-Fock (BHF) calculations. The first G matrix is to soften the bare force, and the second one is to include the high-order correlations of the interaction in medium. The first G -matrix calculation for two-nucleon interaction should be done in the center-of-mass coordinate. As another alternative BHF approach, we have adopted the Vlow-k technique to soften the interaction and used the G matrix to include high-order correlations. The Vlow-k renormalization leads to high-momentum and low-momentum components of the interaction decoupled. With the Vlow-k potential, we have performed the BHF calculations for finite nuclei. The G -matrix elements with exact Pauli exclusions are calculated in the self-consistent BHF basis. To see effects from further possible correlations beyond BHF, we have simultaneously performed renormalized BHF (RBHF) calculations with the same potential. In RBHF, the mean field derived from realistic forces is modified by introducing the particle-occupation depletion resulting from many-body correlations. The ground-state energies and radii of the closed-shell nuclei, 4He, 16O, and 40Ca, have been investigated. The convergences of the BHF and RBHF calculations have been discussed and compared with other ab initio calculations with the same potential.
Hartree-Fock Cluster Study of Interstitial Transition Metals in Silicon
Broer, R.; Aissing, G.; Nieuwpoort, W.C.; Feiner, L.F.
1986-01-01
Results are presented of a Hartree-Fock cluster study of interstitial Ti, V, Cr, and Mn impurities in silicon. A Si10 cluster models the nearest Si atoms around a tetrahedral interstitial site in crystalline Si. The dangling bonds of the Si atoms are saturated by hydrogens. The effect of the Si core
Method of renormalization potential for one model of Hartree-Fock-Slater type
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
Koopmans' theorem in the statistical Hartree-Fock theory
Pain, Jean-Christophe, E-mail: jean-christophe.pain@cea.fr [CEA, DAM, DIF, F-91297 Arpajon (France)
2011-07-28
In this short paper, the validity of Koopmans' theorem in the Hartree-Fock theory at non-zero temperature (Hartree-Fock statistical theory) is investigated. It is shown that Koopmans' theorem does not apply in the grand-canonical ensemble, due to a missing contribution to the energy proportional to the interaction between two electrons belonging to the same orbital. The Hartree-Fock statistical theory has also been applied in the canonical ensemble (Blenski et al 1997 Phys. Rev. E 55 R4889) for the purpose of photo-absorption calculations. In that case, the Hartree-Fock self-consistent field equations are derived in the super-configuration approximation. It is shown that Koopmans' theorem does not hold in the canonical ensemble, but a restricted version of the theorem can be obtained by assuming that a particular quantity multiplying the interaction matrix element in the expression of the energy does not change during the removal of an electron.
Qiu, Yiheng; Henderson, Thomas M.; Scuseria, Gustavo E.
2016-09-01
Spin-projected Hartree-Fock is written as a particle-hole excitation ansatz over a symmetry-adapted reference determinant. Remarkably, this expansion has an analytic expression that we were able to decipher. While the form of the polynomial expansion is universal, the excitation amplitudes need to be optimized. This is equivalent to the optimization of orbitals in the conventional projected Hartree-Fock framework of non-orthogonal determinants. Using the inverse of the particle-hole expansion, we similarity transform the Hamiltonian in a coupled-cluster style theory. The left eigenvector of the non-Hermitian Hamiltonian is constructed in a similar particle-hole expansion fashion, and we show that to numerically reproduce variational projected Hartree-Fock results, one needs as many pair excitations in the bra as the number of strongly correlated entangled pairs in the system. This single-excitation polynomial similarity transformation theory is an alternative to our recently presented double excitation theory, but supports projected Hartree-Fock and coupled cluster simultaneously rather than interpolating between them.
Restricted Closed Shell Hartree Fock Roothaan Matrix Method Applied to Helium Atom Using Mathematica
Acosta, César R.; Tapia, J. Alejandro; Cab, César
2014-01-01
Slater type orbitals were used to construct the overlap and the Hamiltonian core matrices; we also found the values of the bi-electron repulsion integrals. The Hartree Fock Roothaan approximation process starts with setting an initial guess value for the elements of the density matrix; with these matrices we constructed the initial Fock matrix.…
Hartree-Fock Cluster Study of Interstitial Transition Metals in Silicon
Broer, R.; Aissing, G.; Nieuwpoort, W.C.; Feiner, L.F.
Results are presented of a Hartree-Fock cluster study of interstitial Ti, V, Cr, and Mn impurities in silicon. A Si10 cluster models the nearest Si atoms around a tetrahedral interstitial site in crystalline Si. The dangling bonds of the Si atoms are saturated by hydrogens. The effect of the Si core
Perturbative calculation of the Sternheimer anti-shielding factor with Hartree-Fock atomic orbitals
2012-01-01
We report a calculation of the Sternheimer anti-shielding factor, \\gamma, by means of first order perturbation theory. In quality of basis functions, we use Hartree-Fock electronic orbitals, expanded on hydrogenic atomic states. The computed \\gamma(r) for Fe^{3+} and Cu^{1+} inner electronic cores are reported and compared with literature values, obtained from alternative methodologies.
Approaching the Hartree-Fock limit for organotransition metal complexes
Schaefer, III, Henry F. [Univ. of Texas, Austin, TX (United States). Dept. of Chemistry. Inst. for Theoretical Chemistry; Univ. of California, Berkeley, CA (United States). Dept. of Chemistry. Lawrence Berkeley Lab.
1981-04-01
In theoretical studies of the electronic structure of organometallic complexes, the choice of basis set is critical, much more so than for analogous studies of molecules containing only H, C, N, and O. In this paper, this problem is discussed in the light of structural predictions for the transition metal hydrides MH, MH_{2}, and MH_{4}, for the fluorides MF_{2} and MF_{3}, and for Ni(CO)_{4}, Ni(C_{2}H_{4})_{3}, (CO)_{3}NiCH_{2}, and Ni(C_{4}H_{4})_{2}.
Bierón, Jacek; Indelicato, Paul; Jönsson, Per; Pyykkö, Pekka
2009-01-01
The multiconfiguration Dirac-Hartree-Fock (MCDHF) model has been employed to calculate the expectation values for the hyperfine splittings of the 5d96s2 2D3/2 and 5d96s2 2D5/2 levels of atomic gold. One-, two-, and three-body electron correlation effects involving all 79 electrons have been included in a systematic manner. The approximation employed in this study is equivalent to a Complete Active Space (CAS) approach. Calculated electric field gradients, together with experimental values of the electric quadrupole hyperfine structure constants, allow us to extract a nuclear electric quadrupole moment Q(197Au)=521.5(5.0) mb.
Dziedzic, J; Hill, Q; Skylaris, C-K
2013-12-07
We present a method for the calculation of four-centre two-electron repulsion integrals in terms of localised non-orthogonal generalised Wannier functions (NGWFs). Our method has been implemented in the ONETEP program and is used to compute the Hartree-Fock exchange energy component of Hartree-Fock and Density Functional Theory (DFT) calculations with hybrid exchange-correlation functionals. As the NGWFs are optimised in situ in terms of a systematically improvable basis set which is equivalent to plane waves, it is possible to achieve large basis set accuracy in routine calculations. The spatial localisation of the NGWFs allows us to exploit the exponential decay of the density matrix in systems with a band gap in order to compute the exchange energy with a computational effort that increases linearly with the number of atoms. We describe the implementation of this approach in the ONETEP program for linear-scaling first principles quantum mechanical calculations. We present extensive numerical validation of all the steps in our method. Furthermore, we find excellent agreement in energies and structures for a wide variety of molecules when comparing with other codes. We use our method to perform calculations with the B3LYP exchange-correlation functional for models of myoglobin systems bound with O2 and CO ligands and confirm that the same qualitative behaviour is obtained as when the same myoglobin models are studied with the DFT+U approach which is also available in ONETEP. Finally, we confirm the linear-scaling capability of our method by performing calculations on polyethylene and polyacetylene chains of increasing length.
Multiconfiguration hartree-fock theory for pseudorelativistic systems: The time-dependent case
Hajaiej, Hichem
2014-03-01
In [Setting and analysis of the multi-configuration time-dependent Hartree-Fock equations, Arch. Ration. Mech. Anal. 198 (2010) 273-330] the third author has studied in collaboration with Bardos, Catto and Mauser the nonrelativistic multiconfiguration time-dependent Hartree-Fock system of equations arising in the modeling of molecular dynamics. In this paper, we extend the previous work to the case of pseudorelativistic atoms. We show the existence and the uniqueness of global-in-time solution to the underlying system under technical assumptions on the energy of the initial data and the charge of the nucleus. Moreover, we prove that the result can be extended to the case of neutron stars when the number of electrons is less than a critical number N cr. © 2014 World Scientific Publishing Company.
Brueckner-Hartree-Fock and its renormalized calculations for finite nuclei
Hu, B S; Ma, Y Z; Wu, Q; Sun, Z H
2016-01-01
We have performed self-consistent Brueckner-Hartree-Fock (BHF) and its renormalized theory to the structure calculations of finite nuclei. The $G$-matrix is calculated within the BHF basis, and the exact Pauli exclusion operator is determined by the BHF spectrum. Self-consistent occupation probabilities are included in the renormalized Brueckner-Hartree-Fock (RBHF). Various systematics and convergences are studies. Good results are obtained for the ground-state energy and radius. RBHF can give a more reasonable single-particle spectrum and radius. We present a first benchmark calculation with other {\\it ab initio} methods using the same effective Hamiltonian. We find that the BHF and RBHF results are in good agreement with other $\\it{ab}$ $\\it{initio}$ methods.
Mazurek, A. P.; Sadlej-Sosnowska, N.
2000-11-01
A comparison of the ab initio quantum chemical methods: Hartree-Fock (HF) and hybrid density functional theory (DFT)/B3LYP for the treatment of tautomeric equilibria both in the gas phase and in the solution is made. The solvent effects were investigated in terms of the self-consistent reaction field (SCRF). Ionization potentials (IP), calculated by DFT/B3LYP, are also compared with those calculated previously within the HF frame.
Generalization of Cramer's rule and its application to the projection of Hartree-Fock wave function
Hage-Hassan, Mehdi
2009-01-01
We generalize the Cramer's rule of linear algebra. We apply it to calculate the spectra of nucleus by applying Hill-Wheeler projection operator to Hartree-Fock wave function, and to derive L\\"owdin formula and Thouless theorem. We derive by an elementary method the infinitesimal or L\\"owdin projection operators and its integral representation to be useful for the projection of Slater determinant.
The Dielectric Permittivity of Crystals in the reduced Hartree-Fock approximation
Cancès, Eric
2009-01-01
In a recent article (Canc\\`es, Deleurence and Lewin, Commun. Math. Phys., 281 (2008), pp. 129-177), we have rigorously derived, by means of bulk limit arguments, a new variational model to describe the electronic ground state of insulating or semiconducting crystals in the presence of local defects. In this so-called reduced Hartree-Fock model, the ground state electronic density matrix is decomposed as $\\gamma = \\gamma^0_{\\rm per} + Q_{\
On the solution of the Hartree-Fock-Bogoliubov equations by the conjugate gradient method
Egido, J.L. [Universidad Autonoma de Madrid (Spain). Dept. de Fisica Teorica; Lessing, J. [Universidad Autonoma de Madrid (Spain). Dept. de Fisica Teorica; Martin, V. [Analisis Numerico, Facultad de Informatica, Universidad Politecnica de Madrid, E-28660 Boadilla del Monte, Madrid (Spain); Robledo, L.M. [Universidad Autonoma de Madrid (Spain). Dept. de Fisica Teorica
1995-11-06
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.).
Optimized $\\delta$ expansion for relativistic nuclear models
Krein, G I; Peres-Menezes, D; Nielsen, M; Pinto, M B
1998-01-01
The optimized $\\delta$-expansion is a nonperturbative approach for field theoretic models which combines the techniques of perturbation theory and the variational principle. This technique is discussed in the $\\lambda \\phi^4$ model and then implemented in the Walecka model for the equation of state of nuclear matter. The results obtained with the $\\delta$ expansion are compared with those obtained with the traditional mean field, relativistic Hartree and Hartree-Fock approximations.
On the NP-completeness of the Hartree-Fock method for translationally invariant systems
Whitfield, James D
2014-01-01
The self-consistent field method utilized for solving the Hartree-Fock (HF) problem and the closely related Kohn-Sham problem, is typically thought of as one of the cheapest methods available to quantum chemists. This intuition has been developed from the numerous applications of the self-consistent field method to a large variety of molecular systems. However, in terms of its worst-case computational complexity, the HF problem is NP-complete. In this work, we investigate how far one can push the boundaries of the NP-completeness by investigating restricted instances of HF. We have constructed two new NP-complete variants of the problem. The first is a set of Hamiltonians whose translationally invariant Hartree-Fock solutions are trivial, but whose broken symmetry solutions are NP-complete. Second, we demonstrate how to embed instances of spin glasses into translationally invariant Hartree-Fock instances and provide a numerical example. These findings are the first steps towards understanding in which cases t...
A Nonlinear Model for Relativistic Electrons at Positive Temperature
Hainzl, Christian; Lewin, Mathieu; Seiringer, Robert
2008-01-01
We study the relativistic electron-positron field at positive temperature in the Hartree-Fock-approximation. We consider both the case with and without exchange term, and investigate the existence and properties of minimizers. Our approach is non-perturbative in the sense that the relevant electron subspace is determined in a self-consistent way. The present work is an extension of previous work by Hainzl, Lewin, S\\'er\\'e, and Solovej where the case of zero temperature was considered.
Time-dependent Hartree-Fock studies of the dynamical fusion threshold
Nakatsukasa Takashi
2012-12-01
Full Text Available A microscopic description of dynamical fusion threshold in heavy ion collisions is performed in the framework of time-dependent Hartree-Fock (TDHF theory using Skyrme energy density functional (EDF. TDHF fusion threshold is in a better agreement with experimental fusion barrier. We find that the onset of extra push lies at the effective fissility 33, which is consistent with the prediction of Swiateckis macroscopic model. The extra push energy in our TDHF simulation is systematically smaller than the prediction in macroscopic model. The important dynamical effects and the way to fit the parameter might be responsible for the different results.
Projected gradient algorithms for Hartree-Fock and density matrix functional theory calculations
Cancès, Eric; Pernal, Katarzyna
2008-04-01
We present projected gradient algorithms designed for optimizing various functionals defined on the set of N-representable one-electron reduced density matrices. We show that projected gradient algorithms are efficient in minimizing the Hartree-Fock or the Müller-Buijse-Baerends functional. On the other hand, they converge very slowly when applied to the recently proposed BBk (k =1,2,3) functionals [O. Gritsenko et al., J. Chem. Phys. 122, 204102 (2005)]. This is due to the fact that the BBk functionals are not proper functionals of the density matrix.
Superdeformed rotational bands in the mercury region. A cranked Skyrme-Hartree-Fock-Bogoliubov study
Gall, B. (Centre de Spectrometrie Nucleaire et de Spectrometrie de Masse, 91 Orsay (France)); Bonche, P. (Service de Physique Theorique, DSM, CE Saclay, 91 Gif-sur-Yvette (France)); Dobaczewski, J. (Inst. of Theoretical Physics, Warsaw Univ., Warsaw (Poland)); Flocard, H. (Div. de Physique Theorique, Inst. de Physique Nucleaire, 91 Orsay (France)); Heenen, P.H. (Physique Nucleaire Theorique, Univ. Libre de Bruxelles (Belgium))
1994-05-01
A study of rotational properties of the ground superdeformed bands in [sup 190]Hg, [sup 192]Hg, [sup 194]Hg, and [sup 194]Pb is presented. We use the cranked Hartree-Fock-Bogoliubov method with the SkM* parametrization of the Skyrme force in the particle-hole channel and a seniority interaction in the pairing channel. An approximate particle number projection is performed by means of the Lipkin-Nogami prescription. We analyze the proton and neutron quasiparticle routhians in connection with the present information on about thirty presently observed superdeformed bands in nuclei close neighbours of [sup 192]Hg (orig.)
Superdeformed rotational bands in the mercury region; a cranked Skyrme-Hartree-Fock-Bogoliubov study
Gall, B.; Bonche, P.; Dobaczewski, J.; Flocard, H.; Heenen, P. -H.
1994-01-01
URL: http://www-spht.cea.fr/articles/T94/011 http://fr.arxiv.org/abs/nucl-th/9312011; International audience; A study of rotational properties of the ground superdeformed bands in $ ^{190} {\\rm Hg,} $ $ ^{192} {\\rm Hg,} $ $ ^{194} {\\rm Hg,} $ and $ ^{194} {\\rm Pb} $ is presented. We use the cranked Hartree-Fock-Bogoliubov method with the SkM$ ^\\ast $ parametrization of the Skyrme force in the particle-hole channel and a seniority interaction in the pairing channel. An approximate particle num...
Superdeformed rotational bands in the mercury region. A cranked Skyrme-Hartree-Fock-Bogoliubov study
Gall, B.; Bonche, P.; Dobaczewski, J.; Flocard, H.; Heenen, P.-H.
1994-09-01
A study of rotational properties of the ground superdeformed bands in190Hg,192Hg,194Hg, and194Pb is presented. We use the cranked Hartree-Fock-Bogoliubov method with the SkM* parametrization of the Skyrme force in the particle-hole channel and a seniority interaction in the pairing channel. An approximate particle number projection is performed by means of the Lipkin-Nogami prescription. We analyze the proton and neutron quasiparticle routhians in connection with the present information on about thirty presently observed superdeformed bands in nuclei close neighbours of192Hg.
Superdeformed rotational bands in the Mercury region. A cranked Skyrme-Hartree-Fock-Bogoliubov study
Gall, B. [Paris-11 Univ., 91 - Orsay (France). Centre de Spectrometrie Nucleaire et de Spectrometrie de Masse; Bonche, P. [CEA Centre d`Etudes de Saclay, 91 - Gif-sur-Yvette (France). Service de Physique Theorique; Dobaczewski, J. [Warsaw Univ. (Poland). Inst. Fizyki Teoretycznej; Heenen, P.H. [Universite Libre de Bruxelles (Belgium). Physique Nucleaire Theorique; Flocard, H.
1993-12-17
A study of rotational properties of the ground superdeformed bands in {sup 190}Hg, {sup 192}Hg, {sup 194}Hg, and {sup 194}Pb is presented. The cranked Hartree-Fock-Bogolyubov method is used with the SkM* parametrization of the Skyrme force in the particle-hole channel and a seniority interaction in the pairing channel. An approximate particle number projection is performed by means of the Lipkin-Nogami prescription. The proton and neutron quasiparticle rhouthians are analyzed in connection with the present information on about thirty presently observed superdeformed bands in nuclei close neighbours of {sup 192}Hg. (authors). 53 refs., 14 figs.
Olshanii, Maxim; Pricoupenko, Ludovic
2001-05-01
We introduce a novel one-parametric family of zero-range pseudopotentials hatV^Λ(r) = g_Λ δ(r) [ partialr + Λ ] (r \\cdot ) with g_Λ = fracg_01-Λ a and g0 = 4πhbar^2 a/m , whose scattering length a does not depend on the free parameter Λ. No exact (after the zero-range approximation has been made) many-body observable depends on it, although approximate treatments differ for different Λ (M. Olshanii and L. Pricoupenko, mat/0101275>). We incorporate these pseudopotentials in the Hartree-Fock-Bogoliubov variational formalism, whose conventional (Λ=0) version is known to exhibit UV-divergencies, inconsistencies with both Hugenholtz-Pines theorem and many-body T-matrix calculations, and inability to develop an energy minimum for the atomic condensate leading to a molecular condensate instead. Using Λ as a new variational parameter we resolve all inconsistencies of the Hartree-Fock-Bogoliubov formalism known so far, with no ad hoc modifications of the theory.
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.
Lewis, Cannada A; Valeev, Edward F
2015-01-01
Clustered Low Rank (CLR) framework for block-sparse and block-low-rank tensor representation and computation is described. The CLR framework depends on 2 parameters that control precision: one controlling the CLR block rank truncation and another that controls screening of small contributions in arithmetic operations on CLR tensors. As these parameters approach zero CLR representation and arithmetic become exact. There are no other ad-hoc heuristics, such as domains. Use of the CLR format for the order-2 and order-3 tensors that appear in the context of density fitting (DF) evaluation of the Hartree-Fock (exact) exchange significantly reduced the storage and computational complexities below their standard $\\mathcal{O}(N^3)$ and $\\mathcal{O}(N^4)$ figures. Even for relatively small systems and realistic basis sets CLR-based DF HF becomes more efficient than the standard DF approach, and significantly more efficient than the conventional non-DF HF, while negligibly affecting molecular energies and properties.
Pototzky, K J; Reinhard, P -G; Nesterenko, V O
2010-01-01
We present a systematic analysis of the description of odd nuclei by the Skyrme-Hartree-Fock approach augmented with pairing in BCS approximation and blocking of the odd nucleon. Current and spin densities in the Skyrme functional produce time-odd mean fields (TOMF) for odd nuclei. Their effect on basic properties (binding energies, odd-even staggering, separation energies and spectra) is investigated for the three Skyrme parameterizations SkI3, SLy6, and SV-bas. About 1300 spherical and axially-deformed odd nuclei with 16 < Z < 92 are considered. The calculations demonstrate that the TOMF effect is generally small, although not fully negligible. The influence of the Skyrme parameterization and the consistency of the calculations are much more important. With a proper choice of the parameterization, a good description of binding energies and their differences is obtained, comparable to that for even nuclei. The description of low-energy excitation spectra of odd nuclei is of varying quality depending on...
Caffarel, Michel; Scemama, Anthony; Ramírez-Solís, Alejandro
2014-01-01
We present a comparative study of the spatial distribution of the spin density (SD) of the ground state of CuCl2 using Density Functional Theory (DFT), quantum Monte Carlo (QMC), and post-Hartree-Fock wavefunction 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 of the copper atom and the delocalization of the 3d hole over the chlorine atoms. It is shown here that qualitatively different results for SD are obtained from these various quantum-chemical approaches. At the DFT level, the spin density distribution is directly related to the amount of Hartree-Fock exchange introduced in hybrid functionals. At the QMC level, Fixed-node Diffusion Monte Carlo (FN-DMC) results for SD are strongly dependent on the nodal structure of the trial wavefunction employed (here, Hartree-Fock or Kohn-Sham with a particula...
Amour, Laurent; 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.
Constrained Hartree-Fock Theory and Study of Deformed Structures of Closed Shell Nuclei
Praharaj, Choudhury
2016-03-01
We have studied some N or Z = 50 nuclei in a microscopic model with effective interaction in a reasonably large shell model space. Excitation of particles across 50 shell closure leads to well-deformed excited prolate configurations. The potential energy surfaces of nuclei are studied using Hartree-Fock theory with quadrupole constraint to explore the various deformed configurations of N = 50 nuclei 82Ge , 84Se and 86Kr . Energy spectra are calculated from various intrinsic states using Peierls-Yoccoz angular momentum projection technique. Results of spectra and electromagnetic moments and transitions will be presented for N = 50 nuclei and for Z = 50 114Sn nucleus. Supported by Grant No SB/S2/HEP-06/2013 of DST.
Twist-averaged boundary conditions for nuclear pasta Hartree-Fock calculations
Schuetrumpf, B
2015-01-01
Background: Nuclear pasta phases, present in the inner crust of neutron stars, are associated with nucleonic matter at sub-saturation densities arranged in regular shapes. Those complex phases, residing in a layer which is approximately 100 m thick, impact many features of neutron stars. Theoretical quantum-mechanical simulations of nuclear pasta are usually carried out in finite 3D boxes assuming periodic boundary conditions (PBC). The resulting solutions are affected by spurious finite-size effects. Purpose: In order to remove spurious finite-size effects, it is convenient to employ twist-averaged boundary conditions (TABC) used in condensed matter, nuclear matter, and lattice QCD applications. In this work, we study the effectiveness of TABC in the context of pasta phases simulations within nuclear density functional theory. Methods: We perform Skyrme-Hartree-Fock calculations in three dimensions by implementing Bloch boundary conditions. The TABC averages are obtained by means of Gauss-Legendre integratio...
Quasi-particle Continuum and Resonances in the Hartree-Fock-Bogoliubov Theory
Pei, J. C. [University of Tennessee, Knoxville (UTK) & Oak Ridge National Laboratory (ORNL); Kruppa, Andras Tibor [ORNL; Nazarewicz, Witold [ORNL
2011-01-01
The quasi-particle energy spectrum of the Hartree-Fock-Bogoliubov (HFB) equations contains discrete bound states, resonances, and non-resonant continuum states. We study the structure of the unbound quasi-particle spectrum of weakly bound nuclei within several methods that do not rely on imposing scattering or outgoing boundary conditions. Various approximations are examined to estimate resonance widths. It is shown that the stabilization method works well for all HFB resonances except for very narrow ones. The Thomas-Fermi approximation to the non-resonant continuum has been shown to be very effective, especially for coordinate-space HFB calculations in large boxes that involve huge amounts of discretized quasi-particle continuum states.
Quasiparticle continuum and resonances in the Hartree-Fock-Bogoliubov theory
Pei, Junchen [ORNL; Kruppa, A. T. [Joint Institute for Heavy Ion Research, Oak Ridge; Nazarewicz, W. [University of Tennessee, Knoxville (UTK) & Oak Ridge National Laboratory (ORNL)
2011-01-01
The quasi-particle energy spectrum of the Hartree-Fock-Bogoliubov (HFB) equations contains discrete bound states, resonances, and non-resonant continuum states. We study the structure of the unbound quasi-particle spectrum of weakly bound nuclei within several methods that do not rely on imposing scattering or outgoing boundary conditions. Various approximations are examined to estimate resonance widths. It is shown that the stabilization method works well for all HFB resonances except for very narrow ones. The Thomas-Fermi approximation to the non-resonant continuum has been shown to be very effective, especially for coordinate-space HFB calculations in large boxes that involve huge amounts of discretized quasi-particle continuum states.
Comparative study of metal cluster fission in Hartree-Fock and LDA
Lyalin, A; Greiner, W; Lyalin, Andrey; Solov'yov, Andrey; Greiner, Walter
2001-01-01
Fission of doubly charged metal clusters is studied using the open-shell two-center deformed jellium Hartree-Fock model and Local Density Approximation. Results of calculations of the electronic structure and fission barriers for the symmetric and asymmetric channels associated with the following processes Na_{10}^{2+} --> Na_{7}^{+} + Na_{3}^{+}, Na_{18}^{2+} --> Na_{15}^{+} + Na_{3}^{+} and Na_{18}^{2+} --> 2 Na_{9}^{+} are presented. The role of the exact exchange and many-body correlation effects in metal clusters fission is analysed. It is demonstrated that the influence of many-electron correlation effects on the height of the fission barrier is more profound if the barrier arises nearby or beyond the scission point. The importance of cluster deformation effects in the fission process is elucidated with the use of the overlapping-spheroids shape parametrization allowing one an independent variation of deformations in the parent and daughter clusters.
Ab-initio Hartree-Fock study of tritium desorption from Li{sub 2}O
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)
Kjærgaard, Thomas; Jørgensen, Poul; Thorvaldsen, Andreas;
2009-01-01
-orbital density-matrix based formulation of response theory and use London atomic orbitals to parametrize the magnetic field dependence. It yields a computational procedure which is both gauge-origin independent and suitable for linear-scaling at the level of time-dependent Hartree-Fock and density functional......A Lagrangian approach has been used to derive gauge-origin independent expressions for two properties that rationalize magneto-optical activity, namely the Verdet constant V(ω) of the Faraday effect and the B term of magnetic circular dichroism. The approach is expressed in terms of an atomic...... theory. The formulation includes a modified preconditioned conjugated gradient algorithm, which projects out the excited state component from the solution to the linear response equation. This is required when solving one of the response equations for the determination of the B term and divergence...
On the problem of representability and the Bogolyubov-Hartree-Fock theory
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
Akamatsu, Hirofumi; Kumagai, Yu; Oba, Fumiyasu; Fujita, Koji; Murakami, Hideo; Tanaka, Katsuhisa; Tanaka, Isao
2011-06-01
A superexchange mechanism between Eu2+ 4f spins via the 3d states of nonmagnetic Ti4+ ions is proposed through first-principles calculations based on a hybrid Hartree-Fock density functional approach to explain G-type antiferromagnetism in EuTiO3. This mechanism is supported by systematic calculations for related Eu2+-based perovskite oxides. In EuTiO3, the competition between the antiferromagnetic superexchange and an indirect ferromagnetic exchange via the Eu 5d states leads to a delicate balance between antiferromagnetic and ferromagnetic phases. The superexchange mechanism involving the Ti 3d states hints at the microscopic origin of the strong spin-lattice coupling in EuTiO3.
Potential energy curves for Mo2: multi-component symmetry-projected Hartree-Fock and beyond
Bytautas, Laimutis; Jiménez-Hoyos, Carlos A.; Rodríguez-Guzmán, R.; Scuseria, Gustavo E.
2014-07-01
The molybdenum dimer is an example of a transition metal system with a formal sextuple bond that constitutes a challenging case for ab initio quantum chemistry methods. In particular, the complex binding pattern in the Mo2 molecule requires a high-quality description of non-dynamic and dynamic electron correlation in order to yield the correct shape of the potential energy curve. The present study examines the performance of a recently implemented multi-component symmetry projected Hartree-Fock (HF) approach. In this work, the spin and spatial symmetries of a trial wavefunction written in terms of non-orthogonal Slater determinants are deliberately broken and then restored in a variation-after-projection framework. The resulting symmetry-projected HF wavefunctions, which possess well-defined quantum numbers, can account for static and some dynamic correlations. A single symmetry-projected configuration in a D∞hS-UHF or a D∞hKS-UHF framework offers a reasonable description of the potential energy curve of Mo2, though the binding energy is too small for the former. Our multi-component strategy offers a way to improve on the single configuration result in a systematic way towards the exact wavefunction: in the def2-TZVP basis set considered in this study, a 7-determinant multi-component D∞hS-UHF approach yields a bond length of 2.01 Å, in good agreement with experimental results, while the predicted binding energy is 39.2 mhartree. The results of this exploratory study suggest that a multi-component symmetry-projected HF stategy is a promising alternative in a high-accuracy description of the electronic structure of challenging systems. We also present and discuss some benchmark calculations based on the CEEIS-FCI (correlation energy extrapolation by intrinsic scaling - full configuration interaction) method for selected geometries.
Neese, Frank
2007-10-28
The zero-field splitting (ZFS) (expressed in terms of the D tensor) is the leading spin-Hamiltonian parameter for systems with a ground state spin S>12. To first order in perturbation theory, the ZFS arises from the direct spin-spin dipole-dipole interaction. To second order, contributions arise from spin-orbit coupling (SOC). The latter contributions are difficult to treat since the SOC mixes states of different multiplicities. This is an aspect of dominant importance for the correct prediction of the D tensor. In this work, the theory of the D tensor is discussed from the point of view of analytic derivative theory. Starting from a general earlier perturbation treatment [F. Neese and E. I. Soloman, Inorg. Chem. 37, 6568 (1998)], straightforward response equations are derived that are readily transferred to the self-consistent field (SCF) Hartree-Fock (HF) or density functional theory (DFT) framework. The main additional effort in such calculations arises from the solution of nine sets of nonstandard coupled-perturbed SCF equations. These equations have been implemented together with the spin-orbit mean-field representation of the SOC operator and a mean-field treatment of the direct spin-spin interaction into the ORCA electronic structure program. A series of test calculations on diatomic molecules with accurately known zero-field splittings shows that the new approach corrects most of the shortcomings of previous DFT based methods and, on average, leads to predictions within 10% of the experimental values. The slope of the correlation line is essentially unity for the B3LYP and BLYP functionals compared to approximately 0.5 in previous treatments.
Adaptive multi-resolution 3D Hartree-Fock-Bogoliubov solver for nuclear structure
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
The classical limit of the time dependent Hartree-Fock equation. I. The Weyl symbol of the solution
Amour, Laurent; Nourrigat, Jean
2011-01-01
We study the time evolution of the Weyl symbol of a solution of the time dependent Hartree Fock equation, assuming that for t=0, it has a Weyl symbol which is integrable in the phase space, such as all its derivatives. We prove that the solution has the same property for all t, and we give an asymptotic expansion, in L1 sense, of this Weyl symbol.
Systematic study of even-even nuclei with Hartree-Fock+BCS method using Skyrme SIII force
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)
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.
The Hartree-Fock exchange effect on the CO adsorption by the boron nitride nanocage
Vessally, E.; Soleimani-Amiri, S.; Hosseinian, A.; Edjlali, L.; Bekhradnia, A.
2017-03-01
We studied the effect of Hartree-Fock (HF) exchange percentage of a density functional on the adsorption properties and electronic sensitivity of the B12N12 nanocluster to CO molecule. It was found that by an increase in the %HF, the LUMO level is nearly constant while the HOMO level is strongly stabilized, expanding the HOMO-LUMO gap (Eg). Also, the volume of the all structures decreased and the sensitivity of the B12N12 is slightly increased to CO molecule. For the pristine B12N12 cluster, the B66 and B64 bonds are about 1.43 and 1.49 Å at 10% HF, and 1.23 and 1.26 Å at 100% HF, respectively. The HF exchange between 10-20% may predict an accurate Eg for the B12N12 system. We concluded that functionals with a large %HF such as M06-HF, and M06-2X may significantly overestimate the Eg, and bond strength. We obtained a parabolic relationship between the %HF and the adsorption energy of CO molecule on the B12N12 cluster. Also, an increase in the %HF predicts a larger charge transfer from the CO molecule to the cage.
Exact exchange potential evaluated solely from occupied Kohn-Sham and Hartree-Fock solutions
Cinal, M
2011-01-01
The reported new algorithm determines the exact exchange potential v_x in a iterative way using energy and orbital shifts (ES, OS) obtained - with finite-difference formulas - from the solutions (occupied orbitals and their energies) of the Hartree-Fock-like equation and the Kohn-Sham-like equation, the former used for the initial approximation to v_x and the latter - for increments of ES and OS due to subsequent changes of v_x. Thus, solution of the differential equations for OS, used by Kummel and Perdew (KP) [Phys. Rev. Lett. 90, 043004 (2003)], is avoided. The iterated exchange potential, expressed in terms of ES and OS, is improved by modifying ES at odd iteration steps and OS at even steps. The modification formulas are related to the OEP equation (satisfied at convergence) written as the condition of vanishing density shift (DS) - they are obtained, respectively, by enforcing its satisfaction through corrections to approximate OS and by determining optimal ES that minimize the DS norm. The proposed met...
Angular-momentum projection for Hartree-Fock and RPA with realistic interactions
Erler, Bastian; Roth, Robert [Institut fuer Kernphysik, TU Darmstadt (Germany)
2012-07-01
Hartree-Fock (HF) with a Hamiltonian constructed from similarity transformed realistic NN potentials plus 3N contact interactions provides a good starting point for the description of closed shell nuclei. In conjunction with Many-Body-Perturbation-Theory, experimental ground-state energies and radii are well reproduced. To describe collective excitations, the Random-Phase-Approximation (RPA) is the method of choice. Beyond closed shells, e.g. in the sd-shell region, ground-states might exhibit intrinsic deformation, resulting in HF states where angular-momentum ceases to be a good quantum number. Lab-frame observables, like ground-state energies or rotational bands can be recovered from the intrinsic states via angular-momentum projection. We study axially deformed even-even sd-shell nuclei, namely {sup 20}Ne, {sup 28}Si and {sup 32}S. Starting from a HF ground state obtained by exact angular-momentum projection, we use the RPA to study collective excitations. The transition strengths obtained from the RPA are projected to good angular momentum in an exact formalism, without resorting to popular approximations. We investigate the effect of deformed intrinsic states on giant resonances.
Aryal, M. M.; Maharjan, N. B.; Paudyal, D. D.; Mishra, D. R.; Byahut, S. R.; Scheicher, R. H.; Badu, S. R.; Jeong, J.; Chow, Lee; Das, T. P.
2008-03-01
Using the first-principles Hartree-Fock Cluster Procedure, we have studied the electronic structures of pure chain like Selenium and Tellurium, pure ring structured Selenium, Tellurium impurity in chain and ring-structured Selenium and Selenium impurity in chain-structured Tellurium chain. For our investigations in all the systems we have carried out convergence studies with respect to variational basis set sizes,sizes of clusters and electron correlation effects using many-body perturbation theory. Using our calculated electronic field-gradient parameters q in the pure chain systems and employing the experimental quadrupole coupling constants (e^2qQ), the values Q(^77Se)=(0.50±0.04) 10-28 m^2 and Q(^125Te)=-(0.2±0.02) 10-28m^2. Results will also be presented for the asymmetry parameters η for the pure chain systems and the e^2qQ and η for ^77Se in selenium ring. Our calculated values for e^2qQ and η for the impurity systems will also be presented and compared with available experimental data and earlier theoretical results.
Hartree-Fock Many-Body Perturbation Theory for Nuclear Ground-States
Tichai, Alexander; Binder, Sven; Roth, Robert
2016-01-01
We investigate the order-by-order convergence behavior of many-body perturbation theory (MBPT) as a simple and efficient tool to approximate the ground-state energy of closed-shell nuclei. To address the convergence properties directly, we explore perturbative corrections up to 30th order and highlight the role of the partitioning for convergence. The use of a simple Hartree-Fock solution to construct the unperturbed basis leads to a convergent MBPT series for soft interactions, in contrast to, e.g., a harmonic oscillator basis. For larger model spaces and heavier nuclei, where a direct high-order MBPT calculation in not feasible, we perform third-order calculation and compare to advanced ab initio coupled-cluster calculations for the same interactions and model spaces. We demonstrate that third-order MBPT provides ground-state energies for nuclei up into tin isotopic chain that are in excellent agreement with the best available coupled-cluster results at a fraction of the computational cost.
Coordinate-Space Hartree-Fock-Bogoliubov Solvers for Superfluid Fermi Systems in Large Boxes
Pei, J. C. [University of Tennessee (UTK) and Oak Ridge National Laboratory (ORNL); Fann, George I [ORNL; Harrison, Robert J [ORNL; Nazarewicz, W. [University of Tennessee (UTK) and Oak Ridge National Laboratory (ORNL); Hill, Judith C [ORNL; Galindo, Diego A [ORNL; Jia, Jun [ORNL
2012-01-01
The self-consistent Hartree-Fock-Bogoliubov problem in large boxes can be solved accurately in the coordinate space with the recently developed solvers HFB-AX (2D) and MADNESS-HFB (3D). This is essential for the description of superfluid Fermi systems with complicated topologies and significant spatial extend, such as fissioning nuclei, weakly-bound nuclei, nuclear matter in the neutron star rust, and ultracold Fermi atoms in elongated traps. The HFB-AX solver based on B-spline techniques uses a hybrid MPI and OpenMP programming model for parallel computation for distributed parallel computation, within a node multi-threaded LAPACK and BLAS libraries are used to further enable parallel calculations of large eigensystems. The MADNESS-HFB solver uses a novel multi-resolution analysis based adaptive pseudo-spectral techniques to enable fully parallel 3D calculations of very large systems. In this work we present benchmark results for HFB-AX and MADNESS-HFB on ultracold trapped fermions.
On the problem of representability and the Bogolyubov-Hartree-Fock theory
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
A simple and efficient dispersion correction to the Hartree-Fock theory.
Yoshida, Tatsusada; Mashima, Akira; Sasahara, Katsunori; Chuman, Hiroshi
2014-02-15
One of the most challenging problems in computational chemistry and in drug discovery is the accurate prediction of the binding energy between a ligand and a protein receptor. It is well known that the binding energy calculated with the Hartree-Fock molecular orbital theory (HF) lacks the dispersion interaction energy that significantly affects the accuracy of the total binding energy of a large molecular system. We propose a simple and efficient dispersion energy correction to the HF theory (HF-Dtq). The performance of HF-Dtq was compared with those of several recently proposed dispersion corrected density functional theory methods (DFT-Ds) as to the binding energies of 68 small non-covalent complexes. The overall performance of HF-Dtq was found to be nearly equivalent to that of more sophisticated B3LYP-D3. HF-Dtq will thus be a useful and powerful method for accurately predicting the binding energy between a ligand and a protein, albeit it is a simple correction procedure based on HF.
Parallel and Low-Order Scaling Implementation of Hartree-Fock Exchange Using Local Density Fitting.
Köppl, Christoph; Werner, Hans-Joachim
2016-07-12
Calculations using modern linear-scaling electron-correlation methods are often much faster than the necessary reference Hartree-Fock (HF) calculations. We report a newly implemented HF program that speeds up the most time-consuming step, namely, the evaluation of the exchange contributions to the Fock matrix. Using localized orbitals and their sparsity, local density fitting (LDF), and atomic orbital domains, we demonstrate that the calculation of the exchange matrix scales asymptotically linearly with molecular size. The remaining parts of the HF calculation scale cubically but become dominant only for very large molecular sizes or with many processing cores. The method is well parallelized, and the speedup scales well with up to about 100 CPU cores on multiple compute nodes. The effect of the local approximations on the accuracy of computed HF and local second-order Møller-Plesset perturbation theory energies is systematically investigated, and default values are established for the parameters that determine the domain sizes. Using these values, calculations for molecules with hundreds of atoms in combination with triple-ζ basis sets can be carried out in less than 1 h, with just a few compute nodes. The method can also be used to speed up density functional theory calculations with hybrid functionals that contain HF exchange.
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.
Rayka, Milad; Shahbazian, Shant
2016-01-01
In this communication, an effective set of the Hartree-Fock equations are derived only for electrons of the muonic systems, i.e., molecules containing a positively charged muon, conceiving the muon as a quantum oscillator. In these equations, a non-Coulombic potential is added to the orthodox coulomb and exchange potential energy terms, which describes the interaction of the muon and electrons effectively. The explicit form of the effective potential depends on the nature of muon vibrations and is derived for a combination of Cartesian Gaussian functions that are 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 the case of MuCN molecule, which results from replacing the proton of HCN molecule with a muon. The developed effective Hartree-Fock 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...
Study of superdeformation at zero spin with Skyrme-Hartree-Fock method
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)
Symbolic computation of the Hartree-Fock energy from a chiral EFT three-nucleon interaction at N 2LO
Gebremariam, B.; Bogner, S. K.; Duguet, T.
2010-06-01
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 2LO. 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 summaryProgram title: SymbHFNNN Catalogue identifier: AEGC_v1_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 2LO 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 2LO is cast into a form suitable for an automatic simplification of
Pernpointner, M.
2004-11-01
In this paper we present the third-order extension of the four-component one-particle propagator method in the non-Dyson version of the algebraic diagrammatic construction (ADC) for the calculation of valence ionization energies. Relativistic and electron correlation effects are incorporated consistently by starting from the Dirac-Hamiltonian. The ADC equations derived from the Feynman diagrams can hereby be used in their spin-orbital form and need not be transformed to the spin-free version as required for a nonrelativistic treatment. For the calculation of the constant self-energy contribution the Dyson expansion method was implemented being superior to a perturbational treatment of Σ(∞). The Dirac-Hartree-Fock- (DHF-) ADC(3) was applied to the calculation of valence photoionization spectra of the noble gas atoms, carbon monoxide and ICN now also reproducing spin-orbit features in the spectrum. Comparison with DHF-ADC(2), nonrelativistic ADC(3), and experimental data was made in order to demonstrate the characteristics and performance of the method.
Staker, Joshua T
2013-01-01
We make numerical comparison of spectra from angular-momentum projection on Hartree-Fock states with spectra from configuration-interaction nuclear shell-model calculations, all carried out in the same model spaces (in this case the sd, lower pf, and p-sd_5/2 shells) and using the same input Hamiltonians. We find, unsurprisingly, that the low-lying excitation spectra for rotational nuclides are well reproduced, but the spectra for vibrational nuclides, and more generally the complex specta for odd-A and odd-odd nuclides are less well reproduced in detail.
Miyasita, Mitiyasu, E-mail: miyasita.mitiyasu@gmail.com [Graduate School of Science and Engineering, Shinshu University, Ueda 386-8567 (Japan); Higuchi, Katsuhiko [Graduate School of Advanced Science of Matter, Hiroshima University, Higashi-Hiroshima 739-8527 (Japan); Higuchi, Masahiko [Department of Physics, Faculty of Science, Shinshu University, Matsumoto 390-8621 (Japan)
2012-07-15
We present an alternative scheme for calculating the unrestricted Hartree-Fock (HF) equation. The scheme is based on the variational method utilizing the sophisticated basis functions that include no adjustable parameters. The validity of the present scheme is confirmed by actual calculations of the boron and neon atoms. The total energy of the present scheme is lower than that of the conventional restrictive HF equation, but higher than that of the CI method. Also, the resultant wave function satisfies the electron-nucleus cusp condition.
El Aouad, N.; Dobaczewski, J.; Dudek, J.; Li, X.; Luo, W.D.; Molique, H.; Bouguettoucha, A.; Byrski, Th.; Beck, F.A.; Curien, D.; Duchene, G.; Finck, Ch.; Kharraja, B
2000-08-28
Structure of eight experimentally known superdeformed bands in the nucleus {sup 151}Tb is analyzed using the results of the Hartree-Fock and Woods-Saxon cranking approaches. It is demonstrated that far going detailed similarities between the two approaches exist and predictions related to the structure of rotational bands calculated within the two models are nearly parallel. An interpretation scenario for the structure of the superdeformed bands is presented and predictions related to the exit spins are made. Small but systematic discrepancies between experiment and theory, analyzed in terms of the dynamical moments, J{sup (2)}, are shown to exist. These discrepancies can be parametrized in terms of a scaling factor f, such that modifications J{sup (1),(2)}{yields}fJ{sup (1),(2)} together with the implied scaling of the frequencies {omega}{yields}f{sup -1}{omega}, correspond systematically better with the experimental data (f{approx_equal}0.9) for both the Woods-Saxon and Hartree-Fock with Skyrme SkM* interactions. The pairing correlations taken into account by using the particle-number-projection technique are shown to increase the disagreement. Sources of these systematic discrepancies are discussed -- they are most likely related to the not yet optimal parametrization of the nuclear interactions used.
Ragot, Sébastien
2008-04-01
The ground-state Hartree-Fock (HF) wavefunction of Hooke's atom is not known in closed form, contrary to the exact solution. The single HF orbital involved has thus far been studied using expansion techniques only, leading to slightly disparate energies. Therefore, the present letter aims at proposing alternative definitions of the HF wavefunction. First, the HF limit is ascertained using a simple expansion, which makes it possible to formulate explicit expressions of HF properties. The resulting energy, 2.038 438 871 8 Eh, is found stable at the tenth digit. Second and more instructive, an analysis of the Hartree equation makes it possible to infer a remarkably simple and accurate HF orbital, i.e., φHF(r)=nHFe-αr2√r2+β2, leading to an energy exceeding by 5.76×10-7 Eh only the above HF limit. This orbital makes it possible to obtain (near) Hartree-Fock properties in closed form, which in turn enables handy comparisons with exact quantities.
Small, David W; Sundstrom, Eric J; Head-Gordon, Martin
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 + H2 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 O2, 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.
Cui, Yao; Bulik, Ireneusz W; Jiménez-Hoyos, Carlos A; Henderson, Thomas M; Scuseria, Gustavo E
2013-10-21
We study the spectra of the molecular orbital Hessian (stability matrix) and random-phase approximation (RPA) Hamiltonian of broken-symmetry Hartree-Fock solutions, focusing on zero eigenvalue modes. After all negative eigenvalues are removed from the Hessian by following their eigenvectors downhill, one is left with only positive and zero eigenvalues. Zero modes correspond to orbital rotations with no restoring force. These rotations determine states in the Goldstone manifold, which originates from a spontaneously broken continuous symmetry in the wave function. Zero modes can be classified as improper or proper according to their different mathematical and physical properties. Improper modes arise from symmetry breaking and their restoration always lowers the energy. Proper modes, on the other hand, correspond to degeneracies of the wave function, and their symmetry restoration does not necessarily lower the energy. We discuss how the RPA Hamiltonian distinguishes between proper and improper modes by doubling the number of zero eigenvalues associated with the latter. Proper modes in the Hessian always appear in pairs which do not double in RPA. We present several pedagogical cases exemplifying the above statements. The relevance of these results for projected Hartree-Fock methods is also addressed.
Weimer, Martin; Hieringer, Wolfgang; Sala, Fabio Della; Goerling, Andreas
2005-02-21
The electronic and optical properties of extended functionalized carbyne chains, polyynes and cumulenes, are investigated with the localized Hartree-Fock method, with conventional Kohn-Sham methods, and with the Hartree-Fock method. It is found that even for very long polyynes the carbon-carbon bond lengths within a polyyne alternate while for long cumulenes no carbon-carbon bond length alternation occurs. Polyynes exhibit a finite HOMO-LUMO gap even if they become very long while cumulenes are found to become metallic in the limit of long chain lengths. The geometry and the electro-optical properties of polyynes cannot be influenced significantly by simple sp-{sigma}-bonded end groups. The optically active {sup 1}{sigma}{sub u}{sup +} <- X{sup 1}{sigma}{sub g}{sup +} electronic transition in polyynes is investigated by time-dependent density-functional theory (TDDFT). The known systematic underestimation of excitation energies in large chain-like systems by TDDFT methods is also found for the systems considered here. Deficiencies in the commonly used exchange-correlation kernels are identified as the main source of this shortcoming of TDDFT methods. Unphysical Coulomb self-interactions present in conventional Kohn-Sham potentials seem to not contribute significantly to the problem.
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.
Goerigk, Lars; Collyer, Charles A; Reimers, Jeffrey R
2014-12-18
We demonstrate the importance of properly accounting for London dispersion and basis-set-superposition error (BSSE) in quantum-chemical optimizations of protein structures, factors that are often still neglected in contemporary applications. We optimize a portion of an ensemble of conformationally flexible lysozyme structures obtained from highly accurate X-ray crystallography data that serve as a reliable benchmark. We not only analyze root-mean-square deviations from the experimental Cartesian coordinates, but also, for the first time, demonstrate how London dispersion and BSSE influence crystallographic R factors. Our conclusions parallel recent recommendations for the optimization of small gas-phase peptide structures made by some of the present authors: Hartree-Fock theory extended with Grimme's recent dispersion and BSSE corrections (HF-D3-gCP) is superior to popular density functional theory (DFT) approaches. Not only are statistical errors on average lower with HF-D3-gCP, but also the convergence behavior is much better. In particular, we show that the BP86/6-31G* approach should not be relied upon as a black-box method, despite its widespread use, as its success is based on an unpredictable cancellation of errors. Using HF-D3-gCP is technically straightforward, and we therefore encourage users of quantum-chemical methods to adopt this approach in future applications.
Simenel, Cédric; Kedziora, David J
2011-01-01
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 {\\textsc{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...
Kalinowski, Jaroslaw; Wennmohs, Frank; Neese, Frank
2017-07-11
A resolution of identity based implementation of the Hartree-Fock method on graphical processing units (GPUs) is presented that is capable of handling basis functions with arbitrary angular momentum. For practical reasons, only functions up to (ff|f) angular momentum are presently calculated on the GPU, thus leaving the calculation of higher angular momenta integrals on the CPU of the hybrid CPU-GPU environment. Speedups of up to a factor of 30 are demonstrated relative to state-of-the-art serial and parallel CPU implementations. Benchmark calculations with over 3500 contracted basis functions (def2-SVP or def2-TZVP basis sets) are reported. The presented implementation supports all devices with OpenCL support and is capable of utilizing multiple GPU cards over either MPI or OpenCL itself.
Thiele, Robert; Son, Sang-Kil [Center for Free-Electron Laser Science, DESY, 22607 Hamburg (Germany); Ziaja, Beata [Center for Free-Electron Laser Science, DESY, 22607 Hamburg (Germany); Institute of Nuclear Physics, Polish Academy of Sciences, Radzikowskiego 152, 31-342 Krakow (Poland); Santra, Robin [Center for Free-Electron Laser Science, DESY, 22607 Hamburg (Germany); Department of Physics, University of Hamburg, 20355 Hamburg (Germany)
2013-07-01
X-ray free-electron lasers (XFELs) are a promising tool for the structural determination of macro- and biomolecules, using coherent diffractive imaging. During imaging, the intense XFEL pulses also efficiently ionize the molecules, so it is important to estimate how the charged environment within the molecule modifies atomic properties, in comparison to the case of an isolated atom. Here, we apply the XATOM toolkit to obtain predictions on the modified ionization thresholds and rates of some photoinduced processes in carbon. The Hartree-Fock-Slater model is extended to include the electron screening and ion correlation effects, induced by external charges. With this extended model, we obtain predictions on modifications of orbital energies, photoabsorption cross sections, Auger decay rates, fluorescence emission rates, and atomic scattering factors as a function of the density and temperature of the surrounding charges. Our results have implications for the studies of dynamics within XFEL irradiated samples, in particular for those dedicated to coherent diffraction imaging.
Application of a solvable model to test the accuracy of the time-dependent Hartree-Fock method
Bouayad, N. [Blida Univ. (Algeria). Inst. de Phys.; Zettili, N. [Blida Univ. (Algeria). Inst. de Phys.]|[Department of Physics, King Fahd University of Petroleum and Minerals, Dhahran 31261 (Saudi Arabia)
1996-11-11
This work deals with the application of a solvable model to study the accuracy of a nuclear many-body approximation method. Using a new exactly solvable model, we carry out here a quantitative test of the accuracy of the time-dependent Hartree-Fock (TDHF) method. The application of the TDHF method to the model reveals that the model is suitable for describing various forms of collective motion: harmonic and anharmonic oscillations as well as rotations. We then show that, by properly quantizing the TDHF results, the TDHF approximation method yields energy spectra that are in very good agreement with their exact counterparts. This work shows that the model offers a rich and comprehensive framework for studying the various aspects of the TDHF method and also for assessing quantitatively its accuracy. (orig.).
Application of a solvable model to test the accuracy of the time-dependent Hartree-Fock method
Bouayad, Nouredine; Zettili, Nouredine
1996-02-01
This work deals with the application of a solvable model to study the accuracy of a nuclear many-body approximation method. Using a new exactly solvable model, we carry out here a quantitative test of the accuracy of the time-dependent Hartree-Fock (TDHF) method. The application of the TDHF method to the model reveals that the model is suitable for describing various forms of collective motion: harmonic and anharmonic oscillations as well as rotations. We then show that, by properly quantizing the TDHF results, the TDHF approximation method yields energy spectra that are in very good agreement with their exact counterparts. This work shows that the model offers a rich and comprehensive framework for studying the various aspects of the TDHF method and also for assessing quantitatively its accuracy.
Greenman, Loren; Haxton, Daniel J; McCurdy, C William
2016-01-01
We have verified a mechanism for Raman excitation of atoms through continuum levels previously obtained by quantum optimal control using the multi-configurational time-dependent Hartree-Fock (MCTDHF) method. This mechanism, which was obtained at the time-dependent configuration interaction singles (TDCIS) level of theory, involves sequentially exciting an atom from the ground state to an intermediate core-hole state using a long pump pulse, and then transferring this population to the target Raman state with a shorter Stokes pulse. This process represents the first step in a multidimensional x-ray spectroscopy scheme that will provide a local probe of valence electronic correlations. Although at the optimal pulse intensities at the TDCIS level of theory the MCTDHF method predicts multiple ionization of the atom, at slightly lower intensities (reduced by a factor of about 4) the TDCIS mechanism is shown to hold qualitatively. Quantitatively, the MCTDHF populations are reduced from the TDCIS calculations by a f...
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.
Jansík, Branislav; Høst, Stinne; Johansson, Mikael P; Olsen, Jeppe; Jørgensen, Poul; Helgaker, Trygve
2009-07-21
A hierarchical optimisation strategy has been introduced for minimising the Hartree-Fock/Kohn-Sham energy, consisting of three levels (3L): an atom-in-a-molecule optimisation, a valence-basis molecular optimisation, and a full-basis molecular optimisation. The density matrix formed at one level is used as a starting density matrix at the next level with no loss of information. To ensure a fast and reliable convergence to a minimum, the augmented Roothaan-Hall (ARH) algorithm is used in both the valence-basis and full-basis molecular optimisations. The performance of the ARH-3L method is compared with standard optimisation algorithms. Both for efficiency and reliability, we recommend to use the ARH-3L algorithm.
Kuwahara, Riichi; Tadokoro, Yoichi; Ohno, Kaoru
2014-08-28
In this paper, we calculate kinetic and potential energy contributions to the electronic ground-state total energy of several isolated atoms (He, Be, Ne, Mg, Ar, and Ca) by using the local density approximation (LDA) in density functional theory, the Hartree-Fock approximation (HFA), and the self-consistent GW approximation (GWA). To this end, we have implemented self-consistent HFA and GWA routines in our all-electron mixed basis code, TOMBO. We confirm that virial theorem is fairly well satisfied in all of these approximations, although the resulting eigenvalue of the highest occupied molecular orbital level, i.e., the negative of the ionization potential, is in excellent agreement only in the case of the GWA. We find that the wave function of the lowest unoccupied molecular orbital level of noble gas atoms is a resonating virtual bound state, and that of the GWA spreads wider than that of the LDA and thinner than that of the HFA.
Smeyers, Y.G.; Delgado-Barrio, G.
1976-05-01
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.
Sil, T; Reinhard, P G; Shlomo, S; Sil, Tapas
2006-01-01
We provide accurate assessments of the consequences of violations of self-consistency in Hartree-Fock (HF) based random phase approximation (RPA) calculations of the centroid energy $E_{cen}$ of isoscalar and isovector giant resonances of multi-polarities $L=0-3$ in a wide range of nuclei. This is done by carrying out highly accurate HF-RPA calculations neglecting the particle-hole (ph) spin-orbit or Coulomb interaction in the RPA and comparing with the fully self-consistent HF-RPA results. We find that the shifts in the value of $E_{cen}$ due to self-consistency violation associated with the spin-orbit and Coulomb interactions are comparable or larger than the current experimental errors in $E_{cen}$.
Relativity and the chemistry of UF6 : A molecular Dirac-Hartree-Fock-CI study
de Jong, W.A.; Nieuwpoort, W.C
1996-01-01
The electronic structure and bonding of UF6 and UF6- are studied within a relativistic framework using the MOLFDIR program package. A stronger bonding but more ionic molecule is found if one compares the relativistic with the nonrelativistic results. The first peak in the photoelectron spectrum of
Salah, Wa'el; Hassouneh, Ola
2017-04-01
We computed the energy levels, oscillator strengths f_{ij}, the radiative transition rates A_{ij}, the Landé g -factor, the magnetic dipole moment and the electric quadrupole hyperfine constants of the intermediate Rydberg series ns [k]J ( 4 ≤ n ≤ 6), nd [k]J (3 ≤ n ≤ 4), np [k]J (4 ≤ n ≤ 5) relative to the ground state 3p6 1S0 for neutral argon atom spectra. The values are obtained in the framework of the multiconfiguration Dirac-Hartree-Fock (MCDHF) approach. In this approach, Breit interaction, leading quantum electrodynamics (QED) effects and self-energy correction are taken into account. Moreover, these spectroscopic parameters have been calculated for many levels belonging to the configuration 3p54s, 3p55s, 3p56s, 3p53d, 3p54d, 3p54p, 3p55p as well as for transitions between levels 3p54s-3p54p, 3p54p-3p53d, 3p54p-3p55s, 3p55s-3p55p and 3p55p-3p56s. The large majority of the lines from the 4p-5s and 4p-3d, 5s-5p and 5p-6s transition arrays have been observed and the calculations are consistent with the J -file-sum rule. The obtained theoretical values are compared with previous experimental and theoretical data available in the literature. An overall satisfactory agreement is noticed allowing assessing the reliability of our data.
Gontchar, I. I.; Bhattacharya, R.; Chushnyakova, M. V.
2014-03-01
We calculate the capture (fusion) cross sections for nine reactions involving spherical nuclei: O16 + O16, Si28, Zr92, Sm144, Pb208; Si28 + Si28, Zr92, Pb208; S32 + Pb208. For six of them precision data are available in the literature. Analysis of these precision data within the framework of the single-barrier penetration model based on the Woods-Saxon profile for the strong nucleus-nucleus interaction potential (SnnP) gave rise to the problem of the apparently large diffuseness of the SnnP [Newton et al., Phys. Rev. C 70, 024605 (2004), 10.1103/PhysRevC.70.024605]. Our fluctuation-dissipation trajectory model is based on the double-folding approach with the density-dependent M3Y NN forces including the finite-range exchange part. For the nuclear matter density the Skyrme-Hartree-Fock approach including the tensor interaction is applied. The resulting nucleus-nucleus potential possesses rather small (normal) diffuseness. The strength of the radial friction KR is used as the free parameter of the model. It turns out that for four of the five reactions induced by O16 (except O16 + Pb208) the calculated cross sections cannot be brought into agreement with the data within the experimental errors. This suggests that the calculated nuclear density is incorrect for O16. For the reactions not involving O16 and, surprisingly, for the O16 + Pb208 reaction the agreement with the data within 2-5% is achieved at KR=1.2×10-2 to 3.0×10-2MeV-1zs which is in accord with the previous works.
Yoshida, Tatsusada; Hayashi, Takahisa; Mashima, Akira; Sasahara, Katsunori; Chuman, Hiroshi
2016-01-15
Accurate prediction of the intermolecular interaction energy (ΔEbind) has been a challenging and serious problem. Current in silico drug screening demands efficient and accurate evaluation of ΔEbind for ligands and their target proteins. It is desirable that ΔEbind including the dispersion interaction energy (Edisp) is calculated using a post-Hartree-Fock (HF) theory, such as the high-order coupled-cluster one, with a larger basis set. However, it remains computationally too expensive to apply such a one to large molecular systems. As another problem, it is necessary to consider the contribution of the basis set superposition error (BSSE) in calculation of ΔEbind. In Bioorg. Med. Chem. Lett. 2014 and 2015, we proposed simple and efficient corrections of dispersion and BSSE for the HF theory, which is not able to express the dispersion interaction energy correctly. The current Letter, as the final one in the series, aims to verify the HF theory enhanced by the dispersion correction (HF-Dtq) in the light of reproducibility of 'accurate' intermolecular ligand-protein interaction energy values, with comprehensive comparison with the MP2 and recently proposed various DFT-D theories. Taking ΔEbind calculated with the coupled-cluster theory coupled with a complete basis set as a reference, ΔEbind of over a hundred small sized noncovalent complexes as well as real ligand-protein complexes models was systematically examined in terms of accuracy and computational cost. The comprehensive comparison in the current work showed that HF-Dtq is a practical and reliable approach for in silico drug screening and quantitative structure-activity relationships.
Phillips, Jordan J; Peralta, Juan E
2011-01-21
We assess the dependence of magnetic exchange couplings on the variation of Hartree-Fock exchange (HFX) admixture in global hybrid functionals and the range-separation parameter ω in range-separated hybrid functionals in a set of 12 spin-1/2 binuclear transition metal complexes. The global hybrid PBEh (hybrid Perdew-Burke-Ernzerhof) and range-separated hybrids HSE (Heyd-Scuseria-Ernzerhof) and LC-ωPBE (long-range corrected hybrid PBE) are employed for this assessment, and exchange couplings are calculated from energy differences within the framework of the spin-projected approach. It is found that these functionals perform optimally for magnetic exchange couplings with 35% HFX admixture for PBEh, ω = 0.50 a.u.(-1) for LC-ωPBE, and ω at or near 0.0 a.u.(-1) for HSE (which corresponds to PBEh). We find that in their standard respective forms, LC-ωPBE slightly outperforms PBEh, while PBEh with 35% HFX yields exchange couplings closer to experiment than those of LC-ωPBE with ω = 0.50 a.u.(-1). Additionally, we show that the profile of exchange couplings with respect to ω in HSE is appreciably flat from 0 to 0.2 a.u.(-1). This combined with the fact that HSE is computationally more tractable than global hybrids makes HSE an attractive alternative for the evaluation of exchange couplings in extended systems. These results are rationalized with respect to how varying the parameters within these functionals affects the delocalization of the magnetic orbitals, and conclusions are made regarding the relative importance of range separation versus global mixing of HFX for the calculation of exchange couplings.
Langhoff, S. R.; Scott, W. R.; Suzuki, N.; Chong, D. P.
1979-01-01
Ordinary Rayleigh-Schroudinger perturbation theory with Moller-Plesset (RSMP) partitioning is used to calculate second- and third-order correlation corrections to the CHF polarizability and dipole moment of the water molecule by a finite-field procedure. Pade approximants are found to be useful in accelerating the convergence of the property perturbation expansions. Field-induced polarization functions suitable for polarizability calculations are determined. The average polarizability calculated, neglecting vibrational averaging, with Dunning's (9s5p/4s-4s2p/2s) contracted GTO basis set augmented by field-induced lslp2d/lp polarization functions is within 3 per cent of the experimental result. Correlation corrections to the dipole moment and polarizability of the water molecule calculated by the finite-field RSMP and single + double excitation CI(SDCI) methods for the same basis set are found to be in close agreement. The RSMP approach has the advantages of being size-consistent and of being capable of greater efficiency than the SCDI method. Comparative calculations carried out using Epstein-Nesbet partitioning show that through third order RSEN correlation perturbation expansions for the dipole moment and polarizability are less rapidly convergent than RSMP expansions. However, reasonable accord with RSMP results can be achieved by using Pade approximants to accelerate the convergence of RSEN energy perturbation expansions. The convergence of RSMP property correlation expansions based on the zeroth-order uncoupled-Hartree-Fock (UCHF) and coupled-Hartree-Fock (CHF) approximations are compared through third order. Whereas the CHF + RSMP expansions are for practical purposes fully converged, the UCHF + RSMP expansions are not adequately converged.
Karasiev, V.; López-Boada, R.
1998-09-01
The line-integral method developed by van Leeuwen and Baerends [Phys. Rev. A 51, 170 (1995)] is applied to the calculation of the differences of correlation energy functional values ΔEDFTc=EDFTc[ρHF]- EDFTc[ρexact], where ρHF is the Hartree-Fock density and ρexact is the near-exact one (DFT is density-functional theory). From the Kohn-Sham wave functions yielding Hartree-Fock and the near-exact densities, the corresponding noninteracting kinetic energies and the exchange energies are calculated. An approximate relation between EDFTc[ρHF] and the conventional quantum chemistry correlation energy is presented, accurate to <=4μ hartree for the isoelectronic series of He, and Li, and for the Be atom.
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.
$\\it{Ab}$ $\\it{initio}$ nuclear many-body perturbation calculations in the Hartree-Fock basis
Hu, Baishan; Sun, Zhonghao; Vary, James P; Li, Tong
2016-01-01
Starting from realistic nuclear forces, the chiral N$^3$LO and JISP16, we have applied many-body perturbation theory (MBPT) to the structure of closed-shell nuclei, $^4$He and $^{16}$O. The two-body N$^3$LO interaction is softened by a similarity renormalization group transformation while JISP16 is adopted without renormalization. The MBPT calculations are performed within the Hartree-Fock (HF) bases. The angular momentum coupled scheme is used, which can reduce the computational task. Corrections up to the third order in energy and up to the second order in radius are evaluated. Higher-order corrections in the HF basis are small relative to the leading-order perturbative result. Using the anti-symmetrized Goldstone diagram expansions of the wave function, we directly correct the one-body density for the calculation of the radius, rather than calculate corrections to the occupation propabilities of single-particle orbits as found in other treatments. We compare our results with other methods where available a...
Dubey, Archana; Badu, S. R.; Scheicher, R. H.; Sahoo, N.; Pink, R. H.; Schulte, A.; Saha, H. P.; Chow, Lee; Nagamine, K.; Das, T. P.
2008-03-01
The observation of paramagnetic susceptibility [1] in Oxy-Hb from measurements over a broad temperature range has stimulated interest in the occurrence of a low-lying excited triplet state close to the ground singlet state of Oxy-Hb. An earlier theoretical investigation [2] has shown the existence of such a triplet state providing support to the interpretation of the susceptibility data [1]. Support for the low-lying excited triplet state has been augmented recently [3] from microscopic relaxation rate measurements for muon attached to the heme group of Oxy-Hb. We are studying by first principles Hartree-Fock procedure the energies and the electronic wave functions of the ground and triplet states and the quantitative theoretical prediction of muon magnetic hyperfine interaction in room temperature μSR measurements on Oxy-Hb. Results will be presented for hyperfine interactions of muon and other nuclei in Oxy-Hb [1] M.Cerdonio etal. Proc. Nat. Acad. Sci USA 75, 4916(1978). [2] Zalek S. Herman and Gilda H Loew JACS 102, 1815(1980).[ 3] K. Nagamine etal Proc. Jpn. Acad.Ser.B 83,120(2007).
Xu Sun; You-song Gu; Xue-qiang Wang; Yue Zhang
2012-01-01
The electronic properties and stability of Li-doped ZnO with various defects have been studied by calculating the electronic structures and defect formation energies via first-principles calculations using hybrid Hartree-Fock and density functional methods.The results from formation energy calculations show that Li pair complexes have the lowest formation energy in most circumstances and they consume most of the Li content in Li doped ZnO,which make the p-type conductance hard to obtain.The formation of Li pair complexes is the main obstacle to realize p-type conductance in Li doped ZnO.However,the formation energy of Lizn decreases as environment changes from Zn-rich to O-rich and becomes more stable than that of Li-pair complexes at highly O-rich environment.Therefore,p-type conductance can be obtained by Li doped ZnO grown or post annealed in oxygen rich atmosphere.
Saravanan, S. P.; Sankar, A.; Parimala, K.
2017-01-01
The complete structural and vibrational analysis of the 2,5-Difluoronitrobenzene (DNB) was carried out by Hartree-Fock (HF) and density functional theory (DFT) method (B3LYP) with 6-311++G (d,p) basis set. The fundamental vibrations are assigned on the basis of the potential energy distribution (PED) of the vibrational modes calculated with scaled quantum mechanics (SQM) method. Using the time-dependent density functional theory (TD-DFT) method, electronic absorption spectra of the title compound have been predicted and a good agreement with the experimental ones is determined. 13C and 1H NMR spectra were recorded and chemical shifts of the molecule were calculated using the gauge independent atomic orbital (GIAO) method. The hyperconjugative interaction energy (E(2)) and electron densities of donor (i) and acceptor (j) bonds were calculated using natural bond orbital (NBO) analysis. In addition, molecular electrostatic potential (MEP) and atomic charges were calculated using B3LYP/6-311++G (d,p) level of theory. Moreover, thermodynamic properties (heat capacities, entropy, enthalpy and Gibb's free energy) of the title compound at different temperatures were calculated.
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
Goriely, S.; Chamel, N.; Pearson, J. M.
2016-03-01
Extending our earlier work, a new family of three Hartree-Fock-Bogoliubov (HFB) mass models, labeled HFB-30, HFB-31, and HFB-32, is presented, along with their underlying interactions, BSk30, BSk31, and BSk32, respectively. The principle new feature is a purely phenomenological pairing term that depends on the density gradient. This enables us to have a bulk pairing term that is fitted to realistic nuclear-matter calculations in which for the first time the self-energy corrections are included, while the behavior of the nucleon effective masses in asymmetric homogeneous nuclear matter is significantly improved. Furthermore, in the particle-hole channel all the highly realistic constraints of our earlier work are retained. In particular, the unconventional Skyrme forces containing t4 and t5 terms are still constrained to fit realistic equations of state of neutron matter stiff enough to support the massive neutron stars PSR J1614-2230 and PSR J0348+0432. All unphysical long-wavelength spin and spin-isospin instabilities of nuclear matter, including the unphysical transition to a polarized state in neutron-star matter, are eliminated. Our three interactions are characterized by values of the symmetry coefficient J of 30, 31, and 32 MeV, respectively. The best fit to the database of 2353 nuclear masses is found for model HFB-31 (J =31 MeV ) with a model error of 0.561 MeV. This model also fits the charge-radius data with an root-mean-square error of 0.027 fm.
Shell evolution at N=20 in the constrained relativistic mean field approach
无
2008-01-01
The shell evolution at N = 20, a disappearing neutron magic number observed experimentally in very neutron-rich nuclides, is investigated in the constrained relativistic mean field (RMF) theory. The trend of the shell closure observed experimentally towards the neutron drip-line can be reproduced. The predicted two-neutron separation energies, neutron shell gap energies and deformation parameters of ground states are shown as well. These results are compared with the recent Hartree-Fock-Bogliubov (HFB-14) model and the available experimental data. The perspective towards a better understanding of the shell evolution is discussed.
Chushnyakova, M. V.; Bhattacharya, R.; Gontchar, I. I.
2014-07-01
Background: In our previous paper [Gontchar et al., Phys. Rev. C 89, 034601 (2014), 10.1103/PhysRevC.89.034601] we have calculated the capture (fusion) excitation functions for several reactions with O16,Si28, and S32 nuclei as the projectiles and Zr92,Sm144, and Pb208 nuclei as the targets. These calculations were performed by using our fluctuation-dissipation trajectory model based on the double-folding approach with the density-dependent M3Y NN forces that include the finite range exchange part. For the nuclear matter density the Hartree-Fock approach with the SKP coefficient set that includes the tensor interaction was applied. It was found that for most of the reactions induced by O16 the calculated cross sections cannot be brought into agreement with the data. This suggested that the deviation in the calculated nuclear density for O16 from the experimental one was crucial. Method: The SKX parameter set is used to obtain the nuclear densities. Reactions with C12 and S36 as the projectiles and Pb204 as the target are included in the analysis in addition to those of the previous paper. Only data that correspond to the collision energy Ec.m.>1.1UB0 (UB0 is the s-wave fusion barrier height) are included in the analysis. The radial friction strength KR is used as the individual adjustable parameter for each reaction. Results: For all 13 reactions (91 points) it is possible to reach an agreement with the experimental fusion cross sections within 10%. Only at ten points does the deviation exceed 5%. The value of KR, which provides the best agreement with the data in general, decreases as the system gets heavier in accord with the previous paper [Gontchar et al., Phys. Rev. C 89, 034601 (2014), 10.1103/PhysRevC.89.034601]. A universal analytical approximation for the dependence of KR upon the Coulomb barrier height is found. Conclusions: The developed model is able to reproduce the above-barrier portion of the fusion excitation function within 5% with a probability of
Simenel, Cédric; Golabek, Cédric; Kedziora, David J.
2011-10-01
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 produce transfermium
Dyall, Kenneth G.
1992-01-01
The effect of omission of two-electron integrals involving basis functions for the small component of the wavefunction on the eigenvalue spectrum in the Dirac-Hartree-Fock problem is studied. From an analysis of the Fock matrix it is shown that omission of these integrals moves the negative-energy states down, not up. Their complete omission does not give rise to intruder states. The appearance of intruder states occurs when only some of the core integrals are omitted, due to the nature of particular contraction schemes used for the core basis functions. Use of radially localized functions rather than atomic functions alleviates the intruder state problem.
Forte, G; March, N H; Pucci, R
2014-01-01
The Hartree-Fock (HF) method, supplemented by low-order Moller-Plesset (MP2) perturbation theory, has been utilized to predict the nuclear geometry, assuming planarity, of a low-lying isomer of the free space cluster BOSi$_2$. The planar structure found at equilibrium geometry is shown to be stable against small amplitude molecular vibrations. Finally, some brief comments are made on the possible relevance of the above free-space cluster geometry to the known B-O defects which limit the improvement of minority carrier lifetime in a form of p-type silicon.
Forte, G.; Angilella, G. G. N.; March, N. H.; Pucci, R.
2014-07-01
The Hartree-Fock (HF) method, supplemented by low-order Møller-Plesset (MP2) perturbation theory, has been utilized to predict the nuclear geometry, assuming planarity, of a low-lying isomer of the free space cluster BOSi2. The planar structure found at equilibrium geometry is shown to be stable against small amplitude molecular vibrations. Finally, some brief comments are made on the possible relevance of the above free-space cluster geometry to the known B-O defects which limit the improvement of minority carrier lifetime in a form of p-type silicon.
Maschio, Lorenzo; Kirtman, Bernard; Rérat, Michel; Orlando, Roberto; Dovesi, Roberto
2013-10-28
We present a fully analytical formulation for calculating Raman intensities of crystalline periodic systems using a local basis set. Numerical differentiation with respect to atomic coordinates and with respect to wavevectors is entirely avoided as is the determination of crystal orbital coefficient derivatives with respect to nuclear displacements. Instead, our method utilizes the orbital energy-weighted density matrix and is based on the self-consistent solution of first- and second-order Coupled Perturbed Hartree-Fock/Kohn-Sham equations for the electronic response to external electric fields at the equilibrium geometry. This method has also been implemented in the Crystal program, which uses a Gaussian type basis set.
Zhou, Fuyang; Li, Jiguang; Wang, Jianguo
2015-01-01
The multi-configuration Dirac-Hartree-Fock method was employed to calculate the total and excitation energies, oscillator strengths and hyperfine structure constants for low-lying levels of Sm I. In the first-order perturbation approximation, we systematically analyzed correlation effects from each electrons and electron pairs. It was found that the core correlations are of importance for physical quantities concerned. Based on the analysis, the important configuration state wave functions were selected to constitute atomic state wave functions. By using this computational model, our excitation energies, oscillator strengths, and hyperfine structure constants are in better agreement with experimental values than earlier theoretical works.
Martínez, E; Rincon, L
2002-01-01
Theoretical results of photoemission energy spectral of the atomic sulfur and of the SO sub 2 molecule, adsorbed over surfaces of Ni(110) and Ni(l l l) clusters, are reported in this work. Clusters with 11, 13, 15 and 17 atoms of Ni were used for the model. The calculations were done by Hartree-Fock method, and basis sets of type STO-NG and p-q1G (p3,6; q= 2,3; N= 3,6) were used. The ionization potentials (IP) were interpreted within the Koopmans Theorem. The results obtained for the IP of 1s, 2s and 2p orbitals are 2472.03 eV, 238.14 eV and 173.55 eV, respectively; while for the same orbitals of the sulfur in SO sub 2 these values are 2481.30 eV, 246.61 eV and 182.17 eV. The theoretical results were compared with experimental results reported in the references, and the error ranges are between 5 eV and 30 eV, in agreement with the standard for the Hartree-Fock method. (Author)
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...
Kussmann, Jörg; Ochsenfeld, Christian
2007-11-28
A density matrix-based time-dependent self-consistent field (D-TDSCF) method for the calculation of dynamic polarizabilities and first hyperpolarizabilities using the Hartree-Fock and Kohn-Sham density functional theory approaches is presented. The D-TDSCF method allows us to reduce the asymptotic scaling behavior of the computational effort from cubic to linear for systems with a nonvanishing band gap. The linear scaling is achieved by combining a density matrix-based reformulation of the TDSCF equations with linear-scaling schemes for the formation of Fock- or Kohn-Sham-type matrices. In our reformulation only potentially linear-scaling matrices enter the formulation and efficient sparse algebra routines can be employed. Furthermore, the corresponding formulas for the first hyperpolarizabilities are given in terms of zeroth- and first-order one-particle reduced density matrices according to Wigner's (2n+1) rule. The scaling behavior of our method is illustrated for first exemplary calculations with systems of up to 1011 atoms and 8899 basis functions.
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
Bučinský, Lukáš
2015-05-11
"Kramers pairs symmetry breaking" is evaluated at the 2-component (2c) Kramers unrestricted and/or general complex Hartree-Fock (GCHF) level of theory, and its analogy with "spin contamination" at the 1-component (1c) unrestricted Hartree-Fock (UHF) level of theory is emphasized. The GCHF "Kramers pairs symmetry breaking" evaluation is using the square of overlaps between the set of occupied spinorbitals with the projected set of Kramers pairs. In the same fashion, overlaps between α and β orbitals are used in the evaluation of "spin contamination" at the UHF level of theory. In this manner, UHF Š2 expectation value is made formally extended to the GCHF case. The directly evaluated GCHF expectation value of the Š2 operator is considered for completeness. It is found that the 2c GCHF Kramers pairs symmetry breaking has a very similar extent in comparison to the 1c UHF spin contamination. Thus higher excited states contributions to the 1c and 2c unrestricted wave functions of open shell systems have almost the same extent and physical consequences. Moreover, it is formally shown that a single determinant wave function in the restricted open shell Kramers case has the expectation value of K2 operator equal to the negative number of open shell electrons, while the eigenvalue of K2 for the series of simple systems (H, He, He*-triplet, Li and Li*-quartet) are found to be equal to minus the square of the number of open shell electrons. The concept of unpaired electron density is extended to the GCHF regime and compared to UHF and restricted open shell Hartree-Fock spin density. The "collinear" and "noncollinear" analogs of spin density at the GCHF level of theory are considered as well. Spin contamination and/or Kramers pairs symmetry breaking, spin populations and spin densities are considered for H2O+, Cl, HCl+, phenoxyl radical (C6H5O) as well as for Cu, Cu2+, Fe and the [OsCl5(1H-pyrazole)]- anion. The 1c and 2c unpaired electron density representation is found
Ucun, Fatih; Sağlam, Adnan; Güçlü, Vesile
2007-06-01
The molecular structures, vibrational frequencies and corresponding vibrational assignments of xanthine and its methyl derivatives (caffeine and theobromine) have been calculated using ab initio Hartree-Fock (HF) and density functional theory (B3LYP) methods with 6-31G(d, p) basis set level. The calculations were utilized to the CS symmetries of the molecules. The obtained vibrational frequencies and optimised geometric parameters (bond lengths and bond angles) were seen to be well agreement with the experimental data. The used scale factors which have been obtained the ratio of the frequency values of the strongest peaks in the calculated and experimental spectra seem to cause the gained vibrations well corresponding to the experimental ones. Theoretical infrared intensities and Raman activities are also reported.
Ebata, Shuichiro; Inakura, Tsunenori
2014-01-01
Systematic investigations of the electric dipole (E1) modes of excitation are performed using the canonical-basis time-dependent Hartree-Fock-Bogoliubov (Cb-TDHFB) theory. The Cb-TDHFB is able to describe dynamical pairing correlations in excited states of nuclear systems. We apply the method to the real-time calculation of linear response in even-even nuclei with Skyrme functionals. Effects of shell structure, neutron skin, deformation, and neutron chemical potential (separation energy) are studied in a systematic way. This reveals a number of characteristic features of the low-energy E1 modes. We also find a universal behavior in the low-energy E1 modes for heavy neutron-rich isotopes, which suggests the emergence of decoupled E1 peaks beyond N = 82.
Gundra, Kondayya
2011-01-01
Pariser-Parr-Pople (P-P-P) model Hamiltonian is employed frequently to study the electronic structure and optical properties of $\\pi$-conjugated systems. In this paper we describe a Fortran 90 computer program which uses the P-P-P model Hamiltonian to solve the Hartree-Fock (HF) equation for infinitely long, one-dimensional, periodic, $\\pi$-electron systems. The code is capable of computing the band structure, as also the linear optical absorption spectrum, by using the tight-binding (TB) and the HF methods. Furthermore, using our program the user can solve the HF equation in the presence of a finite external electric field, thereby, allowing the simulation of gated systems. We apply our code to compute various properties of polymers such as $trans$-polyacetylene ($t$-PA), poly-\\emph{para}-phenylene (PPP), and armchair and zigzag graphene nanoribbons, in the infinite length limit.
Inakura, T.; Mizutori, S.; Yamagami, M.; Matsuyanagi, K. E-mail: ken@ruby.scphys.kyoto-u.ac.jp
2002-11-18
With the use of the symmetry-unrestricted cranked Skyrme-Hartree-Fock method in the three-dimensional coordinate-mesh representation, we have carried out a systematic theoretical search for the superdeformed and hyperdeformed rotational bands in the mass A=30-50 region. Along the N=Z line, we have found superdeformed solutions in {sup 32}S, {sup 36}Ar, {sup 40}Ca, {sup 44}Ti, and hyperdeformed solutions in {sup 36}Ar, {sup 40}Ca, {sup 44}Ti, {sup 48}Cr. The superdeformed band in {sup 40}Ca is found to be extremely soft against both the axially symmetric (Y{sub 30}) and asymmetric (Y{sub 31}) octupole deformations. An interesting role of symmetry breaking in the mean field is pointed out.
Inakura, T.; Yamagami, M.; Matsuyanagi, K. [Kyoto Univ., Dept. of Physics, Kyoto (Japan); Mizutori, S. [Kansai Women' s College, Dept. of Human Science, Kashiwara, Osaka (Japan)
2003-02-01
With the use of the symmetry-unrestricted cranked Skyrme-Hartree-Fock method in the three-dimensional coordinate-mesh representation, we have carried out a systematic theoretical search for the superdeformed and hyperdeformed rotational bands in the mass A=30-50 region. Along the N=Z line, we have found superdeformed solutions in {sup 32}S, {sup 36}Ar, {sup 40}Ca, {sup 44}Ti, and hyperdeformed solutions in {sup 36}Ar, {sup 40}Ca, {sup 44}Ti, {sup 48}Cr. The superdeformed band in {sup 40}Ca is found to be extremely soft against both the axially symmetric (Y{sub 30}) and asymmetric (Y{sub 31}) octupole deformations. An interesting role of symmetry breaking in the mean field is pointed out. (author)
Inakura, T.; Mizutori, S.; Yamagami, M.; Matsuyanagi, K.
2002-11-01
With the use of the symmetry-unrestricted cranked Skyrme-Hartree-Fock method in the three-dimensional coordinate-mesh representation, we have carried out a systematic theoretical search for the superdeformed and hyperdeformed rotational bands in the mass A=30-50 region. Along the N= Z line, we have found superdeformed solutions in 32S, 36Ar, 40Ca, 44Ti, and hyperdeformed solutions in 36Ar, 40Ca, 44Ti, 48Cr. The superdeformed band in 40Ca is found to be extremely soft against both the axially symmetric ( Y30) and asymmetric ( Y31) octupole deformations. An interesting role of symmetry breaking in the mean field is pointed out.
Joshi, Bhawani Datt; Srivastava, Anubha; Tandon, Poonam; Jain, Sudha
2011-11-01
Yohimbine hydrochloride (YHCl) is an aphrodisiac and promoted for erectile dysfunction, weight loss and depression. The optimized geometry, total energy, potential energy surface and vibrational wavenumbers of yohimbine hydrochloride have been determined using ab initio, Hartree-Fock (HF) and density functional theory (DFT/B3LYP) method with 6-311++G(d,p) basis set. A complete vibrational assignment is provided for the observed Raman and IR spectra of YHCl. The UV absorption spectrum was examined in ethanol solvent and compared with the calculated one in gas phase as well as in solvent environment (polarizable continuum model, PCM) using TD-DFT/6-31G basis set. These methods are proposed as a tool to be applied in the structural characterization of YHCl. The calculated highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) with frontier orbital gap are presented.
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.
Investigation of Properties of Exotic Nuclei in Non-relativistic and Relativistic Models
2001-01-01
Properties of exotic nuclei are described by non-relativistic and relativistic models. The relativistic mean field theory predicts one proton halo in 26,27,28P and two proton halos in 27,28,29S, recently, one proton halo in 26,27,28P has been found experimentally in MSU lab. The relativistic Hartree-Fock theory has been used to investigate the contribution of Fock term and isovector mesons to the properties of exotic nuclei. It turns out that the influence of the Fock term and isovector mesons on the properties of neutron extremely rich nuclei is very different from that of near stable nuclei. Meanwhile, the deformed Hartree-Fock-Bogoliubov theory has been employed to describe the ground state properties of the isotopes for some light nuclei.
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.
Kondayya, Gundra; Shukla, Alok
2012-03-01
Pariser-Parr-Pople (P-P-P) model Hamiltonian is employed frequently to study the electronic structure and optical properties of π-conjugated systems. In this paper we describe a Fortran 90 computer program which uses the P-P-P model Hamiltonian to solve the Hartree-Fock (HF) equation for infinitely long, one-dimensional, periodic, π-electron systems. The code is capable of computing the band structure, as also the linear optical absorption spectrum, by using the tight-binding and the HF methods. Furthermore, using our program the user can solve the HF equation in the presence of a finite external electric field, thereby, allowing the simulation of gated systems. We apply our code to compute various properties of polymers such as trans-polyacetylene, poly- para-phenylene, and armchair and zigzag graphene nanoribbons, in the infinite length limit. Program summaryProgram title: ppp_bulk.x Catalogue identifier: AEKW_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEKW_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.: 87 464 No. of bytes in distributed program, including test data, etc.: 2 046 933 Distribution format: tar.gz Programming language: Fortran 90 Computer: PCs and workstations Operating system: Linux, Code was developed and tested on various recent versions of 64-bit Fedora including Fedora 14 (kernel version 2.6.35.12-90). Classification: 7.3 External routines: This program needs to link with LAPACK/BLAS libraries compiled with the same compiler as the program. For the Intel Fortran Compiler we used the ACML library version 4.4.0, while for the gfortran compiler we used the libraries supplied with the Fedora distribution. Nature of problem: The electronic structure of one-dimensional periodic π-conjugated systems is an intense area of research at
Schimeczek, C.; Engel, D.; Wunner, G.
2014-05-01
Our previously published code for calculating energies and bound-bound transitions of medium-Z elements at neutron star magnetic field strengths [D. Engel, M. Klews, G. Wunner, Comp. Phys. Comm. 180, 3-2-311 (2009)] was based on the adiabatic approximation. It assumes a complete decoupling of the (fast) gyration of the electrons under the action of the magnetic field and the (slow) bound motion along the field under the action of the Coulomb forces. For the single-particle orbitals this implied that each is a product of a Landau state and an (unknown) longitudinal wave function whose B-spline coefficients were determined self-consistently by solving the Hartree-Fock equations for the many-electron problem on a finite-element grid. In the present code we go beyond the adiabatic approximation, by allowing the transverse part of each orbital to be a superposition of Landau states, while assuming that the longitudinal part can be approximated by the same wave function in each Landau level. Inserting this ansatz into the energy variational principle leads to a system of coupled equations in which the B-spline coefficients depend on the weights of the individual Landau states, and vice versa, and which therefore has to be solved in a doubly self-consistent manner. The extended ansatz takes into account the back-reaction of the Coulomb motion of the electrons along the field direction on their motion in the plane perpendicular to the field, an effect which cannot be captured by the adiabatic approximation. The new code allows for the inclusion of up to 8 Landau levels. This reduces the relative error of energy values as compared to the adiabatic approximation results by typically a factor of three (1/3 of the original error) and yields accurate results also in regions of lower neutron star magnetic field strengths where the adiabatic approximation fails. Further improvements in the code are a more sophisticated choice of the initial wave functions, which takes into
G(U)M(U)(S), Sedat; (O)ZDO(G)AN, Telhat
2004-01-01
Hartree-Fock-Roothaan (HFR) calculations for ground states of some atoms, i.e. He, Be, Ne, Ar, and Kr have been performed using minimal basis sets of Slater type orbitals (STOs) with integer and noninteger principal quantum numbers (integer n-STOs and noninteger n-STOs). The obtained total energies for these atoms using minimal basis sets of integer n-STOs are in good agreement with those in the previous literature. On the other hand, for the case of minimal basis sets of noninteger n-STOs, although the calculated total energies of these atoms agree well with the results in literature, some striking results have been obtained for atoms Ar and Kr. Our computational results for the energies of atoms Ar and Kr are slightly better than those in literature, by amount of 0.00222 and 0.000054 a.u., respectively. The improvement in the energies of atoms Ar and Kr may result from the efficient calculations of one-center two-electron integrals over noninteger n-STOs. For some atomic ions in their ground state,HFR calculations have been carried out using minimal basis sets of noninteger n-STOs. The obtained total energies for these atomic ions are substantially lower than those available in literature.
Seel, M.; Ladik, J.
1985-10-01
Hartree-Fock Green's-function studies of end effects on the core-level structure of metallic and insulating quasi-one-dimensional model polymers reveal additional core peaks outside the bulk bands. In the metallic case, shifts to both lower (~-150 meV) and higher (~+50 meV) binding energies are observed, whereas in the insulating case, split-off peaks occur only at the lower-binding-energy side (~-150 meV). It is shown that a positive or negative net valence population alone does not determine the direction of the shift. The binding-energy changes are determined by a detailed balance between the energy loss due to a decrease in the electron-nuclear attraction and the energy gain due to a decrease in the electron-electron repulsion experienced by the core electrons of the end atoms. This can probably also explain why for some metal surfaces, shifts towards lower, and for others, shifts towards higher, binding energies are found. In the valence region of the investigated lithium chains, the ends do not produce localized end states.
Nemykin, Victor N; Hadt, Ryan G
2006-10-01
Influence of molecular geometry, type of exchange-correlation functional, and contraction scheme of basis set applied at the iron nuclei have been tested in the calculation of 57Fe Mössbauer isomer shifts and quadrupole splittings for a wide range of ligand types, as well as oxidation and spin states, in inorganic and organometallic systems. It has been found that uncontraction of the s-part of Wachter's full-electron basis set at the iron nuclei does not appreciably improve the calculated isomer shifts. The observed correlations for all tested sets of geometries are close to each other and predominantly depend on the employed exchange-correlation functional with B3LYP functional being slightly better as compared to BPW91. Both hybrid (B3LYP) and pure (BPW91) exchange-correlation functionals are suitable for the calculation of isomer shifts in organometallic compounds. Surprisingly, it has been found that the hybrid B3LYP exchange-correlation functional completely fails in accurate prediction of quadrupole splittings in ferrocenes, while performance of the pure BPW91 functional for the same systems was excellent. This observation has been explained on the basis of relationship between the amount of Hartree-Fock exchange involved in the applied exchange-correlation functional and the calculated HOMO-LUMO energy gap in ferrocenes. On the basis of this explanation, use of only pure exchange-correlation functionals has been suggested for accurate prediction of Mössbauer spectra parameters in ferrocenes.
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.
Mariji, Hodjat
2016-01-01
The nucleon single-particle energies (SPEs) of the selected closed shell nuclei; that is, 16O, 40Ca, and 56Ni, 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 AV18 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,rho), with the Heaviside functions, the role of n(k,rho) on 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 b...
Agrawal, B K
2004-01-01
We provide for the first time accurate assessments of the consequences of violations of self-consistency in the Hartree-Fock based random phase approximation (RPA) as commonly used to calculate the energy $E_c$ of the nuclear breathing mode. Using several Skyrme interactions we find that the self-consistency violated by ignoring the spin-orbit interaction in the RPA calculation causes a spurious enhancement of the breathing mode energy for spin unsaturated systems. Contrarily, neglecting the Coulomb interaction in the RPA or performing the RPA calculations in the TJ scheme underestimates the breathing mode energy. Surprisingly, our results for the $^{90}$Zr and $^{208}$Pb nuclei for several Skyrme type effective nucleon-nucleon interactions having a wide range of nuclear matter incompressibility ($K_{nm} \\sim 215 - 275$ MeV) and symmetry energy ($J \\sim 27 - 37$ MeV) indicate that the net uncertainty ($\\delta E_c \\sim 0.3$ MeV) is comparable to the experimental one.
Dobaczewski, J.; Olbratowski, P.
2005-05-01
We describe the new version (v2.08k) of the code HFODD which solves the nuclear Skyrme-Hartree-Fock or Skyrme-Hartree-Fock-Bogolyubov problem by using the Cartesian deformed harmonic-oscillator basis. Similarly as in the previous version (v2.08i), all symmetries can be broken, which allows for calculations with angular frequency and angular momentum tilted with respect to the mass distribution. In the new version, three minor errors have been corrected. New Version Program SummaryTitle of program: HFODD; version: 2.08k Catalogue number: ADVA Catalogue number of previous version: ADTO (Comput. Phys. Comm. 158 (2004) 158) Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADVA Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Does the new version supersede the previous one: yes Computers on which this or another recent version has been tested: SG Power Challenge L, Pentium-II, Pentium-III, AMD-Athlon Operating systems under which the program has been tested: UNIX, LINUX, Windows-2000 Programming language used: Fortran Memory required to execute with typical data: 10M words No. of bits in a word: 64 No. of lines in distributed program, including test data, etc.: 52 631 No. of bytes in distributed program, including test data, etc.: 266 885 Distribution format:tar.gz Nature of physical problem: The nuclear mean-field and an analysis of its symmetries in realistic cases are the main ingredients of a description of nuclear states. Within the Local Density Approximation, or for a zero-range velocity-dependent Skyrme interaction, the nuclear mean-field is local and velocity dependent. The locality allows for an effective and fast solution of the self-consistent Hartree-Fock equations, even for heavy nuclei, and for various nucleonic ( n-particle n-hole) configurations, deformations, excitation energies, or angular momenta. Similar Local Density Approximation in the particle-particle channel, which is equivalent to using a zero
Aerts, Patrick Johan Coenraad
1986-01-01
Computational Theoretical Chemnistry is a research area which, as far as electronic structure problems are concerned, encompasses essentially the development of theoretically sound, yet computionally feasable quantum mechanical models for atoms melecules and the solid state. ... Zie: Introduction
Relativistic heavy ion collisions with realistic non-equilibrium mean fields
Fuchs, C; Wolter, H H
1996-01-01
We study the influence of non-equilibrium phase space effects on the dynamics of heavy ion reactions within the relativistic BUU approach. We use realistic Dirac-Brueckner-Hartree-Fock (DBHF) mean fields determined for two-Fermi-ellipsoid configurations, i.e. for colliding nuclear matter, in a local phase space configuration approximation (LCA). We compare to DBHF mean fields in the local density approximation (LDA) and to the non-linear Walecka model. The results are further compared to flow data of the reaction Au on Au at 400 MeV per nucleon measured by the FOPI collaboration. We find that the DBHF fields reproduce the experiment if the configuration dependence is taken into account. This has also implications on the determination of the equation of state from heavy ion collisions.
Relativistic Effects and Three-Nucleon Forces in Nuclear Matter and Nuclei
Müther, Herbert; Ma, Zhongyu
2016-01-01
We review a large body of predictions obtained within the framework of relativistic meson theory together with the Dirac-Brueckner-Hartree-Fock approach to nuclear matter and finite nuclei. The success of this method has been largely related to its ability to take into account important three-body effects. Therefore, the overarching theme of this article is the interpretation of the so-called "Dirac effects" as an effective three-nucleon force. We address the equation of state of isospin symmetric and asymmetric nucleonic matter and related issues, ranging from proton and neutron density distributions to momentum distributions and short-range correlations. A central part of the discussion is devoted to the optical model potential for nucleon-nucleus scattering. We also take the opportunity to explore similarities and differences with predictions based on the increasingly popular chiral effective field theory.
Sundholm, Dage; Olsen, Jeppe
1993-04-01
The atomic quadrupole moments Qzz of Be(2s2p;3P2), Al(3p;2P3/2), In(5p;2P3/2), Ne(2p53s3P2), Ar(3p54s;3P2), Kr(4p55s;3P2), and Xe(5p56s;3P2) have been calculated using a finite-element multiconfiguration Hartree-Fock method. The obtained Qzz(Be) of 2.265 a.u. agrees with previously calculated values. The calculated Qzz(Al) and Qzz(In) of 2.579 and 3.165 a.u. are in good agreement with the experimental values of 2.53(15) a.u. and 2.94(10) a.u. A large s-d polarization contribution to the Qzz of the rare gases is found in the present calculations. The correlation contributions from double (D), triple (T), and quadruple (Q) excitations to the Qzz of the rare gases alternate; the total DTQ correlation contribution is negligibly small for Ne, Ar, and Kr, while the DTQ correlation contribution to the Qzz(Xe) is 25% of the final Qzz. The final values are Qzz(Ne)=-0.0506 a.u., Qzz(Ar)=-0.0553 a.u., Qzz(Kr)=+0.0601 a.u., and Qzz(Xe)=+0.4505 a.u., as compared to the experimental values of -0.048(5) a.u., -0.042(4) a.u., +0.046(5) a.u., and +0.30(3) a.u. for Ne, Ar, Kr, and Xe, respectively.
A systematic sequence of relativistic approximations.
Dyall, Kenneth G
2002-06-01
An approach to the development of a systematic sequence of relativistic approximations is reviewed. The approach depends on the atomically localized nature of relativistic effects, and is based on the normalized elimination of the small component in the matrix modified Dirac equation. Errors in the approximations are assessed relative to four-component Dirac-Hartree-Fock calculations or other reference points. Projection onto the positive energy states of the isolated atoms provides an approximation in which the energy-dependent parts of the matrices can be evaluated in separate atomic calculations and implemented in terms of two sets of contraction coefficients. The errors in this approximation are extremely small, of the order of 0.001 pm in bond lengths and tens of microhartrees in absolute energies. From this approximation it is possible to partition the atoms into relativistic and nonrelativistic groups and to treat the latter with the standard operators of nonrelativistic quantum mechanics. This partitioning is shared with the relativistic effective core potential approximation. For atoms in the second period, errors in the approximation are of the order of a few hundredths of a picometer in bond lengths and less than 1 kJ mol(-1) in dissociation energies; for atoms in the third period, errors are a few tenths of a picometer and a few kilojoule/mole, respectively. A third approximation for scalar relativistic effects replaces the relativistic two-electron integrals with the nonrelativistic integrals evaluated with the atomic Foldy-Wouthuysen coefficients as contraction coefficients. It is similar to the Douglas-Kroll-Hess approximation, and is accurate to about 0.1 pm and a few tenths of a kilojoule/mole. The integrals in all the approximations are no more complicated than the integrals in the full relativistic methods, and their derivatives are correspondingly easy to formulate and evaluate.
de Lara-Castells, María Pilar; Fernández-Perea, Ricardo; Madzharova, Fani; Voloshina, Elena
2016-06-01
The adsorption of noble gases on metallic surfaces represents a paradigmatic case of van-der-Waals (vdW) interaction due to the role of screening effects on the corrugation of the interaction potential [J. L. F. Da Silva et al., Phys. Rev. Lett. 90, 066104 (2003)]. The extremely small adsorption energy of He atoms on the Mg(0001) surface (below 3 meV) and the delocalized nature and mobility of the surface electrons make the He/Mg(0001) system particularly challenging, even for state-of-the-art vdW-corrected density functional-based (vdW-DFT) approaches [M. P. de Lara-Castells et al., J. Chem. Phys. 143, 194701 (2015)]. In this work, we meet this challenge by applying two different procedures. First, the dispersion-corrected second-order Möller-Plesset perturbation theory (MP2C) approach is adopted, using bare metal clusters of increasing size. Second, the method of increments [H. Stoll, J. Chem. Phys. 97, 8449 (1992)] is applied at coupled cluster singles and doubles and perturbative triples level, using embedded cluster models of the metal surface. Both approaches provide clear evidences of the anti-corrugation of the interaction potential: the He atom prefers on-top sites, instead of the expected hollow sites. This is interpreted as a signature of the screening of the He atom by the metal for the on-top configuration. The strong screening in the metal is clearly reflected in the relative contribution of successively deeper surface layers to the main dispersion contribution. Aimed to assist future dynamical simulations, a pairwise potential model for the He/surface interaction as a sum of effective He-Mg pair potentials is also presented, as an improvement of the approximation using isolated He-Mg pairs.
Boblest, S.; Meyer, D.; Wunner, G.
2014-11-01
We present a quantum Monte Carlo application for the computation of energy eigenvalues for atoms and ions in strong magnetic fields. The required guiding wave functions are obtained with the Hartree-Fock-Roothaan code described in the accompanying publication (Schimeczek and Wunner, 2014). Our method yields highly accurate results for the binding energies of symmetry subspace ground states and at the same time provides a means for quantifying the quality of the results obtained with the above-mentioned Hartree-Fock-Roothaan method. Catalogue identifier: AETV_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AETV_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.: 72 284 No. of bytes in distributed program, including test data, etc.: 604 948 Distribution format: tar.gz Programming language: C++. Computer: Cluster of 1-˜500 HP Compaq dc5750. Operating system: Linux. Has the code been vectorized or parallelized?: Yes. Code includes MPI directives. RAM: 500 MB per node Classification: 2.1. External routines: Boost::Serialization, Boost::MPI, LAPACK BLAS Nature of problem: Quantitative modelings of features observed in the X-ray spectra of isolated neutron stars are hampered by the lack of sufficiently large and accurate databases for atoms and ions up to the last fusion product iron, at high magnetic field strengths. The predominant amount of line data in the literature has been calculated with Hartree-Fock methods, which are intrinsically restricted in precision. Our code is intended to provide a powerful tool for calculating very accurate energy values from, and thereby improving the quality of, existing Hartree-Fock results. Solution method: The Fixed-phase quantum Monte Carlo method is used in combination with guiding functions obtained in Hartree-Fock
Hamel, Sébastien; Casida, Mark E.; Salahub, Dennis R.
2001-05-01
The Roothaan-Hartree-Fock (HF) method has been implemented in deMon-DynaRho within the resolution-of-the-identity (RI) auxiliary-function approximation. While previous studies have focused primarily upon the effect of the RI approximation on total energies, very little information has been available regarding the effect of the RI approximation on orbital energies, even though orbital energies play a central role in many theories of ionization and excitation. We fill this gap by testing the accuracy of the RI approximation against non-RI-HF calculations using the same basis sets, for the occupied orbital energies and an equal number of unoccupied orbital energies of five small molecules, namely CO, N2, CH2O, C2H4, and pyridine (in total 102 orbitals). These molecules have well-characterized excited states and so are commonly used to test and validate molecular excitation spectra computations. Of the deMon auxiliary basis sets tested, the best results are obtained with the (44) auxiliary basis sets, yielding orbital energies to within 0.05 eV, which is adequate for analyzing typical low resolution polyatomic molecule ionization and excitation spectra. Interestingly, we find that the error in orbital energies due to the RI approximation does not seem to increase with the number of electrons. The absolute RI error in the orbital energies is also roughly related to their absolute magnitude, being larger for the core orbitals where the magnitude of orbital energy is large and smallest where the molecular orbital energy is smallest. Two further approximations were also considered, namely uniterated ("zero-order") and single-iteration ("first-order") calculations of orbital energies beginning with a local density approximation initial guess. We find that zero- and first-order orbital energies are very similar for occupied but not for unoccupied orbitals, and that the first-order orbital energies are fairly close to the corresponding fully converged values. Typical root
Matta, Chérif F
2010-04-30
This article compares molecular properties and atomic properties defined by the quantum theory of atoms in molecules (QTAIM) obtained from three underlying levels of theory: MP2(full), density functional theory (DFT) (B3LYP), and Hartree-Fock (H-F). The same basis set (6-311++G(d,p)) has been used throughout the study. The calculations and comparisons were applied to a set of 30 small molecules representing common fragments of biological molecules. The molecular properties investigated are the energies and the electrostatic moments (up to and including the quadrupoles), and the atomic properties include electron populations (and atomic charge), atomic dipolar and quadrupolar polarizations, atomic volumes, and corrected and raw atomic energies. The Cartesian distance between dipole vectors and the Frobenius distance between the quadrupole tensors calculated at the three levels of theory provide a measure of their correlation (or lack thereof). With the exception of energies (atomic and molecular), it is found that both DFT and H-F are in excellent agreement with MP2, especially with regards to the electrostatic mutipoles up to the quadrupoles, but DFT and MP2 agree better in almost all studied properties (with the exception of molecular geometries). QTAIM properties whether obtained from H-F, DFT(B3LYP), or MP2 calculations when used in the construction of empirical correlations with experiment such as quantitative structure-activity-(or property)-relationships (QSAR/QSPR) are equivalent (because the properties calculated at the three levels are very highly correlated among themselves with r(2) typically >0.95, and therefore preserving trends). These results suggest that the massive volume of results that were published in the older literature at the H-F level is valid especially when used to study trends or in QSAR or QSPR studies, and, as long as our test set of molecules is representative, there is no pressing need to re-evaluate them at other levels of theory
Schimeczek, C.; Engel, D.; Wunner, G.
2012-07-01
Our previously published code for calculating energies and bound-bound transitions of medium-Z elements at neutron star magnetic field strengths [D. Engel, M. Klews, G. Wunner, Comput. Phys. Comm. 180 (2009) 302-311] was based on the adiabatic approximation. It assumes a complete decoupling of the (fast) gyration of the electrons under the action of the magnetic field and the (slow) bound motion along the field under the action of the Coulomb forces. For the single-particle orbitals this implied that each is a product of a Landau state and an (unknown) longitudinal wave function whose B-spline coefficients were determined self-consistently by solving the Hartree-Fock equations for the many-electron problem on a finite-element grid. In the present code we go beyond the adiabatic approximation, by allowing the transverse part of each orbital to be a superposition of Landau states, while assuming that the longitudinal part can be approximated by the same wave function in each Landau level. Inserting this ansatz into the energy variational principle leads to a system of coupled equations in which the B-spline coefficients depend on the weights of the individual Landau states, and vice versa, and which therefore has to be solved in a doubly self-consistent manner. The extended ansatz takes into account the back-reaction of the Coulomb motion of the electrons along the field direction on their motion in the plane perpendicular to the field, an effect which cannot be captured by the adiabatic approximation. The new code allows for the inclusion of up to 8 Landau levels. This reduces the relative error of energy values as compared to the adiabatic approximation results by typically a factor of three (1/3 of the original error), and yields accurate results also in regions of lower neutron star magnetic field strengths where the adiabatic approximation fails. Further improvements in the code are a more sophisticated choice of the initial wave functions, which takes into
Nuclear structure for the crust of neutron stars and exotic nuclei
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.)
Schunck, N; McDonnell, J; Satula, W; Sheikh, J A; Staszczak, A; Stoitsov, M; Toivanen, P
2011-01-01
We describe the new version (v2.49s) 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...
Komorovsky, Stanislav; Repisky, Michal; Malkin, Elena; Demissie, Taye B; Ruud, Kenneth
2015-08-11
We present an implementation of the nuclear spin-rotation (SR) constants based on the relativistic four-component Dirac-Coulomb Hamiltonian. This formalism has been implemented in the framework of the Hartree-Fock and Kohn-Sham theory, allowing assessment of both pure and hybrid exchange-correlation functionals. In the density-functional theory (DFT) implementation of the response equations, a noncollinear generalized gradient approximation (GGA) has been used. The present approach enforces a restricted kinetic balance condition for the small-component basis at the integral level, leading to very efficient calculations of the property. We apply the methodology to study relativistic effects on the spin-rotation constants by performing calculations on XHn (n = 1-4) for all elements X in the p-block of the periodic table and comparing the effects of relativity on the nuclear SR tensors to that observed for the nuclear magnetic shielding tensors. Correlation effects as described by the density-functional theory are shown to be significant for the spin-rotation constants, whereas the differences between the use of GGA and hybrid density functionals are much smaller. Our calculated relativistic spin-rotation constants at the DFT level of theory are only in fair agreement with available experimental data. It is shown that the scaling of the relativistic effects for the spin-rotation constants (varying between Z(3.8) and Z(4.5)) is as strong as for the chemical shieldings but with a much smaller prefactor.
Grimm, Shu-Ya Lisa
We have developed a general method to calculate the incoherent scattering cross section for complex molecules for photon energy ranging from 1 keV to 130 keV. Within this energy range the binding energy of an electron in a biosystem is comparable to the energy of the incident photon, thus we need to take into account the effect of binding energy in calculations of the total scattering cross section. Also the energy acquired by the scattered electron is in the high energy range, and therefore we are required to use relativistic treatment in our calculations. In our Theory we show the derivation of incoherent scattering function. The calculation of the incoherent scattering function involves matrix elements between two molecular wave functions. With Sharma's analytical formula we are able to expand one of the wave functions to the center of the other wave function, enabling us to perform the calculation of incoherent scattering function for molecules which require multi-center integrals. We explain briefly how one obtains the wave function of a molecule in the Hartree-Fock self-consistent field approximation. Since there are no available molecular wave functions for large molecules such as glucose and Gly-Pro-Pro sequence protein (which are important molecules in biosystems) we develop and use the molecular wave functions using the overlap effect only for large molecules. We further apply the calculated incoherent scattering function to calculate the total incoherent scattering cross section for a molecule. We perform the calculations of incoherent scattering function and total incoherent scattering cross sections for H2O,/ HCN, Glucose, and Gly-Pro-Pro protein molecules. For H2O,/ HCN molecules we calculate the incoherent scattering function using both Hartree-Fock (HF) self-consistent field wave functions and overlap- effect-only wave functions. We further apply these two calculated incoherent scattering functions obtained by Hartree-Fock (HF) self-consistent field
Mackrodt, W. C.
1999-02-01
First principles periodic Hartree-Fock calculations are reported for the P4 2/ mnm(rutile), I4 1/ amd(anatase), Pbca(brookite), Pnma(ramsdellite), Pcbn(colombite), Fdoverline3m(spinel), and Imma(orthorhombic) polymorphs of TiO 2, from which the predicted order of stability is The calculated difference in energy between the rutile and anatase structures is 0.02-0.06 eV, in good agreement with a recent local density approximation (LDA) estimate of 0.033 eV and an experiment enthalpy difference of 0.05 eV. The corresponding Hartree-Fock and LDA differences for the brookite structure are 0.06 and 0.058 eV, respectively. The calculated volumes, which are based on isotropic volume-optimized Hartree-Fock energies, are also in good agreement with recent LDA calculations and with experiment. Spin-unrestricted calculations are reported for the Fmoverline3m, Imma, Pnma, and P4 2/ mmmof LiTiO 2, where the stability is in the order The only reported phase for LiTiO 2is Fmoverline3m, for which the calculated volume is in good agreement with experiment. From the relative stabilities of TiO 2and LiTiO 2, the relative lithium insertion potentials corresponding to TiO 2 → LiTiO 2are deduced, with a maximum variation of 1.6 eV for the different polymorphic routes. The maximum voltage predicted is that for the Immaroute which is ˜1 eV larger than that for Pnma. Direct comparisons with the calculated energy for C2/ mLi 0.5MnO 2 → LiMnO 2lead to an estimate of the voltage for ImmaTiO 2 → LiTiO 2of ˜1.3 eV, which is ˜2.5 eV anodicto the Mn system. The corresponding values for the Pnmapolymorphic route are ˜3 and ˜3.5 eV, respectively. Mulliken population analyses indicate that lithium is completely ionized in LiTiO 2and that the charge transfer is predominantly to the oxygen sublattice. There is a rehybridization of the titanium valence orbitals leading to a slight increase in the 3 dpopulation and strong localization of spin density at the titanium sites with local moments of
Inakura, T; Yamagami, M; Matsuyanagi, K
2002-01-01
With the use of the symmetry-unrestricted cranked Skyrme-Hartree-Fock method in the three-dimensional coordinate-mesh representation, we have carried out a systematic theoretical search for the superdeformed and hyperdeformed rotational bands in the mass A=30-50 region. Along the N=Z line, we have found superdeformed solutions in sup 3 sup 2 S, sup 3 sup 6 Ar, sup 4 sup 0 Ca, sup 4 sup 4 Ti, and hyperdeformed solutions in sup 3 sup 6 Ar, sup 4 sup 0 Ca, sup 4 sup 4 Ti, sup 4 sup 8 Cr. The superdeformed band in sup 4 sup 0 Ca is found to be extremely soft against both the axially symmetric (Y sub 3 sub 0) and asymmetric (Y sub 3 sub 1) octupole deformations. An interesting role of symmetry breaking in the mean field is pointed out.
Lacivita, Valentina; Rérat, Michel; Kirtman, Bernard; Ferrero, Mauro; Orlando, Roberto; Dovesi, Roberto
2009-11-01
The high-frequency dielectric ɛ and the first nonlinear electric susceptibility χ(2) tensors of crystalline potassium dihydrogen phosphate (KH2PO4) are calculated by using the coupled perturbed Hartree-Fock and Kohn-Sham methods as implemented in the CRYSTAL code. The effect of basis sets of increasing size on ɛ and χ(2) is explored. Five different levels of theory, namely, local-density approximation, generalized gradient approximation (PBE), hybrids (B3LYP and PBE0), and HF are compared using the experimental and theoretical structures corresponding not only to the tetragonal geometry I4d2 at room temperature but also to the orthorhombic phase Fdd2 at low temperature. Comparison between the two phases and their optical behavior is made. The calculated results for the tetragonal phase are in good agreement with the experimental data.
Lee, Y.S.
1977-11-01
The effects of the 4f shell of electrons and the relativity of valence electrons are compared. The effect of 4f shell (lanthanide contraction) is estimated from the numerical Hartree-Fock (HF) calculations of pseudo-atoms corresponding to Hf, Re, Au, Hg, Tl, Pb and Bi without 4f electrons and with atomic numbers reduced by 14. The relativistic effect estimated from the numerical Dirac-Hartree-Fock (DHF) calculations of those atoms is comparable in the magnitude with that of the 4f shell of electrons. Both are larger for 6s than for 5d or 6p electrons. The various relativistic effects on valence electrons are discussed in detail to determine the proper level of the approximation for the valence electron calculations of systems with heavy elements. An effective core potential system has been developed for heavy atoms in which relativistic effects are included in the effective potentials.
Rajat K. Chaudhuri
2003-12-01
Full Text Available Abstract: The coupled cluster based linear response theory which is applicable to the direct calculation of atomic and molecular properties are presented and applied to compute the ionization potentials and excitation energies of light and moderately heavy atoms. The eÃ‚Â®ect of electron correlation on the ground and excited states is studied using Hartree-Fock, Dirac-Fock and approximate two-component relativistic spinors.
Ahamad, Shakeb; Patra, S K
2012-01-01
The ground state and first intrinsic excited state of superheavy nuclei with Z=120 and N=160-204 are investigated using both non-relativistic Skyrme-Hartree-Fock and the axially deformed Relativistic Mean Field formalisms. We employ a simple BCS pairing approach for calculating the energy contribution from pairing interaction. The results for isotopic chain of binding energy, quadrupole deformation parameter, two neutron separation energies and some other observables are compared with the FRDM and some recent macroscopic-microscopic calculations. We predict superdeformed ground state solutions for almost all the isotopes. Considering the possibility of magic neutron number, two different mode of \\alpha-decay chains (292)120 and (304)120 are also studied within these frameworks. The Q_{\\alpha}-values and the half-life T^{\\alpha}_{1/2} for these two different mode of decay chains are compared with FRDM and recent macroscopic-microscopic calculations. The calculation is extended for the \\alpha-decay chains of 29...
Generalized quantum similarity in atomic systems: A quantifier of relativistic effects
Martín, A. L.; Angulo, J. C.; Antolín, J.; López-Rosa, S.
2017-02-01
Quantum similarity between Hartree-Fock and Dirac-Fock electron densities reveals the depth of relativistic effects on the core and valence regions in atomic systems. The results emphasize the relevance of differences in the outermost subshells, as pointed out in recent studies by means of Shannon-like functionals. In this work, a generalized similarity functional allows us to go far beyond the Shannon-based analyses. The numerical results for systems throughout the Periodic Table show that discrepancies between the relativistic and non-relativistic descriptions are patently governed by shell-filling patterns.
Claudino, D; Gargano, R; Carvalho-Silva, Valter H; E Silva, Geraldo M; da Cunha, W F
2016-07-21
The present paper concludes our series of kinetics studies on the reactions involved in the complex mechanism of nitrogen trifluoride decomposition. Two other related reactions that, along with this mechanism, take part in an efficient boron nitride growth process are also investigated. We report results concerning two abstraction reactions, namely NF2 + N ⇄ 2NF and NF3 + NF ⇄ 2NF2, and two dissociations, N2F4 ⇄ 2NF2 and N2F3 ⇄ NF2 + NF. State-of-the-art electronic structure calculations at the CCSD(T)/cc-pVTZ level of theory were considered to determine geometries and frequencies of reactants, products, and transition states. Extrapolation of the energies to the complete basis set limit was used to obtain energies of all the species. We applied transition state theory to compute thermal rate constants including Wigner, Eckart, Bell, and deformed theory corrections in order to take tunneling effects into account. The obtained results are in good agreement with the experimental data available in the literature and are expected to provide a better phenomenological understanding of the NF3 decomposition role in the boron nitride growth for a wide range of temperature values.
Shen, Xiaozhi; Liu, Juan; Zhou, Fuyang
2016-10-01
Wavefunctions were determined using the multi-configuration Dirac-Hartree-Fock method. The core-core, core-valence, valence correlation, Breit interaction and quantum electrodynamics effects, as well as some higher-order correlation effects, were considered to obtain accurate wavelengths (λ), oscillator strengths (gf) and transition rates (A) of 2s22p2 - 2s2p3, 2s2p3 - 2s22pnl (n ≥ 3) and 2s2p3 - 2s2p23s E1 transitions. The branching ratio of 2s2p3 5S^o_2 (namely Aλ2143.45/Aλ2139.68) based on the latest calculation of 2.462 ± 0.119 is recommended for the determination of a nebula's electron temperature and electron density. The largest calculated gf value of 2s2p3 - 2s22p4p is λ630.65, differing from that of λ1060.2 (i.e. 2s2p3 3P^o_2 - 2s22p4p 3S1) that was observed with the largest intensities in the Orion Nebula spectrum. In addition, the energy levels and the splittings of 2s2p3, the extremely difficult calculations of the rates of two-electron one-photon transitions as well as those of the very small intercombination A of 2s2p3 5S^o_2 were studied in detail. Because of the weak spin-orbit interaction, accurately calculating the levels 3P^o_{1,2,0} (or 3D^o_{3,2,1}) and their transition matrix elements is very sensitive to relativistic and electron correlation effects. A special case for this is when the transition operators synchronously applied to wavefunctions with regard to 2s2p3 3Po and 2s22pnl (n = 4) become extremely sensitive to some higher-order correlation effects.
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.
Andrea Alparone
2014-05-01
Structural, energetic, spectroscopic, linear and nonlinear optical (NLO) properties of the environmental mutagens 1- and 3-nitro-6-azabenzo[]pyrene -oxides were characterized by means of Hartree-Fock as well as B3LYP and CAM-B3LYP density functional theory computations. The NLO investigations were performed for the second harmonic generation (SHG) and electro-optical Pockels effect (EOPE) at the incident wavelength of 1064 nm. The results show that, the predicted structures, vibrational spectra, nucleus independent chemical shifts, ionization energy, electron affinity as well as electronic polarizabilities are little influenced by the position of the nitro substituent. Differently, the dipole moment () and the first-order hyperpolarizabilities () are significantly dependent on the isomerization. The rather different mutagenic activity of the investigated isomers could be related to their diverse polarity. At the CAM-B3LYP level, when passing from the 1- to the 3-nitro-6-azabenzo[a]pyrene -oxide isomer, the datum increases by about 5 D (a factor of three), whereas the static and dynamic values decrease by ca. 50%. Dipole moment measurement and SHG and EOPE NLO techniques are potentially useful to distinguish these important environmental mutagens.
Mamedov, B. A.; Çopuroğlu, E.
2016-06-01
In this work, we study the effects of self-friction field on the states of a single configuration of closed and open shells by using the Combined Hartree-Fock-Roothaan equations for atomic-molecular and nuclear systems. Here, we present a program that implements the evaluation of the various properties of atoms and molecular systems with respect to the various values of self-friction quantum numbers. An especially fast and accurate algorithm for the calculation of the self-friction multicenter molecular integrals is obtained by using one-range addition theorems. To demonstrate the action of self-friction field on the atomic and molecular systems we have performed the calculations of H2O, CH3, CH2 and NH3 molecules. For the derivations of the orbital, kinetic and total energies and linear combination coefficients, the results are given for various values of self-friction quantum numbers. For various values of self-friction quantum numbers the obtained results of the orbital, kinetic and total energies and linear combination coefficients have been analyzed.
He, Xiao; Ryu, Shinsei; Hirata, So
2014-01-14
Finite-temperature extensions of ab initio Gaussian-basis-set spin-restricted Hartree-Fock (HF) and second-order many-body perturbation (MP2) theories are implemented for infinitely extended, periodic, one-dimensional solids and applied to the Peierls and charge-density-wave (CDW) transitions in polyyne and all-trans polyacetylene. The HF theory predicts insulating CDW ground states for both systems in their equidistant structures at low temperatures. In the same structures, they turn metallic at high temperatures. Starting from the "dimerized" low-temperature equilibrium structures, the systems need even higher temperatures to undergo a Peierls transition, which is accompanied by geometric as well as electronic distortions from dimerized to non-dimerized forms. The conventional finite-temperature MP2 theory shows a sign of divergence in any phase at any nonzero temperature and is useless. The renormalized finite-temperature MP2 (MP2R) theory is divergent only near metallic electronic structures, but is well behaved elsewhere. MP2R also predicts CDW and Peierls transitions occurring at two different temperatures. The effect of electron correlation is primarily to lower the Peierls transition temperature.
Relativistic calculation of the SeH{sub 2} and TeH{sub 2} photoelectron spectra
Pernpointner, Markus [Theoretische Chemie, Universitaet Heidelberg, Im Neuenheimer Feld 229, D-69120 Heidelberg (Germany)], E-mail: Markus.Pernpointner@pci.uni-heidelberg.de
2006-10-26
Photoelectron (PE) spectra provide detailed insight into the electronic structure of atoms, molecules and solids. Hereby electron correlation and relativistic effects influence the structure of the PE spectrum in a complicated way necessitating a consistent theoretical treatment. By embedding the one-particle propagator technique in a four-component framework the interplay between relativistic and correlation effects can be described correctly. In this article the Dirac-Hartree-Fock algebraic diagrammatic construction scheme (DHF-ADC) together with recent applications is reviewed and fully relativistic PE spectra of SeH{sub 2} and TeH{sub 2} in combination with basis set studies are presented.
Linear response at the 4-component relativistic level
Saue, T.; Jensen, Hans Jørgen Aagaard
2003-01-01
The theory, implementation, and application of linear response at the 4-component relativistic closed-shell Hartree-Fock level based on the concept of quasienergy and time averaging are reported. As such, an efficient AO-driven algorithm is obtained by assigning specific Hermiticity and time...... reversal symmetry to the trial vectors used in the solution of the reduced response equations. The given implementation has a quite general structure and thereby allows the calculation of a wide range of second-order properties such as polarizabilities, magnetizabilities, as well as NMR parameters....
Hydrodynamic Approaches in Relativistic Heavy Ion Reactions
de Souza, Rafael Derradi; Kodama, Takeshi
2016-01-01
We review several facets of the hydrodynamic description of the relativistic heavy ion collisions, starting from the historical motivation to the present understandings of the observed collective aspects of experimental data, especially those of the most recent RHIC and LHC results. In this report, we particularly focus on the conceptual questions and the physical foundations of the validity of the hydrodynamic approach itself. We also discuss recent efforts to clarify some of the points in this direction, such as the various forms of derivations of relativistic hydrodynamics together with the limitations intrinsic to the traditional approaches, variational approaches, known analytic solutions for special cases, and several new theoretical developments. Throughout this review, we stress the role of course-graining procedure in the hydrodynamic description and discuss its relation with the physical observables through the analysis of a hydrodynamic mapping of a microscopic transport model. Several questions to...
Diabatic constrained relativistic mean field approach
L"u, H F; Meng, J
2005-01-01
A diabatic (configuration-fixed) constrained approach to calculate the potential energy surface (PES) of the nucleus is developed in the relativistic mean field model. The potential energy surfaces of $^{208}$Pb obtained from both adiabatic and diabatic constrained approaches are investigated and compared. The diabatic constrained approach enables one to decompose the segmented PES obtained in usual adiabatic approaches into separate parts uniquely characterized by different configurations, to define the single particle orbits at very deformed region by their quantum numbers, and to obtain several well defined deformed excited states which can hardly be expected from the adiabatic PES's.
Schunck, N.; Dobaczewski, J.; McDonnell, J.; Satuła, W.; Sheikh, J. A.; Staszczak, A.; Stoitsov, M.; Toivanen, P.
2012-01-01
We describe the new version (v2.49t) of the code HFODD which solves the nuclear Skyrme-Hartree-Fock (HF) or Skyrme-Hartree-Fock-Bogolyubov (HFB) problem by using the Cartesian deformed harmonic-oscillator basis. In the new version, we have implemented the following physics features: (i) the isospin mixing and projection, (ii) the finite-temperature formalism for the HFB and HF + BCS methods, (iii) the Lipkin translational energy correction method, (iv) the calculation of the shell correction. A number of specific numerical methods have also been implemented in order to deal with large-scale multi-constraint calculations and hardware limitations: (i) the two-basis method for the HFB method, (ii) the Augmented Lagrangian Method (ALM) for multi-constraint calculations, (iii) the linear constraint method based on the approximation of the RPA matrix for multi-constraint calculations, (iv) an interface with the axial and parity-conserving Skyrme-HFB code HFBTHO, (v) the mixing of the HF or HFB matrix elements instead of the HF fields. Special care has been paid to using the code on massively parallel leadership class computers. For this purpose, the following features are now available with this version: (i) the Message Passing Interface (MPI) framework, (ii) scalable input data routines, (iii) multi-threading via OpenMP pragmas, (iv) parallel diagonalization of the HFB matrix in the simplex-breaking case using the ScaLAPACK library. Finally, several little significant errors of the previous published version were corrected. New version program summaryProgram title:HFODD (v2.49t) Catalogue identifier: ADFL_v3_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADFL_v3_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU General Public Licence v3 No. of lines in distributed program, including test data, etc.: 190 614 No. of bytes in distributed program, including test data, etc.: 985 898 Distribution
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
Lantri, T. [Laboratory of Technology and Solid’s Properties, Faculty of Sciences and Technology, Abdelhamid Ibn Badis University, BP 227, Mostaganem 27000 (Algeria); Bentata, S., E-mail: sam_bentata@yahoo.com [Laboratory of Technology and Solid’s Properties, Faculty of Sciences and Technology, Abdelhamid Ibn Badis University, BP 227, Mostaganem 27000 (Algeria); Bouadjemi, B.; Benstaali, W. [Laboratory of Technology and Solid’s Properties, Faculty of Sciences and Technology, Abdelhamid Ibn Badis University, BP 227, Mostaganem 27000 (Algeria); Bouhafs, B. [Modelling and Simulation in Materials Science Laboratory, Djillali Liabès University of Sidi Bel-Abbès, 22000 Sidi Bel-Abbes (Algeria); Abbad, A. [Laboratory of Technology and Solid’s Properties, Faculty of Sciences and Technology, Abdelhamid Ibn Badis University, BP 227, Mostaganem 27000 (Algeria); Modelling and Simulation in Materials Science Laboratory, Djillali Liabès University of Sidi Bel-Abbès, 22000 Sidi Bel-Abbes (Algeria); Zitouni, A. [Laboratory of Technology and Solid’s Properties, Faculty of Sciences and Technology, Abdelhamid Ibn Badis University, BP 227, Mostaganem 27000 (Algeria)
2016-12-01
Using the first-principle calculations, we have investigated the structural, elastic, optoelectronic and magnetic properties of Co{sub 2}MnSi Heusler alloy. Based on the density functional theory (DFT) and hiring the full-potential linearized augmented plane wave (FP-LAPW) method, we have used five approaches: the Hybrid on-site exact exchange, the Local Spin Density Approximation (LSDA), the LSDA+U, the Generalized Gradient Approximation GGA and GGA+U; where the Hubbard on-site Coulomb interaction correction U is calculated by constraint local density approximation for Co and Mn atoms. Our results show that the highly-ordered Co{sub 2}MnSi alloy is a ductile, stiff and anisotropic material. It has a half-metallic ferromagnetic character with an integer magnetic moment of 5 µB which is in good agreement with the Slater-Pauling rule. - Highlights: • Each approach gives a half magnetic compound. • EECE gives the largest gap. • Elastic properties show a stiff, ductile and anisotropic material. • Electronic properties are similar for the five approaches. • Total magnetic moment is the same for the five approaches (5 µB).
Lantri, T.; Bentata, S.; Bouadjemi, B.; Benstaali, W.; Bouhafs, B.; Abbad, A.; Zitouni, A.
2016-12-01
Using the first-principle calculations, we have investigated the structural, elastic, optoelectronic and magnetic properties of Co2MnSi Heusler alloy. Based on the density functional theory (DFT) and hiring the full-potential linearized augmented plane wave (FP-LAPW) method, we have used five approaches: the Hybrid on-site exact exchange, the Local Spin Density Approximation (LSDA), the LSDA+U, the Generalized Gradient Approximation GGA and GGA+U; where the Hubbard on-site Coulomb interaction correction U is calculated by constraint local density approximation for Co and Mn atoms. Our results show that the highly-ordered Co2MnSi alloy is a ductile, stiff and anisotropic material. It has a half-metallic ferromagnetic character with an integer magnetic moment of 5 μB which is in good agreement with the Slater-Pauling rule.
Relativistic Hartree-Bogoliubov description of the halo nuclei
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.
Electron correlation within the relativistic no-pair approximation
Almoukhalalati, Adel; Knecht, Stefan; Jensen, Hans Jørgen Aa.; Dyall, Kenneth G.; Saue, Trond
2016-08-01
This paper addresses the definition of correlation energy within 4-component relativistic atomic and molecular calculations. In the nonrelativistic domain the correlation energy is defined as the difference between the exact eigenvalue of the electronic Hamiltonian and the Hartree-Fock energy. In practice, what is reported is the basis set correlation energy, where the "exact" value is provided by a full Configuration Interaction (CI) calculation with some specified one-particle basis. The extension of this definition to the relativistic domain is not straightforward since the corresponding electronic Hamiltonian, the Dirac-Coulomb Hamiltonian, has no bound solutions. Present-day relativistic calculations are carried out within the no-pair approximation, where the Dirac-Coulomb Hamiltonian is embedded by projectors eliminating the troublesome negative-energy solutions. Hartree-Fock calculations are carried out with the implicit use of such projectors and only positive-energy orbitals are retained at the correlated level, meaning that the Hartree-Fock projectors are frozen at the correlated level. We argue that the projection operators should be optimized also at the correlated level and that this is possible by full Multiconfigurational Self-Consistent Field (MCSCF) calculations, that is, MCSCF calculations using a no-pair full CI expansion, but including orbital relaxation from the negative-energy orbitals. We show by variational perturbation theory that the MCSCF correlation energy is a pure MP2-like correlation expression, whereas the corresponding CI correlation energy contains an additional relaxation term. We explore numerically our theoretical analysis by carrying out variational and perturbative calculations on the two-electron rare gas atoms with specially tailored basis sets. In particular, we show that the correlation energy obtained by the suggested MCSCF procedure is smaller than the no-pair full CI correlation energy, in accordance with the underlying
Parallel, grid-adaptive approaches for relativistic hydro and magnetohydrodynamics
Keppens, R.; Meliani, Z.; van Marle, A. J.; Delmont, P.; Vlasis, A.; van der Holst, B.
2012-01-01
Relativistic hydro and magnetohydrodynamics provide continuum fluid descriptions for gas and plasma dynamics throughout the visible universe. We present an overview of state-of-the-art modeling in special relativistic regimes, targeting strong shock-dominated flows with speeds approaching the speed
Nonlinear approach to ternary scission
Kartavenco, V G
2002-01-01
Description of three-center configuration within mean-field approaches meets uncertainties to select a peculiar set of constraints. We suggest to use the inverse mean field method to solve single-particle Schroedinger equation, instead of constrained selfconsistent Hartree-Fock equations. It is shown, that it is possible to simulate one-dimensional three-center system in the approximation of reflectless single- particle potentials (authors)
Nucleon Spin Content in a Relativistic Quark Potential Model Approach
DONG YuBing; FENG QingGuo
2002-01-01
Based on a relativistic quark model approach with an effective potential U(r) = (ac/2)(1 + γ0)r2, the spin content of the nucleon is investigated. Pseudo-scalar interaction between quarks and Goldstone bosons is employed to calculate the couplings between the Goldstone bosons and the nucleon. Different approaches to deal with the center of mass correction in the relativistic quark potential model approach are discussed.
Relativistic Thermodynamics: A Modern 4-Vector Approach
J. Güémez
2011-01-01
Full Text Available Using the Minkowski relativistic 4-vector formalism, based on Einstein's equation, and the relativistic thermodynamics asynchronous formulation (Grøn (1973, the isothermal compression of an ideal gas is analyzed, considering an electromagnetic origin for forces applied to it. This treatment is similar to the description previously developed by Van Kampen (van Kampen (1969 and Hamity (Hamity (1969. In this relativistic framework Mechanics and Thermodynamics merge in the first law of relativistic thermodynamics expressed, using 4-vector notation, such as ΔUμ = Wμ + Qμ, in Lorentz covariant formulation, which, with the covariant formalism for electromagnetic forces, constitutes a complete Lorentz covariant formulation for classical physics.
Nonrelativistic mean-field description of the deformation of Λ hypernuclei
无
2009-01-01
The deformations of light Λ hypernuclei are studied in an extended nonrelativistic deformed Skyrme-Hartree-Fock approach with realistic modern nucleonic Skyrme forces,pairing correlations,and a microscopical lambda-nucleon interaction derived from Brueckner-Hartree-Fock calculations.Compared to the large effect of an additional Λ particle on nuclear deformation in the light soft nuclei within relativistic mean field method,this effect is much smaller in the nonrelativistic mean-field approximation.
Iliaš, M.; Jensen, Hans Jørgen Aagaard; Bast, R.;
2013-01-01
better convergence of magnetisabilities with respect to the basis set size is observed compared to calculations employing a common gauge origin. In fact, it is mandatory to use London atomic orbitals unless you want to use ridiculously large basis sets. Relativistic effects on magnetisabilities are found......The use of magnetic-field dependent London atomic orbitals, also called gauge including atomic orbitals, is known to be an efficient choice for accurate non-relativistic calculations of magnetisabilities. In this work, the appropriate formulas were extended and implemented in the framework...... 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...
Efficient two-component relativistic method for large systems
Nakai, Hiromi [Department of Chemitsry and Biochemistry, School of Advanced Science and Engineering, Waseda University, Tokyo 169-8555 (Japan); Research Institute for Science and Engineering, Waseda University, Tokyo 169-8555 (Japan); CREST, Japan Science and Technology Agency, 4-1-8 Honcho, Kawaguchi, Saitama 332-0012 (Japan); Elements Strategy Initiative for Catalysts and Batteries (ESICB), Kyoto University, Katsura, Kyoto 615-8520 (Japan)
2015-12-31
This paper reviews a series of theoretical studies to develop efficient two-component (2c) relativistic method for large systems by the author’s group. The basic theory is the infinite-order Douglas-Kroll-Hess (IODKH) method for many-electron Dirac-Coulomb Hamiltonian. The local unitary transformation (LUT) scheme can effectively produce the 2c relativistic Hamiltonian, and the divide-and-conquer (DC) method can achieve linear-scaling of Hartree-Fock and electron correlation methods. The frozen core potential (FCP) theoretically connects model potential calculations with the all-electron ones. The accompanying coordinate expansion with a transfer recurrence relation (ACE-TRR) scheme accelerates the computations of electron repulsion integrals with high angular momenta and long contractions.
Electron correlation within the relativistic no-pair approximation
Almoukhalalati, Adel; Knecht, Stefan; Jensen, Hans Jørgen Aa
2016-01-01
This paper addresses the definition of correlation energy within 4-component relativistic atomic and molecular calculations. In the nonrelativistic domain the correlation energy is defined as the difference between the exact eigenvalue of the electronic Hamiltonian and the Hartree-Fock energy....... In practice, what is reported is the basis set correlation energy, where the "exact" value is provided by a full Configuration Interaction (CI) calculation with some specified one-particle basis. The extension of this definition to the relativistic domain is not straightforward since the corresponding......-like correlation expression, whereas the corresponding CI correlation energy contains an additional relaxation term. We explore numerically our theoretical analysis by carrying out variational and perturbative calculations on the two-electron rare gas atoms with specially tailored basis sets...
Relativistic wave equations: an operational approach
Dattoli, G.; Sabia, E.; Górska, K.; Horzela, A.; Penson, K. A.
2015-03-01
The use of operator methods of an algebraic nature is shown to be a very powerful tool to deal with different forms of relativistic wave equations. The methods provide either exact or approximate solutions for various forms of differential equations, such as relativistic Schrödinger, Klein-Gordon, and Dirac. We discuss the free-particle hypotheses and those relevant to particles subject to non-trivial potentials. In the latter case we will show how the proposed method leads to easily implementable numerical algorithms.
Relativistic heavy-atom effects on heavy-atom nuclear shieldings
Lantto, Perttu; Romero, Rodolfo H.; Gómez, Sergio S.; Aucar, Gustavo A.; Vaara, Juha
2006-11-01
The principal relativistic heavy-atom effects on the nuclear magnetic resonance (NMR) shielding tensor of the heavy atom itself (HAHA effects) are calculated using ab initio methods at the level of the Breit-Pauli Hamiltonian. This is the first systematic study of the main HAHA effects on nuclear shielding and chemical shift by perturbational relativistic approach. The dependence of the HAHA effects on the chemical environment of the heavy atom is investigated for the closed-shell X2+, X4+, XH2, and XH3- (X =Si-Pb) as well as X3+, XH3, and XF3 (X =P-Bi) systems. Fully relativistic Dirac-Hartree-Fock calculations are carried out for comparison. It is necessary in the Breit-Pauli approach to include the second-order magnetic-field-dependent spin-orbit (SO) shielding contribution as it is the larger SO term in XH3-, XH3, and XF3, and is equally large in XH2 as the conventional, third-order field-independent spin-orbit contribution. Considering the chemical shift, the third-order SO mechanism contributes two-thirds of the difference of ˜1500ppm between BiH3 and BiF3. The second-order SO mechanism and the numerically largest relativistic effect, which arises from the cross-term contribution of the Fermi contact hyperfine interaction and the relativistically modified spin-Zeeman interaction (FC/SZ-KE), are isotropic and practically independent of electron correlation effects as well as the chemical environment of the heavy atom. The third-order SO terms depend on these factors and contribute both to heavy-atom shielding anisotropy and NMR chemical shifts. While a qualitative picture of heavy-atom chemical shifts is already obtained at the nonrelativistic level of theory, reliable shifts may be expected after including the third-order SO contributions only, especially when calculations are carried out at correlated level. The FC/SZ-KE contribution to shielding is almost completely produced in the s orbitals of the heavy atom, with values diminishing with the principal
A two-dimensional approach to relativistic positioning systems
Coll, B; Morales, J A; Coll, Bartolom\\'{e}; Ferrando, Joan Josep; Morales, Juan Antonio
2006-01-01
A relativistic positioning system is a physical realization of a coordinate system consisting in four clocks in arbitrary motion broadcasting their proper times. The basic elements of the relativistic positioning systems are presented in the two-dimensional case. This simplified approach allow to explain and to analyze the properties and interest of these new systems. The positioning system defined by geodesic emitters in flat metric is developed in detail. The information that the data generated by a relativistic positioning system give on the space-time metric interval is analyzed, and the interest of these results in gravimetry is pointed out.
Hanni, Matti; Lantto, Perttu; Ilias, Miroslav
2007-01-01
Relativistic effects on the 129Xe nuclear magnetic resonance shielding and 131Xe nuclear quadrupole coupling (NQC) tensors are examined in the weakly bound Xe2 system at different levels of theory including the relativistic four-component Dirac-Hartree-Fock (DHF) method. The intermolecular...... interaction-induced binary chemical shift d, the anisotropy of the shielding tensor ?s, and the NQC constant along the internuclear axis ?ll are calculated as a function of the internuclear distance. DHF shielding calculations are carried out using gauge-including atomic orbitals. For comparison, the full...... leading-order one-electron Breit-Pauli perturbation theory (BPPT) is applied using a common gauge origin. Electron correlation effects are studied at the nonrelativistic (NR) coupled-cluster singles and doubles with perturbational triples [CCSD(T)] level of theory. The fully relativistic second...
Hot neutron matter from a Self-Consistent Green's Functions approach
Rios, A; Vidaña, I
2008-01-01
A systematic study of the microscopic and thermodynamical properties of pure neutron matter at finite temperature within the Self-Consistent Green's Function approach is performed. The model dependence of these results is analyzed by both comparing the results obtained with two different microscopic interactions, the CD-BONN and the Argonne V18 potentials, and by analyzing the results obtained with other approaches, such as the Brueckner--Hartree--Fock approximation, the variational approach and the virial expansion.
Time-dependent HF approach to SHE dynamics
Umar, A. S.; Oberacker, V. E.
2015-12-01
We employ the time-dependent Hartree-Fock (TDHF) method to study various aspects of the reactions utilized in searches for superheavy elements. These include capture cross-sections, quasifission, prediction of PCN, and other interesting dynamical quantities. We show that the microscopic TDHF approach provides an important tool to shed some light on the nuclear dynamics leading to the formation of superheavy elements.
Mapping the Generator Coordinate Method to the Coupled Cluster Approach
Stuber, Jason L
2015-01-01
The generator coordinate method (GCM) casts the wavefunction as an integral over a weighted set of non-orthogonal single determinantal states. In principle this representation can be used like the configuration interaction (CI) or shell model to systematically improve the approximate wavefunction towards an exact solution. In practice applications have generally been limited to systems with less than three degrees of freedom. This bottleneck is directly linked to the exponential computational expense associated with the numerical projection of broken symmetry Hartree-Fock (HF) or Hartree-Fock-Bogoliubov (HFB) wavefunctions and to the use of a variational rather than a bi-variational expression for the energy. We circumvent these issues by choosing a hole-particle representation for the generator and applying algebraic symmetry projection, via the use of tensor operators and the invariant mean (operator average). The resulting GCM formulation can be mapped directly to the coupled cluster (CC) approach, leading...
A variational approach to resistive relativistic plasmas
Andersson, N; Hawke, I
2016-01-01
We develop an action principle to construct the field equations for a multi-fluid system containing charge-neutral fluids, plasmas, and dissipation (via resistive interactions), by combining the standard, Maxwell action and minimal coupling of the electromagnetic field with a recently developed action for relativistic dissipative fluids. We use a pull-back formalism from spacetime to abstract matter spaces to build unconstrained variations for both the charge-neutral fluids and currents making up the plasmas. Using basic linear algebra techniques, we show that a general "relabeling" invariance exists for the abstract matter spaces. With the field equations in place, a phenomenological model for the resistivity is developed, using as constraints charge conservation and the Second Law of Thermodynamics. A minimal model for a system of electrons, protons, and heat is developed using the Onsager procedure for incorporating dissipation.
A variational approach to resistive relativistic plasmas
Andersson, N.; Comer, G. L.; Hawke, I.
2017-06-01
We develop an action principle to construct the field equations for a multi-fluid system containing charge-neutral fluids, plasmas, and dissipation (via resistive interactions), by combining the standard, Maxwell action and minimal coupling of the electromagnetic field with a recently developed action for relativistic dissipative fluids. We use a pull-back formalism from spacetime to abstract matter spaces to build unconstrained variations for both the charge-neutral fluids and currents making up the plasmas. Using basic linear algebra techniques, we show that a general ‘relabeling’ invariance exists for the abstract matter spaces. With the field equations in place, a phenomenological model for the resistivity is developed, using as constraints charge conservation and the Second Law of Thermodynamics. A minimal model for a system of electrons, protons, and heat is developed using the Onsager procedure for incorporating dissipation.
Cherenkov loss factor of short relativistic bunches:general approach
Baturin, S S
2013-01-01
The interaction of short relativistic charged particle bunches with waveguides and other accelerator system components is a critical issue for the development of X-ray FELs (free electron lasers) and linear collider projects. Wakefield Cherenkov losses of short bunches have been studied previously for resistive wall, disk-loaded, corrugated and dielectric loaded waveguides. It was noted in various publications [1] that if the slowdown layer is thin, the Cherenkov loss factor of a short bunch does not depend on the guiding system material and is a constant for any given transverse cross section dimensions of the waveguides. In this paper, we consider a new approach to the analysis of loss factors for relativistic short bunches and formulate a general integral relation that allows calculation of the loss factor for a short relativistic bunch passing an arbitrary waveguide system. The loss factors calculated by this new method for various types of waveguides with arbitrary thickness slowdown layers, including in...
Big Data Meets Quantum Chemistry Approximations: The Δ-Machine Learning Approach.
Ramakrishnan, Raghunathan; Dral, Pavlo O; Rupp, Matthias; von Lilienfeld, O Anatole
2015-05-12
Chemically accurate and comprehensive studies of the virtual space of all possible molecules are severely limited by the computational cost of quantum chemistry. We introduce a composite strategy that adds machine learning corrections to computationally inexpensive approximate legacy quantum methods. After training, highly accurate predictions of enthalpies, free energies, entropies, and electron correlation energies are possible, for significantly larger molecular sets than used for training. For thermochemical properties of up to 16k isomers of C7H10O2 we present numerical evidence that chemical accuracy can be reached. We also predict electron correlation energy in post Hartree-Fock methods, at the computational cost of Hartree-Fock, and we establish a qualitative relationship between molecular entropy and electron correlation. The transferability of our approach is demonstrated, using semiempirical quantum chemistry and machine learning models trained on 1 and 10% of 134k organic molecules, to reproduce enthalpies of all remaining molecules at density functional theory level of accuracy.
Big Data meets Quantum Chemistry Approximations: The $\\Delta$-Machine Learning Approach
Ramakrishnan, Raghunathan; Rupp, Matthias; von Lilienfeld, O Anatole
2015-01-01
Chemically accurate and comprehensive studies of the virtual space of all possible molecules are severely limited by the computational cost of quantum chemistry. We introduce a composite strategy that adds machine learning corrections to computationally inexpensive approximate legacy quantum methods. After training, highly accurate predictions of enthalpies, free energies, entropies, and electron correlation energies are possible, for significantly larger molecular sets than used for training. For thermochemical properties of up to 16k constitutional isomers of C$_7$H$_{10}$O$_2$ we present numerical evidence that chemical accuracy can be reached. We also predict electron correlation energy in post Hartree-Fock methods, at the computational cost of Hartree-Fock, and we establish a qualitative relationship between molecular entropy and electron correlation. The transferability of our approach is demonstrated, using semi-empirical quantum chemistry and machine learning models trained on 1 and 10\\% of 134k organ...
Huynh, Tri H V; Shim, Irene; Bohr, Henrik; Abrahamsen, Bjarke; Nielsen, Birgitte; Jensen, Anders A; Bunch, Lennart
2012-06-14
The excitatory amino acid transporters (EAATs) play essential roles in regulating the synaptic concentration of the neurotransmitter glutamate in the mammalian central nervous system. To date, five subtypes have been identified, named EAAT1-5 in humans, and GLAST, GLT-1, EAAC1, EAAT4, and EAAT5 in rodents, respectively. In this paper, we present the design, synthesis, and pharmacological evaluation of seven 7-N-substituted analogues of UCPH-101/102. Analogue 9 inhibited EAAT1 in the micromolar range (IC(50) value 20 μM), whereas analogues 8 and 10 were inactive (IC(50) values >100 μM). The diastereomeric pairs 11a/11b and 12a/12b were separated by HPLC and the absolute configuration assigned by VCD technique in combination with ab initio Hartree-Fock calculations. Analogues 11a (RS-isomer) and 12b (RR-isomer) inhibited EAAT1 (IC(50) values 5.5 and 3.8 μM, respectively), whereas analogues 11b (SS-isomer) and 12a (SR-isomer) failed to inhibit EAAT1 uptake (IC(50) values >300 μM).
Mean field approaches for $\\Xi^-$ hypernuclei and current experimental data
Sun, T T; Sagawa, H; Schulze, H -J; Meng, J
2016-01-01
Motivated by the recently observed hypernucleus (Kiso event) $^{15}_{\\Xi}$C ($^{14}$N$+\\Xi^-$), we identify the state of this system theoretically within the framework of the relativistic-mean-field and Skyrme-Hartree-Fock models. The $\\Xi N$ interactions are constructed to reproduce the two possibly observed $\\Xi^-$ removal energies, $4.38\\pm 0.25$ MeV or $1.11\\pm 0.25$ MeV. The present result is preferable to be $^{14}{\\rm N}({\\rm g.s.})+\\Xi^-(1p)$, corresponding to the latter value.
Equation of State in a Generalized Relativistic Density Functional Approach
Typel, Stefan
2015-01-01
The basic concepts of a generalized relativistic density functional approach to the equation of state of dense matter are presented. The model is an extension of relativistic mean-field models with density-dependent couplings. It includes explicit cluster degrees of freedom. The formation and dissolution of nuclei is described with the help of mass shifts. The model can be adapted to the description of finite nuclei in order to study the effect of $\\alpha$-particle correlations at the nuclear surface on the neutron skin thickness of heavy nuclei. Further extensions of the model to include quark degrees of freedom or an energy dependence of the nucleon self-energies are outlined.
Gourlaouen, Christophe; Piquemal, Jean-Philip; Saue, Trond; Parisel, Olivier
2006-01-30
Hartree-Fock and DFT (B3LYP) nonrelativistic (scalar relativistic pseudopotentials for the metallic cation) and relativistic (molecular four-component approach coupled to an all-electron basis set) calculations are performed on a series of six nd10 (n+1)s0 [M(H2O)]p+ complexes to investigate their geometry, either planar C2v or nonplanar C(s). These complexes are, formally, entities originating from the complexation of a water molecule to a metallic cation: in the present study, no internal reorganization has been found, which ensures that the complexes can be regarded as a water molecule interacting with a metallic cation. For [Au(H2O)]+ and [Hg(H2O)]2+, it is observed that both electronic correlation and relativistic effects are required to recover the C(s) structures predicted by the four-component relativistic all-electron DFT calculations. However, including the zero-point energy corrections makes these shallow C(s) minima vanish and the systems become floppy. In all other systems, namely [Cu(H2O)]+, [Zn(H2O)]2+, [Ag(H2O)]+, and [Cd(H2O)]2+, all calculations predict a C2v geometry arising from especially flat potential energy surfaces related to the out-of-plane wagging vibration mode. In all cases, our computations point to the quasi-perfect transferability of the atomic pseudopotentials considered toward the molecular species investigated. A rationalization of the shape of the wagging potential energy surfaces (i.e., single well vs. double well) is proposed based on the Constrained Space Orbital Variation decompositions of the complexation energies. Any way of stabilizing the lowest unoccupied orbital of the metallic cation is expected to favor charge-transfer (from the highest occupied orbital(s) of the water ligand), covalence, and, consequently, C(s) structures. The CSOV complexation energy decompositions unambiguously reveal that such stabilizations are achieved by means of relativistic effects for [Au(H2O)]+, and, to a lesser extent, for [Hg(H2O)]2
Quantum regime of a free-electron laser: relativistic approach
Kling, Peter; Sauerbrey, Roland; Preiss, Paul; Giese, Enno; Endrich, Rainer; Schleich, Wolfgang P.
2017-01-01
In the quantum regime of the free-electron laser, the dynamics of the electrons is not governed by continuous trajectories but by discrete jumps in momentum. In this article, we rederive the two crucial conditions to enter this quantum regime: (1) a large quantum mechanical recoil of the electron caused by the scattering with the laser and the wiggler field and (2) a small energy spread of the electron beam. In contrast to our recent approach based on nonrelativistic quantum mechanics in a co-moving frame of reference, we now pursue a model in the laboratory frame employing relativistic quantum electrodynamics.
Heinz, U; Denicol, G S; Martinez, M; Nopoush, M; Noronha, J; Ryblewski, R; Strickland, M
2015-01-01
Several recent results are reported from work aiming to improve the quantitative precision of relativistic viscous fluid dynamics for relativistic heavy-ion collisions. The dense matter created in such collisions expands in a highly anisotropic manner. Due to viscous effects this also renders the local momentum distribution anisotropic. Optimized hydrodynamic approaches account for these anisotropies already at leading order in a gradient expansion. Recently discovered exact solutions of the relativistic Boltzmann equation in anisotropically expanding systems provide a powerful testbed for such improved hydrodynamic approximations. We present the latest status of our quest for a formulation of relativistic viscous fluid dynamics that is optimized for applications to relativistic heavy-ion collisions.
Bozkaya, Uğur
2014-09-28
General analytic gradient expressions (with the frozen-core approximation) are presented for density-fitted post-HF methods. An efficient implementation of frozen-core analytic gradients for the second-order Møller-Plesset perturbation theory (MP2) with the density-fitting (DF) approximation (applying to both reference and correlation energies), which is denoted as DF-MP2, is reported. The DF-MP2 method is applied to a set of alkanes, conjugated dienes, and noncovalent interaction complexes to compare the computational cost of single point analytic gradients with MP2 with the resolution of the identity approach (RI-MP2) [F. Weigend and M. Häser, Theor. Chem. Acc. 97, 331 (1997); R. A. Distasio, R. P. Steele, Y. M. Rhee, Y. Shao, and M. Head-Gordon, J. Comput. Chem. 28, 839 (2007)]. In the RI-MP2 method, the DF approach is used only for the correlation energy. Our results demonstrate that the DF-MP2 method substantially accelerate the RI-MP2 method for analytic gradient computations due to the reduced input/output (I/O) time. Because in the DF-MP2 method the DF approach is used for both reference and correlation energies, the storage of 4-index electron repulsion integrals (ERIs) are avoided, 3-index ERI tensors are employed instead. Further, as in case of integrals, our gradient equation is completely avoid construction or storage of the 4-index two-particle density matrix (TPDM), instead we use 2- and 3-index TPDMs. Hence, the I/O bottleneck of a gradient computation is significantly overcome. Therefore, the cost of the generalized-Fock matrix (GFM), TPDM, solution of Z-vector equations, the back transformation of TPDM, and integral derivatives are substantially reduced when the DF approach is used for the entire energy expression. Further application results show that the DF approach introduce negligible errors for closed-shell reaction energies and equilibrium bond lengths.
Bozkaya, Uğur, E-mail: ugur.bozkaya@atauni.edu.tr [Department of Chemistry, Atatürk University, Erzurum 25240, Turkey and Department of Chemistry, Middle East Technical University, Ankara 06800 (Turkey)
2014-09-28
General analytic gradient expressions (with the frozen-core approximation) are presented for density-fitted post-HF methods. An efficient implementation of frozen-core analytic gradients for the second-order Møller–Plesset perturbation theory (MP2) with the density-fitting (DF) approximation (applying to both reference and correlation energies), which is denoted as DF-MP2, is reported. The DF-MP2 method is applied to a set of alkanes, conjugated dienes, and noncovalent interaction complexes to compare the computational cost of single point analytic gradients with MP2 with the resolution of the identity approach (RI-MP2) [F. Weigend and M. Häser, Theor. Chem. Acc. 97, 331 (1997); R. A. Distasio, R. P. Steele, Y. M. Rhee, Y. Shao, and M. Head-Gordon, J. Comput. Chem. 28, 839 (2007)]. In the RI-MP2 method, the DF approach is used only for the correlation energy. Our results demonstrate that the DF-MP2 method substantially accelerate the RI-MP2 method for analytic gradient computations due to the reduced input/output (I/O) time. Because in the DF-MP2 method the DF approach is used for both reference and correlation energies, the storage of 4-index electron repulsion integrals (ERIs) are avoided, 3-index ERI tensors are employed instead. Further, as in case of integrals, our gradient equation is completely avoid construction or storage of the 4-index two-particle density matrix (TPDM), instead we use 2- and 3-index TPDMs. Hence, the I/O bottleneck of a gradient computation is significantly overcome. Therefore, the cost of the generalized-Fock matrix (GFM), TPDM, solution of Z-vector equations, the back transformation of TPDM, and integral derivatives are substantially reduced when the DF approach is used for the entire energy expression. Further application results show that the DF approach introduce negligible errors for closed-shell reaction energies and equilibrium bond lengths.
Effective approach to non-relativistic quantum mechanics
Jacobs, David M
2015-01-01
Boundary conditions on non-relativistic wavefunctions are generally not completely constrained by the basic precepts of quantum mechanics, so understanding the set of possible self-adjoint extensions of the Hamiltonian is required. For real physical systems, non-trivial self-adjoint extensions have been used to model contact potentials when those interactions are expected a priori. However, they must be incorporated into the effective description of any quantum mechanical system in order to capture possible short-distance physics that does not decouple in the low energy limit. Here, an approach is described wherein an artificial boundary is inserted at an intermediate scale on which boundary conditions may encode short-distance effects that are hidden behind the boundary. Using this approach, an analysis is performed of the free particle, harmonic oscillator, and Coulomb potential in three dimensions. Requiring measurable quantities, such as spectra and cross sections, to be independent of this artificial bou...
Kinetic approach to a relativistic Bose-Einstein condensate
Meistrenko, Alex; Zhou, Kai; Greiner, Carsten
2015-01-01
We apply a Boltzmann approach to the kinetic regime of a relativistic Bose-Einstein condensate of scalar bosons by decomposing the one-particle distribution function in a condensate part and a non-zero momentum part of excited modes, leading to a coupled set of evolution equations which are then solved efficiently with an adaptive higher order Runge-Kutta scheme. We compare our results to the partonic cascade Monte-Carlo simulation BAMPS for an underpopulated but far from equilibrium case of massless bosons. Motivated by the color glass condensate initial conditions in QCD with a strongly overpopulated initial glasma state, we also discuss the time evolution starting from an overpopulated initial distribution function of massive scalar bosons.
Entropy-limited hydrodynamics: a novel approach to relativistic hydrodynamics
Guercilena, Federico; Radice, David; Rezzolla, Luciano
2017-07-01
We present entropy-limited hydrodynamics (ELH): a new approach for the computation of numerical fluxes arising in the discretization of hyperbolic equations in conservation form. ELH is based on the hybridisation of an unfiltered high-order scheme with the first-order Lax-Friedrichs method. The activation of the low-order part of the scheme is driven by a measure of the locally generated entropy inspired by the artificial-viscosity method proposed by Guermond et al. (J. Comput. Phys. 230(11):4248-4267, 2011, doi: 10.1016/j.jcp.2010.11.043). Here, we present ELH in the context of high-order finite-differencing methods and of the equations of general-relativistic hydrodynamics. We study the performance of ELH in a series of classical astrophysical tests in general relativity involving isolated, rotating and nonrotating neutron stars, and including a case of gravitational collapse to black hole. We present a detailed comparison of ELH with the fifth-order monotonicity preserving method MP5 (Suresh and Huynh in J. Comput. Phys. 136(1):83-99, 1997, doi: 10.1006/jcph.1997.5745), one of the most common high-order schemes currently employed in numerical-relativity simulations. We find that ELH achieves comparable and, in many of the cases studied here, better accuracy than more traditional methods at a fraction of the computational cost (up to {˜}50% speedup). Given its accuracy and its simplicity of implementation, ELH is a promising framework for the development of new special- and general-relativistic hydrodynamics codes well adapted for massively parallel supercomputers.
Relativistic Approach to the Hydrogen Atom in a Minimal Length Scenario
Francisco, Ronald Oliveira; Oakes, Thiago Luiz Antonacci; Fabris, Julio Cesar; Nogueira, Jose Alexandre, E-mail: jose.nogueira@ufes.br [Universidade Federal do Espirito Santo (UFES), Vitoria, ES (Brazil). Departamento de Fisica
2014-07-01
We show that relativistic contributions to the ground-state energy of the hydrogen atom from a minimal length introduced by a Lorentz-covariant algebra are more important than non-relativistic contributions; the nonrelativistic approach is therefore unsuitable. We compare our result with experimental data to estimate an upper bound of the order 10{sup -20}m for the minimal length. (author)
Large amplitude motion with a stochastic mean-field approach
Yilmaz Bulent
2012-12-01
Full Text Available In the stochastic mean-field approach, an ensemble of initial conditions is considered to incorporate correlations beyond the mean-field. Then each starting point is propagated separately using the Time-Dependent Hartree-Fock equation of motion. This approach provides a rather simple tool to better describe fluctuations compared to the standard TDHF. Several illustrations are presented showing that this theory can be rather effective to treat the dynamics close to a quantum phase transition. Applications to fusion and transfer reactions demonstrate the great improvement in the description of mass dispersion.
On kaonic deuterium. Quantum field theoretic and relativistic covariant approach
Ivanov, A N; Faber, M; Fuhrmann, H; Ivanova, V A; Marton, J; Troitskaya, N I; Zmeskal, J
2004-01-01
We study kaonic deuterium, the bound K^-d state A_{K d}. Within a quantum field theoretic and relativistic covariant approach we derive the energy level displacement of the ground state of kaonic deuterium in terms of the amplitude of K^-d scattering for arbitrary relative momenta. Near threshold our formula reduces to the well-known DGBT formula. The S-wave amplitude of K^-d scattering near threshold is defined by the resonances Lambda(1405), Sigma(1750) and a smooth elastic background, and the inelastic channels K^- d -> NY and K^- d -> NY pion, with Y = Sigma^{+/-}, Sigma^0 and Lambda^0, where the final-state interactions play an important role. The Ericson-Weise formula for the S-wave scattering length of K^-d scattering is derived. The total width of the energy level of the ground state of kaonic deuterium is estimated using the theoretical predictions of the partial widths of the two-body decays A_{Kd} -> NY and experimental data on the rates of the NY-pair production in the reactions K^-d -> NY. We obt...
On kaonic hydrogen. Quantum field theoretic and relativistic covariant approach
Ivanov, A N; Faber, M; Marton, J; Troitskaya, N I; Zmeskal, J
2003-01-01
We study kaonic hydrogen, the bound K^-p state A_(Kp). Within a quantum field theoretic and relativistic covariant approach we derive the energy level displacement of the ground state of kaonic hydrogen in terms of the amplitude of K^-p scattering for arbitrary energies. The amplitude of low-energy K^-p scattering near threshold is defined by the contributions of three resonances Lambda(1405), Lambda(1800) and Sigma^0(1750) and a smooth elastic background. The amplitudes of inelastic channels of low-energy K^-p scattering fit experimental data on near threshold behaviour of the cross sections and the experimental data by the DEAR Collaboration. We use the soft-pion technique (leading order in Chiral Perturbation Theory) for the calculate of the partial width of the radiative decay of pionic hydrogen A_(pi p) -> n + gamma and the Panofsky ratio. The theoretical prediction for the Panofsky ratio agrees well with experimental data. We apply the soft-kaon technique (leading order in Chiral Perturbation Theory) to...
On kaonic hydrogen. Quantum field theoretic and relativistic covariant approach
Ivanov, A. N.; Cargnelli, M.; Faber, M.; Marton, J.; Troitskaya, N. I.; Zmeskal, J.
2004-07-01
We study kaonic hydrogen, the bound K - p state A K p . Within a quantum field theoretic and relativistic covariant approach we derive the energy level displacement of the ground state of kaonic hydrogen in terms of the amplitude of K - p scattering for arbitrary relative momenta. The amplitude of low-energy K - p scattering near threshold is defined by the contributions of three resonances Λ(1405), Λ(1800) and Σ^0(1750) and a smooth elastic background. The amplitudes of inelastic channels of low-energy K - p scattering fit experimental data on the near-threshold behaviour of the cross-sections and the experimental data by the DEAR Collaboration. We use the soft-pion technique (leading order in Chiral Perturbation Theory) for the calculation of the partial width of the radiative decay of pionic hydrogen A_{π p} to n + γ and the Panofsky ratio. The theoretical prediction for the Panofsky ratio agrees well with experimental data. We apply the soft-kaon technique (leading order in Chiral Perturbation Theory) to the calculation of the partial widths of radiative decays of kaonic hydrogen A_{Kp} to Λ^0 + γ and A_{K p} to Σ^0 + γ. We show that the contribution of these decays to the width of the energy level of the ground state of kaonic hydrogen is less than 1%.
Approaches to relativistic positioning around Earth and error estimations
Puchades, Neus
2016-01-01
In the context of relativistic positioning, the coordinates of a given user may be calculated by using suitable information broadcast by a 4-tuple of satellites. Our 4-tuples belong to the Galileo constellation. Recently, we estimated the positioning errors due to uncertainties in the satellite world lines (U-errors). A distribution of U-errors was obtained, at various times, in a set of points covering a large region surrounding Earth. Here, the positioning errors associated to the simplifying assumption that photons move in Minkowski space-time (S-errors) are estimated and compared with the U-errors. Both errors have been calculated for the same points and times to make comparisons possible. For a certain realistic modeling of the world line uncertainties, the estimated S-errors have proved to be smaller than the U-errors, which shows that the approach based on the assumption that the Earth's gravitational field produces negligible effects on photons may be used in a large region surrounding Earth. The appl...
Gamow-Teller Resonance of 90Zr in a Relativistic Approach
马中玉; 陈宝秋
2003-01-01
We establish the formalism of nuclear spin-isospin excitations, especially the Gamow-Teller resonance in a fully consistent relativistic random-phase approximation. A relativistic form of the Landau-Migdal parameter g′ is adopted as a residual spin-isospin correlation force. In the non-relativistic limit it reproduces the excitation energy of the giant Gamow-Teller resonance state obtained in the non-relativistic model. The Gamow-Teller resonance for finite nuclei is investigated in a relativistic approach for the first time. It is found that the Ikeda sum rule of90Zr is quenched about 8% in the Hartree as well as the correlated strengths due to the poles of the negative Dirac states at energies above 1 GeV.
Safronova, M S; Derevianko, S A
1999-01-01
Removal energies and hyperfine constants of the lowest four $ns, np_{1/2}$ and $np_{3/2}$ states in Na, K, Rb and Cs are calculated; removal energies of the n=7--10 states and hyperfine constants of the n=7 and 8 states in Fr are also calculated. The calculations are based on the relativistic single-double (SD) approximation in which single and double excitations of Dirac-Hartree-Fock (DHF) wave functions are included to all-orders in perturbation theory. Using SD wave functions, accurate values of removal energies, electric-dipole matrix elements and static polarizabilities are obtained, however, SD wave functions give poor values of magnetic-dipole hyperfine constants for heavy atoms. To obtain accurate values of hyperfine constants for heavy atoms, we include triple excitations partially in the wave functions. The present calculations provide the basis for reevaluating PNC amplitudes in Cs and Fr.
Quantum Geometry: Relativistic energy approach to cooperative electron-nucleary-transition spectrum
Ольга Юрьевна Хецелиус
2014-11-01
Full Text Available An advanced relativistic energy approach is presented and applied to calculating parameters of electron-nuclear 7-transition spectra of nucleus in the atom. The intensities of the spectral satellites are defined in the relativistic version of the energy approach (S-matrix formalism, and gauge-invariant quantum-electrodynamical perturbation theory with the Dirac-Kohn-Sham density-functional zeroth approximation.
Bast, Radovan; Juselius, Jonas [Centre for Theoretical and Computational Chemistry (CTCC), Department of Chemistry, University of Tromso, N-9037 Tromso (Norway); Saue, Trond [Institut de Chimie de Strasbourg, CNRS et Universite Louis Pasteur, Laboratoire de Chimie Quantique, 4, rue Blaise Pascal, BP 1032, F-67070 Strasbourg (France)], E-mail: tsaue@chimie.u-strasbg.fr
2009-02-17
We present a 4-component relativistic implementation for calculating the magnetically induced current density within Hartree-Fock and Kohn-Sham linear response theory using a common gauge origin. We demonstrate how the current density can be decomposed into paramagnetic and diamagnetic contributions by calculating separately the contributions from rotations between positive-energy orbitals and contributions from rotations between the occupied positive-energy orbitals and the virtual negative-energy orbitals, respectively. This methodology is applied to the study of the magnetically induced current density in benzene and the group 15 heteroaromatic compounds C{sub 5}H{sub 5}E (E = N, P, As, Sb, Bi). Quantitative values for the magnetically induced ring currents are obtained by numerical integration over the current flow. We have found that the diatropic ring current is sustained for the entire series of the group 15 heteroaromatic compounds-the induced ring current susceptibility of bismabenzene being 76% of the benzene result. Having employed two hybrid and two nonhybrid generalized gradient approximation functionals, the results are found to be rather insensitive to the choice of the density functional approximation. The relativistic effect is relatively small, reaching its maximum of 8% for bismabenzene. The presented 4-component relativistic methodology opens up the possibility to visualize magnetically induced current densities of aromatic heavy-element systems with both scalar relativistic and spin-orbit effects included.
The q overlineq relativistic interaction in the Wilson loop approach
Brambilla, N.; Vairo, A.
1998-05-01
We study the q overlineq relativistic interaction starting from the Feynman-Schwinger representation of the gauge-invariant quark-antiquark Green function. We focus on the one-body limit and discuss the obtained non-perturbative interaction kernel of the Dirac equation.
Donker, H. C.; Katsnelson, M. I.; De Raedt, H.; Michielsen, K.
2016-09-01
The logical inference approach to quantum theory, proposed earlier De Raedt et al. (2014), is considered in a relativistic setting. It is shown that the Klein-Gordon equation for a massive, charged, and spinless particle derives from the combination of the requirements that the space-time data collected by probing the particle is obtained from the most robust experiment and that on average, the classical relativistic equation of motion of a particle holds.
A Conic Section Approach to the Relativistic Reflection Law
Maesumi, Mohsen
2016-01-01
We consider the reflection of light, from a stationary source, off of a uniformly moving flat mirror, and derive the relativistic reflection law using well-known properties of conic sections. The effective surface of reflection (ESR) is defined as the loci of intersection of all beams, emanating from the source at a given time, with the moving mirror. Fermat principle of least time is then applied to ESR and it is shown that, assuming the independence of speed of light, the result is identical with the relativistic reflection law. For a uniformly moving mirror ESR is a conic and the reflection law becomes a case of bi-angular equation of the conic, with the incident and reflected beams coinciding with the focal rays of the conic. A short calculus-based proof for accelerating mirrors is also given.
Relativistic corrections to the central force problem in a generalized potential approach
Singh, Ashmeet
2014-01-01
We present a novel technique to obtain the relativistic corrections to the central force problem in the Lagrangian formulation, using a generalized potential energy. Throughout the paper, we focus on the attractive inverse square law central force. The generalised potential can be made a part of the regular classical lagrangian which can reproduce the relativistic force equation upto second order in $|\\vec{v}|/c$. We then go on to derive the relativistically corrected Hamiltonian from the Lagrangian and estimate the corrections to the total energy of the system. We employ our methodology to calculate the relativistic correction to the circular orbit in attractive gravitational force. We also estimate to the first order energy correction in the ground state of the hydrogen atom in the semi-classical approach. Our predictions in both problems give the reasonable agreement with the known results. Thus we feel that this work has pedagogical value and can be used by undergraduate students to better understand the ...
Role of deformation on giant resonances within the QRPA approach and the Gogny force
Peru, S
2008-01-01
Fully consistent axially-symmetric-deformed Quasi-particle Random Phase Approximation (QRPA) calculations have been performed, in which the same Gogny D1S effective force has been used for both the Hartree-Fock-Bogolyubov mean field and the QRPA approaches. Giant resonances calculated in deformed $^{26-28}$Si and $^{22-24}$Mg nuclei as well as in the spherical $^{30}$Si and $^{28}$Mg isotopes are presented. Theoretical results for isovector-dipole and isoscalar monopole, quadrupole, and octupole responses are presented and the impact of the intrinsic nuclear deformation is discussed.
A generating functional approach to the sd-model with strong correlations
Yu.A.Izyumov
2005-01-01
Full Text Available A Kadanoff-Baym-type generating functional approach, earlier developed by the authors to strongly correlated systems, is applied to the sd-model with strong sd-coupling. Formalism of the Hubbard X-operators was used, and equation for electron Green's function was derived with functional derivatives over external fluctuating fields. Iterations in this equation generate a perturbation theory near the atomic limit. Hartree-Fock type approximation is developed within the framework of this theory, and the problem of a metal-insulator phase transition in sd-model is discussed.
Meson Structure in a Relativistic Many-Body Approach
Llanes-Estrada, F J; Llanes-Estrada, Felipe J.; Cotanch, Stephen R.
2000-01-01
Results from an extensive relativistic many-body analysis utilizing a realistic effective QCD Hamiltonian are presented for the meson spectrum. A comparative numerical study of the BCS, TDA and RPA treatments provides new, significant insight into the condensate structure of the vacuum, the chiral symmetry governance of the pion and the meson spin, orbital and flavor mass splitting contributions. In contrast to a previous glueball application, substantial quantitative differences are computed between TDA and RPA for the light quark sector with the pion emerging as a Goldstone boson only in the RPA.
A String Motivated Approach to the Relativistic Point Particle
Tuite, M P; Tuite, Michael; Sen, Siddhartha
2003-01-01
Using concepts developed in string theory, Cohen, Moore, Nelson and Polchinski calculated the propagator for a relativistic point particle. Following these authors we extend the technique to include the case of closed world lines. The partition function found corresponds to the Feynmann and Schwinger proper time formalism. We also explicitly verify that the partition function is equivalent to the usual path length action partition function. As an example of a sum over closed world lines, we compute the Euler-Heisenberg effective Lagrangian in a novel way.
From RHIC to LHC: A relativistic diffusion approach
Kuiper, R; Kuiper, Rolf; Wolschin, Georg
2007-01-01
We investigate the energy dependence of stopping and hadron production in high-energy heavy-ion collisions based on a three-sources Relativistic Diffusion Model. The transport coefficients are extrapolated from Au + Au and Cu + Cu at RHIC energies (sqrt{s_NN)=19.6 - 200 GeV) to Pb + Pb at LHC energies sqrt{s_NN)= 5.52 TeV. Rapidity distributions for net protons, and pseudorapidity spectra for produced charged particles in central collisions are compared to data at RHIC energies, and discussed for several extrapolations to LHC energies.
DONG Yu-Bing; FENG Qing-Guo
2002-01-01
Based on a relativistic quark model approach, the transition properties of the first nucleon resonance △(1232), and the coupling constants gπNN, g△πN are investigated. Tvo different vays to remove the center of mass motion are considered. The results of the relativistic approaches with and without center ofmass correction are compared with those of nonrelativistic constituent quark model. Moreover, pion meson cloud effect on these calculated observables is explicitly addressed. Better results are obtained by taking the pion meson cloud into account.
Relativistic bound state approach to fundamental forces including gravitation
Morsch H.P.
2012-06-01
Full Text Available To describe the structure of particle bound states of nature, a relativistic bound state formalism is presented, which requires a Lagrangian including scalar coupling of two boson fields. The underlying mechanisms are quite complex and require an interplay of overlapping boson fields and fermion-antifermion production. This gives rise to two potentials, a boson-exchange potential and one identified with the long sought confinement potential in hadrons. With minimal requirements, two elementary massless fermions (quantons - with and without charge - and one gauge boson, hadrons and leptons but also atoms and gravitational systems are described by bound states with electric and magnetic coupling between the charges and spins of quantons. No need is found for colour, Higgs-coupling and supersymmetry.
A nonextensive statistics approach for Langmuir waves in relativistic plasmas
V. Muñoz
2006-01-01
Full Text Available The nonextensive statistics formalism proposed by Tsallis has found many applications in systems with memory effects, long range spatial correlations, and in general whenever the phase space has fractal or multi-fractal structure. These features may appear naturally in turbulent or non-neutral plasmas. In fact, the equilibrium distribution functions which maximize the nonextensive entropy strongly resemble the non-Maxwellian particle distribution functions observed in space and laboratory and turbulent pure electron plasmas. In this article we apply the Tsallis entropy formalism to the problem of longitudinal oscillations in a proton-electron plasma. In particular, we study the equilibrium distribution function and the dispersion relation of longitudinal oscillations in a relativistic plasma, finding interesting differences with the nonrelativistic treatment.
Donker, H. C.; Katsnelson, M. I.; De Raedt, H.; Michielsen, K.
The logical inference approach to quantum theory, proposed earlier De Raedt et al. (2014), is considered in a relativistic setting. It is shown that the Klein-Gordon equation for a massive, charged, and spinless particle derives from the combination of the requirements that the space-time data
Donker, H. C.; Katsnelson, M. I.; De Raedt, H.; Michielsen, K.
2016-01-01
The logical inference approach to quantum theory, proposed earlier De Raedt et al. (2014), is considered in a relativistic setting. It is shown that the Klein-Gordon equation for a massive, charged, and spinless particle derives from the combination of the requirements that the space-time data colle
Bargmann-Michel-Telegdi equation and one-particle relativistic approach
Della Selva, A; Masperi, L
1995-01-01
A reexamination of the semiclassical approach of the relativistic electron indicates a possible variation of its helicity for electric and magnetic static fields applied along its global motion due to zitterbewegung effects, proportional to the anomalous part of the magnetic moment.
Relativistic Many-Body Hamiltonian Approach to Mesons
Llanes-Estrada, F J; Llanes-Estrada, Felipe J.; Cotanch, Stephen R.
2002-01-01
We represent QCD at the hadronic scale by means of an effective Hamiltonian, $H$, formulated in the Coulomb gauge. As in the Nambu-Jona-Lasinio model, chiral symmetry is explicity broken, however our approach is renormalizable and also includes confinement through a linear potential with slope specified by lattice gauge theory. This interaction generates an infrared integrable singularity and we detail the computationally intensive procedure necessary for numerical solution. We focus upon applications for the $u, d, s$ and $c$ quark flavors and compute the mass spectrum for the pseudoscalar, scalar and vector mesons. We also perform a comparative study of alternative many-body techniques for approximately diagonalizing $H$: BCS for the vacuum ground state; TDA and RPA for the excited hadron states. The Dirac structure of the field theoretical Hamiltonian naturally generates spin-dependent interactions, including tensor, spin-orbit and hyperfine, and we clarify the degree of level splitting due to both spin an...
Group-theoretical approach to relativistic eikonal physics
Leon, J.; Quiros, M. (Instituto de Enstructura de la Materia, C.S.I.C., Madrid (Spain); Departamento de Matematica, Universidad Complutense, Campus de Alcala (Spain)); Ramirez Mittelbrunn, J. (Instituto de Estructura de la Materia, C.S.I.C., Madrid (Spain))
1977-09-01
A contraction of the Poincare group is performed leading to the eikonal approximation. Invariants, one-particle states, spinning particles and some interaction problems are studied with the following results: momenta of ultrarelativistic particles behave as lightlike, the little group being E/sub 2/, spin behaves as that of zero-mass particles, helicity being conserved in the presence of interactions. The full eikonal results are rederived for Green's functions, wave functions, etc. The way for computing corrections due to transverse momenta and spin-dependent interactions is outlined. A parallel analysis is made for the infinite-momentum frame, the similarities and differences between this formalism and the eikonal approach being disclosed.
Pan, Jun-Yang; Xie, Yi
2015-02-01
With tremendous advances in modern techniques, Einstein's general relativity has become an inevitable part of deep space missions. We investigate the relativistic algorithm for time transfer between the proper time τ of the onboard clock and the Geocentric Coordinate Time, which extends some previous works by including the effects of propagation of electromagnetic signals. In order to evaluate the implicit algebraic equations and integrals in the model, we take an analytic approach to work out their approximate values. This analytic model might be used in an onboard computer because of its limited capability to perform calculations. Taking an orbiter like Yinghuo-1 as an example, we find that the contributions of the Sun, the ground station and the spacecraft dominate the outcomes of the relativistic corrections to the model.
Relativistic three-body quark model of light baryons based on hypercentral approach
Aslanzadeh, M.; Rajabi, A. A.
2015-05-01
In this paper, we have treated the light baryons as a relativistic three-body bound system. Inspired by lattice QCD calculations, we treated baryons as a spin-independent three-quark system within a relativistic three-quark model based on the three-particle Klein-Gordon equation. We presented the analytical solution of three-body Klein-Gordon equation with employing the constituent quark model based on a hypercentral approach through which two- and three-body forces are taken into account. Herewith the average energy values of the up, down and strange quarks containing multiplets are reproduced. To describe the hyperfine structure of the baryon, the splittings within the SU(6)-multiplets are produced by the generalized Gürsey Radicati mass formula. The considered SU(6)-invariant potential is popular "Coulomb-plus-linear" potential and the strange and non-strange baryons spectra are in general well reproduced.
A "horizon adapted" approach to the study of relativistic accretion flows onto rotating black holes
Font, J A; Papadopoulos, P P; Font, José A.; Ibanez, José M.; Papadopoulos, Philippos
1998-01-01
We present a new geometrical approach to the study of accretion flows onto rotating (Kerr) black holes. Instead of Boyer-Lindquist coordinates, the standard choice in all existing numerical simulations in the literature, we employ the simplest example of a horizon adapted coordinate system, the Kerr-Schild coordinates. This choice eliminates boundary ambiguities and unphysical divergent behavior at the event horizon. Computations of Bondi-Hoyle accretion onto extreme Kerr black holes, performed here for the first time, demonstrate the key advantages of this procedure. We argue it offers the best approach to the numerical study of the, observationally, increasingly more accesible relativistic inner region around black holes.
Zhang, Hong Lin; Sampson, D.H. (Pennsylvania State Univ., University Park, PA (USA). Dept. of Astronomy)
1990-10-22
The rapid relativistic distorted wave method of Zhang et al for excitation, which uses the atomic structure data of Sampson et al, has been extended to ionization. In this approach the same Dirac-Fock-Slater potential evaluated using a single mean configuration is used in calculating the orbitals of all electrons bound and free. Values for the cross sections Q for ionization of various ions have been calculated and generally good agreement is obtained with other recent relativistic calculations. When results are expressed in terms of the reduced ionization cross section Q{sub R}, which is proportional to I{sup 2}Q, they are close to the non-relativistic Coulomb-Born-Exchange values of Moores et al for hydrogenic ions except for high Z and/or high energies. This suggests that fits of the Q{sub R} to simple functions of the impact electron energy in threshold units with coefficients that are quite slowly varying functions of an effective Z can probably be made. This would be convenient for plasma modeling applications. 24 refs., 2 tabs.
Exchange interaction in pyrochlore vanadates Lu2V2O7 and Y2V2O7: Ab initio approach
Nazipov, D. V.; Nikiforov, A. E.; Chernyshev, V. A.
2016-10-01
The exchange interaction in vanadates with the pyrochlore structure, namely, Lu2V2O7 and Y2V2O7, has been investigated using the first-principles approach. The isotropic exchange coupling constants have been determined. The calculations have been performed within the unrestricted Hartree-Fock (UHF) approximation, as well as in the framework of the density functional theory (DFT), using hybrid functionals. It has been shown that, in the description of the exchange interaction in the compounds under investigation, the nonlocal Hartree-Fock exchange should be taken into account. The splitting patterns of the 3 d 1 level of the V4+ ion in the crystal field have been obtained within the model approach. The calculation has been carried out in the approximation of point charges taking into account the spin-orbit interaction. It has been revealed that the "orbital liquid" state cannot be observed in the compounds under investigation, because the exchange interaction energy is significantly less than the energy spacing between the ground state and the first excited state. The orbital ordering has been analyzed, and the spin density maps have been constructed.
The OIV 1407.3\\AA /1401.1\\AA\\ emission-line ratio in a plasma
Nessib, Nabil Ben; Qindeel, Rabia; Sahal-Bréchot, Sylvie; Dimitrijević, Milan S
2013-01-01
Line ratio of O IV 1407.3 \\AA/1401.1 \\AA\\- is calculated using mostly our own atomic and collisional data. Energy levels and oscillator strengths needed for this calculation have been calculated using a Hartree-Fock relativistic (HFR) approach. The electron collision strengths introduced in the statistic equilibrium equations are fitted by Line ratio of O IV 1407.3 \\AA/1401.1 \\AA\\- is calculated using mostly our own atomic and collisional data. Energy levels and oscillator strengths needed for this calculation have been calculated using a Hartree-Fock relativistic (HFR) approach. The electron collision strengths introduced in the statistic equilibrium equations are fitted by polynomials for different energies. Comparison has also been made with available theoretical results. The provided line ratio has been obtained for a set of electron densities from $10^{8}$ cm$^{-3}$ to $10^{13}$ cm$^{-3}$ and for a fixed temperature of 50 000 K.
A Geometrical Approach to Hojman Theorem of a Rotational Relativistic Birkhoffian System
ZHANGYi
2004-01-01
A geometrical approach to the Hojman theorem of a rotational relativistic Birkhoffian system is presented.The differential equations of motion of the system are established. According to the invariance of differential equations under infinitesimal transformation, the determining equations of Lie symmetry are constructed. A new conservation law of the system, called Hojman theorem, is obtained, which is the generalization of previous results given sequentially by Hojman, Zhang, and Luo et al. In terms of the theory of modern differential geometry a proof of the theorem is given.
Shell-model-like Approach (SLAP) for the Nuclear Properties in Relativistic Mean field Theory
MENG Jie; GUO Jian-you; LIU Lang; ZHANG Shuang-quan
2006-01-01
A Shell-model-like approach suggested to treat the pairing correlations in relativistic mean field theory is introduced,in which the occupancies thus obtained have been iterated back into the densities.The formalism and numerical techniques are given in detail.As examples,the ground state properties and low-lying excited states for Ne isotopes are studied.The results thus obtained are compared with the data available.The binding energies,the odd-even staggering,as well as the tendency for the change of the shapes in Ne isotopes are correctly reproduced.
A fully relativistic approach for calculating atomic data for highly charged ions
Sampson, Douglas H. [Department of Astronomy and Astrophysics, Pennsylvania State University, University Park, PA 16802 (United States); Zhang Honglin [Applied Physics Division, Los Alamos National Laboratory, Los Alamos, NM 87545 (United States)], E-mail: zhang@lanl.gov; Fontes, Christopher J. [Applied Physics Division, Los Alamos National Laboratory, Los Alamos, NM 87545 (United States)], E-mail: cjf@lanl.gov
2009-07-15
We present a review of our fully relativistic approach to calculating atomic data for highly charged ions, highlighting a research effort that spans twenty years. Detailed discussions of both theoretical and numerical techniques are provided. Our basic approach is expected to provide accurate results for ions that range from approximately half ionized to fully stripped. Options for improving the accuracy and range of validity of this approach are also discussed. In developing numerical methods for calculating data within this framework, considerable emphasis is placed on techniques that are robust and efficient. A variety of fundamental processes are considered including: photoexcitation, electron-impact excitation, electron-impact ionization, autoionization, electron capture, photoionization and photorecombination. Resonance contributions to a variety of these processes are also considered, including discussions of autoionization, electron capture and dielectronic recombination. Ample numerical examples are provided in order to illustrate the approach and to demonstrate its usefulness in providing data for large-scale plasma modeling.
A fully relativistic approach for calculating atomic data for highly charged ions
Zhang, Hong Lin [Los Alamos National Laboratory; Fontes, Christopher J [Los Alamos National Laboratory; Sampson, Douglas H [PENNSYLVANIA STATE UNIV
2009-01-01
We present a review of our fully relativistic approach to calculating atomic data for highly charged ions, highlighting a research effort that spans twenty years. Detailed discussions of both theoretical and numerical techniques are provided. Our basic approach is expected to provide accurate results for ions that range from approximately half ionized to fully stripped. Options for improving the accuracy and range of validity of this approach are also discussed. In developing numerical methods for calculating data within this framework, considerable emphasis is placed on techniques that are robust and efficient. A variety of fundamental processes are considered including: photoexcitation, electron-impact excitation, electron-impact ionization, autoionization, electron capture, photoionization and photorecombination. Resonance contributions to a variety of these processes are also considered, including discussions of autoionization, electron capture and dielectronic recombination. Ample numerical examples are provided in order to illustrate the approach and to demonstrate its usefulness in providing data for large-scale plasma modeling.
Relativistic coupled-cluster calculations of transition properties in highly charged inert-gas ions
Nandy, D. K.
2016-11-01
We have carried out an extensive investigation of various spectroscopic properties of highly charged inert-gas ions using a relativistic coupled-cluster method through a one-electron detachment procedure. In particular, we have calculated the atomic states 2 s22 p53/2 2P, 2 s22 p51/2 2P, and 2 s 2 p61/2 2S in F-like inert-gas ions; 3 s23 p53/2 2P, 3 s23 p51/2 2P, and 3 s 3 p61/2 2S states in Cl-like Kr, Xe, and Rn; and 4 s24 p53/2 2P, 4 s24 p51/2 2P, and 4 s 4 p61/2 2S states in Br-like Xe and Rn. Starting from a single-reference Dirac-Hartree-Fock wave function, we construct our exact atomic states by including the dynamic correlation effects in an all-order perturbative fashion. Employing this method, we estimate the ionization potential energies of three low-lying orbitals present in their respective closed-shell configurations. Since the considered highly charged inert-gas ions exhibit huge relativistic effects, we have taken into account the corrections due to Breit interaction as well as from the dominant quantum electrodynamic correction such as vacuum polarization and self-energy effects in these systems. Using our calculated relativistic atomic wave functions and energies, we accurately determine various transition properties such as wavelengths, line strengths, oscillator strengths, transition probabilities, and lifetimes of the excited states.
Sensing and reconstruction of arbitrary light-in-flight paths by a relativistic imaging approach
Laurenzis, Martin; Klein, Jonathan; Bacher, Emmanuel; Metzger, Nicolas; Christnacher, Frank
2016-10-01
Transient light imaging is an emerging technology and interesting sensing approach for fundamental multidisciplinary research ranging from computer science to remote sensing. Recent developments in sensor technologies and computational imaging has made this emerging sensing approach a candidate for next generation sensor systems with rapidly increasing maturity but still relay on laboratory technology demonstrations. At ISL, transient light sensing is investigated by time correlated single photon counting (TCSPC). An eye-safe shortwave infrared (SWIR) TCSPC setup, consisting of an avalanche photodiode array and a pulsed fiber laser source, is used to investigate sparsely scattered light while propagating through air. Fundamental investigation of light in light are carried out with the aim to reconstruct the propagation path of arbitrary light paths. Light pulses are observed in light at various propagation angles and distances. As demonstrated, arbitrary light paths can be distinguished due to a relativistic effect leading to a distortion of temporal signatures. A novel method analyzing the time difference of arrival (TDOA) is carried out to determine the propagation angle and distance with respect to this relativistic effect. Based on our results, the performance of future laser warning receivers can be improved by the use of single photon counting imaging devices. They can detect laser light even when the laser does not directly hit the sensor or is passing at a certain distance.
Description of Drip-Line Nuclei within Relativistic Mean-Field Plus BCS Approach
Yadav, H L; Toki, H
2004-01-01
Recently it has been demonstrated, considering Ni and Ca isotopes as prototypes, that the relativistic mean-field plus BCS (RMF+BCS) approach wherein the single particle continuum corresponding to the RMF is replaced by a set of discrete positive energy states for the calculation of pairing energy provides a good approximation to the full relativistic Hartree-Bogoliubov (RHB) description of the ground state properties of the drip-line neutron rich nuclei. The applicability of RMF+BCS is essentially due to the fact that the main contribution to the pairing correlations is provided by the low-lying resonant states. General validity of this approach is demonstrated by the detailed calculations for the ground state properties of the chains of isotopes of O, Ca, Ni, Zr, Sn and Pb nuclei. The TMA and NL-SH force parameter sets have been used for the effective mean-field Lagrangian. Comprehensive results for the two neutron separation energy, rms radii, single particle pairing gaps and pairing energies etc. are pres...
VISSER, O; VISSCHER, L; AERTS, PJC; NIEUWPOORT, WC
1992-01-01
We present results of all-electron molecular relativistic (Hartree-Fock-Dirac) and nonrelativistic (Hartree-Fock) calculations followed by a complete open shell configuration interaction (COSCI) calculation on an EuO6(9-) cluster in a Ba2GdNbO6 crystal. The results include the calculated energies of
VISSER, O; VISSCHER, L; AERTS, PJC; NIEUWPOORT, WC
1992-01-01
We present results of all-electron molecular relativistic (Hartree-Fock-Dirac) and nonrelativistic (Hartree-Fock) calculations followed by a complete open shell configuration interaction (COSCI) calculation on an EuO6(9-) cluster in a Ba2GdNbO6 crystal. The results include the calculated energies of
The grasp2K relativistic atomic structure package
Jönsson, P.; He, X.; Froese Fischer, C.; Grant, I. P.
2007-10-01
Xeon, 3.06 GHz Operating system: Suse LINUX RAM: 500 MB or more Classification: 2.1 Nature of problem: Prediction of atomic spectra—atomic energy levels, oscillator strengths, and radiative decay rates—using a 'fully relativistic' approach. Solution method: Atomic orbitals are assumed to be four-component spinor eigenstates of the angular momentum operator, j=l+s, and the parity operator Π=βπ. Configuration state functions (CSFs) are linear combinations of Slater determinants of atomic orbitals, and are simultaneous eigenfunctions of the atomic electronic angular momentum operator, J, and the atomic parity operator, P. Approximate atomic state functions (ASFs) are linear combinations of CSFs. A variational functional may be constructed by combining expressions for the energies of one or more ASFs. Average energy level (EAL) functionals are weighted sums of energies of all possible ASFs that may be constructed from a set of CSFs; the number of ASFs is then the same as the number of CSFs. Extended optimal level (EOL) functionals are weighted sums of energies of some subset of ASFs. Radial functions may be determined by numerically solving the multiconfiguration Dirac-Hartree-Fock (MCDHF) equations that define an extremum of the variational functional by the self-consistent-field (SCF) method. Lists of CSFs are generated from a set of reference CSFs and rules for deriving other CSFs from these. Expansion coefficients are obtained using sparse-matrix methods for solving the relativistic configuration interaction (CI) problem. Transition properties for pairs of ASFs are computed from matrix elements of multipole operators of the electromagnetic field. Biorthogonal transformation methods are employed so that all matrix elements between CSFs can be evaluated using Racah algebra. Restrictions: The maximum number of radial orbitals is limited to 120 by the packing algorithm used for 32-bit integers. The maximum size of a multiconfiguration (MC) calculation, as measured
Zhang, Hong Lin; Sampson, Douglas H.
1990-11-01
The rapid relativistic distorted-wave method of Zhang, Sampson, and Mohanty [Phys. Rev. A 40, 616 (1989)] for excitation, which uses the atomic-structure data of Sampson et al. [Phys. Rev. A 40, 604 (1989)], has been extended to ionization. In this approach the same Dirac-Fock-Slater potential evaluated using a single mean configuration is used in calculating the orbitals of all electrons bound and free. Values for the cross sections Q for ionization of various ions have been calculated, and generally good agreement is obtained with other recent relativistic calculations. When results are expressed in terms of the reduced ionization cross section QR, which is proportional to I2Q, they are close to the nonrelativistic Coulomb-Born-exchange values of Moores, Golden, and Sampson [J. Phys. B 13, 385 (1980)] for hydrogenic ions except for high Z and/or high energies. This suggests that fits of the QR to simple functions of the impact electron energy in threshold units with coefficients that are quite slowly varying functions of an effective Z can probably be made. This would be convenient for plasma-modeling applications.
Cannoni, Mirco [Universidad de Huelva, Departamento de Fisica Aplicada, Facultad de Ciencias Experimentales, Huelva (Spain)
2016-03-15
We find an exact formula for the thermally averaged cross section times the relative velocity left angle σv{sub rel} right angle with relativistic Maxwell-Boltzmann statistics. The formula is valid in the effective field theory approach when the masses of the annihilation products can be neglected compared with the dark matter mass and cut-off scale. The expansion at x = m/T >> 1 directly gives the nonrelativistic limit of left angle σv{sub rel} right angle, which is usually used to compute the relic abundance for heavy particles that decouple when they are nonrelativistic. We compare this expansion with the one obtained by expanding the total cross section σ(s) in powers of the nonrelativistic relative velocity vr. We show the correct invariant procedure that gives the nonrelativistic average left angle σv{sub rel} right angle {sub nr} coinciding with the large x expansion of left angle σv{sub rel} right angle in the comoving frame. We explicitly formulate flux, cross section, thermal average, collision integral of the Boltzmann equation in an invariant way using the true relativistic relative v{sub rel}, showing the uselessness of the Moeller velocity and further elucidating the conceptual and numerical inconsistencies related with its use. (orig.)
Ghizzo, A.; Bertrand, P. [Institut Jean Lamour-UMR 7168, University of Lorraine, BP 239 F-54506 Vandoeuvre les Nancy (France)
2013-08-15
A one-dimensional multistream formalism is extended for the study of temperature anisotropy driven Weibel-type instabilities in collisionless and relativistic plasma. The formulation is based on a Hamiltonian reduction technique using the invariance of generalized canonical momentum in transverse direction. The Vlasov-Maxwell model is expressed in terms of an ensemble of one-dimensional Vlasov-type equations, coupled together with the Maxwell equations in a self-consistent way. Although the model is fundamentally nonlinear, this first of three companion papers focuses on the linear aspect. Dispersion relations of the Weibel instability are derived in the linear regime for different kinds of polarization of the electromagnetic potential vector. The model allows new unexpected insights on the instability: enhanced growth rates for the Weibel instability are predicted when a dissymmetric distribution is considered in p{sub ⊥}. In the case of a circular polarization, a simplification of the linear analysis can be obtained by the introduction of the “multiring” approach allowing to extend the analytical model of Yoon and Davidson [Phys. Rev. A 35, 2718 (1987)]. Applications of this model are left to the other two papers of the series where specific problems are addressed pertaining to the nonlinear and relativistic dynamics of magnetically trapped particles met in the saturation regime of the Weibel instability.
Sahoo, Raghunath
2016-01-01
This lecture note covers Relativistic Kinematics, which is very useful for the beginners in the field of high-energy physics. A very practical approach has been taken, which answers "why and how" of the kinematics useful for students working in the related areas.
Luciano, Rezzolla
2013-01-01
Relativistic hydrodynamics is a very successful theoretical framework to describe the dynamics of matter from scales as small as those of colliding elementary particles, up to the largest scales in the universe. This book provides an up-to-date, lively, and approachable introduction to the mathematical formalism, numerical techniques, and applications of relativistic hydrodynamics. The topic is typically covered either by very formal or by very phenomenological books, but is instead presented here in a form that will be appreciated both by students and researchers in the field. The topics covered in the book are the results of work carried out over the last 40 years, which can be found in rather technical research articles with dissimilar notations and styles. The book is not just a collection of scattered information, but a well-organized description of relativistic hydrodynamics, from the basic principles of statistical kinetic theory, down to the technical aspects of numerical methods devised for the solut...
Erler, Bastian
2012-07-18
Realistic nucleon-nucleon interactions transformed via the Unitary Correlation Operator Method (UCOM) or the Similarity Renormalization Group (SRG) have proven to be a suitable starting point for the description of closed-shell nuclei via mean-field methods like Hartree-Fock (HF). This allows the treatment of a number of heavy nuclei with realistic nucleon-nucleon interactions, which would otherwise only be possible with phenomenological interactions. To include three-nucleon forces in an approximate way, the UCOM or SRG transformed interactions can be augmented by a three-body contact interaction, which is necessary to reproduce measured charge radii. However, many interesting nuclei, including those near the neutron drip line, are far away from closed shells. These nuclei are of great importance for modeling nucleosynthesis processes in the universe, but experiments can only be performed at a few research facilities. In this work, the Hartree Fock (HF) approach with realistic interactions is extended to light deformed nuclei. Pairing correlations are not taken into account. A crucial step in this process is to allow deformed ground states on the mean-field level, as only nuclei with at least one closed shell can be described with spherical HF ground states. To restore the rotational symmetry in the lab frame, exact angular-momentum projection (AMP) is implemented. Constrained HF calculations are used for an approximate variation after projection approach. The AMP-HF description of open-shell nuclei is on par with the pure HF description of closed-shell nuclei. Charge-radii and systematics of binding energies agree well with experiment. However, missing correlations, lead to an underestimated absolute value of the binding energy. Projection on higher angular momenta approximately reproduces the energy systematics of rotational bands. To describe collective excitations, the Random Phase Approximation (RPA) constitutes a well tested approach, which can also be
Model operator approach to the Lamb shift calculations in relativistic many-electron atoms
Shabaev, V M; Yerokhin, V A
2013-01-01
A model operator approach to calculations of the QED corrections to energy levels in relativistic many-electron atomic systems is developed. The model Lamb shift operator is represented by a sum of local and nonlocal potentials which are defined using the results of ab initio calculations of the diagonal and nondiagonal matrix elements of the one-loop QED operator with H-like wave functions. The model operator can be easily included in any calculations based on the Dirac-Coulomb-Breit Hamiltonian. Efficiency of the method is demonstrated by comparison of the model QED operator results for the Lamb shifts in many-electron atoms and ions with exact QED calculations.
Olejniczak, Malgorzata; Gomes, Andre Severo Pereira
2016-01-01
We report an implementation of the nuclear magnetic resonance (NMR) shielding ($\\sigma$), isotope-independent indirect spin-spin coupling ($K$) and the magnetizability ($\\xi$) tensors in the frozen density embedding (FDE) scheme using the four-component (4c) relativistic Dirac--Coulomb (DC) Hamiltonian and the non-collinear spin density functional theory (SDFT). The formalism takes into account the magnetic balance between the large and the small components of molecular spinors and assures the gauge-origin independence of NMR shielding and magnetizability results. This implementation has been applied to hydrogen-bonded HXH$\\cdots$OH$_2$ complexes (X = Se, Te, Po) and compared with the supermolecular calculations and with the approach based on the integration of the magnetically induced current density vector. A comparison with the approximate Zeroth-Order Regular Approximation (ZORA) Hamiltonian indicates non-negligible differences in $\\sigma$ and $K$ in the HPoH$\\cdots$OH$_2$ complex, and calls for a thourou...
Magnetic moments of 33Mg in the time-odd relativistic mean field approach
无
2009-01-01
The configuration-fixed deformation constrained relativistic mean field approach with time-odd component has been applied to investigate the ground state properties of 33Mg with effective interaction PK1.The ground state of 33Mg has been found to be prolate deformed,β2=0.23,with the odd neutron in 1/2[330] orbital and the energy -251.85 MeV which is close to the data -252.06 MeV.The magnetic moment -0.9134 μN is obtained with the effective electromagnetic current which well reproduces the data -0.7456 μN self-consistently without introducing any parameter.The energy splittings of time reversal conjugate states,the neutron current,the energy contribution from the nuclear magnetic potential,and the effect of core polarization are discussed in detail.
Ghizzo, A. [Institut Jean Lamour UMR 7163, Université de Lorraine, BP 239 F-54506 Vandoeuvre les Nancy (France)
2013-08-15
The saturation of the Weibel instability in the relativistic regime is investigated within the Hamiltonian reduction technique based on the multistream approach developed in paper I in the linear case and in paper II for the nonlinear saturation. In this work, the study is compared with results obtained by full kinetic 1D2V Vlasov-Maxwell simulations based on a semi-Lagrangian technique. For a temperature anisotropy, qualitatively different regimes are realized depending on the excitation of the longitudinal (plasma) electric field, in contrast with the existing theories of the Weibel instability based on their purely transverse characters. The emphasis here is on gaining a better understanding of the nonlinear aspects of the Weibel instability. The multistream model offers an alternate way to make calculations or numerical experiments more tractable, when only a few moments of the velocity distribution of the plasma are considered.
Calzetta, Esteban; Kandus, Alejandra
2016-12-01
We develop a purely hydrodynamic formalism to describe collisional, anisotropic instabilities in a relativistic plasma, that are usually described with kinetic theory tools. Our main motivation is the fact that coarse-grained models of high particle number systems give more clear and comprehensive physical descriptions of those systems than purely kinetic approaches, and can be more easily tested experimentally as well as numerically. Also they make it easier to follow perturbations from linear to nonlinear regimes. In particular, we aim at developing a theory that describes both a background nonequilibrium fluid configurations and its perturbations, to be able to account for the backreaction of the latter on the former. Our system of equations includes the usual conservation laws for the energy-momentum tensor and for the electric current, and the equations for two new tensors that encode the information about dissipation. To make contact with kinetic theory, we write the different tensors as the moments of a nonequilibrium one-particle distribution function (1pdf) which, for illustrative purposes, we take in the form of a Grad-like ansatz. Although this choice limits the applicability of the formalism to states not far from equilibrium, it retains the main features of the underlying kinetic theory. We assume the validity of the Vlasov-Boltzmann equation, with a collision integral given by the Anderson-Witting prescription, which is more suitable for highly relativistic systems than Marle’s (or Bhatnagar, Gross and Krook) form, and derive the conservation laws by taking its corresponding moments. We apply our developments to study the emergence of instabilities in an anisotropic, but axially symmetric background. For small departures of isotropy we find the dispersion relation for normal modes, which admit unstable solutions for a wide range of values of the parameter space.
Poszwa, A.; Rutkowski, A.
2007-03-01
The binding energies and magnetic susceptibilities for states evolving from 1s1/2 , 2s1/2 , 2p1/2 , 2p3/2 , 3s1/2 , 3d3/2 , and 3d5/2 are calculated using power-series solutions of the Dirac equation for hydrogenic atoms in static and uniform magnetic B . The accuracy of the binding energies for low and medium magnetic fields exceeds that of previous variational calculations. In the low-magnetic-field limit the highly accurate values of energies are used to determine the relativistic Paschen-Back effect and relativistic magnetic susceptibilities by expansion of the fully relativistic energy into power series of the parameter B/Z2 . The linear term of this series is related to the relativistic Paschen-Back effect and the square term is proportional to the relativistic dipole magnetic susceptibility of the atom.
Haba, Z
2009-02-01
We discuss relativistic diffusion in proper time in the approach of Schay (Ph.D. thesis, Princeton University, Princeton, NJ, 1961) and Dudley [Ark. Mat. 6, 241 (1965)]. We derive (Langevin) stochastic differential equations in various coordinates. We show that in some coordinates the stochastic differential equations become linear. We obtain momentum probability distribution in an explicit form. We discuss a relativistic particle diffusing in an external electromagnetic field. We solve the Langevin equations in the case of parallel electric and magnetic fields. We derive a kinetic equation for the evolution of the probability distribution. We discuss drag terms leading to an equilibrium distribution. The relativistic analog of the Ornstein-Uhlenbeck process is not unique. We show that if the drag comes from a diffusion approximation to the master equation then its form is strongly restricted. The drag leading to the Tsallis equilibrium distribution satisfies this restriction whereas the one of the Jüttner distribution does not. We show that any function of the relativistic energy can be the equilibrium distribution for a particle in a static electric field. A preliminary study of the time evolution with friction is presented. It is shown that the problem is equivalent to quantum mechanics of a particle moving on a hyperboloid with a potential determined by the drag. A relation to diffusions appearing in heavy ion collisions is briefly discussed.
High-Order Fully General-Relativistic Hydrodynamics: new Approaches and Tests
Radice, David; Galeazzi, Filippo
2013-01-01
We present a new approach for achieving high-order convergence in fully general-relativistic hydrodynamic simulations. The approach is implemented in WhiskyTHC, a new code that makes use of state-of-the-art numerical schemes and was key in achieving, for the first time, higher than second-order convergence in the calculation of the gravitational radiation from inspiraling binary neutron stars Radice et al. (2013). Here, we give a detailed description of the algorithms employed and present results obtained for a series of classical tests involving isolated neutron stars. In addition, using the gravitational-wave emission from the late inspiral and merger of binary neutron stars, we make a detailed comparison between the results obtained with the new code and those obtained when using standard second-order schemes commonly employed for matter simulations in numerical relativity. We find that even at moderate resolutions and for binaries with large compactness, the phase accuracy is improved by a factor 50 or mo...
Self-consistent approach for Bose-condensed atoms in optical lattices
V.I. Yukalov
2013-06-01
Full Text Available Bose atoms in optical lattices are considered at low temperatures and weak interactions, when Bose-Einstein condensate is formed. A self-consistent approach, based on the use of a representative statistical ensemble, is employed, guaranteeing a gapless spectrum of collective excitations and the validity of conservation laws. In order to show that the approach is applicable to both weak and tight binding, the problem is treated in the Bloch as well as in the Wannier representations. Both these ways result in similar expressions that are compared for the self-consistent Hartree-Fock-Bogolubov approximation. A convenient general formula for the superfluid fraction of atoms in an optical lattice is derived.
A molecular dynamics approach to dissipative relativistic hydrodynamics: propagation of fluctuations
Shahsavar, Leila; Montakhab, Afshin
2016-01-01
Relativistic generalization of hydrodynamic theory has attracted much attention from a theoretical point of view. However, it has many important practical applications in high energy as well as astrophysical contexts. Despite various attempts to formulate relativistic hydrodynamics, no definitive consensus has been achieved. In this work, we propose to test the predictions of four types of \\emph{first-order} hydrodynamic theories for non-perfect fluids in the light of numerically exact molecular dynamics simulations of a fully relativistic particle system in the low density regime. In this regard, we study the propagation of density, velocity and heat fluctuations in a wide range of temperatures using extensive simulations and compare them to the corresponding analytic expressions we obtain for each of the proposed theories. As expected in the low temperature classical regime all theories give the same results consistent with the numerics. In the high temperature extremely relativistic regime, not all conside...
Cannoni, Mirco
2015-01-01
We find an exact formula for the thermally averaged cross section times the relative velocity $\\langle \\sigma v_{\\text{rel}} \\rangle$ with relativistic Maxwell-Boltzmann statistics. The formula is valid in the effective field theory approach when the masses of the annihilation products can be neglected compared with the dark matter mass and cut-off scale. The expansion at $x=m/T\\gg 1$ directly gives the nonrelativistic limit of $\\langle \\sigma v_{\\text{rel}}\\rangle$ which is usually used to compute the relic abundance for heavy particles that decouple when they are nonrelativistic. We compare this expansion with the one obtained by expanding the total cross section $\\sigma(s)$ in powers of the nonrelativistic relative velocity $v_r$. We show the correct invariant procedure that gives the nonrelativistic average $\\langle \\sigma_{nr} v_r \\rangle_{nr}$ coinciding with the large $x$ expansion of $\\langle \\sigma v_{\\text{rel}}\\rangle$ in the comoving frame. We explicitly formulate flux, cross section, thermal aver...
Salazar-Ramírez, M.; Ojeda-Guillén, D.; Mota, R. D.
2016-09-01
We study a relativistic quantum particle in cosmic string spacetime in the presence of a magnetic field and a Coulomb-type scalar potential. It is shown that the radial part of this problem possesses the su(1 , 1) symmetry. We obtain the energy spectrum and eigenfunctions of this problem by using two algebraic methods: the Schrödinger factorization and the tilting transformation. Finally, we give the explicit form of the relativistic coherent states for this problem.
The Brueckner-Hartree-Fock Equation of State for Nuclear Matter and Neutron Skin
Qing-Yang, Bu; Zeng-Hua, Li; Hans-Josef, Schulze
2016-03-01
Not Available Supported by the National Natural Science Foundation of China under Grant Nos 11075037 and 11475045, the Scientific Research Foundation for the Returned Overseas Chinese Scholars of the Ministry of Education of China, the Fundamental Research Funds for the Central Universities of China, the Shanghai Leading Academic Discipline Project under Grant No B107, and the ‘NewCompStar’, COST Action MP1304.
Predicting bond strength from a single Hartree-Fock ground state using the localized pair model.
Hennessey, Dylan C; Sheppard, Brendan J H; Mackenzie, Dalton E C K; Pearson, Jason K
2014-12-14
We present an application of the recently introduced Localized Pair Model (LPM) [Z. A. Zielinksi and J. K. Pearson, Comput. Theor. Chem., 2013, 1003, 7990] to characterize and quantify properties of the chemical bond in a series of substituted benzoic acid molecules. By computing interelectronic distribution functions for doubly-occupied Edmiston-Ruedenberg localized molecular orbitals (LMOs), we show that chemically intuitive electron pairs may be uniquely classified and bond strength may be predicted with remarkable accuracy. Specifically, the HF/u6-311G(d,p) level (where u denotes a complete uncontraction of the basis set) is used to generate the relevant LMOs and their respective interelectronic distribution functions can be linearly correlated to the well-known Hammett σp or σm parameters with near-unity correlation coefficients.
Hartree-Fock and density functional theory study of alpha-cyclodextrin conformers.
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.
$L^2$ Analysis of the Multi-Configuration Time-Dependent Hartree-Fock Equations
Mauser, Norbert J
2010-01-01
The multiconfiguration methods are widely used by quantum physicists and chemists for numerical approximation of the many electron Schr\\"odinger equation. Recently, first mathematically rigorous results were obtained on the time-dependent models, e.g. short-in-time well-posedness in the Sobolev space $H^2$ for bounded interactions (C. Lubichand O. Koch} with initial data in $H^2$, in the energy space for Coulomb interactions with initial data in the same space (Trabelsi, Bardos et al.}, as well as global well-posedness under a sufficient condition on the energy of the initial data (Bardos et al.). The present contribution extends the analysis by setting an $L^2$ theory for the MCTDHF for general interactions including the Coulomb case. This kind of results is also the theoretical foundation of ad-hoc methods used in numerical calculation when modification ("regularization") of the density matrix destroys the conservation of energy property, but keeps invariant the mass.
Hyper Raman spectra calculated in a time-dependent Hartree-Fock method
Mohammed, Abdelsalam; Ågren, Hans; Ringholm, Magnus; Thorvaldsen, Andreas J.; Ruud, Kenneth
2012-10-01
Hyper Raman scattering (HRS) of the benzonitrile (BN) and 1,3,5-trinitro-1,3,5-triazacyclohexane (RDX) molecules is studied by means of ab initio calculations. The computational procedure employs a recently developed methodology for the analytic calculations of frequency-dependent polarizability gradients of arbitrary order, including perturbation dependent basis sets. The result are compared to normal Raman scattering (NRS) and coherent anti-Stokes Raman scattering (CARS) that previously have been studied using the same technology. It is found that some suppressed or silent modes in CARS and NRS spectra are clearly seen in HRS, and that although under general excitation conditions the HRS intensities are much lower than for CARS and NRS, HRS provides complementary information useful for target identification.
Adaptive Multi-resolution 3D Hartree-Fock-Bogoliubov Solver for Nuclear Structure
Pei, Junchen; Harrison, Robert; Nazarewicz, Witold; Shi, Yue; Thornton, Scott
2014-01-01
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, they 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. To describe complex superfluid many-fermion systems, we introduce an adaptive pseudo-spectral method for solving self-consistent equations of nuclear density functional theory in three dimensions, without symmetry restrictions. The new adaptive mult...
Theoretical Studies on Two Possible Conformers of TNDAIW at Hartree-Fock Level
WU Yu-kai; OU Yu-xiang; LIU Zhi-guo; MENG Zheng; ,LIU Jin-quan; CHEN Bo-ren
2005-01-01
Tetranitrodiazidoacetylhexaazaisowurtzitane (TNDAIW) is a novel polyazapolycyclic caged polyazidonitramine explosive first synthesized in our laboratory. Two possible conformers of TNDAIW with Cs symmetry were fully optimized using the HF/6-31G(d) level of theory. TNDAIW with the optimized geometries probably exists, and is predicted to be more stable than epsilon-hexanitrohexaazoisowurtzitane (epsilon-CL-20) based on the lengths of N-N, C-C and C-N bonds. The impact and shock sensitivities are lower for the possible conformers of TNDAIW than those for epsilon-CL-20. TNDAIW with the optimized possible conformers is estimated to be a promising novel high energy density explosive.
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)
Dipole response in neutron-rich nuclei within self-consistent approaches using realistic potentials
Lo Iudice N.
2015-01-01
Full Text Available A nucleon-nucleon chiral potential with a corrective density dependent term simulating a three-body force is used in a self-consistent calculation of the dipole strength distribution in neutron-rich nuclei, with special attention to the low-lying spectra associated to the pygmy resonance. A Hartree-Fock-Bogoliubov basis is generated and adopted in Tamm-Dancoff and random-phase approximations and, then, in an equation of motion approach which includes a basis of two-phonon states. The direct use of the mentioned chiral potential improves the description of both giant and pygmy dipole modes with respect to other realistic interactions. Moreover, the inclusion of the two-phonon states induces a pronounced fragmentation of the giant resonance and enhances the density of the low-lying levels in the pygmy region in agreement with recent experiments.
Self-consistent RPA and the time-dependent density matrix approach
Schuck, P. [Institut de Physique Nucleaire, Orsay (France); CNRS et Universite Joseph Fourier, Laboratoire de Physique et Modelisation des Milieux Condenses, Grenoble (France); Tohyama, M. [Kyorin University School of Medicine, Mitaka, Tokyo (Japan)
2016-10-15
The time-dependent density matrix (TDDM) or BBGKY (Bogoliubov, Born, Green, Kirkwood, Yvon) approach is decoupled and closed at the three-body level in finding a natural representation of the latter in terms of a quadratic form of two-body correlation functions. In the small amplitude limit an extended RPA coupled to an also extended second RPA is obtained. Since including two-body correlations means that the ground state cannot be a Hartree-Fock state, naturally the corresponding RPA is upgraded to Self-Consistent RPA (SCRPA) which was introduced independently earlier and which is built on a correlated ground state. SCRPA conserves all the properties of standard RPA. Applications to the exactly solvable Lipkin and the 1D Hubbard models show good performances of SCRPA and TDDM. (orig.)
Time-resolved photoabsorption in finite systems: A first-principles NEGF approach
Perfetto, E.; Uimonen, A.-M.; van Leeuwen, R.; Stefanucci, G.
2016-03-01
We describe a first-principles NonEquilibrium Green's Function (NEGF) approach to time-resolved photoabsortion spectroscopy in atomic and nanoscale systems. The method is used to highlight a recently discovered dynamical correlation effect in the spectrum of a Krypton gas subject to a strong ionizing pump pulse. We propose a minimal model that captures the effect, and study the performance of time-local approximations versus time-nonlocal ones. In particular we implement the time-local Hartree-Fock and Markovian second Born (2B) approximation as well as the exact adiabatic approximation within the Time-Dependent Density Functional Theory framework. For the time-nonlocal approximation we instead use the 2B one. We provide enough convincing evidence for the fact that a proper description of the spectrum of an evolving admixture of ionizing atoms requires the simultaneous occurrence of correlation and memory effects.
Fission half-lives of super-heavy nuclei in a microscopic approach
Warda, M
2012-01-01
A systematic study of 160 heavy and super-heavy nuclei is performed in the Hartree-Fock-Bogoliubov approach with the finite range and density dependent Gogny force with the D1S parameter set. We show calculations in several approximations: with axially symmetric and reflexion symmetric wave functions, with axially symmetric and non-reflexion symmetric wave functions and finally some representative examples with triaxial wave functions are also discussed. Relevant properties of the ground state and along the fission path are thoroughly analyzed. Fission barriers, Q$_\\alpha$-factors and lifetimes with respect to fission and $\\alpha$-decay as well as other observables are discussed. Larger configuration spaces and more general HFB wave functions as compared to previous studies provide a very good agreement with the experimental data.
Oliveira, Diego F.M., E-mail: diegofregolente@gmail.com [Institute for Multiscale Simulations, Friedrich-Alexander Universität, D-91052, Erlangen (Germany); Leonel, Edson D., E-mail: edleonel@rc.unesp.br [Departamento de Estatística, Matemática Aplicada e Computação, UNESP, Univ. Estadual Paulista, Av. 24A, 1515, Bela Vista, 13506-900, Rio Claro, SP (Brazil); Departamento de Física, UNESP, Univ. Estadual Paulista, Av. 24A, 1515, 13506-900, Rio Claro, SP (Brazil)
2012-11-01
We study some dynamical properties for the problem of a charged particle in an electric field considering both the low velocity and relativistic cases. The dynamics for both approaches is described in terms of a two-dimensional and nonlinear mapping. The structure of the phase spaces is mixed and we introduce a hole in the chaotic sea to let the particles to escape. By changing the size of the hole we show that the survival probability decays exponentially for both cases. Additionally, we show for the relativistic dynamics, that the introduction of dissipation changes the mixed phase space and attractors appear. We study the parameter space by using the Lyapunov exponent and the average energy over the orbit and show that the system has a very rich structure with infinite family of self-similar shrimp shaped embedded in a chaotic region.
Relativistic two-body bound states in scalar QFT: variational basis-state approach
Emami-Razavi, Mohsen [Centre for Research in Earth and Space Science, York University, Toronto, Ontario, M3J 1P3 (Canada); Darewych, Jurij W [Department of Physics and Astronomy, York University, Toronto, Ontario, M3J 1P3 (Canada)
2006-08-15
We use the Hamiltonian formalism of quantum field theory and the variational basis-state method to derive relativistic coupled-state wave equations for scalar particles interacting via a massive or massless mediating scalar field (the scalar Yukawa model). A variational trial state comprised of two and four Fock-space states is used to derive coupled wave equations for a relativistic two (and four) body system. Approximate, variational two-body ground-state solutions of the relativistic equations are obtained for various strengths of coupling, for both massive and massless mediating fields. The results show that the inclusion of virtual pairs has a large effect on the two-body binding energy at strong coupling. A comparison of the two-body binding energies with other calculations is presented.
A Non-Perturbative, Finite Particle Number Approach to Relativistic Scattering Theory
Lindesay, James V
2001-05-11
We present integral equations for the scattering amplitudes of three scalar particles, using the Faddeev channel decomposition, which can be readily extended to any finite number of particles of any helicity. The solution of these equations, which have been demonstrated to be calculable, provide a non-perturbative way of obtaining relativistic scattering amplitudes for any finite number of particles that are Lorentz invariant, unitary, cluster decomposable and reduce unambiguously in the non-relativistic limit to the non-relativistic Faddeev equations. The aim of this program is to develop equations which explicitly depend upon physically observable input variables, and do not require ''renormalization'' or ''dressing'' of these parameters to connect them to the boundary states.
Recurrence relation for relativistic atomic matrix elements
Martínez y Romero, R P; Salas-Brito, A L
2000-01-01
Recurrence formulae for arbitrary hydrogenic radial matrix elements are obtained in the Dirac form of relativistic quantum mechanics. Our approach is inspired on the relativistic extension of the second hypervirial method that has been succesfully employed to deduce an analogous relationship in non relativistic quantum mechanics. We obtain first the relativistic extension of the second hypervirial and then the relativistic recurrence relation. Furthermore, we use such relation to deduce relativistic versions of the Pasternack-Sternheimer rule and of the virial theorem.
Relativistic small-core pseudopotentials for actinium, thorium, and protactinium.
Weigand, Anna; Cao, Xiaoyan; Hangele, Tim; Dolg, Michael
2014-04-03
Small-core pseudopotentials for actinium, thorium, and protactinium have been energy-adjusted to multiconfiguration Dirac-Hartree-Fock reference data based on the Dirac-Coulomb-Breit Hamiltonian and the Fermi nucleus model. Corresponding optimized valence basis sets of polarized valence quadruple-ζ quality are presented. Atomic test calculations for the first four ionization potentials show satisfactory results at both the Hartree-Fock and the multireference averaged coupled-pair functional level. Highly correlated Fock-space coupled cluster calculations demonstrate that the new pseudopotentials yield ionization potentials, which are in excellent agreement with corresponding all-electron results and experimental data. The pseudopotentials and basis sets supplement a similar set previously published for uranium.
Multiple chiral doublet candidate nucleus $^{105}$Rh in a relativistic mean-field approach
Li, Jian; Meng, J; 10.1103/PhysRevC.83.037301
2011-01-01
Following the reports of two pairs of chiral doublet bands observed in $^{105}$Rh, the adiabatic and configuration-fixed constrained triaxial relativistic mean-field (RMF) calculations are performed to investigate their triaxial deformations with the corresponding configuration and the possible multiple chiral doublet (M$\\chi$D) phenomenon. The existence of M$\\chi$D phenomenon in $^{105}$Rh is highly expected.
An su(1, 1) algebraic approach for the relativistic Kepler-Coulomb problem
Salazar-Ramirez, M; Granados, V D [Escuela Superior de Fisica y Matematicas, Instituto Politecnico Nacional, Ed. 9, Unidad Profesional Adolfo Lopez Mateos, 07738 Mexico DF (Mexico); MartInez, D [Universidad Autonoma de la Ciudad de Mexico, Plantel Cuautepec, Av. La Corona 320, Col. Loma la Palma, Delegacion Gustavo A. Madero, 07160 Mexico DF (Mexico); Mota, R D, E-mail: dmartinezs77@yahoo.com.m [Unidad Profesional Interdisciplinaria de Ingenieria y TecnologIas Avanzadas, IPN. Av. Instituto Politecnico Nacional 2580, Col. La Laguna Ticoman, Delegacion Gustavo A. Madero, 07340 Mexico DF (Mexico)
2010-11-07
We apply the Schroedinger factorization method to the radial second-order equation for the relativistic Kepler-Coulomb problem. From these operators we construct two sets of one-variable radial operators which are realizations for the su(1, 1) Lie algebra. We use this algebraic structure to obtain the energy spectrum and the supersymmetric ground state for this system.
The $q\\overline{q}$ relativistic interaction in the Wilson loop approach
Brambilla, Nora; Brambilla, Nora; Vairo, Antonio
1997-01-01
We study the $q \\bar{q}$ relativistic interaction starting from the Feynman-Schwinger representation of the gauge-invariant quark-antiquark Green function. We focus on the one-body limit and discuss the obtained non-perturbative interaction kernel of the Dirac equation.
The $q \\bar{q}$ relativistic interaction in the Wilson loop approach
Brambilla, Nora; Vairo, Antonio
1997-01-01
We study the $q \\bar{q}$ relativistic interaction starting from the Feynman-Schwinger representation of the gauge-invariant quark-antiquark Green function. We focus on the one-body limit and discuss the obtained non-perturbative interaction kernel of the Dirac equation.
A Dynamical Approach to the Exterior Geometry of a Perfect Fluid as a Relativistic Star
Fathi, Mohsen
2011-01-01
The aim of this article is to compare some of the solution classes, which were presented for a perfect charged fluid in Ref. [8], through studying the motion of a test charged particle on a relativistic charged star. We will show that how the interior solutions of such star, can affect its exterior geometry, by illustrating the corresponding effective potentials.
Koh, Meng-Hock [Universiti Teknologi Malaysia, Skudai, Johor (Malaysia); Univ. Bordeaux, CENBG, UMR5797, Gradignan (France); CNRS, IN2P3, CENBG, UMR5797, Gradignan (France); Duc, Dao Duy [Ton Duc Thang University, Division of Nuclear Physics, Ho Chi Minh City (Viet Nam); Ton Duc Thang University, Faculty of Applied Sciences, Ho Chi Minh City (Viet Nam); Nhan Hao, T.V. [Duy Tan University, Center of Research and Development, Danang (Viet Nam); Hue University, Center for Theoretical and Computational Physics, College of Education, Hue City (Viet Nam); Long, Ha Thuy [Hanoi University of Sciences, Vietnam National University, Hanoi (Viet Nam); Quentin, P. [Universiti Teknologi Malaysia, Skudai, Johor (Malaysia); Univ. Bordeaux, CENBG, UMR5797, Gradignan (France); CNRS, IN2P3, CENBG, UMR5797, Gradignan (France); Ton Duc Thang University, Division of Nuclear Physics, Ho Chi Minh City (Viet Nam); Bonneau, L. [Univ. Bordeaux, CENBG, UMR5797, Gradignan (France); CNRS, IN2P3, CENBG, UMR5797, Gradignan (France)
2016-01-15
In four well-deformed heavy odd nuclei, the energies of low-lying rotational band heads have been determined microscopically within a self-consistent Hartree-Fock-plus-BCS approach with blocking. A Skyrme nucleon-nucleon effective interaction has been used together with a seniority force to describe pairing correlations. Only such states which are phenomenologically deemed to be related to single-particle excitations have been considered. The polarization effects, including those associated with the genuine time-reversal symmetry breaking have been fully taken into account within our model assumptions. The calculated spectra are in reasonably good qualitative agreement with available data for the considered odd-neutron nuclei. This is not so much the case for the odd-proton nuclei. A potential explanation for such a difference in behavior is proposed. (orig.)
Antimagnetic rotation in 108,110In with tilted axis cranking relativistic mean-field approach
Sun, Wu-Ji; Xu, Hai-Dan; Li, Jian; Liu, Yong-Hao; Ma, Ke-Yan; Yang, Dong; Lu, Jing-Bing; Ma, Ying-Jun
2016-08-01
Based on tilted axis cranking relativistic mean-field theory within point-coupling interaction PC-PK1, the rotational structure and the characteristic features of antimagnetic rotation for ΔI = 2 bands in 108,110In are studied. Tilted axis cranking relativistic mean-field calculations reproduce the experimental energy spectrum well and are in agreement with the experimental I ∼ ω plot, although the calculated spin overestimates the experimental values. In addition, the two-shears-like mechanism in candidate antimagnetic rotation bands is clearly illustrated and the contributions from two-shears-like orbits, neutron (gd) orbits above Z = 50 shell and Z = 50, N = 50 core are investigated microscopically. The predicted B(E2), dynamic moment of inertia ℑ(2), deformation parameters β and γ, and ℑ(2)/B(E2) ratios in tilted axis cranking relativistic mean-field calculations are discussed and the characteristic features of antimagnetic rotation for the bands before and after alignment are shown. Supported by National Natural Science Foundation of China (11205068, 11205069, 11405072, 11475072, 11547308) and China Postdoctoral Science Foundation (2012M520667)
Fission Barrier for 240Pu in the Quadrupole Constrained Relativistic Mean Field Approach
L(U) Hong-Feng; GENG Li-Sheng; MENG Jie
2006-01-01
@@ The fission barrier for 240Pu is investigated beyond the second saddle point in the potential energy surface by the constrained relativistic mean field method with the newly proposed parameter set PK1. The microscopic correction for the centre-of-mass motion is essential to provide the correct potential energy surface. The shell effects that stabilize the nuclei against the fission is also investigated by the Strutinsky method. The shapes for the ground state, fission isomer and saddle-points, etc, are studied in detail.
Relativistic many-body theory a new field-theoretical approach
Lindgren, Ingvar
2016-01-01
This revised second edition of the author’s classic text offers readers a comprehensively updated review of relativistic atomic many-body theory, covering the many developments in the field since the publication of the original title. In particular, a new final section extends the scope to cover the evaluation of QED effects for dynamical processes. The treatment of the book is based upon quantum-field theory, and demonstrates that when the procedure is carried to all orders of perturbation theory, two-particle systems are fully compatible with the relativistically covariant Bethe-Salpeter equation. This procedure can be applied to arbitrary open-shell systems, in analogy with the standard many-body theory, and it is also applicable to systems with more than two particles. Presently existing theoretical procedures for treating atomic systems are, in several cases, insufficient to explain the accurate experimental data recently obtained, particularly for highly charged ions. The main text is divided into...
Harmonic balance approach to the periodic solutions of the (an)harmonic relativistic oscillator
Belendez, Augusto [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain)], E-mail: a.belendez@ua.es; Pascual, Carolina [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain)
2007-11-19
The first-order harmonic balance method via the first Fourier coefficient is used to construct two approximate frequency-amplitude relations for the relativistic oscillator for which the nonlinearity (anharmonicity) is a relativistic effect due to the time line dilation along the world line. Making a change of variable, a new nonlinear differential equation is obtained and two procedures are used to approximately solve this differential equation. In the first the differential equation is rewritten in a form that does not contain a square-root expression, while in the second the differential equation is solved directly. The approximate frequency obtained using the second procedure is more accurate than the frequency obtained with the first due to the fact that, in the second procedure, application of the harmonic balance method produces an infinite set of harmonics, while in the first procedure only two harmonics are produced. Both approximate frequencies are valid for the complete range of oscillation amplitudes, and excellent agreement of the approximate frequencies with the exact one are demonstrated and discussed. The discrepancy between the first-order approximate frequency obtained by means of the second procedure and the exact frequency never exceeds 1.6%. We also obtained the approximate frequency by applying the second-order harmonic balance method and in this case the relative error is as low 0.31% for all the range of values of amplitude of oscillation A.
A Study of Multi-Λ Hypernuclei Within Spherical Relativistic Mean-Field Approach
Rather, Asloob A.; Ikram, M.; Usmani, A. A.; Kumar, B.; Patra, S. K.
2017-09-01
This research article is a follow up of an earlier work by M. Ikram et al., reported in Int. J. Mod. Phys. E 25, 1650103 (2016) where we searched for Λ magic numbers in experimentally confirmed doubly magic nucleonic cores in light to heavy mass region (i.e., 16 O-208 P b) by injecting Λ's into them. In the present manuscript, working within the state of the art relativistic mean field theory with the inclusion of ΛN and ΛΛ interaction in addition to nucleon-meson NL 3∗ effective force, we extend the search of lambda magic numbers in multi- Λ hypernuclei using the predicted doubly magic nucleonic cores 292120, 304120, 360132, 370132, 336138, 396138 of the elusive superheavy mass regime. In analogy to well established signatures of magicity in conventional nuclear theory, the prediction of hypernuclear magicities is made on the basis of one-, two- Λ separation energy (S Λ,S 2Λ) and two lambda shell gaps (δ 2Λ) in multi- Λ hypernuclei. The calculations suggest that the Λ numbers 92, 106, 126, 138, 184, 198, 240, and 258 might be the Λ shell closures after introducing the Λ's in the elusive superheavy nucleonic cores. The appearance of new lambda shell closures apart from the nucleonic ones predicted by various relativistic and non-relativistic theoretical investigations can be attributed to the relatively weak strength of the spin-orbit coupling in hypernuclei compared to normal nuclei. Further, the predictions made in multi- Λ hypernuclei under study resembles closely the magic numbers in conventional nuclear theory suggested by various relativistic and non-relativistic theoretical models. Moreover, in support of the Λ shell closure, the investigation of Λ pairing energy and effective Λ pairing gap has been made. We noticed a very close agreement of the predicted Λ shell closures with the survey made on the pretext of S Λ, S 2Λ, and δ 2Λ except for the appearance of magic numbers corresponding to Λ = 156 which manifest in Λ effective
Relativistic GLONASS and geodesy
Mazurova, E. M.; Kopeikin, S. M.; Karpik, A. P.
2016-12-01
GNSS technology is playing a major role in applications to civil, industrial and scientific areas. Nowadays, there are two fully functional GNSS: American GPS and Russian GLONASS. Their data processing algorithms have been historically based on the Newtonian theory of space and time with only a few relativistic effects taken into account as small corrections preventing the system from degradation on a fairly long time. Continuously growing accuracy of geodetic measurements and atomic clocks suggests reconsidering the overall approach to the GNSS theoretical model based on the Einstein theory of general relativity. This is essentially more challenging but fundamentally consistent theoretical approach to relativistic space geodesy. In this paper, we overview the basic principles of the relativistic GNSS model and explain the advantages of such a system for GLONASS and other positioning systems. Keywords: relativistic GLONASS, Einstein theory of general relativity.
Exact Relativistic 'Antigravity' Propulsion
Felber, F S
2006-01-01
The Schwarzschild solution is used to find the exact relativistic motion of a payload in the gravitational field of a mass moving with constant velocity. At radial approach or recession speeds faster than 3^-1/2 times the speed of light, even a small mass gravitationally repels a payload. At relativistic speeds, a suitable mass can quickly propel a heavy payload from rest nearly to the speed of light with negligible stresses on the payload.
Exact Relativistic `Antigravity' Propulsion
Felber, Franklin S.
2006-01-01
The Schwarzschild solution is used to find the exact relativistic motion of a payload in the gravitational field of a mass moving with constant velocity. At radial approach or recession speeds faster than 3-1/2 times the speed of light, even a small mass gravitationally repels a payload. At relativistic speeds, a suitable mass can quickly propel a heavy payload from rest nearly to the speed of light with negligible stresses on the payload.
Spectral line shifts of alkali atoms in liquid helium: a relativistic density functional approach
Anton, J [Universitaet Kassel, Institut fuer Physik, 34109 Kassel (Germany); Mukherjee, P K [Indian Association for the Cultivation of Science, Jadavpur, Kolkata-700 032 (India); Fricke, B [Universitaet Kassel, Institut fuer Physik, 34109 Kassel (Germany); Fritzsche, S [Universitaet Kassel, Institut fuer Physik, 34109 Kassel (Germany)
2007-06-28
Excitation line shifts of the principal resonance transitions in alkali atoms sodium and cesium embedded inside the liquid helium environment have been calculated using four-component relativistic density functional theory. The effect of the liquid helium environment is assumed to be represented by a cluster of 14 atoms surrounding the central alkali atom. The estimated blue shift of the principal resonance line {sup 2}S {yields}{sup 2}P is 22.8 nm for Na and 16.7 nm for Cs. The result for Cs is in good agreement with the experimental shift of 18.2 nm. In the absence of the experimental data for Na, our result is compared with those of other theoretical estimates.
Pétri, J
2014-01-01
The close vicinity of neutron stars remains poorly constrained by observations. Although plenty of data are available for the peculiar class of pulsars we are still unable to deduce the underlying plasma distribution in their magnetosphere. In the present paper, we try to unravel the magnetospheric structure starting from basic physics principles and reasonable assumptions about the magnetosphere. Beginning with the monopole force-free case, we compute accurate general-relativistic solutions for the electromagnetic field around a slowly rotating magnetized neutron star. Moreover, here we address this problem by including the important effect of plasma screening. This is achieved by solving the time-dependent Maxwell equations in a curved space-time following the 3+1~formalism. We improved our previous numerical code based on pseudo-spectral methods in order to allow for possible discontinuities in the solution. Our algorithm based on a multi-domain decomposition of the simulation box belongs to the discontinu...
General relativistic radiative transfer in hot astrophysical plasmas a characteristic approach
Zane, S; Nobili, L; Erna, M; Zane, Silvia; Turolla, Roberto; Nobili, Luciano; Erna, Myris
1996-01-01
In this paper we present a characteristic method for solving the transfer equation in differentially moving media in a curved spacetime. The method is completely general, but its capabilities are exploited at best in presence of symmetries, when the existence of conserved quantities allows to derive analytical expressions for the photon trajectories in phase space. In spherically--symmetric, stationary configurations the solution of the transfer problem is reduced to the integration of a single ordinary differential equation along the bi--parametric family of characteristic rays. Accurate expressions for the radiative processes relevant to continuum transfer in a hot astrophysical plasma have been used in evaluating the source term, including relativistic e--p, e--e bremsstrahlung and Compton scattering. A numerical code for the solution of the transfer problem in moving media in a Schwarzschild spacetime has been developed and tested. Some applications, concerning ``hot'' and ``cold'' accretion onto non--rot...
Brown, Natalie
In this thesis we solve the Feshbach-Villars equations for spin-zero particles through use of matrix continued fractions. The Feshbach-Villars equations are derived from the Klein-Gordon equation and admit, for the Coulomb potential on an appropriate basis, a Hamiltonian form that has infinite symmetric band-matrix structure. The corresponding representation of the Green's operator of such a matrix can be given as a matrix continued fraction. Furthermore, we propose a finite dimensional representation for the potential operator such that it retains some information about the whole Hilbert space. Combining these two techniques, we are able to solve relativistic quantum mechanical problems of a spin-zero particle in a Coulomb-like potential with a high level of accuracy.
A general relativistic approach to the Navarro-Frenk-White (NFW) galactic halos
Matos, T; Sussman, R A; Matos, Tonatiuh; Nunez, Dario; Sussman, Roberto A
2004-01-01
In order to study their interplay with large scale cosmic evolution and with relativistic effects, such as gravitational lenses, quintessence sources or gravitational waves, we construct a post-Newtonian fluid framework for the "Navarro-Frenk-White'' (NFW) models of galactic halos that follow from N-body numerical simulations. Since these simulations are unable to resolve regions very near the halo center, the extrapolation of the fitting formula leads to a spherically averaged "universal'' density profile that diverges at the origin. We remove this inconvenient feature by replacing a small central region of the NFW halo with an interior Schwarzschild solution with constant density, continuously matched to the remaining NFW spacetime. A model of a single halo, as an isolated object with finite mass, follows by smoothly matching the NFW spacetime to a Schwarzschild vacuum exterior along the virial radius, the physical "cut-off'' customarily imposed, as the mass associated with NFW profiles diverges asymptotica...
Asymmetric Neutrino Reaction in Magnetized Proto-Neutron Stars in Fully Relativistic Approach
Yasutake Nobutoshi
2012-02-01
Full Text Available We calculate asymmetric neutrino absorption and scattering cross sections on hot and dense magnetized neutron-star matter including hyperons in fully relativistic mean-field theory. The absorption/scattering cross sections are suppressed/enhanced incoherently in the direction of the magnetic field B = Bẑ. The asymmetry is 2–4% at the matter density ρ0 ≤ ρB ≤ 3ρ0 and temperature T ≤ 40MeV for B = 2 × 1017G. Then we solve the Boltzmann equation for the neutrino transport in 1D attenuation approximation, and get the result that the kick velocity becomes about 300 km/s for the proto-neutron star with 168 solar mass at T = 20MeV.
Demianski, Marek
2013-01-01
Relativistic Astrophysics brings together important astronomical discoveries and the significant achievements, as well as the difficulties in the field of relativistic astrophysics. This book is divided into 10 chapters that tackle some aspects of the field, including the gravitational field, stellar equilibrium, black holes, and cosmology. The opening chapters introduce the theories to delineate gravitational field and the elements of relativistic thermodynamics and hydrodynamics. The succeeding chapters deal with the gravitational fields in matter; stellar equilibrium and general relativity
A general relativistic approach to the Navarro Frenk White galactic halos
Matos, Tonatiuh; Núñez, Darío; Sussman, Roberto A.
2004-11-01
Although galactic dark matter halos are basically Newtonian structures, the study of their interplay with large-scale cosmic evolution and with relativistic effects, such as gravitational lenses, quintessence sources or gravitational waves, makes it necessary to obtain adequate relativistic descriptions for these self-gravitating systems. With this purpose in mind, we construct a post-Newtonian fluid framework for the 'Navarro Frenk White' (NFW) models of galactic halos that follow from N-body numerical simulations. Since these simulations are unable to resolve regions very near the halo centre, the extrapolation of the fitting formula leads to a spherically averaged 'universal' density profile that diverges at the origin. We remove this inconvenient feature by replacing a small central region of the NFW halo with an interior Schwarzschild solution with constant density, continuously matched to the remaining NFW spacetime. A model of a single halo, as an isolated object with finite mass, follows by smoothly matching the NFW spacetime to a Schwarzschild vacuum exterior along the virial radius, the physical 'cut-off' customarily imposed, as the mass associated with NFW profiles diverges asymptotically. Numerical simulations assume weakly interacting collisionless particles, hence we suggest that NFW halos approximately satisfy an 'ideal gas' type of equation of state, where mass-density is the dominant rest-mass contribution to matter-energy, with the internal energy contribution associated with an anisotropic kinetic pressure. We show that, outside the central core, this pressure and the mass density roughly satisfy a polytropic relation. Since stellar polytropes are the equilibrium configurations in Tsallis' non-extensive formalism of statistical mechanics, we argue that NFW halos might provide a rough empirical estimate of the free parameter q of Tsallis' formalism.
Bai, Hong-Bo; Zhang, Zhen-Hua; Li, Xiao-Wei
2016-11-01
Ground state properties for Mg isotopes, including binding energies, one- and two-neutron separation energies, pairing energies, nuclear matter radii and quadrupole deformation parameters, are obtained from the self-consistent relativistic mean field (RMF) model with the pairing correlations treated by a shell-mode-like approach (SLAP), in which the particle-number is conserved and the blocking effects are treated exactly. The experimental data, including the binding energies and the one- and two-neutron separation energies, which are sensitive to the treatment of pairing correlations and block effects, are well reproduced by the RMF+SLAP calculations. Supported by NSFC (11465001,11275098, 11275248, 11505058,11165001) and Natural Science Foundation of Inner Mongolia of China (2016BS0102)
Bliokh, Konstantin Y
2011-01-01
We consider the relativistic deformation of quantum waves and mechanical bodies carrying intrinsic angular momentum (AM). When observed in a moving reference frame, the centroid of the object undergoes an AM-dependent transverse shift. This is the relativistic analogue of the spin Hall effect, which occurs in free space without any external fields. Remarkably, the shifts of the geometric and energy centroids differ by a factor of 2, and both centroids are crucial for the correct Lorentz transformations of the AM tensor. We examine manifestations of the relativistic Hall effect in quantum vortices, mechanical flywheel, and discuss various fundamental aspects of the phenomenon. The perfect agreement of quantum and relativistic approaches allows applications at strikingly different scales: from elementary spinning particles, through classical light, to rotating black-holes.
Souza, V. M. C. E. S.; Vieira, L.; Alves, L. R.; Da Silva, L. A.; Koga, D.; Sibeck, D. G.; Walsh, B.; Kanekal, S. G.; Silveira, M. D.; Medeiros, C.; Mendes, O., Jr.; Marchezi, J.; Rockenbach, M.; Jauer, P. R.; Gonzalez, W.; Baker, D. N.
2015-12-01
A myriad of physical phenomena occur in the inner magnetosphere, in particular at the Earth's radiation belts, which can be a result of the combination of both internal and external processes. However, the connection between physical processes occurring deep within the magnetosphere and external interplanetary drivers it is not yet well understood. In this work we investigate whether a selected set of interplanetary structures affect the local time distribution of three different classes of high energy electron pitch angle distributions (PADs), namely normal, isotropic, and butterfly. We split this work into two parts: initially we focus on the methodology used which employs a Self-Organized Feature Map (SOFM) neural network for identifying different classes of electron PAD shapes in the Van Allen Probes' Relativistic Electron Proton Telescope (REPT) data. The algorithm can categorize the input data into an arbitrary number of classes from which three of them appears the most: normal, isotropic and butterfly. Other classes which are related with these three also emerge and deserve to be addressed in detail in future works. We also discuss the uncertainties of the algorithm. Then, we move to the second part where we describe in details the criteria used for selecting the interplanetary events, and also try to investigate the relation between key parameters characterizing such interplanetary structures and the local time distributions of electron PAD shapes.
Ionization potentials and polarizabilities of superheavy elements from Db to Cn ($Z$=105 to 112)
Dzuba, V A
2016-01-01
Relativistic Hartree-Fock and random phase approximation methods for open shells are used to calculate ionization potentials and static scalar polarizabilities of eight superheavy elements with open $6d$-shell, which include Db, Sg, Bh, Hs, Mt, Ds, Rg and Cn ($Z$=105 to 112). Inter-electron correlations are taken into account with the use of the semi-empirical polarization potential. Its parameters are chosen to fit the known ionization potentials of lighter atoms. Calculations for lighter atoms are also used to illustrate the accuracy of the approach.
Maruyama Tomoyuki
2016-01-01
Full Text Available We study pion production from proton synchrotron radiation in the presence of strong magnetic fields by using the exact proton propagator in a strong magnetic field and explicitly including the anomalous magnetic moment. Results in this exact quantum approach do not agree with those obtained in the semi-classical approach. Then, we find that the anomalous magnetic moment of the proton greatly enhances the production rate by about two orders magnitude, and that the decay width satisfies a robust scaling law.
The Twin Twin Paradox: Exploring Student Approaches to Understanding Relativistic Concepts
Cormier, Sebastien; Steinberg, Richard
2010-01-01
A great deal has long been known about student difficulties connecting real-world experiences with what they are learning in their physics classes, making learning basic ideas of classical physics challenging. Understanding these difficulties has led to the development of many instructional approaches that have been shown to help students make…
Potylitsyn, A. P.; Kolchuzhkin, A. M.; Strokov, S. A.
2016-07-01
A photon spectrum of undulator radiation (UR) is calculated in the semi-classical approach. The UR intensity spectrum is determined by an electron trajectory in the undulator neglecting by energy losses for radiation. Using the Planck's law, the UR photon spectrum can be calculated from the classical intensity spectrum both for linear and nonlinear regimes. The radiation of an electron in a field of strong electromagnetic wave (radiation in the "light" undulator) is considered in the quantum electromagnetic frame. Comparison of results obtained by both approaches has been shown that UR spectra in the whole cone coincide with high accuracy for the case xbeam were simulated with taking into account the discrete process of photon emission along an electron trajectory in both kinds of undulators.
The Fock-Kemmer approach to precursor shock waves in relativistic field theory
Abdullah, Rawand H
2016-01-01
We use distribution theory (generalized functions) to extend and justify the Fock-Kemmer approach to the propagation of precursor shock wave discontinuities in classical and quantum field theory. We apply lightcone causality arguments to propose that shock wave singularities in non-linear classical field theories and in Maxwell's equations for responsive media require a form of classical renormalization analogous to Wilson operator product expansions in quantum field theories.
Unified derivation of exact solutions to the relativistic Coulomb problem: Lie algebraic approach
Panahi, H.; Baradaran, M.; Savadi, A.
2015-10-01
Exact algebraic solutions of the D-dimensional Dirac and Klein-Gordon equations for the Coulomb potential are obtained in a unified treatment. It is shown that two cases are reducible to the same basic equation, which can be solved exactly. Using the Lie algebraic approach, the general exact solutions of the problem are obtained within the framework of representation theory of the sl(2) Lie algebra.
Relativistic quantum mechanics
Horwitz, Lawrence P
2015-01-01
This book describes a relativistic quantum theory developed by the author starting from the E.C.G. Stueckelberg approach proposed in the early 40s. In this framework a universal invariant evolution parameter (corresponding to the time originally postulated by Newton) is introduced to describe dynamical evolution. This theory is able to provide solutions for some of the fundamental problems encountered in early attempts to construct a relativistic quantum theory. A relativistically covariant construction is given for which particle spins and angular momenta can be combined through the usual rotation group Clebsch-Gordan coefficients. Solutions are defined for both the classical and quantum two body bound state and scattering problems. The recently developed quantum Lax-Phillips theory of semigroup evolution of resonant states is described. The experiment of Lindner and coworkers on interference in time is discussed showing how the property of coherence in time provides a simple understanding of the results. Th...
Worldline Variational Approximation: A New Approach to the Relativistic Binding Problem
Barro-Bergflodt, K; Stingl, M
2004-01-01
We determine the lowest bound-state pole of the density-density correlator in the scalar Wick-Cutkosky model where two equal-mass constituents interact via the exchange of mesons. This is done by employing the worldline representation of field theory together with a variational approximation as in Feynman's treatment of the polaron. Unlike traditional methods based on the Bethe-Salpeter equation, self-energy and vertex corrections are (approximately) included as are crossed diagrams. Only vacuum-polarization effects of the heavy particles are neglected. The well-known instability of the model due to self-energy effects leads to large qualitative and quantitative changes compared to traditional approaches which neglect them. We determine numerically the critical coupling constant above which no real solutions of the variational equations exist anymore and show that it is smaller than in the one-body case due to an induced instability. The width of the bound state above the critical coupling is estimated analyt...
Sekizawa, Kazuyuki
2016-01-01
Background: Multinucleon transfer (MNT) and quasifission (QF) processes are dominant processes in low-energy collisions of two heavy nuclei. They are expected to be useful to produce neutron-rich unstable nuclei. Nuclear dynamics leading to these processes depends sensitively on nuclear properties such as deformation and shell structure. Purpose: We elucidate reaction mechanisms of MNT and QF processes involving heavy deformed nuclei, making detailed comparisons between microscopic TDHF calculations and measurements for $^{64}$Ni+$^{238}$U reaction. Methods: Three-dimensional Skyrme-TDHF calculations are performed. Particle-number projection method is used to evaluate MNT cross sections from the TDHF wave function after collision. Results: Fragment masses, total kinetic energy (TKE), scattering angle, contact time, and MNT cross sections are investigated for $^{64}$Ni+$^{238}$U reaction. They show reasonable agreements with measurements. At small impact parameters, collision dynamics depends sensitively on th...
Adachi, H; Kawai, J
2006-01-01
Molecular-orbital calculations for materials design such as alloys, ceramics, and coordination compounds are now possible for experimentalists. Molecuar-orbital calculations for the interpretation of chemical effect of spectra are also possible for experimentalists. The most suitable molecular-orbital calculation method for these purpose is the DV-Xa method, which is robust in such a way that the calculation converges to a result even if the structure of the molecule or solid is impossible in the pressure and temperature ranges on earth. This book specially addresses the methods to design novel materials and to predict the spectralline shape of unknown materials using the DV-Xa molecular-orbital method, but is also useful for those who want to calculate electronic structures of materials using any kind of method.
Papajak, Ewa; Truhlar, Donald G
2011-01-11
We present sets of convergent, partially augmented basis set levels corresponding to subsets of the augmented "aug-cc-pV(n+d)Z" basis sets of Dunning and co-workers. We show that for many molecular properties a basis set fully augmented with diffuse functions is computationally expensive and almost always unnecessary. On the other hand, unaugmented cc-pV(n+d)Z basis sets are insufficient for many properties that require diffuse functions. Therefore, we propose using intermediate basis sets. We developed an efficient strategy for partial augmentation, and in this article, we test it and validate it. Sequentially deleting diffuse basis functions from the "aug" basis sets yields the "jul", "jun", "may", "apr", etc. basis sets. Tests of these basis sets for Møller-Plesset second-order perturbation theory (MP2) show the advantages of using these partially augmented basis sets and allow us to recommend which basis sets offer the best accuracy for a given number of basis functions for calculations on large systems. Similar truncations in the diffuse space can be performed for the aug-cc-pVxZ, aug-cc-pCVxZ, etc. basis sets.
Weberszpil, J; Cherman, A; Helayël-Neto, J A
2012-01-01
The main goal of this paper is to set up the coarse-grained formulation of a fractional Schr\\"odinger equation that incorporates a higher (spatial) derivative term which accounts for relativistic effects at a lowest order. The corresponding continuity equation is worked out and we also identify the contribution of the relativistic correction the quantum potential in the coarse-grained treatment. As a consequence, in the classical regime, we derive the sort of fractional Newtonian law with the quantum potential included and the fractional conterparts of the De Broglies's energy and momentum relations.
Ghizzo, A. [Institut Jean Lamour UMR 7163, Université de Lorraine, BP 239 F-54506 Vandoeuvre les Nancy (France)
2013-08-15
The stationary state with magnetically trapped particles is investigated at the saturation of the relativistic Weibel instability, within the “multiring” model in a Hamiltonian framework. The multistream model and its multiring extension have been developed in Paper I, under the assumption that the generalized canonical momentum is conserved in the perpendicular direction. One dimensional relativistic Bernstein-Greene-Kruskal waves with deeply trapped particles are addressed using similar mathematical formalism developed by Lontano et al.[Phys. Plasmas 9, 2562 (2002); Phys. Plasmas 10, 639 (2003)] using several streams and in the presence of both electrostatic and magnetic trapping mechanisms.
Microscopic Optical Potential of α-Nucleus Elastic Scattering
2008-01-01
<正>The nucleon microscopic optical model potentials (OMP) in the nuclear medium are studied in the framework of the Dirac-Brueckner-Hartree-Fock approach, which are of density- and energy-dependence.
Pairing correlations in an explicitly particle-number conserving approach
Pillet, N; Libert, J
2002-01-01
A method to treat pairing correlations in an explicitly particle-number conserving approach is proposed and discussed. It appears to be both tractable and reliable while using state of the art effective interactions, e.g. of the Skyrme type, for the particle-hole matrix elements. It corresponds to a highly truncated shell-model calculation approach. Its fast convergence in the particle-hole basis is due to the use of single-particle states stemming from an Hartree-Fock-like mean field defined from a one-body density matrix including self-consistently the one-body effect of the correlations. Results obtained in an non-fully consistent fashion, in that the residual interaction is mocked up by a delta interaction, are presented. They mainly confirm most of the physical properties underlying the BCS-like solutions, in particular the paramount importance of pair transfers. However in weak pairing situations, e.g. near subshell- or shell-closures, they provide a microscopic description quite at variance with the us...
A new approach to barrier-top fission dynamics
Bertsch, G. F.; Mehlhaff, J. M.
2016-06-01
We proposed a calculational framework for describing induced fission that avoids the Bohr-Wheeler assumption of well-defined fission channels. The building blocks of our approach are configurations that form a discrete, orthogonal basis and can be characterized by both energy and shape. The dynamics is to be determined by interaction matrix elements between the states rather than by a Hill-Wheeler construction of a collective coordinate. Within our approach, several simple limits can be seen: diffusion; quantized conductance; and ordinary decay through channels. The specific proposal for the discrete basis is to use the Kπ quantum numbers of the axially symmetric Hartree-Fock approximation to generate the configurations. Fission paths would be determined by hopping from configuration to configuration via the residual interaction. We show as an example the configurations needed to describe a fictitious fission decay 32S → 16 O + 16 O. We also examine the geometry of the path for fission of 236U, measuring distances by the number of jumps needed to go to a new Kπ partition.
What is "Relativistic Canonical Quantization"?
Arbatsky, D. A.
2005-01-01
The purpose of this review is to give the most popular description of the scheme of quantization of relativistic fields that was named relativistic canonical quantization (RCQ). I do not give here the full exact account of this scheme. But with the help of this review any physicist, even not a specialist in the relativistic quantum theory, will be able to get a general view of the content of RCQ, of its connection with other known approaches, of its novelty and of its fruitfulness.
Sylvetsky, Nitai; Peterson, Kirk A.; Karton, Amir; Martin, Jan M. L.
2016-06-01
In the context of high-accuracy computational thermochemistry, the valence coupled cluster with all singles and doubles (CCSD) correlation component of molecular atomization energies presents the most severe basis set convergence problem, followed by the (T) component. In the present paper, we make a detailed comparison, for an expanded version of the W4-11 thermochemistry benchmark, between, on the one hand, orbital-based CCSD/AV{5,6}Z + d and CCSD/ACV{5,6}Z extrapolation, and on the other hand CCSD-F12b calculations with cc-pVQZ-F12 and cc-pV5Z-F12 basis sets. This latter basis set, now available for H-He, B-Ne, and Al-Ar, is shown to be very close to the basis set limit. Apparent differences (which can reach 0.35 kcal/mol for systems like CCl4) between orbital-based and CCSD-F12b basis set limits disappear if basis sets with additional radial flexibility, such as ACV{5,6}Z, are used for the orbital calculation. Counterpoise calculations reveal that, while total atomization energies with V5Z-F12 basis sets are nearly free of BSSE, orbital calculations have significant BSSE even with AV(6 + d)Z basis sets, leading to non-negligible differences between raw and counterpoise-corrected extrapolated limits. This latter problem is greatly reduced by switching to ACV{5,6}Z core-valence basis sets, or simply adding an additional zeta to just the valence orbitals. Previous reports that all-electron approaches like HEAT (high-accuracy extrapolated ab-initio thermochemistry) lead to different CCSD(T) limits than "valence limit + CV correction" approaches like Feller-Peterson-Dixon and Weizmann-4 (W4) theory can be rationalized in terms of the greater radial flexibility of core-valence basis sets. For (T) corrections, conventional CCSD(T)/AV{Q,5}Z + d calculations are found to be superior to scaled or extrapolated CCSD(T)-F12b calculations of similar cost. For a W4-F12 protocol, we recommend obtaining the Hartree-Fock and valence CCSD components from CCSD-F12b/cc-pV{Q,5}Z-F12
Hakim, Rémi
1994-01-01
Il existe à l'heure actuelle un certain nombre de théories relativistes de la gravitation compatibles avec l'expérience et l'observation. Toutefois, la relativité générale d'Einstein fut historiquement la première à fournir des résultats théoriques corrects en accord précis avec les faits.
Jones, Bernard J. T.; Markovic, Dragoljub
1997-06-01
Preface; Prologue: Conference overview Bernard Carr; Part I. The Universe At Large and Very Large Redshifts: 2. The size and age of the Universe Gustav A. Tammann; 3. Active galaxies at large redshifts Malcolm S. Longair; 4. Observational cosmology with the cosmic microwave background George F. Smoot; 5. Future prospects in measuring the CMB power spectrum Philip M. Lubin; 6. Inflationary cosmology Michael S. Turner; 7. The signature of the Universe Bernard J. T. Jones; 8. Theory of large-scale structure Sergei F. Shandarin; 9. The origin of matter in the universe Lev A. Kofman; 10. New guises for cold-dark matter suspects Edward W. Kolb; Part II. Physics and Astrophysics Of Relativistic Compact Objects: 11. On the unification of gravitational and inertial forces Donald Lynden-Bell; 12. Internal structure of astrophysical black holes Werner Israel; 13. Black hole entropy: external facade and internal reality Valery Frolov; 14. Accretion disks around black holes Marek A. Abramowicz; 15. Black hole X-ray transients J. Craig Wheeler; 16. X-rays and gamma rays from active galactic nuclei Roland Svensson; 17. Gamma-ray bursts: a challenge to relativistic astrophysics Martin Rees; 18. Probing black holes and other exotic objects with gravitational waves Kip Thorne; Epilogue: the past and future of relativistic astrophysics Igor D. Novikov; I. D. Novikov's scientific papers and books.
Relativistic impulse dynamics.
Swanson, Stanley M
2011-08-01
Classical electrodynamics has some annoying rough edges. The self-energy of charges is infinite without a cutoff. The calculation of relativistic trajectories is difficult because of retardation and an average radiation reaction term. By reconceptuallizing electrodynamics in terms of exchanges of impulses rather than describing it by forces and potentials, we eliminate these problems. A fully relativistic theory using photonlike null impulses is developed. Numerical calculations for a two-body, one-impulse-in-transit model are discussed. A simple relationship between center-of-mass scattering angle and angular momentum was found. It reproduces the Rutherford cross section at low velocities and agrees with the leading term of relativistic distinguishable-particle quantum cross sections (Møller, Mott) when the distance of closest approach is larger than the Compton wavelength of the particle. Magnetism emerges as a consequence of viewing retarded and advanced interactions from the vantage point of an instantaneous radius vector. Radiation reaction becomes the local conservation of energy-momentum between the radiating particle and the emitted impulse. A net action is defined that could be used in developing quantum dynamics without potentials. A reinterpretation of Newton's laws extends them to relativistic motion.
Tailoring approach for obtaining molecular orbitals of large systems
Anuja P Rahalkar; Shridhar R Gadre
2012-01-01
Molecular orbitals (MO’s) within Hartree-Fock (HF) theory are of vital importance as they provide preliminary information of bonding and features such as electron localization and chemical reactivity. The contemporary literature treats the Kohn-Sham orbitals within density functional theory (DFT) equivalently to the MO's obtained within HF framework. The high scaling order of ab initio methods is the main hurdle in obtaining the MO's for large molecular systems. With this view, an attempt is made in the present work to employ molecular tailoring approach (MTA) for obtaining the complete set of MO's including occupied and virtual orbitals, for large molecules at HF and B3LYP levels of theory. The energies of highest occupied and lowest unoccupied molecular orbitals, and hence the band gaps, are accurately estimated by MTA for most of the test cases benchmarked in this study, which include -conjugated molecules. Typically, the root mean square errors of valence MO's are in range of 0.001 to 0.010 a.u. for all the test cases examined. MTA shows a time advantage factor of 2 to 3 over the corresponding actual calculation, for many of the systems reported.
Pramanik, Souvik; Ghosh, Subir
2013-10-01
We have developed a unified scheme for studying noncommutative algebras based on generalized uncertainty principle (GUP) and Snyder form in a relativistically covariant point particle Lagrangian (or symplectic) framework. Even though the GUP-based algebra and Snyder algebra are very distinct, the more involved latter algebra emerges from an approximation of the Lagrangian model of the former algebra. Deformed Poincaré generators for the systems that keep space-time symmetries of the relativistic particle models have been studied thoroughly. From a purely constrained dynamical analysis perspective the models studied here are very rich and provide insights on how to consistently construct approximate models from the exact ones when nonlinear constraints are present in the system. We also study dynamics of the GUP particle in presence of external electromagnetic field.
Comparison of Self-Consistent Skyrme and Gogny Calculations for Light Hg Isotopes
Warda, M; Próchniak, L
2009-01-01
The ground-state properties of neutron-deficient Hg isotopes have been investigated by the constrained self-consistent Hartree-Fock-Bogoliubov approach with the Skyrme and Gogny effective forces. In the case of the Skyrme interaction we h ave also applied the Hartree-Fock+BCS model with the state-dependent $\\delta$-pairing interaction. Potential energy surfaces and pairing properties have been compared for the both types of forces.
Properties of deformed Λ hypernuclei
ZHOU Xian-Rong
2009-01-01
The properties of Be and B isotopes and the corresponding Λ hypernuclei are studied by using a deformed Skyrme Hartree-Fock approach with realistic nucleonic Skyrme forces, pairing correlations, and a microscopically determined lambda-nucleon interaction based on Brueckner-Hartree-Fock calculations of hypernuclear matter. The results suggest that the core nuclei and the corresponding hypernuclei have similar deformations with the same sign.
Scattering in Relativistic Particle Mechanics.
de Bievre, Stephan
The problem of direct interaction in relativistic particle mechanics has been extensively studied and a variety of models has been proposed avoiding the conclusions of the so-called no-interaction theorems. In this thesis we study scattering in the relativistic two-body problem. We use our results to analyse gauge invariance in Hamiltonian constraint models and the uniqueness of the symplectic structure in manifestly covariant relativistic particle mechanics. We first present a general geometric framework that underlies approaches to relativistic particle mechanics. This permits a model-independent and geometric definition of the notions of asymptotic completeness and of Moller and scattering operators. Subsequent analysis of these concepts divides into two parts. First, we study the kinematic properties of the scattering transformation, i.e. those properties that arise solely from the invariance of the theory under the Poincare group. We classify all canonical (symplectic) scattering transformations on the relativistic phase space for two free particles in terms of a single function of the two invariants of the theory. We show how this function is determined by the center of mass time delay and scattering angle and vice versa. The second part of our analysis of the relativistic two-body scattering problem is devoted to the dynamical properties of the scattering process. Hence, we turn to two approaches to relativistic particle mechanics: the Hamiltonian constraint models and the manifestly covariant formalism. Using general geometric arguments, we prove "gauge invariance" of the scattering transformation in the Todorov -Komar Hamiltonian constraint model. We conclude that the scattering cross sections of the Todorov-Komar models have the same angular dependence as their non-relativistic counterpart, irrespective of a choice of gauge. This limits the physical relevance of those models. We present a physically non -trivial Hamiltonian constraint model, starting from
Relativistic effects in atom gravimeters
Tan, Yu-Jie; Shao, Cheng-Gang; Hu, Zhong-Kun
2017-01-01
Atom interferometry is currently developing rapidly, which is now reaching sufficient precision to motivate laboratory tests of general relativity. Thus, it is extremely significant to develop a general relativistic model for atom interferometers. In this paper, we mainly present an analytical derivation process and first give a complete vectorial expression for the relativistic interferometric phase shift in an atom interferometer. The dynamics of the interferometer are studied, where both the atoms and the light are treated relativistically. Then, an appropriate coordinate transformation for the light is performed crucially to simplify the calculation. In addition, the Bordé A B C D matrix combined with quantum mechanics and the "perturbation" approach are applied to make a methodical calculation for the total phase shift. Finally, we derive the relativistic phase shift kept up to a sensitivity of the acceleration ˜1 0-14 m/s 2 for a 10 -m -long atom interferometer.
Relativistic and non-relativistic geodesic equations
Giambo' , R.; Mangiarotti, L.; Sardanashvily, G. [Camerino Univ., Camerino, MC (Italy). Dipt. di Matematica e Fisica
1999-07-01
It is shown that any dynamic equation on a configuration space of non-relativistic time-dependent mechanics is associated with connections on its tangent bundle. As a consequence, every non-relativistic dynamic equation can be seen as a geodesic equation with respect to a (non-linear) connection on this tangent bundle. Using this fact, the relationships between relativistic and non-relativistic equations of motion is studied.
Relativistic non-equilibrium thermodynamics revisited
García-Colin, L S
2006-01-01
Relativistic irreversible thermodynamics is reformulated following the conventional approach proposed by Meixner in the non-relativistic case. Clear separation between mechanical and non-mechanical energy fluxes is made. The resulting equations for the entropy production and the local internal energy have the same structure as the non-relativistic ones. Assuming linear constitutive laws, it is shown that consistency is obtained both with the laws of thermodynamics and causality.
Nonlinear Approach in Nuclear Dynamics
Gridnev, K. A.; Kartavenko, V. G.; Greiner, W.
2002-11-01
Attention is focused on the various approaches that use the concept of nonlinear dispersive waves (solitons) in nonrelativistic nuclear physics. The problem of dynamical instability and clustering (stable fragments formation) in a breakup of excited nuclear systems are considered from the points of view of the soliton concept. It is shown that the volume (spinodal) instability can be associated with nonlinear terms, and the surface (Rayleigh-Taylor type) instability, with the dispersion terms in the evolution equations. The both instabilities may compensate each other and lead to stable solutions (solitons). A static scission configuration in cold ternary fission is considered in the framework of mean field approach. We suggest to use the inverse mean field method to solve single-particle Schrödinger equation, instead of constrained selfconsistent Hartree-Fock equations. It is shown, that it is possible to simulate one-dimensional three-center system in the approximation of reflectless single-particle potentials. The soliton-like solutions of the Korteweg-de Vries equation are using to describe collective excitations of nuclei observed in inelastic alpha-particle and proton scattering. The analogy between fragmentation into parts of nuclei and buckyballs has led us to the idea of light nuclei as quasi-crystals. We establish that the quasi-crystalline structure can be formed when the distance between the alpha-particles is comparable with the length of the De Broglia wave of the alpha-particle. Applying this model to the scattering of alpha-particles we obtain that the form factor of the clusterized nucleus can be factorized into the formfactor of the cluster and the density of clusters in the nucleus. It gives possibility to study the distribution of clusters in nuclei and to resolve what kind of distribution we are dealing with: a surface or volume one.
Zhidkov, A.; Masuda, S.; Bulanov, S. S.; Koga, J.; Hosokai, T.; Kodama, R.
2014-05-01
Nonlinear cascade scattering of intense, tightly focused laser pulses by relativistic electrons is studied numerically in the classical approximation including radiation damping for the quantum parameter ⟨ℏωxray⟩/ɛ <1 and an arbitrary radiation parameter χ. The electron's energy loss, along with its being scattered to the side by the ponderomotive force, makes scattering in the vicinity of a high laser field nearly impossible at high electron energies. The use of a second, copropagating laser pulse as a booster is shown to partially solve this problem.
Relativistic magnetohydrodynamics
Hernandez, Juan; Kovtun, Pavel
2017-05-01
We present the equations of relativistic hydrodynamics coupled to dynamical electromagnetic fields, including the effects of polarization, electric fields, and the derivative expansion. We enumerate the transport coefficients at leading order in derivatives, including electrical conductivities, viscosities, and thermodynamic coefficients. We find the constraints on transport coefficients due to the positivity of entropy production, and derive the corresponding Kubo formulas. For the neutral state in a magnetic field, small fluctuations include Alfvén waves, magnetosonic waves, and the dissipative modes. For the state with a non-zero dynamical charge density in a magnetic field, plasma oscillations gap out all propagating modes, except for Alfvén-like waves with a quadratic dispersion relation. We relate the transport coefficients in the "conventional" magnetohydrodynamics (formulated using Maxwell's equations in matter) to those in the "dual" version of magnetohydrodynamics (formulated using the conserved magnetic flux).
Leardini, Fabrice
2013-01-01
This manuscript presents a problem on special relativity theory (SRT) which embodies an apparent paradox relying on the concept of simultaneity. The problem is represented in the framework of Greek epic poetry and structured in a didactic way. Owing to the characteristic properties of Lorenz transformations, three events which are simultaneous in a given inertial reference system, occur at different times in the other two reference frames. In contrast to the famous twin paradox, in the present case there are three, not two, different inertial observers. This feature provides a better framework to expose some of the main characteristics of SRT, in particular, the concept of velocity and the relativistic rule of addition of velocities.
Braun, M A; Kaptari, L P
2003-01-01
The rescattering contribution to the inclusive and exclusive deuteron electro-disintegration at the values of the Bjorken scaling variable $x=1$, as well as in the so called {\\it cumulative} region ($x>1$) is calculated within a relativistic approach based on the Feynman diagram formalism taking into account colour transparency effects by the inclusion of the {\\it finite formation time} (FFT) of the ejected nucleon via the introduction of the dependence of the scattering amplitude of the ejectile upon its virtuality. In the cumulative region the FFT effects which result from the real part of the ejectile propagator are taken into account. It is found that the relative weight of the rescattering steadily grows with $x$ becoming of the order of unity at $x>1.4\\div 1.5$. At such values of $x$ the finite formation time effects become fairly visible, which may serve for their study at relatively small value of the four-momentum transfer$Q^2$. The relativistic rescattering contribution is compared with the Glauber ...
LETTER TO THE EDITOR: Recurrence relations for relativistic atomic matrix elements
Martínez-y-Romero, R. P.; Núñez-Yépez, H. N.; Salas-Brito, A. L.
2000-05-01
Recurrence formulae for arbitrary hydrogenic radial matrix elements are obtained in the Dirac form of relativistic quantum mechanics. Our approach is inspired by the relativistic extension of the second hypervirial method that has been succesfully employed to deduce an analogous relationship in non-relativistic quantum mechanics. We first obtain the relativistic extension of the second hypervirial and then the relativistic recurrence relation. Furthermore, we use this relation to deduce relativistic versions of the Pasternack-Sternheimer rule and of the virial theorem.
Yao Jiang-Ming; Meng Jie; D. Pena Arteaga; P. Ring
2008-01-01
A full three-dimensional angular momentum projection on top of a triaxial relativistic mean-field calculation is implemented for the first time. The underlying Lagrangian is a point coupling model and pairing correlations are taken into account by a monopole force. This method is applied for the low-lying excited states in 24Mg. Good agreement with the experimental data is found for the ground state properties. A minimum in the potential energy surface for the 2+ state, with β≈ 0.55, γ≈ 10°, is used as the basis to investigate the rotational energyspectrum as well as the corresponding B(E2) transition probabilities as compared to the available data.
M MOUSAVI; M R SHOJAEI
2017-02-01
In this work, we have obtained energy levels and charge radius for the $\\beta$-stability line nucleus, in relativistic shell model. In this model, we considered a close shell for each nucleus containing double magicnumber and a single nucleon energy level. Here we have taken $^{41}$Ca with a single neutron in the $^{40}$Ca core as an illustrative example. Then we have selected the Eckart plus Hulthen potentials for interaction between the coreand the single nucleon. By using parametric Nikiforov–Uvarov (PNU) method, we have calculated the energy values and wave function. Finally, we have calculated the charge radius for 17O, $^{41}$Ca, $^{49}$Ca and $^{57}$Ni. Our results are in agreement with experimental values and hence this model can be applied for similar nuclei.
Avishai, Y.; Mizutani, T.
1980-04-01
We continue our investigation into the theory of coupled πNN-NN systems in succession of an earlier work, in which practical equations and unitarity have been established for all the pertinent amplitudes. First, the equivalence of our theory with that of Mizutani and Koltun is proved. Then, the question of whether theories which adopt the bound-state picture are appropriate for the description of systems of pions and nucleons is carefully discussed. We also show how the equations should be modified when we include the non-pole contribution to the πN P 11 channel. Finally, we extend our equations to include relativity and show how to arrive at numerically solvable equations, with relativistic invariance guaranteed. In the NN sector, these equations contain the two time orderings of the OPEP in a correct manner.
Molecular tailoring approach for exploring structures, energetics and properties of clusters
Shridhar R Gadre; K V Jovan Jose; Anuja P Rahalkar
2010-01-01
Molecular Tailoring Approach (MTA) is a method developed for enabling ab initio calculations on prohibitively large molecules or atomic/molecular clusters. A brief review of MTA, a linear scaling technique based on set inclusion and exclusion principle, is provided. The Molecular Electrostatic Potential (MESP) of smaller clusters is exploited for building initial geometries for the larger ones, followed by MTA geometry optimization. The applications of MTA are illustrated with a few test cases such as (CO2) and Li clusters employing Density Functional theory (DFT) and a nanocluster of orthoboric acid at the Hartree-Fock (HF) level. Further, a discussion on the geometries and energetics of benzene tetramers and pentamers, treated at the Møller-Plesset second order (MP2) perturbation theory, is given. MTA model is employed for evaluating some cluster properties viz. adiabatic ionization potential, MESP, polarizability, Hessian matrix and infrared frequencies. These property evaluations are carried out on a series of test cases and are seen to offer quite good agreement with those computed by an actual calculation. These case studies highlight the advantages of MTA model calculations vis-à-vis the actual ones with reference to the CPU-time, memory requirements and accuracy.
Li, Chenyang; Verma, Prakash; Hannon, Kevin P; Evangelista, Francesco A
2017-08-21
We propose an economical state-specific approach to evaluate electronic excitation energies based on the driven similarity renormalization group truncated to second order (DSRG-PT2). Starting from a closed-shell Hartree-Fock wave function, a model space is constructed that includes all single or single and double excitations within a given set of active orbitals. The resulting VCIS-DSRG-PT2 and VCISD-DSRG-PT2 methods are introduced and benchmarked on a set of 28 organic molecules [M. Schreiber et al., J. Chem. Phys. 128, 134110 (2008)]. Taking CC3 results as reference values, mean absolute deviations of 0.32 and 0.22 eV are observed for VCIS-DSRG-PT2 and VCISD-DSRG-PT2 excitation energies, respectively. Overall, VCIS-DSRG-PT2 yields results with accuracy comparable to those from time-dependent density functional theory using the B3LYP functional, while VCISD-DSRG-PT2 gives excitation energies comparable to those from equation-of-motion coupled cluster with singles and doubles.
Mitin, Alexander V; van Wüllen, Christoph
2006-02-14
A two-component quasirelativistic Hamiltonian based on spin-dependent effective core potentials is used to calculate ionization energies and electron affinities of the heavy halogen atom bromine through the superheavy element 117 (eka-astatine) as well as spectroscopic constants of the homonuclear dimers of these atoms. We describe a two-component Hartree-Fock and density-functional program that treats spin-orbit coupling self-consistently within the orbital optimization procedure. A comparison with results from high-order Douglas-Kroll calculations--for the superheavy systems also with zeroth-order regular approximation and four-component Dirac results--demonstrates the validity of the pseudopotential approximation. The density-functional (but not the Hartree-Fock) results show very satisfactory agreement with theoretical coupled cluster as well as experimental data where available, such that the theoretical results can serve as an estimate for the hitherto unknown properties of astatine, element 117, and their dimers.
Findlater, Alexander D; Zahariev, Federico; Gordon, Mark S
2015-04-16
The local correlation "cluster-in-molecule" (CIM) method is combined with the fragment molecular orbital (FMO) method, providing a flexible, massively parallel, and near-linear scaling approach to the calculation of electron correlation energies for large molecular systems. Although the computational scaling of the CIM algorithm is already formally linear, previous knowledge of the Hartree-Fock (HF) reference wave function and subsequent localized orbitals is required; therefore, extending the CIM method to arbitrarily large systems requires the aid of low-scaling/linear-scaling approaches to HF and orbital localization. Through fragmentation, the combined FMO-CIM method linearizes the scaling, with respect to system size, of the HF reference and orbital localization calculations, achieving near-linear scaling at both the reference and electron correlation levels. For the 20-residue alanine α helix, the preliminary implementation of the FMO-CIM method captures 99.6% of the MP2 correlation energy, requiring 21% of the MP2 wall time. The new method is also applied to solvated adamantine to illustrate the multilevel capability of the FMO-CIM method.
Huzak, M; Deleuze, M S; Hajgató, B
2011-09-14
An analysis using the formalism of crystalline orbitals for extended systems with periodicity in one dimension demonstrates that any antiferromagnetic and half-metallic spin-polarization of the edge states in n-acenes, and more generally in zigzag graphene nanoislands and nanoribbons of finite width, would imply a spin contamination S(2) that increases proportionally to system size, in sharp and clear contradiction with the implications of Lieb's theorem for compensated bipartite lattices and the expected value for a singlet (S = 0) electronic ground state. Verifications on naphthalene, larger n-acenes (n = 3-10) and rectangular nanographene islands of increasing size, as well as a comparison using unrestricted Hartree-Fock theory along with basis sets of improving quality against various many-body treatments demonstrate altogether that antiferromagnetism and half-metallicity in extended graphene nanoribbons will be quenched by an exact treatment of electron correlation, at the confines of non-relativistic many-body quantum mechanics. Indeed, for singlet states, symmetry-breakings in spin-densities are necessarily the outcome of a too approximate treatment of static and dynamic electron correlation in single-determinantal approaches, such as unrestricted Hartree-Fock or Density Functional Theory. In this context, such as the size-extensive spin-contamination to which it relates, half-metallicity is thus nothing else than a methodological artefact.
Simenel, C.; Avez, B. [CEA Saclay, Dept. d' Astrophysique, de Physique des Particules de Physique Nucleaire et de l' Instrumentation Associee (DSM/DAPNIA/SPhN), 91- Gif sur Yvette (France); Lacroix, D. [GANIL, 14 - Caen (France)
2007-07-01
This lecture introduces several microscopic approaches to nuclear dynamics. Our goal is to provide a good description of low energy heavy ions collisions. We study both the formalism and the practical application of the time-dependent Hartree-Fock (TDHF) theory. The TDHF approach gives a mean field dynamics of the system under the assumption of independent particles. As an example, we study the fusion of both spherical and deformed nuclei with TDHF. We also show that nucleon transfer may occur between nuclei below the barrier. These studies allow us to specify the field of applications of TDHF in one hand, and, in the other hand, its intrinsic limitations, as for instance the fact that there is no fusion by tunnel effect with TDHF. It is then important to get rid of the independent particle assumption. We finally present some approaches to go beyond TDHF, including for instance pairing and/or collision term between nucleons, though only few realistic applications have been performed so far. (authors)
Ground State Properties of Neutron Magic Nuclei
Saxena, G
2016-01-01
A systematic study of the ground state properties of the entire chains of even even neutron magic nuclei represented by isotones of traditional neutron magic numbers N = 8, 20, 40, 50, 82 and 126 has been carried out using relativistic mean field (rmf) plus Bardeen Cooper Schrieffer (BCS) approach. Our present investigation includes deformation, binding energy, two proton separation energy, single particle energy, rms radii along with proton and neutron density profiles, etc. Several of these results are compared with the results calculated using non relativistic approach (Skyrme Hartree Fock method) along with available experimental data and indeed they are found with excellent agreement. In addition, the possible locations of the proton and neutron drip lines, the (Z,N) values for the new shell closures, disappearance of traditional shell closures as suggested by the detailed analyzes of results are also discussed in detail.
Relativistic causality and clockless circuits
Matherat, Philippe; 10.1145/2043643.2043650
2011-01-01
Time plays a crucial role in the performance of computing systems. The accurate modelling of logical devices, and of their physical implementations, requires an appropriate representation of time and of all properties that depend on this notion. The need for a proper model, particularly acute in the design of clockless delay-insensitive (DI) circuits, leads one to reconsider the classical descriptions of time and of the resulting order and causal relations satisfied by logical operations. This questioning meets the criticisms of classical spacetime formulated by Einstein when founding relativity theory and is answered by relativistic conceptions of time and causality. Applying this approach to clockless circuits and considering the trace formalism, we rewrite Udding's rules which characterize communications between DI components. We exhibit their intrinsic relation with relativistic causality. For that purpose, we introduce relativistic generalizations of traces, called R-traces, which provide a pertinent des...
Assessment of self-consistent field convergence in spin-dependent relativistic calculations
Nakano, Masahiko; Seino, Junji; Nakai, Hiromi
2016-07-01
This Letter assesses the self-consistent field (SCF) convergence behavior in the generalized Hartree-Fock (GHF) method. Four acceleration algorithms were implemented for efficient SCF convergence in the GHF method: the damping algorithm, the conventional direct inversion in the iterative subspace (DIIS), the energy-DIIS (EDIIS), and a combination of DIIS and EDIIS. Four different systems with varying complexity were used to investigate the SCF convergence using these algorithms, ranging from atomic systems to metal complexes. The numerical assessments demonstrated the effectiveness of a combination of DIIS and EDIIS for GHF calculations in comparison with the other discussed algorithms.
Yue, Yutao; Chachiyo, Teepanis; Rodriguez, Jorge H.
2007-03-01
The direct application of ab-initio methods (Hartree-Fock or density functional theory) to study complete biomolecules has been impossible due to the huge computational cost of fully quantum mechanical calculations. As an initial step towards overcoming this problem, we implemented an ab-initio-based method to predict geometric structures of large metalloproteins using the principle of ``divide and conquer.'' The method has been applied to small test systems showing satisfactory agreement with all-atom ab initio calculations. We have successfully applied the divide and conquer approach to partially optimize the geometry of a ligand-enzyme system, namely NO binding to nitric-oxide reductases (NOR, P450nor). NOR is a metalloenzyme that catalyzes the reduction of NO to N2O. To compare our results with all atom calculations we studied a biochemically relevant subsystem (375 atoms) of the ligand-enzyme complex. The deviation between the divide and conquer geometry and the all atom partial geometry optimization is minor, on order of 10-1 å for bond lengths. The computational cost of the method is moderately expensive making its application to large (bio) molecules plausible. Supported by NSF CAREER Award CHE-0349189 (JHR).
Komissarov, S S; Lyutikov, M
2015-01-01
In this paper we describe a simple numerical approach which allows to study the structure of steady-state axisymmetric relativistic jets using one-dimensional time-dependent simulations. It is based on the fact that for narrow jets with v~c the steady-state equations of relativistic magnetohydrodynamics can be accurately approximated by the one-dimensional time-dependent equations after the substitution z=ct. Since only the time-dependent codes are now publicly available this is a valuable and efficient alternative to the development of a high-specialized code for the time-independent equations. The approach is also much cheaper and more robust compared to the relaxation method. We tested this technique against numerical and analytical solutions found in literature as well as solutions we obtained using the relaxation method and found it sufficiently accurate. In the process, we discovered the reason for the failure of the self-similar analytical model of the jet reconfinement in relatively flat atmospheres a...
Solutions of relativistic radial quasipotential equations
Minh, V.X.; Kadyshevskii, V.G.; Zhidkov, E.P.
1985-11-01
A systematic approach to the investigation of relativistic radial quasipotential equations is developed. The quasipotential equations can be interpreted either as linear equations in finite differences of fourth and second orders, respectively, or as differential equations of infinite order.
Cattaneo, Carlo
2011-01-01
This title includes: Pham Mau Quam: Problemes mathematiques en hydrodynamique relativiste; A. Lichnerowicz: Ondes de choc, ondes infinitesimales et rayons en hydrodynamique et magnetohydrodynamique relativistes; A.H. Taub: Variational principles in general relativity; J. Ehlers: General relativistic kinetic theory of gases; K. Marathe: Abstract Minkowski spaces as fibre bundles; and, G. Boillat: Sur la propagation de la chaleur en relativite.
Relativistic recursion relations for transition matrix elements
Martínez y Romero, R P; Salas-Brito, A L
2004-01-01
We review some recent results on recursion relations which help evaluating arbitrary non-diagonal, radial hydrogenic matrix elements of $r^\\lambda$ and of $\\beta r^\\lambda$ ($\\beta$ a Dirac matrix) derived in the context of Dirac relativistic quantum mechanics. Similar recursion relations were derived some years ago by Blanchard in the non relativistic limit. Our approach is based on a generalization of the second hypervirial method previously employed in the non-relativistic Schr\\"odinger case. An extension of the relations to the case of two potentials in the so-called unshifted case, but using an arbitrary radial function instead of a power one, is also given. Several important results are obtained as special instances of our recurrence relations, such as a generalization to the relativistic case of the Pasternack-Sternheimer rule. Our results are useful in any atomic or molecular calculation which take into account relativistic corrections.
Reactions of Proton Halo Nuclei in a Relativistic Optical Potential
Rashdan, M
2003-01-01
The reaction cross section, sigma sub R; of the proton halo nuclei sup 1 sup 7 Ne and sup 1 sup 2 N on Si is calculated using an optical potential derived from the solution of the Dirac-Brueckner-Bethe-Goldstone equation, starting from the one-boson-exchange potential of Bonn. The nuclear densities are generated from self-consistent Hartree-Fock calculations using the recent Skyrme interaction SKRA. It is found that the enhancement in the reaction cross section found experimentally for the sup 1 sup 7 Ne + Si system in comparison to sup 1 sup 5 O + Si, where sup 1 sup 5 O has been considered as a core of sup 1 sup 7 Ne, is mainly due to the proton halo structure of sup 1 sup 7 Ne which increases the interaction, in the surface and tail regions. Glauber model calculations did not produce this enhancement in sigma sub R for proton halo nuclei
Relativistic frozen core potential scheme with relaxation of core electrons
Nakajima, Yuya; Seino, Junji; Hayami, Masao; Nakai, Hiromi
2016-10-01
This letter proposes a relaxation scheme for core electrons based on the frozen core potential method at the infinite-order Douglas-Kroll-Hess level, called FCP-CR. The core electrons are self-consistently relaxed using frozen molecular valence potentials after the valence SCF calculation is performed. The efficiency of FCP-CR is confirmed by calculations of gold clusters. Furthermore, FCP-CR reproduces the results of the all-electron method for the energies of coinage metal dimers and the core ionization energies and core level shifts of vinyl acetate and three tungsten complexes at the Hartree-Fock and/or symmetry-adapted cluster configuration interaction levels.
Relativistic radiative transfer in relativistic spherical flows
Fukue, Jun
2017-02-01
Relativistic radiative transfer in relativistic spherical flows is numerically examined under the fully special relativistic treatment. We first derive relativistic formal solutions for the relativistic radiative transfer equation in relativistic spherical flows. We then iteratively solve the relativistic radiative transfer equation, using an impact parameter method/tangent ray method, and obtain specific intensities in the inertial and comoving frames, as well as moment quantities, and the Eddington factor. We consider several cases; a scattering wind with a luminous central core, an isothermal wind without a core, a scattering accretion on to a luminous core, and an adiabatic accretion on to a dark core. In the typical wind case with a luminous core, the emergent intensity is enhanced at the center due to the Doppler boost, while it reduces at the outskirts due to the transverse Doppler effect. In contrast to the plane-parallel case, the behavior of the Eddington factor is rather complicated in each case, since the Eddington factor depends on the optical depth, the flow velocity, and other parameters.
Bogdanovich, P; Kisielius, R
2015-01-01
The ab initio quasirelativistic Hartree-Fock method developed specifically for the calculation of spectral parameters of heavy atoms and highly charged ions is used to derive spectral data for the 4s$^2$4p$^5$, 4s$^2$4p$^4$4d and 4s4p$^6$ configurations of the multicharged tungsten ion W$^{39+}$. The relativistic effects are taken into account in the Breit-Pauli approximation for the quasirelativistic Hartree-Fock radial orbitals. The configuration interaction method is applied to include the electron correlation effects. Produced data are compared with existing experimental measurements and theoretical calculations.
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.
Gontchar, I. I.; Chushnyakova, M. V.
2016-08-01
Systematic calculations of the Coulomb barrier parameters for collisions of spherical nuclei are performed within the framework of the double folding approach. The value of the parameter {B}Z={Z}P{Z}T/({A}P{1/3}+{A}T{1/3}) (which estimates the Coulomb barrier height) varies in these calculations from 10 MeV up to 150 MeV. The nuclear densities came from the Hartree-Fock calculations which reproduce the experimental charge densities with good accuracy. For the nucleon-nucleon effective interaction two analytical approximations known in the literature are used: the M3Y and Migdal forces. The calculations show that Migdal interaction always results in the higher Coulomb barrier. Moreover, as B Z increases the difference between the M3Y and Migdal barrier heights systematically increases as well. As the result, the above barrier fusion cross sections calculated dynamically with the M3Y forces and surface friction are in agreement with the data. The cross sections calculated with the Migdal forces are always below the experimental data even without accounting for the dissipation.
Gontchar, Igor
2015-01-01
Systematic calculations of the Coulomb barrier parameters for collisions of spherical nuclei are performed within the framework of the double folding approach. The value of the parameter $B_Z=Z_PZ_T/(A^{1/3}_P+(A^{1/3}_P)$ (which estimates the Coulomb barrier height) varies in these calculations from 10 MeV up to 150 MeV. The nuclear densities came from the Hartree-Fock calculations which reproduce the experimental charge densities with good accuracy. For the nucleon-nucleon effective interaction two analytical approximations known in the literature are used: the M3Y and Migdal forces. The calculations show that Migdal interaction always results in the higher Coulomb barrier. Moreover, as $B_Z$ increases the difference between the M3Y and Migdal barrier heights systematically increases as well. As the result, the above barrier fusion cross sections calculated dynamically with the M3Y forces and surface friction are in agreement with the data. The cross sections calculated with the Migdal forces are always bel...
Abramov, Y A; Volkov, A; Wu, G; Coppens, P
2000-11-01
A new module interfaced to the XD programming package has been used in the evaluation of intermolecular interactions and lattice energies of the crystals of p-nitroaniline, L-asparagine monohydrate and the pentapeptide Boc-Gln-D-Iva-Hyp-Ala-Phol (Boc = butoxycarbonyl, Iva = isovaline = ethylalanine, Phol = phenylalaninol). The electrostatic interactions are evaluated with the atom-centered distributed multipoles from KRMM (kappa'-restricted multipole model) refinements, using the Buckingham expression for non-overlapping charge densities. Results for p-nitroaniline are compared with Hartree-Fock (HF), density functional (DFT) and Moller-Plesset (MP2) supermolecular calculations and with HF and DFT periodic calculations. The HF and DFT methods fail to predict the stability of the p-nitroaniline crystal but the results of the experimental charge-density approach (ECDA) are in good agreement with both MP2 interaction energies and the experimental lattice energy. ECDA results for L-asparagine monohydrate compare well with those from DFT supermolecular and periodic HF calculations. The disorder of the terminal group in the pentapeptide, which persists at the experimental temperature of 20 K, corresponds to an energy difference of only 0.35 kJ mol(-1), which is too small to be reproduced with current methods.
Relativistic Remnants of Non-Relativistic Electrons
Kashiwa, Taro
2015-01-01
Electrons obeying the Dirac equation are investigated under the non-relativistic $c \\mapsto \\infty$ limit. General solutions are given by derivatives of the relativistic invariant functions whose forms are different in the time- and the space-like region, yielding the delta function of $(ct)^2 - x^2$. This light-cone singularity does survive to show that the charge and the current density of electrons travel with the speed of light in spite of their massiveness.
Relativistic Fractal Cosmologies
Ribeiro, Marcelo B
2009-01-01
This article reviews an approach for constructing a simple relativistic fractal cosmology whose main aim is to model the observed inhomogeneities of the distribution of galaxies by means of the Lemaitre-Tolman solution of Einstein's field equations for spherically symmetric dust in comoving coordinates. This model is based on earlier works developed by L. Pietronero and J.R. Wertz on Newtonian cosmology, whose main points are discussed. Observational relations in this spacetime are presented, together with a strategy for finding numerical solutions which approximate an averaged and smoothed out single fractal structure in the past light cone. Such fractal solutions are shown, with one of them being in agreement with some basic observational constraints, including the decay of the average density with the distance as a power law (the de Vaucouleurs' density power law) and the fractal dimension in the range 1 <= D <= 2. The spatially homogeneous Friedmann model is discussed as a special case of the Lemait...
Malaya K Nayak; Rajat K Chaudhuri
2009-09-01
Restricted active space (RAS) configuration interaction (CI) approach is employed to compute the , -odd interaction constant d for the ground ($^{2} \\sum_{1/2}$ ) state of YbF molecule. The present estimate of d = −1.164 × 1025 Hz/e-cm is expected to provide a reliable limit on the electron's electric dipole moment (EDM), e.
Relativistic quantum mechanics
Wachter, Armin
2010-01-01
Which problems do arise within relativistic enhancements of the Schrödinger theory, especially if one adheres to the usual one-particle interpretation, and to what extent can these problems be overcome? And what is the physical necessity of quantum field theories? In many books, answers to these fundamental questions are given highly insufficiently by treating the relativistic quantum mechanical one-particle concept very superficially and instead introducing field quantization as soon as possible. By contrast, this monograph emphasizes relativistic quantum mechanics in the narrow sense: it extensively discusses relativistic one-particle concepts and reveals their problems and limitations, therefore motivating the necessity of quantized fields in a physically comprehensible way. The first chapters contain a detailed presentation and comparison of the Klein-Gordon and Dirac theory, always in view of the non-relativistic theory. In the third chapter, we consider relativistic scattering processes and develop the...
Mean-field models and exotic nuclei
Bender, M.; Buervenich, T.; Maruhn, J.A.; Greiner, W. [Inst. fuer Theoretische Physik, Univ. Frankfurt (Germany); Rutz, K. [Inst. fuer Theoretische Physik, Univ. Frankfurt (Germany)]|[Gesellschaft fuer Schwerionenforschung mbH, Darmstadt (Germany); Reinhard, P.G. [Inst. fuer Theoretische Physik, Univ. Erlangen (Germany)
1998-06-01
We discuss two widely used nuclear mean-field models, the relativistic mean-field model and the (nonrelativistic) Skyrme-Hartree-Fock model, and their capability to describe exotic nuclei. Test cases are superheavy nuclei and neutron-rich Sn isotopes. New information in this regime helps to fix hitherto loosely determined aspects of the models. (orig.)
ZHANG Peng-Fei; RUAN Tu-Nan
2001-01-01
A systematic theory on the appropriate spin operators for the relativistic states is developed. For a massive relativistic particle with arbitrary nonzero spin, the spin operator should be replaced with the relativistic one, which is called in this paper as moving spin. Further the concept of moving spin is discussed in the quantum field theory. A new is constructed. It is shown that, in virtue of the two operators, problems in quantum field concerned spin can be neatly settled.
Relativistic Guiding Center Equations
White, R. B. [PPPL; Gobbin, M. [Euratom-ENEA Association
2014-10-01
In toroidal fusion devices it is relatively easy that electrons achieve relativistic velocities, so to simulate runaway electrons and other high energy phenomena a nonrelativistic guiding center formalism is not sufficient. Relativistic guiding center equations including flute mode time dependent field perturbations are derived. The same variables as used in a previous nonrelativistic guiding center code are adopted, so that a straightforward modifications of those equations can produce a relativistic version.
Relativistic Linear Restoring Force
Clark, D.; Franklin, J.; Mann, N.
2012-01-01
We consider two different forms for a relativistic version of a linear restoring force. The pair comes from taking Hooke's law to be the force appearing on the right-hand side of the relativistic expressions: d"p"/d"t" or d"p"/d["tau"]. Either formulation recovers Hooke's law in the non-relativistic limit. In addition to these two forces, we…
MALFLIET, R
1993-01-01
We discuss the present status of relativistic transport theory. Special emphasis is put on problems of topical interest: hadronic features, thermodynamical consistent approximations and spectral properties.
Clementi, Enrico
2012-06-01
This is the introductory chapter to the AIP Proceedings volume "Theory and Applications of Computational Chemistry: The First Decade of the Second Millennium" where we discuss the evolution of "computational chemistry". Very early variational computational chemistry developments are reported in Sections 1 to 7, and 11, 12 by recalling some of the computational chemistry contributions by the author and his collaborators (from late 1950 to mid 1990); perturbation techniques are not considered in this already extended work. Present day's computational chemistry is partly considered in Sections 8 to 10 where more recent studies by the author and his collaborators are discussed, including the Hartree-Fock-Heitler-London method; a more general discussion on present day computational chemistry is presented in Section 14. The following chapters of this AIP volume provide a view of modern computational chemistry. Future computational chemistry developments can be extrapolated from the chapters of this AIP volume; further, in Sections 13 and 15 present an overall analysis on computational chemistry, obtained from the Global Simulation approach, by considering the evolution of scientific knowledge confronted with the opportunities offered by modern computers.
Approaching Chemical Accuracy with Quantum Monte Carlo
Petruzielo, Frank R.; Toulouse, Julien; Umrigar, C. J.
2012-01-01
International audience; A quantum Monte Carlo study of the atomization energies for the G2 set of molecules is presented. Basis size dependence of diffusion Monte Carlo atomization energies is studied with a single determinant Slater-Jastrow trial wavefunction formed from Hartree-Fock orbitals. With the largest basis set, the mean absolute deviation from experimental atomization energies for the G2 set is 3.0 kcal/mol. Optimizing the orbitals within variational Monte Carlo improves the agreem...
Relativistic Langevin equation for runaway electrons
Mier, J. A.; Martin-Solis, J. R.; Sanchez, R.
2016-10-01
The Langevin approach to the kinetics of a collisional plasma is developed for relativistic electrons such as runaway electrons in tokamak plasmas. In this work, we consider Coulomb collisions between very fast, relativistic electrons and a relatively cool, thermal background plasma. The model is developed using the stochastic equivalence of the Fokker-Planck and Langevin equations. The resulting Langevin model equation for relativistic electrons is an stochastic differential equation, amenable to numerical simulations by means of Monte-Carlo type codes. Results of the simulations will be presented and compared with the non-relativistic Langevin equation for RE electrons used in the past. Supported by MINECO (Spain), Projects ENE2012-31753, ENE2015-66444-R.
Relativistic quantum mechanics; Mecanique quantique relativiste
Ollitrault, J.Y. [CEA Saclay, 91 - Gif-sur-Yvette (France). Service de Physique Theorique]|[Universite Pierre et Marie Curie, 75 - Paris (France)
1998-12-01
These notes form an introduction to relativistic quantum mechanics. The mathematical formalism has been reduced to the minimum in order to enable the reader to calculate elementary physical processes. The second quantification and the field theory are the logical followings of this course. The reader is expected to know analytical mechanics (Lagrangian and Hamiltonian), non-relativistic quantum mechanics and some basis of restricted relativity. The purpose of the first 3 chapters is to define the quantum mechanics framework for already known notions about rotation transformations, wave propagation and restricted theory of relativity. The next 3 chapters are devoted to the application of relativistic quantum mechanics to a particle with 0,1/5 and 1 spin value. The last chapter deals with the processes involving several particles, these processes require field theory framework to be thoroughly described. (A.C.) 2 refs.
Towards relativistic quantum geometry
Ridao, Luis Santiago [Instituto de Investigaciones Físicas de Mar del Plata (IFIMAR), Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Mar del Plata (Argentina); Bellini, Mauricio, E-mail: mbellini@mdp.edu.ar [Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad Nacional de Mar del Plata, Funes 3350, C.P. 7600, Mar del Plata (Argentina); Instituto de Investigaciones Físicas de Mar del Plata (IFIMAR), Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Mar del Plata (Argentina)
2015-12-17
We obtain a gauge-invariant relativistic quantum geometry by using a Weylian-like manifold with a geometric scalar field which provides a gauge-invariant relativistic quantum theory in which the algebra of the Weylian-like field depends on observers. An example for a Reissner–Nordström black-hole is studied.
Relativistic and Non-relativistic Equations of Motion
Mangiarotti, L
1998-01-01
It is shown that any second order dynamic equation on a configuration space $X$ of non-relativistic time-dependent mechanics can be seen as a geodesic equation with respect to some (non-linear) connection on the tangent bundle $TX\\to X$ of relativistic velocities. Using this fact, the relationship between relativistic and non-relativistic equations of motion is studied.
Rehman, M. A.; Qureshi, M. N. S. [Department of Physics, GC University, Kachery Road, Lahore 54000 (Pakistan); Shah, H. A. [Department of Physics, Forman Christian College, Ferozepur Road, Lahore 54600 (Pakistan); Masood, W. [COMSATS, Institute of Information Technology, Park Road, Chak Shehzad, Islamabad 44000 (Pakistan); National Centre for Physics (NCP) Shahdra Valley Road, Islamabad (Pakistan)
2015-10-15
Nonlinear circularly polarized Alfvén waves are studied in magnetized nonrelativistic, relativistic, and ultrarelativistic degenerate Fermi plasmas. Using the quantum hydrodynamic model, Zakharov equations are derived and the Sagdeev potential approach is used to investigate the properties of the electromagnetic solitary structures. It is seen that the amplitude increases with the increase of electron density in the relativistic and ultrarelativistic cases but decreases in the nonrelativistic case. Both right and left handed waves are considered, and it is seen that supersonic, subsonic, and super- and sub-Alfvénic solitary structures are obtained for different polarizations and under different relativistic regimes.
Oscillator strengths and branching fractions of 4d75p-4d75s Rh II transitions
Bouazza, Safa
2017-01-01
This work reports semi-empirical determination of oscillator strengths, transition probabilities and branching fractions for Rh II 4d75p-4d75s transitions in a wide wavelength range. The angular coefficients of the transition matrix, beforehand obtained in pure SL coupling with help of Racah algebra are transformed into intermediate coupling using eigenvector amplitudes of these two configuration levels determined for this purpose; The transition integral was treated as free parameter in the least squares fit to experimental oscillator strength (gf) values found in literature. The extracted value: 5s|r1|4d75p> =2.7426 ± 0.0007 is slightly smaller than that computed by means of ab-initio method. Subsequently to oscillator strength evaluations, transition probabilities and branching fractions were deduced and compared to those obtained experimentally or through another approach like pseudo-relativistic Hartree-Fock model including core-polarization effects.
Isotope shift calculations for D lines of stable and short-lived lithium nuclei
Yu, Geng-Hua; Zhao, Peng-Yi; Xu, Bing-Ming; Yang, Wei; Zhu, Xiao-Ling
2016-11-01
The isotope shifts (ISs) for the 2s2S1/2 to 2p2P J (J = 1/2, 3/2) transitions of the lithium nuclei including the stable and short-lived isotopes are calculated based on the multi-configuration Dirac-Hartree-Fock method and the relativistic configuration interaction approach. The results are in good agreement with the previous theoretical and experimental results within a deviation less than 0.05%. The methods used here could be applied to the IS calculations for other heavier Li-like ions and few-electron systems. Project supported by the Young Scientists Fund of the National Natural Science Foundation of China (Grant No. 11304093), the Fund of the Scientific Research Foundation of Sichuan Provincial Department of Education, China (Grant No. 15ZB0386), and the Fund of the 1315 Project of Chengdu University, China (Grant No. 2081915041).
Integrable Gross-Neveu models with fermion-fermion and fermion-antifermion pairing
Thies, Michael
2014-01-01
The massless Gross-Neveu and chiral Gross-Neveu models are well known examples of integrable quantum field theories in 1+1 dimensions. We address the question whether integrability is preserved if one either replaces the four-fermion interaction in fermion-antifermion channels by a dual interaction in fermion-fermion channels, or if one adds such a dual interaction to an existing integrable model. The relativistic Hartree-Fock-Bogoliubov approach is adequate to deal with the large N limit of such models. In this way, we construct and solve three integrable models with Cooper pairing. We also identify a candidate for a fourth integrable model with maximal kinematic symmetry, the "perfect" Gross-Neveu model. This type of field theories can serve as exactly solvable toy models for color superconductivity in quantum chromodynamics.
Coexistence of phases in asymmetric nuclear matter under strong magnetic fields
Aguirre, R
2014-01-01
The equation of state of nuclear matter is strongly affected by the presence of a magnetic field. Here we study the equilibrium configuration of asymmetric nuclear matter for a wide range of densities, isospin composition, temperatures and magnetic fields. Special attention is paid to the low density and low temperature domain, where a thermodynamical instability exists. Neglecting fluctuations of the Coulomb force, a coexistence of phases is found under such conditions, even for extreme magnetic intensities. We describe the nuclear interaction by using the non--relativistic Skyrme potential model within a Hartree--Fock approach. We found that the coexistence of phases modifies the equilibrium configuration, masking most of the manifestations of the spin polarized matter. However, the compressibility and the magnetic susceptibility show clear signals of this fact. Thermal effects are significative for both quantities, mainly out of the coexistence region.
Quinet, Pascal
2014-09-01
A detailed investigation of the atomic structure and radiative parameters involving the lowest states within the 6p4, 6p36d, 6p37s, 6p37p and 6p37d configurations of neutral polonium is reported in the present paper. Using different physical models based on the pseudo-relativistic Hartree-Fock approach, the influence of intravalence, core-valence and core-core electron correlation on the atomic parameters is discussed in detail. This work allowed us to fix the spectroscopic designation of some experimental level energy values and to provide for the first time a set of reliable oscillator strengths corresponding to 31 Po I spectral lines in the wavelength region from 175 to 987 nm.
REVISED AND EXTENDED ANALYSIS OF FIVE TIMES IONIZED XENON, Xe VI
Gallardo, M.; Raineri, M.; Reyna Almandos, J. [Centro de Investigaciones Opticas (CIOp), CC 3, 1897, Gonnet, La Plata (Argentina); Pagan, C. J. B.; Abrahão, R. A., E-mail: monicar@ciop.unlp.edu.ar, E-mail: cesarpagan@fee.unicamp.br [School of Electrical and Computer Engineering, University of Campinas (UNICAMP), 13083-852, Campinas, SP (Brazil)
2015-01-01
A capillary discharge tube was used to record the Xe spectrum in the 400-5500 Å region. A set of 243 lines of the Xe VI spectrum was observed, and 146 of them were classified for the first time. For all known lines, we calculated the weighted oscillator strengths (gf) and weighted transition probabilities (gA) using the configuration interaction in a relativistic Hartree-Fock approach. The energy matrix was calculated using energy parameters adjusted to fit the experimental energy levels. Core polarization effects were taken into account in our calculations. Experimental energy values and calculated lifetimes are also presented for a set of 88 levels. From these levels, 32 were classified for the first time and 33 had their values revised. Our analysis of the 5s5p5d and 5s5p6s configurations was extended in order to clarify discrepancies among previous works.
Burkatzki, M; Filippi, Claudia; Dolg, M
2008-10-28
We extend our recently published set of energy-consistent scalar-relativistic Hartree-Fock pseudopotentials by the 3d-transition metal elements, scandium through zinc. The pseudopotentials do not exhibit a singularity at the nucleus and are therefore suitable for quantum Monte Carlo (QMC) calculations. The pseudopotentials and the accompanying basis sets (VnZ with n=T,Q) are given in standard Gaussian representation and their parameter sets are presented. Coupled cluster, configuration interaction, and QMC studies are carried out for the scandium and titanium atoms and their oxides, demonstrating the good performance of the pseudopotentials. Even though the choice of pseudopotential form is motivated by QMC, these pseudopotentials can also be employed in other quantum chemical approaches.
Glueball Masses in Relativistic Potential Model
Shpenik, A; Kis, J; Fekete, Yu
2000-01-01
The problem of glueball mass spectra using the relativistic Dirac equation is studied. Also the Breit-Fermi approach used to obtaining hyperfine splitting in glueballs. Our approach is based on the assumption, that the nature and the forces between two gluons are the short-range. We were to calculate the glueball masses with used screened potential.
Azadegan, B.
2013-03-01
of charged particles in a continuous planar potential which is formed by the spatially and thermally averaged action of the individual electrostatic potentials of the crystal atoms of the corresponding plane. Classically, the motion of channeled particles through the crystal resembles transverse oscillations being the source of radiation emission. For electrons of energy less than 100 MeV considered here, planar channeling has to be treated quantum mechanically by a one-dimensional Schrödinger equation for the transverse motion. Hence, this motion of the channeled electrons is restricted to a number of discrete (bound) channeling states in the planar continuum potential, and the emission of channeling radiation is caused by spontaneous electron transitions between these eigenstates. Due to relativistic and Doppler effects, the energy of the emitted photons directed into a narrow forward cone is typically shifted up by about three to five orders of magnitude. Consequently, the observed energy spectrum of channeling radiation is characterized by a number of radiation lines in the energy domain of hard X-rays. Channeling radiation may, therefore, be applied as an intense, tunable, quasi-monochromatic X-ray source. Solution method: The problem consists in finding the electron wave function for the planar continuum potential. Both the wave functions and corresponding energies of channeling states solve the Schrödinger equation of transverse electron motion. In the framework of the so-called many-beam formalism, solving the Schrödinger equation reduces to a eigenvector-eigenvalue problem of a Hermitian matrix. For that the program employs the mathematical tools allocated in the commercial computation software Mathematica. The electric field of the atomic planes in the crystal forces dipole oscillations of the channeled charged particles. In the quantum mechanical approach, the dipole approximation is also valid for spontaneous transitions between bound states. The
The relativistic geoid: redshift and acceleration potential
Philipp, Dennis; Lämmerzahl, Claus; Puetzfeld, Dirk; Hackmann, Eva; Perlick, Volker
2017-04-01
We construct a relativistic geoid based on a time-independent redshift potential, which foliates the spacetime into isochronometric surfaces. This relativistic potential coincides with the acceleration potential for isometric congruences. We show that the a- and u- geoid, defined in a post-Newtonian framework, coincide also in a more general setup. Known Newtonian and post-Newtonian results are recovered in the respective limits. Our approach offers a relativistic definition of the Earth's geoid as well as a description of the Earth itself (or observers on its surface) in terms of an isometric congruence. Being fully relativistic, this notion of a geoid can also be applied to other compact objects such as neutron stars. By definition, this relativistic geoid can be determined by a congruence of Killing observers equipped with standard clocks by comparing their frequencies as well as by measuring accelerations of objects that follow the congruence. The redshift potential gives the correct result also for frequency comparison through optical fiber links as long as the fiber is at rest w.r.t. the congruence. We give explicit expressions for the relativistic geoid in the Kerr spacetime and the Weyl class of spacetimes. To investigate the influence of higher order mass multipole moments we compare the results for the Schwarzschild case to those obtained for the Erez-Rosen and q-metric spacetimes.
Relativistic spherical plasma waves
Bulanov, S. S.; Maksimchuk, A.; Schroeder, C. B.; Zhidkov, A. G.; Esarey, E.; Leemans, W. P.
2012-02-01
Tightly focused laser pulses that diverge or converge in underdense plasma can generate wake waves, having local structures that are spherical waves. Here we study theoretically and numerically relativistic spherical wake waves and their properties, including wave breaking.
Relativistic quantum revivals.
Strange, P
2010-03-26
Quantum revivals are now a well-known phenomena within nonrelativistic quantum theory. In this Letter we display the effects of relativity on revivals and quantum carpets. It is generally believed that revivals do not occur within a relativistic regime. Here we show that while this is generally true, it is possible, in principle, to set up wave packets with specific mathematical properties that do exhibit exact revivals within a fully relativistic theory.
Linker, Gerrit-Jan; Loosdrecht , van Paul H.M.; van Duijnen, Piet Th.; Broer, Ria
2015-01-01
The insulating and conducting phases of (EDO-TTF)(2)PF6 were studied by all electron, periodic Hartre-Fock and hybrid density functional calculations. Electronic properties, such as the electronic band structure, the density of states and the Fermi surface are discussed in relation to the metal-insu
Miranda, R. P.; Fisher, A. J.; Stella, L.; Horsfield, A. P.
2011-06-01
Conjugated polymers have attracted considerable attention in the last few decades due to their potential for optoelectronic applications. A key step that needs optimisation is charge carrier separation following photoexcitation. To understand better the dynamics of the exciton prior to charge separation, we have performed simulations of the formation and dynamics of localised excitations in single conjugated polymer strands. We use a nonadiabatic molecular dynamics method which allows for the coupled evolution of the nuclear degrees of freedom and of multiconfigurational electronic wavefunctions. We show the relaxation of electron-hole pairs to form excitons and oppositely charged polaron pairs and discuss the modifications to the relaxation process predicted by the inclusion of the Coulomb interaction between the carriers. The issue of charge photogeneration in conjugated polymers in dilute solution is also addressed.
Woldu, Ameha Seyoum; Mai, Joachim
2012-01-01
The present study aims to establish the relationship between the reported radical-scavenging activities of flavonoids and some enthalpy changes that may occur during flavonoids' reactions with free radicals. Eight flavonoids were chosen for the study on the basis of their structural merits and reported 1,1-diphenyl-2-picryl-hydrazyl scavenging activities. Enthalpy changes accompanying interconversions between selected conformations (including spin multiplicities) and homolytic dissociations were estimated. A novel relationship exists between the total enthalpy of reaction for the abstraction of two hydrogen atoms from flavonoids, their reported radical-scavenging activities and the enthalpy of the homolytic dissociation of hydrogen molecule (104.206 kcal mol(-1)). Only those flavonoids which could give up two hydrogen atoms with total enthalpy changes well below 104.206 kcal mol(-1) were active radical scavengers. By appealing to equilibrium dynamics, we demonstrated that, for flavonoids to be able to donate hydrogen atoms, the change in enthalpy accompanying the abstraction of two hydrogen atoms needs to be less than 104.206 kcal mol(-1). This condition does not seem to be restricted to flavonoids only but rather generally applicable to chian-breaking antioxidants. Thermodynamical relationships may be the most important factors governing the radical-scavenging reactions of flavonoids and possibly other compounds as well. Nevertheless, a more complete characterization of antioxidants would necessitate kinetic analysis.
Relativistic viscoelastic fluid mechanics.
Fukuma, Masafumi; Sakatani, Yuho
2011-08-01
A detailed study is carried out for the relativistic theory of viscoelasticity which was recently constructed on the basis of Onsager's linear nonequilibrium thermodynamics. After rederiving the theory using a local argument with the entropy current, we show that this theory universally reduces to the standard relativistic Navier-Stokes fluid mechanics in the long time limit. Since effects of elasticity are taken into account, the dynamics at short time scales is modified from that given by the Navier-Stokes equations, so that acausal problems intrinsic to relativistic Navier-Stokes fluids are significantly remedied. We in particular show that the wave equations for the propagation of disturbance around a hydrostatic equilibrium in Minkowski space-time become symmetric hyperbolic for some range of parameters, so that the model is free of acausality problems. This observation suggests that the relativistic viscoelastic model with such parameters can be regarded as a causal completion of relativistic Navier-Stokes fluid mechanics. By adjusting parameters to various values, this theory can treat a wide variety of materials including elastic materials, Maxwell materials, Kelvin-Voigt materials, and (a nonlinearly generalized version of) simplified Israel-Stewart fluids, and thus we expect the theory to be the most universal description of single-component relativistic continuum materials. We also show that the presence of strains and the corresponding change in temperature are naturally unified through the Tolman law in a generally covariant description of continuum mechanics.
Brun-Battistini, D; Sandoval-Villalbazo, A
2016-01-01
Richard C. Tolman analyzed the relation between a temperature gradient and a gravitational field in an equilibrium situation. In 2012, Tolman\\textquoteright s law was generalized to a non-equilibrium situation for a simple dilute relativistic fluid. The result in that scenario, obtained by introducing the gravitational force through the molecular acceleration, couples the heat flux with the metric coefficients and the gradients of the state variables. In the present paper it is shown, by \\textquotedblleft suppressing\\textquotedblright{} the molecular acceleration in Boltzmann\\textquoteright s equation, that a gravitational field drives a heat flux. This procedure corresponds to the description of particle motion through geodesics, in which a Newtonian limit to the Schwarzschild metric is assumed. The effect vanishes in the non-relativistic regime, as evidenced by the direct evaluation of the corresponding limit.
Matveev, Alexei V; Rösch, Notker
2008-06-28
We suggest an approximate relativistic model for economical all-electron calculations on molecular systems that exploits an atomic ansatz for the relativistic projection transformation. With such a choice, the projection transformation matrix is by definition both transferable and independent of the geometry. The formulation is flexible with regard to the level at which the projection transformation is approximated; we employ the free-particle Foldy-Wouthuysen and the second-order Douglas-Kroll-Hess variants. The (atomic) infinite-order decoupling scheme shows little effect on structural parameters in scalar-relativistic calculations; also, the use of a screened nuclear potential in the definition of the projection transformation shows hardly any effect in the context of the present work. Applications to structural and energetic parameters of various systems (diatomics AuH, AuCl, and Au(2), two structural isomers of Ir(4), and uranyl dication UO(2) (2+) solvated by 3-6 water ligands) show that the atomic approximation to the conventional second-order Douglas-Kroll-Hess projection (ADKH) transformation yields highly accurate results at substantial computational savings, in particular, when calculating energy derivatives of larger systems. The size-dependence of the intrinsic error of the ADKH method in extended systems of heavy elements is analyzed for the atomization energies of Pd(n) clusters (n
Solitonic excitations in linearly coherent channels of bilayer quantum Hall stripes
Doiron, C. B.; Côté, R.; Fertig, H. A.
2005-09-01
In some range of interlayer distances, the ground state of the two-dimensional electron gas at filling factor ν=4N+1 with N=0,1,2,… is a coherent stripe phase in the Hartree-Fock approximation. This phase has one-dimensional coherent channels that support charged excitations in the form of pseudospin solitons. In this work, we compute the transport gap of the coherent striped phase due to the creation of soliton-antisoliton pairs using a supercell microscopic unrestricted Hartree-Fock approach. We study this gap as a function of interlayer distance and tunneling amplitude. Our calculations confirm that the soliton-antisoliton excitation energy is lower than the corresponding Hartree-Fock electron-hole pair energy. We compare our results with estimates of the transport gap obtained from a field-theoretic model valid in the limit of slowly varying pseudospin textures.
Pseudospin solitons in the coherent stripe phase of a bilayer quantum Hall system
Doiron, C. B.; Côté, R.; Fertig, H. A.
2006-08-01
In the Hartree-Fock approximation and at total filling factor ν=4N+1, the ground state of the two-dimensional electron gas in a double quantum well system in a quantizing magnetic field is, in some range of interlayer distances, a coherent striped phase. This stripe phase has one-dimensional coherent channels that support charged excitations in the form of pseudospin solitons. In this work, we compute the transport gap of the coherent striped phase due to the creation of soliton-antisoliton pairs using a supercell microscopic unrestricted Hartree-Fock approach. We study the energy gap as a function of interlayer distance and tunneling amplitude. Our calculations confirm that the soliton-antisoliton excitation energy is lower than the corresponding Hartree-Fock electron-hole pair energy.
Quantum correlations in nuclear mean field theory through source terms
Lee, S J
1996-01-01
Starting from full quantum field theory, various mean field approaches are derived systematically. With a full consideration of external source dependence, the stationary phase approximation of an action gives a nuclear mean field theory which includes quantum correlation effects (such as particle-hole or ladder diagram) in a simpler way than the Brueckner-Hartree-Fock approach. Implementing further approximation, the result can be reduced to Hartree-Fock or Hartree approximation. The role of the source dependence in a mean field theory is examined.
García-Fernández, Pablo; Aramburu, Jose Antonio; Moreno, Miguel; Zlatar, Matija; Gruden-Pavlović, Maja
2014-04-08
Vibronic coupling theory shows that the cause for spontaneous instability in systems presenting a nondegenerate ground state is the so-called pseudo-Jahn-Teller effect, and thus its study can be extremely helpful to understand the structure of many molecules. While this theory, based on the mixing of the ground and excited states with a distortion, has been long studied, there are two obscure points that we try to clarify in the present work. First, the operators involved in both the vibronic and nonvibronic parts of the force constant take only into account electron-nuclear and nuclear-nuclear interactions, apparently leaving electron-electron repulsions and the electron's kinetic energy out of the chemical picture. Second, a fully quantitative computational appraisal of this effect has been up to now problematic. Here, we present a reformulation of the pseudo-Jahn-Teller theory that explicitly shows the contributions of all operators in the molecular Hamiltonian and allows connecting the results obtained with this model to other chemical theories relating electron distribution and geometry. Moreover, we develop a practical approach based on Hartree-Fock and density functional theory that allows quantification of the pseudo-Jahn-Teller effect. We demonstrate the usefulness of our method studying the pyramidal distortion in ammonia and its absence in borane, revealing the strong importance of the kinetic energy of the electrons in the lowest a2″ orbital to trigger this instability. The present tool opens a window for exploring in detail the actual microscopic origin of structural instabilities in molecules and solids.
RELATIVISTIC HEAVY ION PHYSICS: A THEORETICAL OVERVIEW.
KHARZEEV,D.
2004-03-28
This is a mini-review of recent theoretical work in the field of relativistic heavy ion physics. The following topics are discussed initial conditions and the Color Glass Condensate; approach to thermalization and the hydrodynamic evolution; hard probes and the properties of the Quark-Gluon Plasma. Some of the unsolved problems and potentially promising directions for future research are listed as well.
A relativistic and autonomous navigation satellite system
Delva, Pacôme; Kostić, Uros; Carloni, Sante
2011-01-01
A relativistic positioning system has been proposed by Bartolom\\'e Coll in 2002. Since then, several group developed this topic with different approaches. I will present a work done in collaboration with Ljubljana University and the ESA Advanced Concepts Team. We developed a concept, Autonomous Basis of Coordinates, in order to take advantage of the full autonomy of a satellite constellation for navigation and positioning, by means of satellite inter-links. I will present the advantages of this new paradigm and a number of potential application for reference systems, geophysics and relativistic gravitation.
Margueron, J
2001-07-01
We study the elementary interactions between neutrinos and dense matter in a proto-neutron star. Equations of state obtained with different nuclear effective interactions (Skyrme, Gogny, Relativistic Lagrangians) are first discussed. Then, we characterize their stability in spin and isospin. We derive magnetic susceptibilities for all isospin asymmetry values as a function of Landau parameters G{sup {pi}}{sup {pi}}{sup '}{sub 0} (where {pi}, {pi}' = proton or neutron). From this work, we select a parametrization for each of the 3 effective forces: Sly230b,D1P,NL3. We calculate the pure neutron matter and asymmetric nuclear matter response functions with and without charge exchange, describing nuclear correlations in both approaches: non-relativistic (Hartree-Fock with Skyrme forces, then complete RPA) and relativistic (in the Hartree approximation). At the end, we calculate neutrino mean free paths neutral current and charged current reactions. Comparisons between relativistic and non-relativistic approaches allow us to identify relativistic effects in nuclear matter at densities as low as twice the saturation density. RPA correlations make the medium more transparent to neutrinos compared to free Fermi gas. The importance of the effective mass in mean free path calculations is also shown. (author)
On the convexity of Relativistic Ideal Magnetohydrodynamics
Ibáñez, José-María; Aloy, Miguel-Ángel; Martí, José-María; Miralles, Juan-Antonio
2015-01-01
We analyze the influence of the magnetic field in the convexity properties of the relativistic magnetohydrodynamics system of equations. To this purpose we use the approach of Lax, based on the analysis of the linearly degenerate/genuinely non-linear nature of the characteristic fields. Degenerate and non-degenerate states are discussed separately and the non-relativistic, unmagnetized limits are properly recovered. The characteristic fields corresponding to the material and Alfv\\'en waves are linearly degenerate and, then, not affected by the convexity issue. The analysis of the characteristic fields associated with the magnetosonic waves reveals, however, a dependence of the convexity condition on the magnetic field. The result is expressed in the form of a generalized fundamental derivative written as the sum of two terms. The first one is the generalized fundamental derivative in the case of purely hydrodynamical (relativistic) flow. The second one contains the effects of the magnetic field. The analysis ...
Relativistic theories of materials
Bressan, Aldo
1978-01-01
The theory of relativity was created in 1905 to solve a problem concerning electromagnetic fields. That solution was reached by means of profound changes in fundamental concepts and ideas that considerably affected the whole of physics. Moreover, when Einstein took gravitation into account, he was forced to develop radical changes also in our space-time concepts (1916). Relativistic works on heat, thermodynamics, and elasticity appeared as early as 1911. However, general theories having a thermodynamic basis, including heat conduction and constitutive equations, did not appear in general relativity until about 1955 for fluids and appeared only after 1960 for elastic or more general finitely deformed materials. These theories dealt with materials with memory, and in this connection some relativistic versions of the principle of material indifference were considered. Even more recently, relativistic theories incorporating finite deformations for polarizable and magnetizable materials and those in which couple s...
Relativistic Quantum Communication
Hosler, Dominic
2013-01-01
In this Ph.D. thesis, I investigate the communication abilities of non-inertial observers and the precision to which they can measure parametrized states. I introduce relativistic quantum field theory with field quantisation, and the definition and transformations of mode functions in Minkowski, Schwarzschild and Rindler spaces. I introduce information theory by discussing the nature of information, defining the entropic information measures, and highlighting the differences between classical and quantum information. I review the field of relativistic quantum information. We investigate the communication abilities of an inertial observer to a relativistic observer hovering above a Schwarzschild black hole, using the Rindler approximation. We compare both classical communication and quantum entanglement generation of the state merging protocol, for both the single and dual rail encodings. We find that while classical communication remains finite right up to the horizon, the quantum entanglement generation tend...
New version: GRASP2K relativistic atomic structure package
Jönsson, P.; Gaigalas, G.; Bieroń, J.; Fischer, C. Froese; Grant, I. P.
2013-09-01
, 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.: 730252 No. of bytes in distributed program, including test data, etc.: 14808872 Distribution format: tar.gz Programming language: Fortran. Computer: Intel Xeon, 2.66 GHz. Operating system: Suse, Ubuntu, and Debian Linux 64-bit. RAM: 500 MB or more Classification: 2.1. Catalogue identifier of previous version: ADZL_v1_0 Journal reference of previous version: Comput. Phys. Comm. 177 (2007) 597 Does the new version supersede the previous version?: Yes Nature of problem: Prediction of atomic properties — atomic energy levels, oscillator strengths, radiative decay rates, hyperfine structure parameters, Landé gJ-factors, and specific mass shift parameters — using a multiconfiguration Dirac-Hartree-Fock approach. Solution method: The computational method is the same as in the previous GRASP2K [1] version except that for v3 codes the njgraf library module [2] for recoupling has been replaced by librang [3,4]. Reasons for new version: New angular libraries with improved performance are available. Also methodology for transforming from jj- to LSJ-coupling has been developed. Summary of revisions: New angular libraries where the coefficients of fractional parentage have been extended to j=9/2, making calculations feasible for the lanthanides and actinides. Inclusion of a new program jj2lsj, which reports the percentage composition of the wave function in LSJ. Transition programs have been modified to produce a file of transition data with one record for each transition in the same format as Atsp2K [C. Froese Fischer, G. Tachiev, G. Gaigalas and M.R. Godefroid, Comput. Phys. Commun. 176 (2007) 559], which identifies each atomic state by the total energy and a label for the CSF with the largest expansion coefficient in LSJ intermediate coupling. Updated to 64-bit architecture. A
Basis set independent calculation of molecular polarizabilities
Talman, James D.
2012-08-01
It is shown that e-F, where F is the Hartree-Fock (HF) operator, can be inverted, for molecular systems, in numerical Cartesian coordinates. The method was originally applied to finding corrections to approximate Hartree-Fock orbitals [J. D. Talman, Phys. Rev. APLRAAN1050-294710.1103/PhysRevA.82.052518 82, 052518 (2010)]. The approach is applied to determine basis set independent dipole polarizabilities for the water molecule using the Sternheimer method within the uncoupled HF and coupled perturbed HF approximations.
Handbook of relativistic quantum chemistry
Liu, Wenjian (ed.) [Peking Univ., Beijing (China). Center for Computational Science and Engineering
2017-03-01
This handbook focuses on the foundations of relativistic quantum mechanics and addresses a number of fundamental issues never covered before in a book. For instance: How can many-body theory be combined with quantum electrodynamics? How can quantum electrodynamics be interfaced with relativistic quantum chemistry? What is the most appropriate relativistic many-electron Hamiltonian? How can we achieve relativistic explicit correlation? How can we formulate relativistic properties? - just to name a few. Since relativistic quantum chemistry is an integral component of computational chemistry, this handbook also supplements the ''Handbook of Computational Chemistry''. Generally speaking, it aims to establish the 'big picture' of relativistic molecular quantum mechanics as the union of quantum electrodynamics and relativistic quantum chemistry. Accordingly, it provides an accessible introduction for readers new to the field, presents advanced methodologies for experts, and discusses possible future perspectives, helping readers understand when/how to apply/develop the methodologies.