Shukla, Alok
1999-01-01
In this paper we present a fully ab initio Hartree-Fock approach aimed at calculating the static structure factor of crystalline insulators at arbitrary values of momentum transfer. In particular, we outline the computation of the incoherent scattering function, the component of the structure factor which governs the incoherent x-ray scattering from solids. The presented theory is applied to crystalline LiF to obtain benchmark Hartree-Fock values for its incoherent scattering function. Benchm...
Implementation of a vector potential method in an ab initio Hartree-Fock code
Tevekeliyska, Violina; Springborg, Michael; Champagne, Benoît; Kirtman, Bernard
2012-12-01
For extended systems exposed to an external, electrostatic field, the presence of the field leads to an extra term (E⃗. P⃗) to the Hamiltonian, where E⃗ is the field vector and P⃗ is the polarization of the system of interest. In order to find out how a polymer chain responds to an external electric perturbation, a field with a charge and a current term for the polarization is added to an ab initio Hartree-Fock Hamiltonian. The polarization expression is taken from an efficient vector potential approach (VPA) [1] for calculating electronic and nuclear responses of infinite periodic systems to finite electric fields and is implemented in the ab initio LCAO-SCF algorithm [3], which computes band structure of regular or helical polymers, taking into account the one-dimensional translational symmetry. A smoothing procedure for numerical differentiation of the orbital coefficients is used in order to calculate self-consistently the charge flow contribution to the polarization.
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)
Jiménez-Hoyos, Carlos A; Scuseria, Gustavo E
2014-01-01
Most {\\em ab initio} calculations on fullerene molecules have been carried out based on the paradigm of the H\\"uckel model. This is consistent with the restricted nature of the independent-particle model underlying such calculations, even in single-reference-based correlated approaches. On the other hand, previous works on some of these molecules using model Hamiltonians have clearly indicated the importance of short-range inter-atomic spin-spin correlations. In this work, we consider {\\em ab initio} non-collinear Hartree--Fock (HF) solutions for representative fullerene systems: the bowl, cage, ring, and pentagon isomers of C$_{20}$, and the larger C$_{30}$, C$_{36}$, C$_{60}$, C$_{70}$, and C$_{84}$ fullerene cages. In all cases but the ring we find that the HF minimum corresponds to a truly non-collinear solution with a torsional spin density wave. Optimized geometries at the generalized HF (GHF) level lead to fully symmetric structures, even in those cases where Jahn-Teller distortions have been previousl...
$\\it{Ab}$ $\\it{initio}$ 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...
Pham, T. LH; Nguyen, T. VB; Lowe, J. A.; Grant, I. P.; Chantler, C. T.
2016-02-01
We investigate the Kβ characteristic radiation and the complex asymmetric structure of photoemission lines of copper, which provides a benchmark for theoretical and experimental studies of x-ray calibration series in transition metals. Ab initio multi-configuration Dirac-Hartree-Fock (MCDHF) calculations have been performed to study the complex open-shell many-electron problem in copper. The biorthogonalization technique permits determination of transition intensities and Einstein A coefficients. The results from our MCDHF calculations demonstrate excellent convergence in transition energies and intensities, as well as gauge invariance to 0.6%. Shake processes caused by single and double spectator vacancies from 3d, 3p, 3s and 4s subshells have also been investigated extensively. MCDHF has been performed to calculate energies and relative intensities of 3d, 3d2, 3p, 3s and 4s satellites, resulting in the total number of configuration states exceeding 100 000 and more than 1500 transition components. Our theoretical calculations of shake-off probabilities using the multi-configuration method in the sudden limit have a high degree of internal consistency with the best available experimental data for copper Kβ . This supports the validity of relativistic atomic theory and sets a new benchmark even for poorly resolved characteristic spectra using current techniques of analysis.
Full text: Silicon and boron adatoms on the Si(111) surface have been studied using atomic clusters and the Hartree-Fock/Density Functional Theory components of the Gaussian94/DFT package. The binding energies for the adatom, Si(A), located at the T4 position, and the Si(A)H species formed by the chemisorption of a single hydrogen atom, have been obtained for the corresponding equilibrium minimum energy configurations. We find that the most stable adatom structure results from boron occupying the S5 substitutional position in the second layer directly below the Si adatom (B-S5 topology). The binding energy of the Si adatom in this case is 7.49eV while the binding energy for the Si adatom without the boron (Si-T4 topology) is only 6.34 eV. When a boron atom is chemisorbed in the T4 position, instead of a silicon atom (B-T4 structure), the binding energy is found to be 5.56 eV. The chemisorption of atomic hydrogen onto these clusters stabilizes the Si-T4 geometry through the formation of a silicon adatom-hydrogen Si(A)H complex located at the three-fold T4 position with a binding energy of 5.18 eV. In contrast to this, a hydrogen bonded Si adatom of the B-S5 structure is observed to move away from its 3-fold T4 position to an adjacent bridge site and give an Si(A)H binding energy of 4.68 eV. Similar reconstruction has been observed when a hydrogen atom chemisorbs onto a boron adatom in the B-T4 topology with the binding energy of the BH complex being 5.03 eV. An interpretation of these results will be given in the context of the available experimental data
The molecular geometry and vibrational frequencies of anhydrous zinc acetate and anhydrous magnesium acetate in the ground state have been calculated using the Hartree- Fock and density functional method (B3LYP) with Lan2dz basic set. calculated data were compared with experimental ones
Full text : The molecular geometry and vibrational frequencies of anhydrous zinc acetate and anhydrous magesium acetate in the ground state have been calculated using the Hartree-Fock and density functional method with 6-31G basic set. The optimized geometric band tengths and bond angles obtained by using HF and DFT show the best agreement with the experimental data. Comparison of the observed fundamental vibrational frequencies of melamine diborate with calculated results by density functional B3LYP and Hatree-Fock methods indicate that B3LYP is superior to the scaled Hatree-Fock approach for molecular vibrational problems
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.
Ab Initio Molecular Dynamics: A Virtual Laboratory
Hobbi Mobarhan, Milad
2014-01-01
In this thesis, we perform ab initio molecular dynamics (MD) simulations at the Hartree-Fock level, where the forces are computed on-the-fly using the Born-Oppenheimer approximation. The theory behind the Hartree-Fock method is discussed in detail and an implementation of this method based on Gaussian basis functions is explained. We also demonstrate how to calculate the analytic energy derivatives needed for obtaining the forces acting on the nuclei. Hartree-Fock calculations on the ground s...
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.
The energetics of the H2O/MgO(001), HCl/MgO(001), and NH3/MgO(001) interface were investigated using the ab initio periodic Hartree-Fock LCAO method and a classical interaction energy model. The QM calculations treated a system that was periodic in two dimensions with the adsorbate approaching a three-layer slab of MgO(001). The authors used an approximation to the classical interaction energy, where the surface is represented by its potential, electric field, and electric field derivatives at the positions of the molecule center of mass, and the molecule is described by its charge, electric dipole, electric quadrupole and polarizability. The potential, electric field and electric field gradient are obtained for the clean three-layer slab using the ab initio periodic Hartree-Fock LCAO method (CRYSTAL) and an optimized split valence basis 8-61G on Mg and 8-51G on O. The charge, electric dipole, and electric quadrupole are calculated using ab initio Hartree-Fock theory (GAUSSIAN-92) with a 6-31G* basis set while the SCF polarizability is determined analytically using the same basis set
Mejías, J. A.; Sanz, Javier Fernández
1995-01-01
Compact model potentials to introduce the effect of spin-dependent environments in ab initio embedded cluster calculations are reported. The groups forming the environment are described by unrestricted Hartree-Fock wave functions. The method is tested for the magnetic description of KNiF3 by using different model clusters. The cluster calculations are done at the unrestricted Hartree-Fock and unrestricted second-order perturbation levels. The obtained values are in excellent agreement with other more sophisticated ab initio calculations if some Ni-F delocalization is allowed. How the superexchange interaction is accounted for in our method is also discussed.
Ab Initio Investigations of the C2F4S Isomers and of Their Interconversions
Shim, Irene; Vallano-Lorenzo, Sandra; Lisbona-Martin, Pilar;
2003-01-01
The transition states and the activation energies for the unobserved isomerization reactions between the three possible C2F4S isomers with divalent sulfur, trifluorothioacetyl fluoride 1, tetrafluorothiirane 2, and trifluoroethenesulfenyl fluoride 3, have been determined by ab initio Hartree-Fock...
GAUSSIAN 76: An ab initio Molecular Orbital Program
Binkley, J. S.; Whiteside, R.; Hariharan, P. C.; Seeger, R.; Hehre, W. J.; Lathan, W. A.; Newton, M. D.; Ditchfield, R.; Pople, J. A.
1978-01-01
Gaussian 76 is a general-purpose computer program for ab initio Hartree-Fock molecular orbital calculations. It can handle basis sets involving s, p and d-type Gaussian functions. Certain standard sets (STO-3G, 4-31G, 6-31G*, etc.) are stored internally for easy use. Closed shell (RHF) or unrestricted open shell (UHF) wave functions can be obtained. Facilities are provided for geometry optimization to potential minima and for limited potential surface scans.
GAUSSIAN 76: an ab initio molecular orbital program
Binkley, J. S.; Whiteside, R.; Hariharan, P. C.; Seeger, R.; Hehre, W. J.; Lathan, W. A.; Newton, M. D.; Ditchfield, R.; Pople, J. A.
1978-06-01
Gaussian 76 is a general-purpose computer program for ab initio Hartree-Fock molecular orbital calculations. It can handle basis sets involving s, p and d-type gaussian functions. Certain standard sets (STO-3G, 4-31G, 6-31G*, etc.) are stored internally for easy use. Closed shell (RHF) or unrestricted open shell (UHF) wave functions can be obtained. Facilities are provided for geometry optimization to potential minima and for limited potential surface scans.
Germacrene D Cyclization: An Ab Initio Investigation
William N. Setzer
2008-01-01
Full Text Available Essential oils that contain large concentrations of germacrene D are typically accompanied by cadinane sesquiterpenoids. The acid-catalyzed cyclization of germacrene D to give cadinane and selinane sesquiterpenes has been computationally investigated using both density functional (B3LYP/6-31G* and post Hartree-Fock (MP2/6-31G** ab initio methods. The calculated energies are in general agreement with experimentally observed product distributions, both from acid-catalyzed cyclizations as well as distribution of the compounds in essential oils.
Multiconfiguration Dirac-Hartree-Fock energy levels and transition probabilities for 3d^5 in Fe IV
Fischer, C. Froese; Rubin, R. H.; M. Rodríguez
2008-01-01
Multiconfiguration Dirac-Hartree-Fock electric quadrupole (E2) and magnetic dipole (M1) transition probabilities are reported for transitions between levels of 3d^5 in [Fe IV]. The accuracy of the ab initio energy levels and the agreement in the length and velocity forms of the line strength for the E2 transitions are used as indicators of accuracy. The present E2 and M1 transition probabilities are compared with earlier Breit-Pauli results and other theories. An extensive set of transition p...
Charge transfer excitations from excited state Hartree-Fock subsequent minimization scheme
Theophilou, Iris; Thanos, S
2014-01-01
Photoinduced charge transfer processes play a key role for novel photovoltaic phenomena and devices. Thus, the development of ab initio methods that allow for accurate and computationally inexpensive treatment of charge transfer excitations is a topic that attracts nowadays a lot of scientific attention. In this paper we extend an approach recently introduced for the description of single and double excitations (M. Tassi, I. Theophilou and S. Thanos, Int. J. Quantum Chem., {113}, 690 (2013), M. Tassi, I. Theophilou and S. Thanos, J. Chem. Phys. {138}, 124107 (2013)) to allow for the description of intermolecular charge transfer excitations. For the description of an excitation where an electron is transferred from a donor system to an acceptor one, it is necessary to keep the excited state orthogonal to the ground sate in order to avoid variational collapse. These conditions are achieved by decomposing the subspace spanned by the Hartree-Fock (HF) ground state orbitals to four subspaces: The subspace spanned ...
Belousov, Roman; Prencipe, Mauro
2014-01-01
The isothermal compression of magnesium perovskite and postperovskite is examined through the F-f plot and the diagnostic plot of Vinet universal model theoretically from the ab initio quantum-mechanical calculations at the hybrid Hartree-Fock / Density Functional Theory level. A purely numerical approach, first time applied in this paper, shows that the discrepancies largely observed between studies on the perovskite and criticized in geophysical applications are due to the inadequate choice...
Misfits in Skyrme-Hartree-Fock
Erler, J; Klüpfel, P.; 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 whe...
Fortran 90 implementation of the Hartree-Fock approach within the CNDO/2 and INDO models
Sahu, Sridhar
2008-01-01
Despite the tremendous advances made by the ab initio theory of electronic structure of atoms and molecules, its applications are still not possible for very large systems. Therefore, semi-empirical model Hamiltonians based on the zero-differential overlap (ZDO) approach such as the Pariser-Parr-Pople, CNDO, INDO, etc. provide attractive, and computationally tractable, alternatives to the ab initio treatment of large systems. In this paper we describe a Fortran 90 computer program developed by us, that uses CNDO/2 and INDO methods to solve Hartree-Fock(HF) equation for molecular systems. The INDO method can be used for the molecules containing the first-row atoms, while the CNDO/2 method is applicable to those containing both the first-, and the second-row, atoms. We have paid particular attention to computational efficiency while developing the code, and, therefore, it allows us to perform calculations on large molecules such as C_60 on small computers within a matter of seconds. Besides being able to comput...
AB INITIO HF AND DFT STUDIES ON MOLECULAR STRUCTURE AND VIBRATIONAL ANALYSIS OF 2,5-DIBROMOPYRIDINE
ÇIRAK, Çağrı; KOÇ, Nurettin
2014-01-01
Theoretical study on molecular structure and vibrational spectra of 2,5-dibromopyridine (2,5-DBP) have been investigated. The optimized geometry, theoretical vibration frequencies and intensities were calculated by using ab initio Hartree-Fock and density functional B3LYP method with 6-31G(d,p) basis sets. The vibrational analysis of title molecule was done and its optimized geometry parameters (bond lengths and bond angles) were given. Scaled theoretical frequencies have been compared with e...
Pedersen, Kim Vestergaard; Christensen, Henrik; Shim, Irene;
2004-01-01
Trichlorothioacetyl chloride 1, tetrachlorothiirane 2, and trichloroethenesulfenyl chloride 3 and the equilibria between them have been investigated by ab initio Hartree-Fock (HF), Møller-Plesset second order perturbation (MP2) calculations, and by Gaussian-3 theory, G3(MP2). The transition state...... of the isomerization reactions have been identified. Also investigated were possible reactions leading to the isomers and their possible decomposition products. The results show that the unobserved isomerization reactions are feasible....
Ramya, T.; Gunasekaran, S.; Ramkumaar, G. R.
2013-10-01
The Fourier Transform Infrared (FTIR) and FT Raman spectra of lamotrigine have been recorded in the region 4000-450 cm-1 and 4000-50 cm-1, respectively. The title compound is used as Antiepileptic drug. The optimized geometry, frequency, and intensities of the vibrational bands of the lamotrigine were obtained by Density Functional Theory (DFT) using B3LYP/631G** basis set and ab initio method at the restricted Hartree Fock/6-31** level. The harmonic vibrational frequencies, Natural population analysis, HOMO-LUMO energy gap, infra red intensities and Raman scattering activities, force constant were calculated by DFT and RHF methods. The quality of lamotrigine under different storage containers were analyzed using UV-Vis spectral technique.
Ab initio non-relativistic spin dynamics
Ding, Feizhi; Goings, Joshua J.; Li, Xiaosong, E-mail: xsli@uw.edu [Department of Chemistry, University of Washington, Seattle, Washington 98195 (United States); Frisch, Michael J. [Gaussian, Inc., 340 Quinnipiac St, Bldg 40, Wallingford, Connecticut 06492 (United States)
2014-12-07
Many magnetic materials do not conform to the (anti-)ferromagnetic paradigm where all electronic spins are aligned to a global magnetization axis. Unfortunately, most electronic structure methods cannot describe such materials with noncollinear electron spin on account of formally requiring spin alignment. To overcome this limitation, it is necessary to generalize electronic structure methods and allow each electron spin to rotate freely. Here, we report the development of an ab initio time-dependent non-relativistic two-component spinor (TDN2C), which is a generalization of the time-dependent Hartree-Fock equations. Propagating the TDN2C equations in the time domain allows for the first-principles description of spin dynamics. A numerical tool based on the Hirshfeld partitioning scheme is developed to analyze the time-dependent spin magnetization. In this work, we also introduce the coupling between electron spin and a homogenous magnetic field into the TDN2C framework to simulate the response of the electronic spin degrees of freedom to an external magnetic field. This is illustrated for several model systems, including the spin-frustrated Li{sub 3} molecule. Exact agreement is found between numerical and analytic results for Larmor precession of hydrogen and lithium atoms. The TDN2C method paves the way for the ab initio description of molecular spin transport and spintronics in the time domain.
Tensor representation techniques in post-Hartree-Fock methods: matrix product state tensor format
Benedikt, Udo; Auer, Henry; Espig, Mike; Hackbusch, Wolfgang; Auer, Alexander A.
2013-09-01
In this proof-of-principle study, we discuss the application of various tensor representation formats and their implications on memory requirements and computational effort for tensor manipulations as they occur in typical post-Hartree-Fock (post-HF) methods. A successive tensor decomposition/rank reduction scheme in the matrix product state (MPS) format for the two-electron integrals in the AO and MO bases and an estimate of the t 2 amplitudes as obtained from second-order many-body perturbation theory (MP2) are described. Furthermore, the AO-MO integral transformation, the calculation of the MP2 energy and the potential usage of tensors in low-rank MPS representation for the tensor contractions in coupled cluster theory are discussed in detail. We are able to show that the overall scaling of the memory requirements is reduced from the conventional N 4 scaling to approximately N 3 and the scaling of computational effort for tensor contractions in post-HF methods can be reduced to roughly N 4 while the decomposition itself scales as N 5. While efficient algorithms with low prefactor for the tensor decomposition have yet to be devised, this ansatz offers the possibility to find a robust approximation with low-scaling behaviour with system and basis-set size for post-HF ab initio methods.
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.
Hartree-Fock many-body perturbation theory for nuclear ground-states
Tichai, Alexander; Langhammer, Joachim; Binder, Sven; Roth, Robert
2016-05-01
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 for the unperturbed basis leads to a convergent MBPT series for soft interactions, in contrast to the divergent MBPT series obtained with a harmonic oscillator basis. For larger model spaces and heavier nuclei, where a direct high-order MBPT calculation is not feasible, we perform third-order calculations and compare to advanced ab initio coupled-cluster results for the same interactions and model spaces. We demonstrate that third-order MBPT provides ground-state energies for nuclei up into the tin isotopic chain in excellent agreement with the best available coupled-cluster calculations at a fraction of the computational cost.
Ab initio theoretical comparative study of magnetic coupling in KNiF3 and K2NiF4s
Moreira, Ibério de Pinho Ribeiro; Illas i Riera, Francesc
1997-01-01
The origin of magnetic coupling in KNiF3 and K2 NiF4 is studied by means of an ab initio cluster model approach. By a detailed study of the mapping between eigenstates of the exact nonrelativistic and spin model Hamiltonians it is possible to obtain the magnetic coupling constant J and to compare ab initio cluster-model values with those resulting from ab initio periodic Hartree-Fock calculations. This comparison shows that J is strongly determined by two-body interactions; this is a surprisi...
Low-lying electronic states of nitrosyl cyanide (NCNO): An ab initio MCHF study
Ab initio multiconfiguration Hartree--Fock calculations of the electronic structure of several low-lying electronic states of nitrosyl cyanide (NCNO) are reported. The essential features of the electronic structure of these states were analyzed to provide a qualitative correlation diagram for the dissociation process NCNO → NC+NO. It is found that the four lowest-lying states 1/sup ,/3A' and 1/sup ,/3A'' are connected directly to ground state products. Excitation energies and geometrical parameters for these states and for the 2- 1A'' and 2- 1A' states are presented. Implications of these findings for NCNO photodissociation processes are discussed
Ab initio calculations of 14N and 15N hyperfine structures
Jönsson, P; Nemouchi, M; Godefroid, M
2010-01-01
Hyperfine structure parameters are calculated for the 2p2(3P)3s 4P_J, 2p2(3P)3p 4Po_J and 2p2(3P)3p 4Do_J levels, using the ab initio multiconfiguration Hartree-Fock method. The theoretical hyperfine coupling constants are in complete disagreement with the experimental values of Jennerich et al. (EPJD 40(2006), 81) deduced from the analysis of the near-infrared Doppler-free saturated absorption spectra.
Ab Initio Calculations of Elastic Constants of Li2O under Pressure
LI Xiao-Feng; CHEN Xiang-Rong; JI Guang-Fu; MENG Chuan-Min
2006-01-01
@@ We investigate the equilibrium lattice constant, bulk modulus, elastic constants and Debye temperature of Li2 O under pressure by using ab initio unrestricted Hartree-Fock (HF) linear combination of atomic orbital (LCAO) periodic approach. The obtained results at zero pressure are well consistent with the available experimental data and other theoretical results. It is found that the elastic constants C11, C12 and C44 and bulk modulus B increase monotonously as pressure increases. Also, the anisotropy will weaken and the Debye temperature will rise with pressure increasing.
Phonon spectrum of lead oxychloride Pb3O2Cl2: Ab initio calculation and experiment
Zakir'yanov, D. O.; Chernyshev, V. A.; Zakir'yanova, I. D.
2016-02-01
IR and Raman spectra of Pb3O2Cl2 in the range of 50-600 cm-1 have been detected for the first time. Ab initio calculations of the crystal structure and the phonon spectrum of Pb3O2Cl2 in the framework of LCAO approach have been performed by the Hartree-Fock method and in the framework of the density functional theory with the use of hybrid functionals. The results of calculations have made it possible to interpret the experimental vibration spectra and reveal silent modes, which do not manifest themselves in these spectra but influence the optical properties of the crystal.
NN Correlations and Relativistic Hartree Fock in Finite Nuclei
Fritz, R
1993-01-01
Two different approximation schemes for the self-consistent solution of the relativistic Brueckner-Hartree-Fock equation for finite nuclei are discussed using realistic One-Boson-Exchange potentials. In a first scheme, the effects of correlations are deduced from a study of nuclear matter and parameterized in terms of an effective $\\sigma$, $\\omega$ and $\\pi$ exchange. Employing this effective interaction relativistic Hartree-Fock equations are solved for finite nuclei \\osi , \\caf\\ and \\cafe . In the second approach the effect of correlations are treated in the Brueckner-Hartree-Fock approximation directly for the finite nuclei, but the modifications of the Dirac spinors in the medium are derived from nuclear matter assuming a local-density approximation. Both approaches yield rather similar results for binding energies and radii in fair agreement with experimental data. The importance of the density dependent correlation effects is demonstrated and different ingredients to the spin-orbit splitting in the she...
Spin-polarized Hartree-Fock approximation at nonzero temperatures
Hong, Suklyun; Mahan, G. D.
1995-06-01
The Hartree-Fock exchange energy is calculated for the spin-polarized electron gas at nonzero temperatures. This calculation is done self-consistently in that the Hartree-Fock self-energy is included self-consistently in the Fermi-Dirac occupation numbers while performing a coupling constant integral. The internal energy and entropy are also considered. We calculate the first and second derivatives of the exchange energy, internal energy, and entropy with respect to number density and/or spin polarization density, which are used for calculations of response functions such as the compressibility and polarization. One should have in mind that our exchange-only scheme using the coupling-constant-integral formalism is different from the usual Hartree-Fock approximation at nonzero temperatures and is indeed its self-consistent generalization.
The Hartree-Fock+BCS and generator coordinate methods
A new method to solve the Hartree-Fock+BCS equations with minimal symmetry requirements is described. It is shown that this method is very accurate, with reasonable computing time. The method can be generalized to study the nuclear dynamics within the generator coordinate method, and some applications examples are presented. (authors) 35 refs., 9 figs
Charge transfer excitations from excited state Hartree-Fock subsequent minimization scheme
Theophilou, Iris, E-mail: i.theophilou@fz-juelich.de [Peter Grunberg Institut (PGI) Forschungszentrum Jülich, D-52425 Jülich (Germany); Tassi, M.; Thanos, S. [Institute for Advanced Materials, Physicochemical Processes, Nanotechnology and Microsystems, ‘Demokritos’ National Center for Scientific Research, 15310 Athens (Greece)
2014-04-28
Photoinduced charge-transfer processes play a key role for novel photovoltaic phenomena and devices. Thus, the development of ab initio methods that allow for an accurate and computationally inexpensive treatment of charge-transfer excitations is a topic that nowadays attracts a lot of scientific attention. In this paper we extend an approach recently introduced for the description of single and double excitations [M. Tassi, I. Theophilou, and S. Thanos, Int. J. Quantum Chem. 113, 690 (2013); M. Tassi, I. Theophilou, and S. Thanos, J. Chem. Phys. 138, 124107 (2013)] to allow for the description of intermolecular charge-transfer excitations. We describe an excitation where an electron is transferred from a donor system to an acceptor one, keeping the excited state orthogonal to the ground state and avoiding variational collapse. These conditions are achieved by decomposing the space spanned by the Hartree-Fock (HF) ground state orbitals into four subspaces: The subspace spanned by the occupied orbitals that are localized in the region of the donor molecule, the corresponding for the acceptor ones and two more subspaces containing the virtual orbitals that are localized in the neighborhood of the donor and the acceptor, respectively. Next, we create a Slater determinant with a hole in the subspace of occupied orbitals of the donor and a particle in the virtual subspace of the acceptor. Subsequently we optimize both the hole and the particle by minimizing the HF energy functional in the corresponding subspaces. Finally, we test our approach by calculating the lowest charge-transfer excitation energies for a set of tetracyanoethylene-hydrocarbon complexes that have been used earlier as a test set for such kind of excitations.
Qualitative breakdown of the unrestricted Hartree-Fock energy
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
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.
Relativistic Hartree-Fock-Bogoliubov theory: ground states and excitations
Long, Wen Hui; Meng, Jie; Giai, Nguyen Van
The covariant density functional (CDF) theory with the Fock diagrams, the indivisible part of the effective nuclear interaction, is introduced, including both the relativistic Hartree-Fock and its extension -- the relativistic Hartree-Fock-Bogoliubov methods. The specific roles played by Fock diagrams, particularly for the new degrees of freedom associated with the π and ρ-tensor fields and the non-local mean fields, are discussed in determining the nuclear energy functional, the shell structure and the evolution, and nuclear isospin excitations. The existing problems and limits of the CDF theory with Fock terms are also discussed, and the perspective on a new algorithm of dealing with the non-local Fock terms is given.
Stability of the complex generalized Hartree-Fock equations
Goings, Joshua J.; Ding, Feizhi; Li, Xiaosong, E-mail: li@chem.washington.edu [Department of Chemistry, University of Washington, Seattle, Washington 98195 (United States); Frisch, Michael J. [Gaussian, Inc., 340 Quinnipiac St., Bldg 40, Wallingford, Connecticut 06492 (United States)
2015-04-21
For molecules with complex and competing magnetic interactions, it is often the case that the lowest energy Hartree-Fock solution may only be obtained by removing the spin and time-reversal symmetry constraints of the exact non-relativistic Hamiltonian. To do so results in the complex generalized Hartree-Fock (GHF) method. However, with the loss of variational constraints comes the greater possibility of converging to higher energy minima. Here, we report the implementation of stability test of the complex GHF equations, along with an orbital update scheme should an instability be found. We apply the methodology to finding the local minima of several spin-frustrated hydrogen rings, as well as the non-collinear molecular magnet Cr{sub 3}, illustrating the utility of the broken symmetry GHF method and some of its lesser-known nuances.
Particle-unstable nuclei in the Hartree-Fock theory
Kruppa, A T; Flocard, Hubert; Liotta, R J
1997-01-01
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 states become square integrable. The method is implemented with Skyrme effective interactions. Several Skyrme parametrizations are tested on four unstable nuclei: 10He, 12O, 26O and 28O.
Quark matter in the Hartree-Fock approximation
An equation of state is computed for quark matter interacting through a phenomenological potential in the Hartree-Fock approximation. It is shown that for color-independent confining potentials, it can be approximated by the Hartree result and leads to a first order mass phase transition. For color-dependent confining potentials, a phase transition from a Fermi sphere to a Fermi shell is possible
Dirac Hartree-Fock for Finite Nuclei Employing realistic Forces
Müther, R. Fritz H.; Machleidt, R.
1993-01-01
We discuss two different approximation schemes for the self-consistent solution of the {\\it relativistic} Brueckner-Hartree-Fock equation for finite nuclei. In the first scheme, the Dirac effects are deduced from corresponding nuclear matter calculations, whereas in the second approach the local-density approximation is used to account for the effects of correlations. The results obtained by the two methods are very similar. Employing a realistic one-boson-exchange potential (Bonn~A), the pre...
General multi-configuration Hartree--Fock program: MCHF77
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
Ab initio study of the optical phonons in 1D antiferromagnet Ca2CuO3
Hoang, Nam Nhat; Nguyen, Thu Hang; Nguyen, Chau
2008-01-01
In the spin 1/2 antiferromagnetic Ca2CuO3 the optical excitation along 1D a Cu-O chain showed the enrichment of forbidden peaks that could not be explained by the group theory. We present the cluster-model ab initio study of these optical phonons based on the Hartree-Fock SCF calculation with the 3-21G basic set. The obtained results showed very good agreement with the observed data. The Cu-O resonances generally showed the lower shifts in Ca2CuO3 than in pure CuO and were primarily composed ...
Chemisorption of group-III metals on the Si(111) and Ge(111) surfaces: An ab initio study
Ricart, J M; Rubio Martínez, Jaime; Illas i Riera, Francesc
1990-01-01
Chemisorption of group-III metal adatoms on Si(111) and Ge(111) has been studied through the ab initio Hartree-Fock method including nonempirical pseudopotentials and using cluster models to simulate the surface. Three different high-symmetry sites (atop, eclipsed, and open) have been considered by using X4H9, X4H7, and X6H9 (X=Si,Ge) cluster models. In a first step, ideal surface geometries have been used. Metal-induced reconstruction upon chemisorption has also been taken into account. Equi...
Derivative discontinuity with localized Hartree-Fock potential
Nazarov, V U
2015-01-01
The localized Hartree-Fock potential has proven to be a computationally efficient alternative to the optimized effective potential, preserving the numerical accuracy of the latter and respecting the exact properties of being self-interaction free and having the correct $-1/r$ asymptotics. In this paper we extend the localized Hartree-Fock potential to fractional particle numbers and observe that it yields derivative discontinuities in the energy as required by the exact theory. The discontinuities are numerically close to those of the computationally more demanding Hartree-Fock method. Our potential enjoys a "direct-energy" property, whereby the energy of the system is given by the sum of the single-particle eigenvalues multiplied by the corresponding occupation numbers. The discontinuities $c_\\uparrow$ and $c_\\downarrow$ of the spin-components of the potential at integer particle numbers $N_\\uparrow$ and $N_\\downarrow$ satisfy the condition $c_\\uparrow N_\\uparrow+c_\\downarrow N_\\downarrow=0$. Thus, joining t...
Carette, T; Argenti, L; Lindroth, E
2013-01-01
We present a robust, ab initio method for addressing atom-light interactions and apply it to photoionization of argon. We use a close-coupling ansatz constructed on a multi-configurational Hartree-Fock description of localized states and B-spline expansions of the electron radial wave functions. In this implementation, the general many-electron problem can be tackled thanks to the use of the ATSP2K libraries [CPC 176 (2007) 559]. In the present contribution, we combine this method with exterior complex scaling, thereby allowing for the computation of the complex partial amplitudes that encode the whole dynamics of the photoionization process. The method is validated on the 3s3p6np series of resonances converging to the 3s extraction. Then, it is used for computing the energy dependent differential atomic delay between 3p and 3s photoemission, and agreement is found with the measurements of Gu\\'enot et al. [PRA 85 (2012) 053424]. The effect of the presence of resonances in the one-photon spectrum on photoioniz...
First Gogny-Hartree-Fock-Bogoliubov nuclear mass model.
Goriely, S; Hilaire, S; Girod, M; Péru, S
2009-06-19
We present the first Gogny-Hartree-Fock-Bogoliubov (HFB) model which reproduces nuclear masses with an accuracy comparable with the best mass formulas. In contrast with the Skyrme-HFB nuclear-mass models, an explicit and self-consistent account of all the quadrupole correlation energies are included within the 5D collective Hamiltonian approach. The final rms deviation with respect to the 2149 measured masses is 798 keV. In addition, the new Gogny force is shown to predict nuclear and neutron matter properties in agreement with microscopic calculations based on realistic two- and three-body forces. PMID:19659002
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.
Relativity and pseudopotentials in the Hartree-Fock-Slater method
The methodological problems involved in electronic structure determinations of compounds containing heavy elements by the Hartree-Fock-Slater scheme are investigated. It is shown that the effect of the inner electrons can be simulated by a so called pseudopotential, so that only the valence electrons have to be treated explicitly which constitutes a considerable reduction of computation time. It is further shown that a pseudopotential calculation is able to achieve an accuracy that is comparable to the results of a calculation including the core. (Auth.)
A Hartree-Fock program for atomic structure calculations
The Hartree-Fock equations for a general open shell atom are described. The matrix equations that result when the single particle orbitals are written in terms of a linear combination of analytic basis functions are derived. Attention is paid to the complexities that occur when open shells are present. The specifics of a working FORTRAN program which is available for public use are described. The program has the flexibility to handle either Slater-type orbitals or Gaussian-type orbitals. It can be obtained over the internet at http://lacebark.ntu.edu.au/j_mitroy/research/atomic.htm Copyright (1999) CSIRO Australia
Bimodal fission in the Skyrme-Hartree-Fock approach
Staszczak, A.; Dobaczewski, J.; Nazarewicz, W.
2006-01-01
Spontaneous-fission properties of 256Fm, 258Fm, and 260Fm isotopes are studied within the Skyrme-Hartree-Fock+BCS framework. In the particle-hole channel we take the Skyrme SkM* effective force, while in the particle-particle channel we employ the seniority pairing interaction. Three static fission paths for all investigated heavy fermium isotopes are found. The analysis of these fission modes allows to describe observed asymmetric fission of 256Fm, as well as bimodal fission of 258Fm and sym...
Quasirelativistic Hartree-Fock equations consistent with Breit-Pauli approach
The properties of the quasirelativistic Hartree-Fock equations are investigated. Different ways of forming the equations are discussed. The relativistic corrections employed in the traditional quasirelativistic Hartree-Fock equations are compared with the ones used within the Breit-Pauli approach. The two-electron contact interactions are revised and the new versions of the quasirelativistic Hartree-Fock equations are considered. The solutions of these equations are compared among themselves and also with those obtained within the Dirac-Fock and nonrelativistic Hartree-Fock approaches. Solution data are provided for some heliumlike, neonlike, and mercurylike ions
Ab initio calculation of the pair potentials of MgB2
Ab initio calculations on model clusters of MgB2 are presented to estimate the pairing potentials of superconductivity. The total energies of the clusters for the restricted Hartree-Fock (RHF) type and unrestricted Hartree-Fock (UHF) type singlet ground states and the triplet state are calculated by the hybrid DFT method of Gaussian G03 program. The energy difference between the UHF singlet state and the triplet state is correlated to the superconducting energy gap 2Δ. The highest occupied molecular orbital (HOMO) and the next HOMO are composed of mostly the 2pσ and the 3s orbitals of boron and 3pσ orbitals of magnesium. These orbitals constitute the spin polarized singlet state which represent the superconducting state. The vibrational frequencies of the singlet and the triplet states are calculated on a model cluster, Mg8B16H10, to find vibrational frequencies, and the results are used to interpret the isotope effects of 10B and 11B for the transition temperatures
ESTUDIO TEÓRICO DE LA MOLÉCULA DE HIDROGENO CALCULO AB-INITIO
N. Quitián
2010-09-01
Full Text Available Utilizando la técnica LCGO-SCF-MO (Combinación Lineal de los Orbitales Moleculares en Orbitales Gausianos, en el método del Campo Auto-Coherente, se determinaron las energías de orbital, la energía electrónica total, la energía de repulsión nuclear y la energía de Hartree-Fock de la molécula de hidrógeno en su estado fundamental, mediante un cálculo ab initio y utilizando una base de funciones gausianas. Los orbitales moleculares fueron desarrollados en términos de una función Is contraída por átomo de hidrógeno, obtenida por la minimización de los coeficientes y de los exponentes de los orbitales gausianos para el átomo aislado. Los resultados obtenidos nos permiten afirmar que la base molecular mejora sensiblemente los resultados, acercándose más al límite de Hartree-Fock.
Dynamics of a semiclassical nuclear Hartree-Fock fluid
The Vlasov equation for the Wigner transform of the one-body density matrix is the semiclassical analogue of the time-dependent Hartree-Fock equation. The dynamics of large amplitude nuclear collective motions are studied using an adiabatic approximation to the Vlasov equation. The theory is a semiclassical limit of the adiabatic time-dependent Hartree-Fock approximation and there are many formal similarities between the two theories. In cases where the collective motion has a generalized scaling property it is possible to solve the first adiabatic equation and find explicit formulae for collective currents, kinetic energies and mass parameters. For effective interactions of the Skyrme type it is possible to go beyond cranking results and to show that inertial parameters do not depend on the effective mass resulting from the interaction. The theory is illustrated by the example of a rotating harmonic oscillator potential and the classical limit of the Inglis formula for the moment of inertia is obtained. When a self-consistency condition is imposed the formula gives a rigid moment of inertia, but not always a rigid flow pattern. (orig.)
Hartree-Fock-Bogoliubov model: a theoretical and numerical perspective
This work is devoted to the theoretical and numerical study of Hartree-Fock-Bogoliubov (HFB) theory for attractive quantum systems, which is one of the main methods in nuclear physics. We first present the model and its main properties, and then explain how to get numerical solutions. We prove some convergence results, in particular for the simple fixed point algorithm (sometimes called Roothaan). We show that it converges, or oscillates between two states, none of them being a solution. This generalizes to the HFB case previous results of Cances and Le Bris for the simpler Hartree-Fock model in the repulsive case. Following these authors, we also propose a relaxed constraint algorithm for which convergence is guaranteed. In the last part of the thesis, we illustrate the behavior of these algorithms by some numerical experiments. We first consider a system where the particles only interact through the Newton potential. Our numerical results show that the pairing matrix never vanishes, a fact that has not yet been proved rigorously. We then study a very simplified model for protons and neutrons in a nucleus. (author)
Tensor factorization of the 2-electron integral matrix is a well-known technique for reducing the computational scaling of ab initio electronic structure methods toward that of Hartree-Fock and density functional theories. The simplest factorization that maintains the positive semidefinite character of the 2-electron integral matrix is the Cholesky factorization. In this paper, we introduce a family of positive semidefinite factorizations that generalize the Cholesky factorization. Using an implementation of the factorization within the parametric 2-RDM method [D. A. Mazziotti, Phys. Rev. Lett. 101, 253002 (2008)], we study several inorganic molecules, alkane chains, and potential energy curves and find that this generalized factorization retains the accuracy and size extensivity of the Cholesky factorization, even in the presence of multi-reference correlation. The generalized family of positive semidefinite factorizations has potential applications to low-scaling ab initio electronic structure methods that treat electron correlation with a computational cost approaching that of the Hartree-Fock method or density functional theory
Hoy, Erik P.; Mazziotti, David A., E-mail: damazz@uchicago.edu [Department of Chemistry and The James Franck Institute, The University of Chicago, Chicago, Illinois 60637 (United States)
2015-08-14
Tensor factorization of the 2-electron integral matrix is a well-known technique for reducing the computational scaling of ab initio electronic structure methods toward that of Hartree-Fock and density functional theories. The simplest factorization that maintains the positive semidefinite character of the 2-electron integral matrix is the Cholesky factorization. In this paper, we introduce a family of positive semidefinite factorizations that generalize the Cholesky factorization. Using an implementation of the factorization within the parametric 2-RDM method [D. A. Mazziotti, Phys. Rev. Lett. 101, 253002 (2008)], we study several inorganic molecules, alkane chains, and potential energy curves and find that this generalized factorization retains the accuracy and size extensivity of the Cholesky factorization, even in the presence of multi-reference correlation. The generalized family of positive semidefinite factorizations has potential applications to low-scaling ab initio electronic structure methods that treat electron correlation with a computational cost approaching that of the Hartree-Fock method or density functional theory.
Hoy, Erik P; Mazziotti, David A
2015-08-14
Tensor factorization of the 2-electron integral matrix is a well-known technique for reducing the computational scaling of ab initio electronic structure methods toward that of Hartree-Fock and density functional theories. The simplest factorization that maintains the positive semidefinite character of the 2-electron integral matrix is the Cholesky factorization. In this paper, we introduce a family of positive semidefinite factorizations that generalize the Cholesky factorization. Using an implementation of the factorization within the parametric 2-RDM method [D. A. Mazziotti, Phys. Rev. Lett. 101, 253002 (2008)], we study several inorganic molecules, alkane chains, and potential energy curves and find that this generalized factorization retains the accuracy and size extensivity of the Cholesky factorization, even in the presence of multi-reference correlation. The generalized family of positive semidefinite factorizations has potential applications to low-scaling ab initio electronic structure methods that treat electron correlation with a computational cost approaching that of the Hartree-Fock method or density functional theory. PMID:26277123
In the example of H2NO, a study has been made of how the choice of Gaussian basis sets influences the constants of hyperfine interaction with 14N. The application of uncontracted, expanded basis sets of the type of (10s5p|5s), (11s7p|6s) can provide a considerable improvement in the results. From a comparison with data on a series of radicals, it has been shown that variations of the constant are due mainly to changes in the geometric parameters of the >N-O fragments. Approximation formulas are proposed for the geometric relationships
Large-scale calculations have been performed using the GRASP2K package to accurately determine the lifetime of levels in 2p53s configuration of neutral neon. In particular, we calculated the hyperfine-induced transition rates from two metastable levels 3P20,0 to the ground state for odd Ne isotopes. It was found that hyperfine interactions drastically quench the lifetime of these two levels.
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.
Ab-initio study of the electronic structure of sup 1 sup 9 F implanted in GaAs and GaN crystals
Park, J H; Cho, H S; Shin, Y N
1998-01-01
We have studied the nuclear quadrupole interaction of a fluorine atom implanted in gallium arsenide and gallium nitride cluster models using the ab-initio Hartree-Fock theory. For the three possible fluorine sites in GaAs and GaN, we have determined the location of the implanted fluorine atom by using a self-consistent calculation, the electric field gradient at the implanted atom, and the electronic structure. Good agreement is found with experimental data wherever they are available. Predictions are made for the implanted fluorine site associated with the total energy and the electric field gradient which are expected to be measurable by a variety of experimental techniques.
Berg, Rolf W.
2007-01-01
), without any empiric adjustments of the harmonic force constants, using constants directly predicted from the Gaussian 03W program. Previously obtained IR absorption and Raman scattering spectra of melts are assigned, by comparing to the ab initio quantum mechanical vibrational analysis results. It is......) calculations were carried out on these various aluminium chloride and oxochloride ions, in assumed isolated gaseous free ionic state, by use of the Gaussian-03W program at the restricted Hartree-Fock (HF) level and with the 6-31+G(d,p) basis set [1]. Without any pre-assumed symmetries and with tight...
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.
Superheavy magic nuclei in Relativistic Hartree-Fock-Bogoliubov theory
The occurrence of the spherical shell closures in superheavy nuclear systems is explored within the relativistic Hartree-Fock-Bogoliubov (RHFB) theory with density- dependent meson-nucleon couplings. We use the two-nucleon gaps δ2n(p) and pairing gaps Δv(π) to characterize the shell effects. The results depend slightly on the forces used, but the general set of magic numbers beyond 208Pb are Z = 120, 138 and N = 172, 184, 228 and 258. Our calculations are in favor of the nuclide 304120 as the next spherical doubly magic nucleus. Combined with the bulk properties of symmetric matter, we find that the shell effects are sensitive to the values of both scalar mass and effective mass. These two masses essentially determine the spin-orbit splittings and single-particle level density, respectively. Furthermore, the breaking of relativistic pseudo-spin symmetry influences the level structure and the occurrence of closed shells.
Study of He isotopes with AMD + Hartree-Fock
We study He isotopes with AMD and AMD + Hartree-Fock, putting stress on the study of 8He. In this paper we represent a single nucleon with the superposition of two Gaussian wave packets. Furthermore we propose a new method to calculate single particle levels, including unoccupied levels. By using the merit of the AMD that it is free from any model assumptions, we study whether deformation and/or clustering exist in any of He isotopes. We investigate the influence of changing the strength of the LS force on He isotopes. We see that the structure of 8He, especially its deformation, is largely dependent on the LS force strength, while that of 6He is not. We study the pairing excitation mechanism by using the wave function projected onto the eigenstate of the angular momentum. (author)
ESTUDIO TEÓRICO DE LA MOLÉCULA DE HIDROGENO CALCULO AB-INITIO
Quitián, N.
2010-01-01
Utilizando la técnica LCGO-SCF-MO (Combinación Lineal de los Orbitales Moleculares en Orbitales Gausianos, en el método del Campo Auto-Coherente), se determinaron las energías de orbital, la energía electrónica total, la energía de repulsión nuclear y la energía de Hartree-Fock de la molécula de hidrógeno en su estado fundamental, mediante un cálculo ab initio y utilizando una base de funciones gausianas. Los orbitales moleculares fueron desarrollados en términos de una función Is contraída p...
Ab initio simulations on rutile-based titania nanowires
Zhukovskii, Yu F.; Evarestov, R. A.
2012-08-01
The rod symmetry groups for monoperiodic (1D) nanostructures have been applied for construction of models for bulk-like TiO2 nanowires (NWs) cut from a rutile-based 3D crystal along the chosen [001] and [110] directions of crystallographic axes. In this study, we have considered nanowires described by both the Ti-atom centered rotation axes as well as the hollow site centered axes passing through the interstitial positions between the Ti and O atoms closest to the axes. The most stable [001]-oriented TiO2 NWs with rhombic cross sections are found to display the energetically preferable {110} facets only while the nanowires with quasi-square sections across the [110] axis are formed by the alternating { 1bar 10 } and {001} facets. For simulations on rutile-based nanowires possessing different diameters for each NW type, we have performed large-scale ab initio Density Functional Theory (DFT) and hybrid DFT-Hartree Fock (DFT-HF) calculations with total geometry optimization within the Generalized Gradient Approximation (GGA) in the form of the Perdew-Becke-Ernzenhof (PBE) exchange-correlation functionals (PBE and PBE0, respectively), using the formalism of linear combination of localized atomic functions (LCAO). We have simulated both structural and electronic properties of TiO2 NWs depending both on orientation and position of symmetry axes as well as on diameter and morphology of nanowires.
Ab initio theoretical comparative study of magnetic coupling in KNiF3sand K2 NiF4s
de P. R. Moreira, Ibério; Illas, Francesc
1997-02-01
The origin of magnetic coupling in KNiF3 and K2 NiF4 is studied by means of an ab initio cluster model approach. By a detailed study of the mapping between eigenstates of the exact nonrelativistic and spin model Hamiltonians it is possible to obtain the magnetic coupling constant J and to compare ab initio cluster-model values with those resulting from ab initio periodic Hartree-Fock calculations. This comparison shows that J is strongly determined by two-body interactions; this is a surprising and unexpected result. The importance of the ligands surrounding the basic metal-ligand-metal interacting unit is reexamined by using two different partitions and the constrained space orbital variation method of analysis. This decomposition enables us to show that this effect is basically environmental. Finally, dynamical electronic correlation effects have found to be critical in determining the final value of the magnetic coupling constant.
A general multi-configuration Hartree-Fock program
Numerical non-relativistic Hartree-Fock results are determined within the multi-configuration approximation for atoms in a bound state. The self-consistent field method of solution is employed. In a multi-configuration calculation the mixing coefficients are adjusted periodically as part of the SCF iteration. Two methods of solution of the differential equations are used, each improving only a single function at a time, and rotations are introduced explicitly to find an energy stationary with respect to a rotation of the orbital basis. The organization of the program is such that the 'frozen core' approximation may be used and orbitals with zero occupation number are allowed. Orbitals in different configurations may be allowed to differ so long as not more than one overlap integral enters into the expression for the interaction and the expressions for off-diagonal energy parameters remain relatively simple. A fixed zero-order approximation may be employed resulting in a considerable saving in computation time in some cases. (Auth.)
Relativistic Hartree-Fock-Bogoliubov predictions of superheavy magic nuclei
The occurrence of spherical shell closures in the superheavy nuclei region is explored in the framework of the relativistic Hartree-Fock-Bogoliubov theory (RHFB), and also with the simpler version of relativistic mean field with quasiparticles, in other words the relativistic Hartree-Bogoliubov (RHB) approximation. Both theoretical frameworks are often used for nuclei in the known regions of the nuclear chart. Shell closures characterized in terms of two-nucleon gaps indicate the magic regions. The results depend slightly on the effective Lagrangians used, but the magic numbers beyond 208Pb are generally predicted to be Z = 120, 138 for protons and N = 172, 184, 228, 258 for neutrons. Shell effects are sensitive to various terms of the mean-field, such as the spin-orbit coupling, the scalar and effective masses. This explains the (relatively small) variations in the predictions, depending on the effective Lagrangians employed. The most complete model (RHFB) favors the nuclide 304 120 as the next spherical doubly-magic nucleus beyond 208Pb
Ripka, G. [Commissariat a l' Energie Atomique, 91 - Saclay (France). Centre d' Etudes Nucleaires
1968-09-01
Most of the content of this thesis is published in english in Advances In Nuclear Physics, Vol. 1 (Editors: Baranger and Vogt - Plenum Press). The Hartree- Fock equations are derived. The expansions of the orbits and the possible symmetries of the Hartree-Fock field are discussed. Wavefunctions of even-even N = Z nuclei are given for 12 {<=} A {<=} 40. The role of the monopole, quadrupole and exchange components of the force are discussed. The multiplicity of the solutions and the effect of the spin-orbit interaction are discussed. Exact angular momentum projection is used to generate rotational bands. The validity of the adiabatic rotational model in light nuclei is discussed. Hartree-Fock calculations are extended to include major-shell mixing in order to obtain quadrupole deformations without the use of effective charge. The incompressibility, of nuclei is discussed and the compatibility between the Hartree-Fock solutions, the Mottelson model of quadrupole deformations and the SU3 states of J.P. Elliott and M. Moshinsky is established. (author) [French] La theorie de Hartree-Fock est appliquee au calcul des fonctions d'onde des noyaux legers deformes. Les equations de Hartree-Fock, les symetries permises et le choix du developpement des orbites sont discutes. Les fonctions d'onde des noyaux pair-pairs N = Z (12 {<=} A {<=} 40) sont tabulees. Les contributions des composantes monopolaires et quadrupolaires ainsi que des termes d'echange de la force nucleon-nucleon sont discutees. La methode de projection de moment cinetique est utilisee pour engendrer les bandes de rotation. La validite du modele rotationnel adiabatique est discutee. Les calculs de Hartree-Fock qui tiennent compte du melange de plusieurs couches majeures dans chaque orbite sont appliques au calcul des deformations quadrupolaires sans l'utilisation de charge effective. L'incompressibilite des noyaux et la compatibilite des fonctions d'onde de Hartree- Fock avec les
On the evaluation of determinantal wave functions in open-shell Hartree-Fock theory
Guseinov, I. I.; DEMİR, Ramazan
2001-01-01
Slater method is modified for the evaluation of determinantal wave functions appearing in open-shell Hartree-Fock (HF) theory [1]. Using modified Slater method we have calculated, as an example, the orbital energies and the wave functions of terms obtained from the electronic configuration of a ground state of an N-atom system in the Hartree-Fock-Roothaan (HFR) approximation. The modified determinantal method introduced in this paper can be of considerable help and importance in the ...
A mathematical and computational review of Hartree-Fock SCF methods in Quantum Chemistry
Echenique, Pablo; Alonso, José Luis
2007-01-01
Abstract We present here a review of the fundamental topics of Hartree-Fock theory in Quantum Chemistry. From the molecular Hamiltonian, using and discussing the Born-Oppenheimer approximation, we arrive to the Hartree and Hartree-Fock equations for the electronic problem. Special emphasis is placed in the most relevant mathematical aspects of the theoretical derivation of the final equations, as well as in the results regarding the existence and uniqueness of the...
Hermes, Matthew R; Hirata, So
2015-09-14
One-dimensional (1D) solids exhibit a number of striking electronic structures including charge-density wave (CDW) and spin-density wave (SDW). Also, the Peierls theorem states that at zero temperature, a 1D system predicted by simple band theory to be a metal will spontaneously dimerize and open a finite fundamental bandgap, while at higher temperatures, it will assume the equidistant geometry with zero bandgap (a Peierls transition). We computationally study these unique electronic structures and transition in polyyne and all-trans polyacetylene using finite-temperature generalizations of ab initio spin-unrestricted Hartree-Fock (UHF) and spin-restricted coupled-cluster doubles (CCD) theories, extending upon previous work [He et al., J. Chem. Phys. 140, 024702 (2014)] that is based on spin-restricted Hartree-Fock (RHF) and second-order many-body perturbation (MP2) theories. Unlike RHF, UHF can predict SDW as well as CDW and metallic states, and unlike MP2, CCD does not diverge even if the underlying RHF reference wave function is metallic. UHF predicts a gapped SDW state with no dimerization at low temperatures, which gradually becomes metallic as the temperature is raised. CCD, meanwhile, confirms that electron correlation lowers the Peierls transition temperature. Furthermore, we show that the results from all theories for both polymers are subject to a unified interpretation in terms of the UHF solutions to the Hubbard-Peierls model using different values of the electron-electron interaction strength, U/t, in its Hamiltonian. The CCD wave function is shown to encompass the form of the exact solution of the Tomonaga-Luttinger model and is thus expected to describe accurately the electronic structure of Luttinger liquids. PMID:26374011
We describe classical-trajectory calculations of sputtering yields for Ar+-ion collisions with a Si(001) surface. The Ar+-Si and short-ranged Si-Si interaction potentials were calculated using the ab initio Hartree-Fock and configuration-interaction methods. The low-energy potential describing the silicon solid is the two- and three-body form due to Stillinger and Weber. We compare the calculated sputtering yields with experiment. The potential-energy surface strongly influences the calculated sputtering yields, and it is found that the most reasonable agreement is obtained from our potentials using the (2 x 1) Si(001) reconstructed surface rather than the bulk-terminated surface. Analysis of the kinetic energy and angular distributions of the sputtered silicon atoms and of cluster yields has provided a mechanism of ejection
Gharabaghi, Masumeh
2016-01-01
In this letter the conceptual and computational implications of the Hartree product type nuclear wavefunction introduced recently within context of the ab initio non-Born-Oppenheimer Nuclear-electronic orbital (NEO) methodology are considered. It is demonstrated that this wavefunction may imply a pseudo-adiabatic separation of the nuclei and electrons and each nucleus is conceived as a quantum oscillator while a non-Coulombic effective Hamiltonian is deduced for electrons. Using variational principle this Hamiltonian is used to derive a modified set of single-component Hartree-Fock equations which are equivalent to the multi-component version derived previously within context of the NEO and, easy to be implemented computationally.
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...
Renison, C Alicia; Fernandes, Kyle D; Naidoo, Kevin J
2015-07-01
This article describes an extension of the quantum supercharger library (QSL) to perform quantum mechanical (QM) gradient and optimization calculations as well as hybrid QM and molecular mechanical (QM/MM) molecular dynamics simulations. The integral derivatives are, after the two-electron integrals, the most computationally expensive part of the aforementioned calculations/simulations. Algorithms are presented for accelerating the one- and two-electron integral derivatives on a graphical processing unit (GPU). It is shown that a Hartree-Fock ab initio gradient calculation is up to 9.3X faster on a single GPU compared with a single central processing unit running an optimized serial version of GAMESS-UK, which uses the efficient Schlegel method for s- and l-orbitals. Benchmark QM and QM/MM molecular dynamics simulations are performed on cellobiose in vacuo and in a 39 Å water sphere (45 QM atoms and 24843 point charges, respectively) using the 6-31G basis set. The QSL can perform 9.7 ps/day of ab initio QM dynamics and 6.4 ps/day of QM/MM dynamics on a single GPU in full double precision. © 2015 Wiley Periodicals, Inc. PMID:25975864
Ab Initio Calculations of Oxosulfatovanadates
Frøberg, Torben; Johansen, Helge
1996-01-01
Restricted Hartree-Fock and multi-configurational self-consistent-field calculations together with secondorder perturbation theory have been used to study the geometry, the electron density, and the electronicspectrum of (VO2SO4)-. A bidentate sulphate attachment to vanadium was found to be stable...... with anO-V-O angle of 72.5 degrees . The calculated spectrum shows bands in reasonable agreement with anexperimental spectrum which has been attributed to (VO2SO4)-. The geometry and the electron density fortwo binuclear vanadium complexes proposed as intermediates in the vanadium catalyzed SO2...
Time-dependent Hartree-Fock Study of Octupole Vibrations in doubly magic nuclei
Simenel, C; Vo-Phuoc, K
2016-01-01
Octupole vibrations are studied in some doubly magic nuclei using the time-dependent Hartree-Fock (TDHF) theory with a Skyrme energy density functional. Through the use of the linear response theory, the energies and transition amplitudes of the low-lying vibrational modes for each of the nuclei were determined. Energies were found to be close to experimental results. However, transition amplitudes, quantified by the deformation parameter $\\beta_3$, are underestimated by TDHF. A comparison with single-particle excitations on the Hartree-Fock ground-state shows that the collective octupole vibrations have their energy lowered due to attractive RPA residual interaction.
Single-particle potential in a relativistic Hartree-Fock mean field approximation
Jaminon, Martine; Mahaux, Claude; Rochus, Pierre
1981-01-01
A relativistic Hartree-Fock mean field approximation is investigated in a model in which the nucléon field interacts with scalar and vector meson fields. The Hartree-Fock potential felt by individual nucléons enters in a relativistic Dirac single-particle equation. It is shown that in the case of symmetric nuclear matter one can always find a potential which is fully equivalent to the most general mean field and which is only the sum of a Lorentz scalar, of one component of a Lorentz tensor a...
Non-plane-wave Hartree-Fock states and nuclear homework potentials
It is shown that non-plane-wave single-particle Hartree-Fock orbitals giving rise to a ''spin-density-wave-like'' structure give lower energy than plane waves beyond a certain relatively low density in both nuclear and neutron matter with homework pair potentials v1 and v2
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....
Coriolis coupling effects in time-dependent Hartree-Fock calculations of ion-atom collisions
Effects on the collision dynamics due to the inclusion of the Coriolis term in the time-dependent Hartree-Fock Hamiltonian are investigated for the He2++He colliding system both at low and high incident energies. Whereas at low energies these effects are perturbative, Coriolis terms produce drastic reductions in charge-exchange cross sections at high energies
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.…
Local covariant density functional constrained by the relativistic Hartree-Fock theory
Liang, H Z; Ring, P; Roca-Maza, X; Zhao, P W; 10.1063/1.4764245
2012-01-01
The recent progress in the localized covariant density functional constrained by the relativistic Hartree-Fock theory is briefly presented by taking the Gamow-Teller resonance in 90Zr as an example. It is shown that the constraints introduced by the Fock terms into the particle-hole residual interactions are straight forward and robust.
Time-dependent Hartree-Fock-Bogoliubov description of the pairing interaction
The time-dependent Hartree-Fock-Bogoliubov (TDHFB) method is applied to a system with a pairing interaction. A semiclassical prescription is used for the evaluation of the two-particle-transfer matrix elements. A comparison of matrix elements and excitation energies obtained in the TDHFB approach and the exact ones shows a very good agreement for large degeneracies. (orig.)
Multiconfiguration Dirac-Hartree-Fock calculations for intercombination lines in silicon-like ions
This paper reports on multiconfiguration Dirac-Hartree-Fock calculations for intercombination lines in highly charged silicon-like ions. Results for wavelengths, fine structure, transition rates, branching ratios and lifetimes are reported and compared with other theories and experiments. A review of the experimental situation is presented, and deviations from expected smooth trends along the sequence are discussed
Multiconfiguration Dirac-Hartree-Fock calculations for intercombination lines in silicon-like ions
Min Huang [Applied Ion Beam Physics Laboratory, Fudan University, Shanghai (China); Andersson, Martin [Department of Physics, Lund University, Lund (Sweden); Brage, Tomas [Department of Physics, Lund University, Lund (Sweden); Hutton, Roger [Lund Observatory, Lund University, Lund (Sweden); Joensson, Per [Applied Mathematics Group, Malmoe University, Malmoe (Sweden); Chen Chongyang [Applied Ion Beam Physics Laboratory, Fudan University, Shanghai (China); Zou Yaming [Applied Ion Beam Physics Laboratory, Fudan University, Shanghai (China)
2005-03-14
This paper reports on multiconfiguration Dirac-Hartree-Fock calculations for intercombination lines in highly charged silicon-like ions. Results for wavelengths, fine structure, transition rates, branching ratios and lifetimes are reported and compared with other theories and experiments. A review of the experimental situation is presented, and deviations from expected smooth trends along the sequence are discussed.
Dąbrowska, Aleksandra; Makowski, Mariusz; Jacewicz, Dagmara; Chylewska, Agnieszka; Chmurzyński, Lech
2008-12-01
UV absorption spectra of methyl 3-azido-6-iodo-2,3,6-trideoxy-α- D- arabino-hexopyranoside were recorded over a wide pH range. On this basis, a relationship between absorbance and pH was plotted, from which deprotonation equilibrium constants of this compound were determined. Further, quantum-mechanical calculations were performed at the ab initio level both in the gas phase by using the Restricted Hartree Fock (RHF), Møller-Plesset (MP2) methods and under consideration of solvation effects within the Polarizable Continuum Model (PCM), which enabled location of preferred protonation and deprotonation centers of this compound. The results provided the basis for discussion of the influence of substituents in the sugar ring on protolytic equilibria occurring in aqueous solutions of 3-azido-2,3-dideoxy sugars.
FRANCHFRI: the Finite-RANge Constrained Hartree-Fock Rapid Iterator
Younes, W; Gogny, D
2007-01-22
The Hartree-Fock code FRANCHFRI, which uses a finite-range nucleon-nucleon interaction, has been written and benchmarked. This code represents a new LLNL capability for realistic calculations in both nuclear-structure and nuclear-reaction physics. The use of a finite-range interaction represents a considerable improvement over other Hartree-Fock codes currently available in the public domain, which rely on zero-range forces. The finite-range force does not simply lead to a more realistic treatment of the nuclear problem, it avoids serious mathematical pathologies inherent to zero-range interactions. This brief and non-technical report introduces the code, its design philosophy, various benchmarks used to test its accuracy, and places it within its proper physics context. The current limitations and planned extensions of the code are also discussed.
Mendez, M P A; Miraglia, J E
2015-01-01
Exchange potentials for specific orbitals of noble gases are calculated by inverting the corresponding Hartree-Fock wavefunctions. This procedure was performed by using a Depurated Inversion Method, which is presented here. The basic idea of the method relies upon the substitution of Hartree-Fock orbitals and eigenvalues into the Kohn-Sham equation. Through inversion, the corresponding effective potential were obtained. A further depuration of the potential should be performed. It consists in a careful optimization which shatters the poles and also ensures the fulfillment of the appropriate boundary conditions. The method is not restricted to the ground state or to a nodeless orbital. It allows to reproduce the input energies and wavefunctions with a remarkable degree of accuracy.
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 ...
Physical interpretation of time-dependent Hartree-Fock density matrix for heavy ion scattering
We suggest a quantum mechanical interpretation of the density matrix of the time-dependent Hartree-Fock theory for heavy ion scattering. We show how with this interpretation the time-dependent Hartree-Fock equations can be derived provided we admit (i) a generalized factorization of a suitably defined average of two-body density matrix elements in terms of a sum of products of the corresponding one-particle elements and (ii) additional semiclassical approximations which convert a sum of products into an antisymmetric product of sums. These ideas, previously recognized within the framework of soliton models, are extended here to include inelastic processes with the excitation of collective modes as the mechanism for producing deep inelastic scattering. An essential feature of the approach is that it provides, in principle, a theoretical method of obtaining exclusive amplitudes. We describe how these might be calculated
On the behaviour of the Hartree-Fock energy at short internuclear distances
Gilka, Natalie; Solovej, Jan Philip; Taylor, Peter R.
2011-01-01
There are well-established mathematical relationships for the energy of a diatomic molecule (the exact energy, but also both the Hartree-Fock and Thomas-Fermi energies) in the limit of large nuclear charge of the atoms and small internuclear distances. We present calculated energies for a number ...... homonuclear diatomic molecules at short internuclear distances for numerical comparison with these established relationships. Intriguingly, they hold in practice for relatively small nuclear charges and for relatively long internuclear distances.......There are well-established mathematical relationships for the energy of a diatomic molecule (the exact energy, but also both the Hartree-Fock and Thomas-Fermi energies) in the limit of large nuclear charge of the atoms and small internuclear distances. We present calculated energies for a number of...
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.
Using finite element method to tackle the hartree-fock equations
It is well know that the Schroedinger equation cannot be solved exactly, except maybe for very simple cases, as it represents a many-body interaction problem. However, it is possible to derive approximations of the Schroedinger equation from variational principles. The Hartree-Fock equations are then generally solved thanks to a set of basis functions, e.g. Gaussians, Slater-type orbitals or plane waves. To avoid to impose a general form to the approximate wave function, we use localized trial functions. We consider here the Finite Element Method as a new approach to solve these Hartree-Fock equations. We shall present the main properties of our computations with the different advantages and drawbacks involved by this strategy. We present numerical results about different electronic systems: such as atoms or molecules (LiH, BeH2).
Šimunek, Ján; Noga, Jozef
2012-12-01
It is shown that the non-terminating expansions of the wave function within the variational coupled cluster singles (VCCS) can be exactly treated by summing up the one-particle density matrix elements in the occupied block using simple recurrence relation. At the same time, this leads to an extremely simple 'a priori' diagonalization free algorithm for the solution of the Hartree-Fock equations. This treatment corresponds to a non-unitary transformation of orbitals, however, preserving the norm and idempotency of the density matrix. The resulting algorithm enables a Hartree-Fock solution with 'a priori' localized orbitals. Similar approach can be applied within the Kohn-Sham theory. Analysis of the VCCS expansion in terms of the generalized perturbation theory is also presented. Numerical results are presented for model systems N2, F2, H2O, NH3 but also for a larger Uracile molecule and an interaction of four Guanine molecules.
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.
Multiconfiguration Dirac-Hartree-Fock calculations for be-like intercombination lines revisited
Multiconfiguration Dirac-Hartree-Fock (MCDHF) calculations for the 2s21S0-2s2p 3P1 intercombination transitions are revisited for the elements N+3-Mg+8, and for Fe+22 where previous results produced transition rates that were too small when compared with similar multiconfiguration Hartree-Fock-Breit-Pauli values. By optimizing on both the first and second eigenvalue for J=1, the wave functions for the 2s2p 3P1 state produced transition rates that are within the uncertainty limits of recent Breit-Pauli calculations. The case of C+2 is also discussed where previous theory and experiment are in excellent agreement. (orig.)
Multiconfiguration Dirac-Hartree-Fock calculations for be-like intercombination lines revisited
Froese Fischer, C. [Vanderbilt Univ., Nashville, TN (United States). Dept. of Computer Science
2000-12-01
Multiconfiguration Dirac-Hartree-Fock (MCDHF) calculations for the 2s{sup 2} {sup 1}S{sub 0}-2s2p {sup 3}P{sub 1} intercombination transitions are revisited for the elements N{sup +3}-Mg{sup +8}, and for Fe{sup +22} where previous results produced transition rates that were too small when compared with similar multiconfiguration Hartree-Fock-Breit-Pauli values. By optimizing on both the first and second eigenvalue for J=1, the wave functions for the 2s2p {sup 3}P{sub 1} state produced transition rates that are within the uncertainty limits of recent Breit-Pauli calculations. The case of C{sup +2} is also discussed where previous theory and experiment are in excellent agreement. (orig.)
A study of Lambda hypernuclei within the Skyrme-Hartree-Fock Model
Guleria, Neelam; Dhiman, Shashi K.; Shyam, Radhey
2011-01-01
We investigate the properties of the single Lambda hypernuclei within a Skyrme-Hartree-Fock (SHF) model. The parameters of the Skyrme type effective lambda-nucleon (Lambda N) interaction are obtained by fitting to the experimental Lambda binding energies of hypernuclei with masses spanning a wide range of the periodic table. Alternative parameter sets are also obtained by omitting nuclei below mass number 16 from the fitting procedure. The SHF calculations are performed for the binding energi...
Strutinsky's shell-correction method is applied in the framework of the Hartree-Fock method developed by Roothaan (HFR) in the atoms and ions with an open shell. Applying the Strutinsky energy averaging to the density matrix define a self-consistently average HFR system as a solution of the variational problem. We derive the explicit expressions for the shell corrections. 3 refs. (author)
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_{\
Charged skyrmions in a system of 2D spin excitons in the Hartree-Fock approximation
The existence of topological defects, known as skyrmions, within the spin excitons energy band of a 2D electron gas under a strong magnetic field at filling factor ν = 1 is investigated within the Hartree-Fock approximation. Using the linear momentum representation, it is shown that the inhomogeneity created in the system by a charged skyrmion can be described by a nonuniform rotation of the spin density operators in a condensate of spin excitons. 13 refs
Time-dependent Hartree-Fock Study of Octupole Vibrations in doubly magic nuclei
Simenel, C; Buete, J.; Vo-Phuoc, K.
2016-01-01
Octupole vibrations are studied in some doubly magic nuclei using the time-dependent Hartree-Fock (TDHF) theory with a Skyrme energy density functional. Through the use of the linear response theory, the energies and transition amplitudes of the low-lying vibrational modes for each of the nuclei were determined. Energies were found to be close to experimental results. However, transition amplitudes, quantified by the deformation parameter $\\beta_3$, are underestimated by TDHF. A comparison wi...
Relativistic description of nuclear systems in the Hartree-Fock approximation
The structure of infinite nuclear matter and finite nuclei is studied in the framework of the relativistic Hartree-Fock approximation. A particular attention is paid to the contribution of isovector mesons. (π,p). A satisfactory description of binding energies and densities can be obtained for light as well as heavy nuclei. The spin-orbit splittings are well reproduced. Connections with non-relativistic formulations are also discussed
Exotic Shapes in $^{32}S$ suggested by the Symmetry-Unrestricted Cranked Hartree-Fock Calculations
Yamagami, M; Yamagami, Masayuki; Matsuyanagi, Kenichi
1998-01-01
High-spin structure of ^{32}S is investigated by means of the cranked Skyrme-Hartree-Fock method in the three-dimensional Cartesian-mesh representation. Some interesting suggestions are obtained: 1) An internal structure change (toward hyperdeformation) may occur at I>20 in the superdeformed band, 2) A non-axial Y_{31} deformed band may appear in the yrast line with 4
Fission of heavy $\\Lambda$ hypernuclei with the Skyrme-Hartree-Fock approach
Minato, F.; Chiba, S.; Hagino, K.
2009-01-01
Fission-related phenomena of heavy $\\Lambda$ hypernuclei are discussed with the constraint Skyrme-Hartree-Fock+BCS (SHF+BCS) method, in which a similar Skyrme-type interaction is employed also for the interaction between a $\\Lambda$ particle and a nucleon. Assuming that the $\\Lambda$ particle adiabatically follows the fission motion, we discuss the fission barrier height of $^{239}_{\\Lambda}$U. We find that the fission barrier height increases slightly when the $\\Lambda$ particle occupies the...
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.
Determination of a silane intermolecular force field potential model from an ab initio calculation
Intermolecular interaction potentials of the silane dimer in 12 orientations have been calculated by using the Hartree-Fock (HF) self-consistent theory and the second-order Moeller-Plesset (MP2) perturbation theory. We employed basis sets from Pople's medium-size basis sets [up to 6-311++G(3df, 3pd)] and Dunning's correlation consistent basis sets (up to the triply augmented correlation-consistent polarized valence quadruple-zeta basis set). We found that the minimum energy orientations were the G and H conformers. We have suggested that the Si-H attractions, the central silicon atom size, and electronegativity play essential roles in weakly binding of a silane dimer. The calculated MP2 potential data were employed to parametrize a five-site force field for molecular simulations. The Si-Si, Si-H, and H-H interaction parameters in a pairwise-additive, site-site potential model for silane molecules were regressed from the ab initio energies.
PSI3: an open-source Ab Initio electronic structure package.
Crawford, T Daniel; Sherrill, C David; Valeev, Edward F; Fermann, Justin T; King, Rollin A; Leininger, Matthew L; Brown, Shawn T; Janssen, Curtis L; Seidl, Edward T; Kenny, Joseph P; Allen, Wesley D
2007-07-15
PSI3 is a program system and development platform for ab initio molecular electronic structure computations. The package includes mature programming interfaces for parsing user input, accessing commonly used data such as basis-set information or molecular orbital coefficients, and retrieving and storing binary data (with no software limitations on file sizes or file-system-sizes), especially multi-index quantities such as electron repulsion integrals. This platform is useful for the rapid implementation of both standard quantum chemical methods, as well as the development of new models. Features that have already been implemented include Hartree-Fock, multiconfigurational self-consistent-field, second-order Møller-Plesset perturbation theory, coupled cluster, and configuration interaction wave functions. Distinctive capabilities include the ability to employ Gaussian basis functions with arbitrary angular momentum levels; linear R12 second-order perturbation theory; coupled cluster frequency-dependent response properties, including dipole polarizabilities and optical rotation; and diagonal Born-Oppenheimer corrections with correlated wave functions. This article describes the programming infrastructure and main features of the package. PSI3 is available free of charge through the open-source, GNU General Public License. PMID:17420978
Fission dynamics within time-dependent Hartree-Fock: Deformation-induced fission
Goddard, Philip; Stevenson, Paul; Rios, Arnau
2015-11-01
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: We explore the ability of dynamic mean-field methods to describe fast fission processes beyond the fission barrier, using the nuclide Pu240 as an example. Methods: Time-dependent Hartree-Fock calculations based on the Skyrme interaction are used to calculate nonadiabatic 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 behavior. Those beginning just beyond the barrier explore large-amplitude motion but do not fission, whereas those beginning beyond the two-fragment pathway crossing fission to final states which differ according to the exact initial deformation. Conclusions: Time-dependent Hartree-Fock is able to give a good qualitative and quantitative description of fast fission, provided one begins from a sufficiently deformed state.
On the NP-completeness of the Hartree-Fock method for translationally invariant systems
Whitfield, James Daniel, E-mail: james.whitfield@univie.ac.at [Vienna Center for Quantum Science and Technology, Department of Physics, University of Vienna, Boltzmanngasse 5, Vienna (Austria); Zimborás, Zoltán, E-mail: z.zimboras@ucl.ac.uk [Department of Computer Science, University College London, Gower Street, WC1E 6BT London (United Kingdom); Department of Theoretical Physics, University of the Basque Country UPV/EHU, P.O. Box 644, E-48080 Bilbao (Spain)
2014-12-21
The self-consistent field method utilized for solving the Hartree-Fock (HF) problem and the closely related Kohn-Sham problem is typically thought of as one of the cheapest methods available to quantum chemists. This intuition has been developed from the numerous applications of the self-consistent field method to a large variety of molecular systems. However, as characterized by its worst-case behavior, the HF problem is NP-complete. In this work, we map out boundaries of the NP-completeness by investigating restricted instances of HF. We have constructed two new NP-complete variants of the problem. The first is a set of Hamiltonians whose translationally invariant Hartree-Fock solutions are trivial, but whose broken symmetry solutions are NP-complete. Second, we demonstrate how to embed instances of spin glasses into translationally invariant Hartree-Fock instances and provide a numerical example. These findings are the first steps towards understanding in which cases the self-consistent field method is computationally feasible and when it is not.
Single-particle potential in a relativistic Hartree-Fock mean field approximation
A relativistic Hartree-Fock mean field approximation is investigated in a model in which the nucleon field interacts with scalar and vector meson fields. The Hartree-Fock potential felt by individual nucleons enters in a relativistic Dirac single-particle equation. It is shown that in the case of symmetric nuclear matter one can always find a potential which is fully equivalent to the most general mean field and which is only the sum of a Lorentz scalar, of one component of a Lorentz tensor and of the fourth component of a Lorentz vector. A non-relativistic potential is derived which yields exactly the same single-particle energies and elastic scattering phase shifts as the relativistic Hartree-Fock potential. Analytical results are presented in the case of nuclear matter. A local density approximation is constructed which enables one to consider finite nuclei. The input parameters of the model can be chosen in such a way that the empirical saturation properties of nuclear matter are well reproduced. Good agreement is obtained between the calculated nonrelativistic potential and the empirical value of the real part of the optical-model potential at low and at intermediate energy. At intermediate energy, the wine-bottle bottom shape which had previously been found for the potential in the framework of the relativistic Hartree approximation is maintained when the Fock contribution is included. (orig.)
Constant resolution of time-dependent Hartree--Fock phase ambiguity
The customary time-dependent Hartree--Fock problem is shown to be ambiguous up to an arbitrary function of time additive to H/sub HF/, and, consequently, up to an arbitrary time-dependent phase for the solution, PHI(t). The ''constant'' (H)'' phase is proposed as the best resolution of this ambiguity. It leads to the following attractive features: (a) the time-dependent Hartree--Fock (TDHF) Hamiltonian, H/sub HF/, becomes a quantity whose expectation value is equal to the average energy and, hence, constant in time; (b) eigenstates described exactly by determinants, have time-dependent Hartree--Fock solutions identical with the exact time-dependent solutions; (c) among all possible TDHF solutions this choice minimizes the norm of the quantity (H--i dirac constant delta/delta t) operating on the ket PHI, and guarantees optimal time evolution over an infinitesimal period; (d) this choice corresponds both to the stationary value of the absolute difference between (H) and (i dirac constant delta/delta t) and simultaneously to its absolute minimal value with respect to choice of the time-dependent phase. The source of the ambiguity is discussed. It lies in the time-dependent generalization of the freedom to transform unitarily among the single-particle states of a determinant at the (physically irrelevant for stationary states) cost of altering only a factor of unit magnitude
On the NP-completeness of the Hartree-Fock method for translationally invariant systems
The self-consistent field method utilized for solving the Hartree-Fock (HF) problem and the closely related Kohn-Sham problem is typically thought of as one of the cheapest methods available to quantum chemists. This intuition has been developed from the numerous applications of the self-consistent field method to a large variety of molecular systems. However, as characterized by its worst-case behavior, the HF problem is NP-complete. In this work, we map out boundaries of the NP-completeness by investigating restricted instances of HF. We have constructed two new NP-complete variants of the problem. The first is a set of Hamiltonians whose translationally invariant Hartree-Fock solutions are trivial, but whose broken symmetry solutions are NP-complete. Second, we demonstrate how to embed instances of spin glasses into translationally invariant Hartree-Fock instances and provide a numerical example. These findings are the first steps towards understanding in which cases the self-consistent field method is computationally feasible and when it is not
Different Hamiltonians and their corresponding rotationally degenerate intrinsic counterparts are employed in the study of 18O nucleus under the normal Hartree-Fock, as well as under six other Hartree-Fock type variational calculation schemes. The results are compared and then assessed in the light of their closeness or otherwise to the full 1s-0d basis shell model calculations for this nucleus. The use of these schemes for other shells is also considered. (author)
The Density-Functional method, with Linear Combination of Atomic Orbitals, has been applied to eight crystals; the lattice equilibrium parameters, and the lattice formation energies have been calculated at the Hartree-Fock level (HF), at the hybrid Hartree-Fock Density-Functional level (DFT/HF), and at the Kohn-Sham Density-Functional level (DFT). The band structures and the electronic charge distributions calculated at the DFT and HF levels are compared
Fission dynamics within time-dependent Hartree-Fock. II. Boost-induced fission
Goddard, Philip; Stevenson, Paul; Rios, Arnau
2016-01-01
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: We explore the ability of dynamic mean-field methods to describe induced fission processes, using quadrupole boosts in the nuclide 240Pu as an example. Methods: Following upon the work presented in Goddard et al. [Phys. Rev. C 92, 054610 (2015)], 10.1103/PhysRevC.92.054610, 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 quickly absorbed by the nucleus. In instantaneous boosts, this leads to fast shape rearrangements and violent dynamics that can ultimately lead to fission. This is a qualitatively different process than the deformation-induced fission. Boosts induced within a finite time window excite the system in a relatively gentler way and do induce fission but with a smaller energy deposition. Conclusions: The fission products obtained using boost-induced fission in time-dependent Hartree-Fock are more asymmetric than the fragments obtained in deformation-induced fission or the corresponding adiabatic approaches.
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. PMID:26016539
Toroidal Super-Heavy Nuclei in Skyrme-Hartree-Fock Approach
Staszczak, Andrzej; Wong, Cheuk-Yin
2008-01-01
Within the self-consistent constraint Skyrme-Hartree-Fock+BCS model (SHF+BCS), we found equilibrium toroidal nuclear density distributions in the region of super-heavy elements. For nuclei with a sufficient oblate deformation ($Q_{20}\\leq$ -200 b), it becomes energetically favourable to change the genus of nuclear surface from 0 to 1, i.e., to switch the shape from a biconcave disc to a torus. The energy of the toroidal (genus=1) SHF+BCS solution relative to the compact (genus=0) ground state...
Cluster decay in osmium isotopes using Hartree-Fock-Bogoliubov theory
Ashok, Nithu; Joseph, Deepthy Maria; Joseph, Antony
2016-02-01
Cluster radioactivity is a rare cold nuclear process which is intermediate between alpha decay and spontaneous fission. The present work is a theoretical investigation of the feasibility of alpha decay and cluster radioactivity from proton rich Osmium (Os) isotopes with mass number ranging from 162-190. Osmium forms a part of the transition region between highly deformed and spherical nuclei. Calculations have been done using unified fission model and Hartree-Fock-Bogoliubov (HFB) theory. We have chosen only those decays with half-lives falling in measurable range. Geiger-Nuttall plot has been successfully reproduced. The isotope which is most favorable to each decay mode has a magic daughter nucleus.
Bogolubov-Hartree-Fock Theory for Strongly Interacting Fermions in the Low Density Limit
Bräunlich, Gerhard; Hainzl, Christian; Seiringer, Robert
2016-06-01
We consider the Bogolubov-Hartree-Fock functional for a fermionic many-body system with two-body interactions. For suitable interaction potentials that have a strong enough attractive tail in order to allow for two-body bound states, but are otherwise sufficiently repulsive to guarantee stability of the system, we show that in the low-density limit the ground state of this model consists of a Bose-Einstein condensate of fermion pairs. The latter can be described by means of the Gross-Pitaevskii energy functional.
Generalized Hartree-Fock-Bogoliubov approach in the description of many-body systems
The quantum mechanical equation for a group of states connected by large probabilities of transitions to each other, i.e. possessing common internal structure, is found. No phenomenological assumptions about the vibrational or rotational character of these states have been used. The equations obtained here can be understood as a direct generalization of the Hartree-Fock-Bogoliubov equation, this scheme including not only the ground state, but some excited states as well. The question of normalization of the density matrix in the generalized space has been solved and the additional solutions of the problem have been excluded. (author)
Hartree-Fock-Bogolubov approximation in the models with general four-fermion interaction
The foundation of this work was established by the lectures of Prof. N.N. Bogolubov (senior) written in the beginning of 1990. We should like to develop some of his ideas connected with Hartree-Fock-Bogolubov method and to show how this approximation works in connection with general equations for Green's functions with source terms for sufficiently general model Hamiltonian of four-fermion interaction type and how, for example, to get some results of superconductivity theory by means of this method. (author). 5 refs
Neutron stars with Hyperons in Dirac-Brueckner-Hartree-Fock approach
Katayama, Tetsuya; Saito, Koichi
2014-01-01
Using the Dirac-Brueckner-Hartree-Fock (DBHF) approach including the hyperon degrees of freedom, we investigate the properties of neutron-star matter. To handle the hyperons in matter, we first examine the importance of the space part of baryon self-energies at high densities, and secondly study the effect of negative-energy states of baryons, which can provide an unambiguous relationship between the in-medium reaction matrices for baryon-baryon scattering and the baryon self-energies. We sol...
Particle-Number Projected Hartree-Fock-Bogoliubov Study with Effective Shell Model Interactions
Maqbool, I; Ganai, P A; Ring, P
2010-01-01
We perform particle-number projected mean-field study using the recently developed symmetry-projected Hartree-Fock-Bogoliubov (HFB) equations. Realistic calculations have been performed in sd- and fp-shell nuclei using the shell model empirical intearctions, USD and GXPFIA. It is demonstrated that the mean-field results for energy surfaces, obtained with these shell model interactions, are quite similar to those obtained using the density functional approaches. Further, it is shown that particle-number projected results, for neutron rich isotopes, can lead to different ground-state shapes in comparison to the bare HFB calculations.
Basic and heavy ion scattering in time dependent Hartree-Fock Theory
Time Dependent Hartree-Fock theory, TDHF, is the most sophisticated, microscopic approach to nuclear dynamics yet practiced. Although it is far from a description of nature it does allow us to examine multiply interactive many-body systems semi quantum mechanically and to visualize otherwise covert processes. Some of the properties of the TDHF equations are stated leaving the interested reader to one of several excellent review articles for the derivations. Some of the applications to the collision of heavy ions are briefly described
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.
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, Cr 2, and NO 2
Veeraraghavan, Srikant
2014-01-01
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. A89, 010502R (2014)]. For strongly correlated systems the SDP approach provides an alternative to the locally optimized Hartree-Fock energies and d...
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. PMID:24697423
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}.
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 = 3He, 4He, Ne, Ar, Kr, and Xe) are calculated and compared with the best estimations from experimental measurements and an atom-bond potential model using the ab initio-assisted fine-tuning of semiempirical parameters. The bound-state energies determined differ by less than 6–7 meV (6%) from the atom-bond potential model. The crucial importance of including incremental 3-body dispersion-type terms is clearly demonstrated, showing that the SAPT(DFT) approach effectively account for these terms. With the deviations from the best experimental-based estimations smaller than 2.3 meV (1.9%), the accuracy of
de Lara-Castells, María Pilar; Bartolomei, Massimiliano; Mitrushchenkov, Alexander O; Stoll, Hermann
2015-11-21
The accuracy and transferability of the electronic structure approach combining dispersionless density functional theory (DFT) [K. Pernal et al., Phys. Rev. Lett. 103, 263201 (2009)] with the method of increments [H. Stoll, J. Chem. Phys. 97, 8449 (1992)], are validated for the interaction between the noble-gas Ne, Ar, Kr, and Xe atoms and coronene/graphene/graphite surfaces. This approach uses the method of increments for surface cluster models to extract intermonomer dispersion-like (2- and 3-body) correlation terms at coupled cluster singles and doubles and perturbative triples level, while periodic dispersionless density functionals calculations are performed to estimate the sum of Hartree-Fock and intramonomer correlation contributions. Dispersion energy contributions are also obtained using DFT-based symmetry-adapted perturbation theory [SAPT(DFT)]. An analysis of the structure of the X/surface (X = Ne, Ar, Kr, and Xe) interaction energies shows the excellent transferability properties of the leading intermonomer correlation contributions across the sequence of noble-gas atoms, which are also discussed using the Drude oscillator model. We further compare these results with van der Waals-(vdW)-corrected DFT-based approaches. As a test of accuracy, the energies of the low-lying nuclear bound states supported by the laterally averaged X/graphite potentials (X = (3)He, (4)He, Ne, Ar, Kr, and Xe) are calculated and compared with the best estimations from experimental measurements and an atom-bond potential model using the ab initio-assisted fine-tuning of semiempirical parameters. The bound-state energies determined differ by less than 6-7 meV (6%) from the atom-bond potential model. The crucial importance of including incremental 3-body dispersion-type terms is clearly demonstrated, showing that the SAPT(DFT) approach effectively account for these terms. With the deviations from the best experimental-based estimations smaller than 2.3 meV (1.9%), the accuracy of
Kühne, Thomas D
2012-01-01
Computer simulations and molecular dynamics in particular, is a very powerful method to provide detailed and essentially exact informations of classical many-body problems. With the advent of \\textit{ab-initio} molecular dynamics, where the forces are computed on-the-fly by accurate electronic structure calculations, the scope of either method has been greatly extended. This new approach, which unifies Newton's and Schr\\"odinger's equations, allows for complex simulations without relying on any adjustable parameter. This review is intended to outline the basic principles as well as a survey of the field. Beginning with the derivation of Born-Oppenheimer molecular dynamics, the Car-Parrinello method as well as novel hybrid scheme that unifies best of either approach are discussed. The predictive power is demonstrated by a series of applications ranging from insulators to semiconductors and even metals in condensed phases.
Self-coherent Hartree-Fock theory and the microscopic symmetries of the nucleus
A possible effects of the C4-symmetry in the superdeformed nuclei of the A ∼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 Q44, the results of the calculation indicate a very weak effect of this kind. Four new superdeformed bands in the 148Gd 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(2) moment very similar to that of the yrast band in 152Dy, 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 (Y30-'pear shapes'; Y31-'banana mode'; Y32-'Td-symmetry' and Y33-'C3-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)
Magnetic coupling constants from a hybrid density functional with 35% Hartree-Fock exchange
Feng, Xiaobing; Harrison, N. M.
2004-09-01
The magnetic coupling constants of KCuF3 , Sr2CuO2Cl2 , La2CuO4 , La2NiO4 , K2NiF4 , KNiF3 , NiF2 , KMnF3 , and MnF2 are calculated with a hybrid density functional, in which 35% of the nonlocal Hartree-Fock exchange is mixed in the general gradient approximation to the density functional theory. The theoretical magnetic coupling constants for these materials with different structures, spins, and magnetic orderings are in good agreement with experiment. Our results improve significantly over the so-called B3LYP hybrid density functional, which usually overestimates the magnetic coupling constants by about 50%. However, the energy gaps from the B3LYP functional are in better agreement with experiment than the hybrid functional with 35% Hartree-Fock exchange, which means that within the current scheme of hybrid density functionals different functionals are needed to better predict different properties of materials.
The spectroscopy of odd-A nuclei, in the 1p and 2s-1d shells, is studied in the framework of the projected Hartree-Fock method and by the generator coordinate method. The nuclear effective interactions of Cohen and Kurath, on the one hand, and of Kuo or Preedom-Wildenthal, on the other hand, are used. The binding energies, the nuclear spectra, the static moments and the electromagnetic transitions obtained by these two approaches are compared to the same quantities given by a complete diagonalization in the shell model basis. This study of light nuclei gives some possibilities to put in order the energy levels by coupled rotational bands. In the microscopic approach, thus we find all the elements of the unified model of Bohr and Mottelson. To give evidence of such a relation, the functions of the angle β, in the integrals of the projection method of Peierls and Yoccoz, for a Slater determinant, are developed in the vicinity of the bounds β = O and β = π. The microscopic coefficients are evaluated in the Hartree-Fock approximation, using the particle-hole formalism. Calculations are made for 20Ne and 21Ne and the resulting microscopic coefficients are compared with the corresponding terms of the unified model of Bohr and Mottelson
Comparative studies of the spectroscopy of CuCl2: DFT versus standard ab initio approaches.
Ramírez-Solís, A; Poteau, R; Vela, A; Daudey, J P
2005-04-22
The X2Pi g-2Sigma g+, X2Pi g-2Delta g, X2Pi g-2Sigma u+, X2Pi g-2Pi u transitions on CuCl2 have been studied using several exchange-correlation functionals from the various types of density functional theory (DFT) approaches like local density approximation (LDA), generalized gradient approximation (GGA), hybrid and meta-GGA. The results are compared with the experience and with those coming from the most sophisticated nondynamic and dynamic electronic correlation treatments using the same relativistic effective core potentials and especially developed basis sets to study the electronic structure of the five lowest states and the corresponding vertical and adiabatic transition energies. The calculated transition energies for three of the hybrid functionals (B3LYP, B97-2, and PBE0) are in very good agreement with the benchmark ab initio results and experimental figures. All of the other functionals largely overestimate the X2Pi g-2Sigma g+ and X2Pi g-2Delta g transition energies, many of them even placing the 2Delta g ligand field state above the charge transfer 2Pi u and 2Sigma u+ states. The relative weight of the Hartree-Fock exchange in the definition of the functional used appears to play a key role in the accurate description of the LambdaSSigma density defined by the orientation of the 3d hole (sigma, pi, or delta) on Cu in the field of both chlorine atoms, but no simple connection of this weight with the quality of the spectra has been found. Mulliken charges and spin densities are carefully analyzed; a possible link between the extent of spin density on the metal for the X2Pi g state and the performance of the various functionals was observed, suggesting that those that lead to the largest values (close to 0.65) are the ones that best reproduce these four transitions. Most functionals lead to a remarkably low ionicity for the three ligand field states even for the best performing functionals, compared to the complete active space (SCF) (21, 14) ab initio
Prediction of possible CaMnO3 modifications using an ab initio minimization data-mining approach.
Zagorac, Jelena; Zagorac, Dejan; Zarubica, Aleksandra; Schön, J Christian; Djuris, Katarina; Matovic, Branko
2014-10-01
We have performed a crystal structure prediction study of CaMnO3 focusing on structures generated by octahedral tilting according to group-subgroup relations from the ideal perovskite type (Pm\\overline 3 m), which is the aristotype of the experimentally known CaMnO3 compound in the Pnma space group. Furthermore, additional structure candidates have been obtained using data mining. For each of the structure candidates, a local optimization on the ab initio level using density-functional theory (LDA, hybrid B3LYP) and the Hartree--Fock (HF) method was performed, and we find that several of the modifications may be experimentally accessible. In the high-pressure regime, we identify a post-perovskite phase in the CaIrO3 type, not previously observed in CaMnO3. Similarly, calculations at effective negative pressure predict a phase transition from the orthorhombic perovskite to an ilmenite-type (FeTiO3) modification of CaMnO3. PMID:25274514
Motegi, Kyosuke; Nakajima, Takahito; Hirao, Kimihiko; Seijo, Luis
2001-04-01
A relativistic ab initio model potential (AIMP) for Pt, Au, and Hg atoms has been developed using a relativistic scheme by eliminating small components (RESC) in which the 5p, 5d, and 6s electrons are treated explicitly. The quality of new RESC-AIMP has been tested by calculating the spectroscopic properties of the hydrides of these elements using the Hartree-Fock and coupled cluster with singles and doubles (CCSD) methods. The agreement with reference all-electron RESC calculations is excellent. The RESC-AIMP method is applied successfully in the investigation of the spectroscopic constants of Au2 and Hg2 using the CCSD method with a perturbative estimate of the contributions of triples. The ground state of Pt2 is also determined by RESC-AIMP with the second-order complete active space perturbation method. The results show that scalar relativistic effects on the valence properties are well described by the RESC-AIMP method. The effect on the basis set superposition error on the spectroscopic constants is also examined.
The multiconfiguration Hartree-Fock method for continuum wave functions has been used to calculate the scattering length and phase shifts over extremely low energies ranging from 0 to 1 eV very accurately for electron-helium scattering. The scattering length is calculated very accurately with wave functions computed exactly at zero energy, resulting in an upper bound of 1.1784. The electron correlation and polarization of the target by the scattering electron, which are very important in these calculations, have been taken into account in an accurate ab initio manner through the configuration-interaction procedure by optimizing both bound and continuum orbitals simultaneously at each kinetic energy of the scattered electron. Detailed results for scattering length, differential, total, and momentum-transfer cross sections obtained from the phase shifts are presented. The present scattering length is found to be in excellent agreement with the experimental result of Andrick and Bitsch [J. Phys. B 8, 402 (1975)] and the theoretical result of O'Malley, Burke, and Berrington [J. Phys. B 12, 953 (1979)]. There is excellent agreement between the present total cross sections and the corresponding experimental measurements of Buckman and Lohmann [J. Phys. B 19, 2547 (1986)]. The present momentum-transfer cross sections also show remarkable agreement with the experimental results of Crompton, Elford, and Robertson [Aust. J. Phys. 23, 667 (1970)
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
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...
Optimal plane-wave Hartree-Fock states for many-fermion systems
The possibility of taking plane-wave orbitals of a Hartree-Fock determinant to fill k space differently from the ''normal'' Fermi sphere is investigated for several two-body potentials including the ''homework'' v0, v1, and v2 - aken from the Reid nucleon-nucleon force - as well as a sum-of-Gaussians potential chosen to fit the deuteron binding and size. A random-search and random-walk numerical algorithm shows that, provided the potential strengths are made large enough, a single-shell ''abnormal'' occupation is always found to be lower in energy than the normal one if sufficient attraction is present in the two-body interaction. No abnormal occupation is possible for, among other pair interactions, the electron or charged-boson fluid, the repulsive square barrier, and a common form of the He-He interaction
Hydrogen Dissociation in Generalized Hartree-Fock Theory: Breaking the diatomic bond
Jerke, Jonathan; Masood, Samina; Tymczak, Cj
Generalized Hartree Fock theory predicts molecular Hydrogen dissociation without correlation. A variational Gaussian-Sinc linear superposition is the basis of 50 calculations with 3-4 significant digits of quality. The spin singlet covalent bond spontaneously breaks into a pair of uncorrelated doublets at atomic separation of 1.22 Angstroms. Quantum spin numbers and energetic comparison with Configuration Interaction theory--correlation--point to a first order phase transition in the molecular Hydrogen bond without correlation. Welch Foundation (Grant J-1675), the ARO (Grant W911Nf-13-1-0162), the Texas Southern University High Performance Computing Center (http:/hpcc.tsu.edu/; Grant PHY-1126251) and NSF-CREST CRCN project (Grant HRD-1137732).
Haxton, Daniel J; McCurdy, C William
2011-01-01
The multiconfiguration time-dependent Hartree-Fock (MCTDHF) method is formulated for treating the coupled electronic and nuclear dynamics of diatomic molecules without the Born- Oppenheimer approximation. The method treats the full dimensionality of the electronic motion, uses no model interactions, and is in principle capable of an exact nonrelativistic description of diatomics in electromagnetic fields. An expansion of the wave function in terms of configurations of orbitals whose dependence on internuclear distance is only that provided by the underlying pro- late spheroidal coordinate system is demonstrated to provide the key simplifications of the working equations that allow their practical solution. Photoionization cross sections are also computed from the MCTDHF wave function in calculations using short pulses.
Self-consistent structure in a relativistic Dirac-Hartree-Fock approximation
Uechi, H
2001-01-01
A self-consistent approximation structure is derived for the Dirac-Hartree-Fock (DHF) approximation in the sigma-omega model of quantum hadrodynamics (QHD), by employing Landau's requirement for a quasiparticle energy in the self-consistent framework of the DHF approximation. The self-consistency condition for nuclear matter approximations, the Hugenholtz-Van Hove theorem, is applied to produce functional equations for self-energies, and solutions of the self-energies are obtained. The Hugenholtz-Van Hove theorem is satisfied exactly, and retardation effects in DHF approximation are self-consistently constructed to preserve the HV theorem. The present approximation is also discussed in terms of the theory of conserving approximations, which leads to the stationary condition of the variation of energy density with respect to self-energies. The present self-consistent calculations may support a theoretical approach to build a conserving structure in nonperturbative, self-consistent nuclear matter approximations...
Hartree-Fock calculation of the differential photoionization cross sections of small Li clusters
Cross sections and angular distribution parameters for the single-photon ionization of all electron orbitals of Li2−8 are systematically computed in a broad interval of the photoelectron kinetic energies for the energetically most stable geometry of each cluster. Calculations of the partial photoelectron continuum waves in clusters are carried out by the single center method within the Hartree-Fock approximation. We study photoionization cross sections per one electron and analyze in some details general trends in the photoionization of inner and outer shells with respect to the size and geometry of a cluster. The present differential cross sections computed for Li2 are in a good agreement with the available theoretical data, whereas those computed for Li3−8 clusters can be considered as theoretical predictions
Cranked-Hartree-Fock-Bogoliubov analysis at the valence maximum: Yrast behaviour of 66170Dy104
Cranked Hartree-Fock Bogoliubov calculations have been performed for the doubly-mid-shell, N=104, Z=66 nucleus 170Dy. Assuming the usual spherical magic shell gaps at nucleon numbers 50, 82 and 126, this represents the nucleus with the maximum number of valence nucleons below 208Pb and as such, might naively be thought to exhibit one of the largest low-lying collectivities in the entire Segre chart. The results of our calculations suggest a robust quadrupole deformation, with very little deviation from axial symmetry up to high spins. These results are compared with other recent calculations performed by us on this nucleus which suggest a favoured, K=6+ (neutron) 2-quasiparticle state which should have an extended decay lifetime (of the order of hours) into the ground state band. (author)
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...
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...
Canonical-basis time-dependent Hartree-Fock-Bogoliubov theory and linear-response calculations
Ebata, Shuichiro; Inakura, Tsunenori; Yoshida, Kenichi; Hashimoto, Yukio; Yabana, Kazuhiro
2010-01-01
We present simple equations for a canonical-basis formulation of the time-dependent Hartree-Fock-Bogoliubov (TDHFB) theory. The equations are obtained from the TDHFB theory with an approximation that the pair potential is assumed to be diagonal in the canonical basis. The canonical-basis formulation significantly reduces the computational cost. We apply the method to linear-response calculations for even-even light nuclei and demonstrate its capability and accuracy by comparing our results with recent calculations of the quasi-particle random-phase approximation with Skyrme functionals. We show systematic studies of E1 strength distributions for Ne and Mg isotopes. The evolution of the low-lying pygmy strength seems to be determined by the interplay of several factors, including the neutron excess, separation energy, neutron shell effects, deformation, and pairing.
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.
Bender, E; Faessler, A; Faessler, Amand
1995-01-01
A multi-configuration mixing approach built on essentially complex, symmetry-projected Hartree-Fock-Bogoliubov (HFB) mean fields is introduced. The mean fields are obtained by variation after projection. The configuration space consists out of the symmetry-projected HFB vacuum and the symmetry-projected two-quasiparticle excitations for even, and the symmetry-projected one-quasiparticle excitations for odd A systems. The underlying complex HFB transformations are assumed to be time-reversal invariant and axially symmetric. The model allows nuclear structure calculations in large model spaces with arbitrary two-body interactions. The approach has been applied to ^{20}Ne and ^{22}Ne. Good agreement with the exact shell model results and considerable improvement with respect to older calculations, in which only real HFB transformations were admitted, is obtained.
Properties of dense, asymmetric nuclear matter in Dirac-Brueckner-Hartree-Fock approach
Katayama, Tetsuya
2013-01-01
Within the Dirac-Brueckner-Hartree-Fock approach, using the Bonn potentials, we investigate the properties of dense, asymmetric nuclear matter and apply it to neutron stars. In the actual calculations of the nucleon self-energies and the energy density of matter, we study in detail the validity of an angle-averaged approximation and an averaging of the total momentum squared of interacting two-nucleons in nuclear matter. For practical use, we provide convenient parametrizations for the equation of state for symmetric nuclear matter and pure neutron matter. We also parametrize the nucleon self-energies in terms of polynomials of nucleon momenta. Those parametrizations can accurately reproduce the numerical results up to high densities.
The time dependent Hartree-Fock-theory for collective nuclear motions
The time-dependent Hartree-Fock theory (TDHF) approximately solves the Schroedinger equation by a variational method in the space of the time-dependent Slater determinants. As the TDHF wave function, similar to the exact solution has the property of being determined completely for all times by the nucleon-nucleon interaction and by assuming initial conditions. TDHF is expected to describe collective motion of nuclei with large amplitudes, too. The subject of this paper is to formulate the TDHF theory and its adiabatic limiting case (ATDHF) suited for setting up a collective Schroedinger equation, to investigate the relations with other theories, and to show the applicability for solving practical problems. (orig./WL)
Single-particle basis in an approximate treatment of the extended time-dependent Hartree-Fock theory
The single-particle basis that can be used in the extended time-dependent Hartree-Fock theory is studied in a simple one-dimensional collision model. It is shown that the conventional set of single-particle states, which are boosted initially with the velocity of the collision, can be used
Bieron, J; Jonsson, P; Bieron, Jacek; Indelicato, Paul; Jonsson, Per
2007-01-01
The multiconfiguration Dirac-Hartree-Fock (MCDHF) model has been employed to calculate the transition rates between the nine lowest levels of radium. The dominant rates were then used to evaluate the radiative lifetimes. The decay of the metastable $ 7s7p ^3 P_0 $ state through 2-photon E1M1 and hyperfine induced channels is also studied.
Bieron, Jacek; Indelicato, Paul; Jonsson, Per
2007-01-01
The multiconfiguration Dirac-Hartree-Fock (MCDHF) model has been employed to calculate the transition rates between the nine lowest levels of radium. The dominant rates were then used to evaluate the radiative lifetimes. The decay of the metastable $ 7s7p \\, ^3 \\! P _0 $ state through 2-photon E1M1 and hyperfine induced channels is also studied.
The multiconfiguration Dirac-Hartree-Fock theory has been employed to calculate the electric dipole moment of the 7s6d 3D2 state of radium induced by the nuclear Schiff moment. The results are dominated by valence and core-valence electron correlation effects. We show that the correlation effects can be evaluated in a converged series of multiconfiguration expansions.
Hartree-Fock ground-state energy of anyons with no Coulomb interaction in the zero effective field
Sitko, P.
1994-01-01
We find, in the Hartree-Fock approximation, the ground-state energy of anyons with no Coulomb interaction in the case when the external magnetic field precisely cancels the average statistical field. From the point of view of the fractional quantum Hall effect statistics transmutations to {\\it superfermions} at filling fractions $\
Hartree-Fock ground-state energy of anyons with no Coulomb interaction in the zero effective field
Sitko, Piotr
1994-05-01
We find, in the Hartree-Fock approximation, the ground-state energy of anyons with no Coulomb interaction in the case when the external magnetic field precisely cancels the average statistical field. From the point of view of the fractional quantum Hall effect it is shown that statistics transmutations to superfermions at filling fractions v = {1}/{2 p} are not energetically favourable.
Umar, A. S.; Oberacker, V. E.
2008-01-01
We present a fully microscopic study of the $^{16}$O+$^{208}$Pb fusion using the density-constrained time-dependent Hartree-Fock theory. The calculated fusion cross-sections are in good agreement with the experimental data for the entire energy range indicating that the incorporation of dynamical effects is crucial in describing heavy-ion fusion.
An effective scheme for selecting basis sets for ab initio calculations
无
2000-01-01
An effective scheme for selecting economical basis sets for ab initio calculations has been proposed for wide-range systems based on the analysis of different functions in the currently used basis sets. Accordingly, the selection of the basis sets should be made according to the different properties and real chemical surrounding of the atoms in the systems. For normal systems, the size and level of the basis sets used for the descriptions of the constituent atoms should be increased from left to right according to the position of the atom in the periodic table. Moreover, the more the atom is negatively charged, the more the basis functions and suitable polarization functions and diffuse functions should be utilized. Whereas, for the positively charged atoms, the size of basis set may be reduced. It is not necessary to use the polarization and diffuse functions for the covalently saturated atoms with normal valence states. However, for the system involving hydrogen-bonding, weak interactions, functional groups, metallic bonding with zero valence or low positive valence, and other sensitive interactions, the polarization and diffuse functions must be used. With this scheme, reliable calculation results may be obtained with suitable basis sets and smaller computational capability. By detailed analysis of a series of systems, it has been demonstrated that this scheme is very practical and effective. This scheme may be used in Hartree-Fock, M?ller-Plesset and density functional theoretical calculations. It is expected that the scheme would find important applications in the extensive calculations of large systems in chemistry, materials science, and life and biological sciences.
Ab initio calculation of Ti NMR shieldings for titanium oxides and halides
Tossell, J. A.
Titanium NMR shielding constants have been calculated using ab initio coupled Hartree-Fock perturbation theory and polarized double-zeta basis sets for TiF 4, TiF 62-, TiCI 4, Ti(OH) 4, Ti(OH 2) 64+, Ti(OH) 4O, and Ti(OH) 3O -. In all cases the calculations were performed at Hartree-Fuck energy-optimized geometries. For Ti(OH) 4 a S4-symmetry geometry with nonlinear ∠ TiOH was employed. Relative shieldings are in reasonable agreement with experiment for TiF 62-, TiCI 4, and Ti(OR) 4, where R = H or alkyl. Ti(OH 2) 64+ is predicted to be more highly shielded than Ti(OH) 4 by about 340 ppm. The five-coordinate complex Ti(OH) 4O, whose calculated structure matches well that measured by extended X-ray absorption fine structure in K 2O · TiO 2 · SiO 2 glass, is actually deshielded compared to Ti(OH) 4 by about 40 ppm. X-ray absorption-near-edge spectral energies have also been calculated for TiF 4, TiCI 4, Ti(OH) 4, and Ti(OH) 4O using an equivalent ionic core virtual-orbital method and the observed reduction in term energy for the five-coordinate species compared to Ti(OH) 4 has been reproduced. Replacement of the H atoms in Ti(OH) 4 by point charges has only a slight effect upon σTi, suggesting a possible means of incorporating second-neighbor effects in NMR calculations for condensed phases.
Ferrari, R. (Univ. di Trento (Italy). Dipt. di Fisica I.N.F.N., Trento (Italy). Gruppo Collegato)
1994-02-28
The formalism introduced in a previous paper is used for discussing the Coulomb interaction of many electrons moving in two space-dimensions in the presence of a strong magnetic field. The matrix element of the coulomb interaction is evaluated in the new basis, whose states are invariant under discrete translations. This paper is devoted to the case of low filling factor, thus the authors limit themselves to the lowest Landau level and to spins all oriented along the magnetic field. For the case of filling factor [nu][sub f] = 1/u they give an Ansatz on the state of many electrons which provides a good approximated solution of the Hartree-Fock equation. For general filling factor [nu][sub f] = u[prime]/u a trial state is given which converges very rapidly to a solution of the self-consistent equation. They generalize the Hartree-Fock equation by considering some correlation: all quantum states are allowed for the u[prime] electrons with the same translation quantum numbers. Numerical results are given for the mean energy and the energy bands, for some values of the filling factor ([nu][sub f] = 1/2, 1/3, 2/3, 1/4, 3/4, 1/5, 2/5, 3/5, 4/5). The results agree numerically with the Charge Density Wave approach. The boundary conditions are shown to be very important: only large systems (degeneracy of Landau level over 200) are not affected by the boundaries. Therefore results obtained on small scale systems are somewhat unreliable. The relevance of the results for the Fractional Quantum Hall Effect is briefly discussed.
The formalism introduced in a previous paper is used for discussing the Coulomb interaction of many electrons moving in two space-dimensions in the presence of a strong magnetic field. The matrix element of the coulomb interaction is evaluated in the new basis, whose states are invariant under discrete translations. This paper is devoted to the case of low filling factor, thus the authors limit themselves to the lowest Landau level and to spins all oriented along the magnetic field. For the case of filling factor νf = 1/u they give an Ansatz on the state of many electrons which provides a good approximated solution of the Hartree-Fock equation. For general filling factor νf = u'/u a trial state is given which converges very rapidly to a solution of the self-consistent equation. They generalize the Hartree-Fock equation by considering some correlation: all quantum states are allowed for the u' electrons with the same translation quantum numbers. Numerical results are given for the mean energy and the energy bands, for some values of the filling factor (νf = 1/2, 1/3, 2/3, 1/4, 3/4, 1/5, 2/5, 3/5, 4/5). The results agree numerically with the Charge Density Wave approach. The boundary conditions are shown to be very important: only large systems (degeneracy of Landau level over 200) are not affected by the boundaries. Therefore results obtained on small scale systems are somewhat unreliable. The relevance of the results for the Fractional Quantum Hall Effect is briefly discussed
The present thesis is divided into two parts. The first part describes the many kind of the formalisms of the Generator Coordinate Hartree-Fock method (GCHFM) and second part describes the computational aspect applied to the GCHFM formalism in its discreet form. The major aim of this work is the development of an alternative method to non-linear parameters optimization (basis set) and later uses these optimized parameters to adjust the weight function into GCHFM method. The study of the weight function when N → ∞ (or for large N), where N represents the number of mesh, is important since the GCHFM theory in its continuous form depend on understanding of such behavior. In this thesis, a detailed study is carried out about the methodologies of the self-consistent solution of the GCHFM and some methodology aspects of non-linear parameters optimization. This work shows that the Generator Coordinate Hartree-Fock method is general and it has as particular case the Hartree-Fock Roothaan method. Some possible variations or combinations around of the characteristics of the GCHFM and a comparison with conventional SCF procedure are reported in this thesis. The piecewise weight function method developed in this work shows to be very good for collective parameter optimizations of the Generator Coordinate (GC). The GCHFM calculations are necessary restrict (GCM-RHF), especially when the calculated value energies approach of its numerical values or Hartree-Fock limit. In the optimization methods of state functions for atomic electronic systems is very common the application of the gradient method and its efficacy is not contested. However, the method describes above allow us to obtain results as good as the gradient method. The basis set generated using the piecewise weight function method for Gaussian type function were used in the Restrict Hartree-Fock (RHF) calculations to obtain the total energies for some atomic electronic systems, such as neutron atoms and ions in
Niazazari, Naser; Zatikyan, Ashkhen L.; Markarian, Shiraz A.
2013-06-01
The hydrogen bonding of 1:1 complexes formed between L-ascorbic acid (LAA) and dimethylsulfoxide (DMSO) has been studied by means of ab initio and density functional theory (DFT) calculations. Solutions of L-ascorbic acid (AA) in dimethylsulfoxide (DMSO) have been studied by means of both FT-IR (4000-220 cm-1) and FT-Raman spectroscopy. Ab initio Hartree-Fock (HF) and DFT methods have been used to determine the structure and energies of stable conformers of various types of L-AA/DMSO complexes in gas phase and solution. The basis sets 6-31++G∗∗ and 6-311+G∗ were used to describe the structure, energy, charges and vibrational frequencies of interacting complexes in the gas phase. The optimized geometric parameters and interaction energies for various complexes at different theories have been estimated. Binding energies have been corrected for basis set superposition error (BSSE) and harmonic vibrational frequencies of the structures have been calculated to obtain the stable forms of the complexes. The self-consistent reaction field (SCRF) has been used to calculate the effect of DMSO as the solvent on the geometry, energy and charges of complexes. The solvent effect has been studied using the Onsager models. It is shown that the polarity of the solvent plays an important role on the structures and relative stabilities of different complexes. The results obtained show that there is a satisfactory correlation between experimental and theoretical predictions.
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
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
Ab initio valence calculations in chemistry
Cook, D B
1974-01-01
Ab Initio Valence Calculations in Chemistry describes the theory and practice of ab initio valence calculations in chemistry and applies the ideas to a specific example, linear BeH2. Topics covered include the Schrödinger equation and the orbital approximation to atomic orbitals; molecular orbital and valence bond methods; practical molecular wave functions; and molecular integrals. Open shell systems, molecular symmetry, and localized descriptions of electronic structure are also discussed. This book is comprised of 13 chapters and begins by introducing the reader to the use of the Schrödinge
Quantum treatment of protons with the reduced explicitly correlated Hartree-Fock approach
The nuclear-electronic orbital (NEO) approach treats select nuclei quantum mechanically on the same level as the electrons and includes nonadiabatic effects between the electrons and the quantum nuclei. The practical implementation of this approach is challenging due to the significance of electron-nucleus dynamical correlation. Herein, we present a general extension of the previously developed reduced NEO explicitly correlated Hartree-Fock (RXCHF) approach, in which only select electronic orbitals are explicitly correlated to each quantum nuclear orbital via Gaussian-type geminal functions. Approximations of the electronic exchange between the geminal-coupled electronic orbitals and the other electronic orbitals are also explored. This general approach enables computationally tractable yet accurate calculations on molecular systems with quantum protons. The RXCHF method is applied to the hydrogen cyanide (HCN) and FHF− systems, where the proton and all electrons are treated quantum mechanically. For the HCN system, only the two electronic orbitals associated with the CH covalent bond are geminal-coupled to the proton orbital. For the FHF− system, only the four electronic orbitals associated with the two FH covalent bonds are geminal-coupled to the proton orbital. For both systems, the RXCHF method produces qualitatively accurate nuclear densities, in contrast to mean field-based NEO approaches. The development and implementation of the RXCHF method provide the framework to perform calculations on systems such as proton-coupled electron transfer reactions, where electron-proton nonadiabatic effects are important
Neutron stars with Hyperons in Dirac-Brueckner-Hartree-Fock approach
Katayama, Tetsuya
2014-01-01
Using the Dirac-Brueckner-Hartree-Fock (DBHF) approach including the hyperon degrees of freedom, we investigate the properties of neutron-star matter. To handle the hyperons in matter, we first examine the importance of the space part of baryon self-energies at high densities, and secondly study the effect of negative-energy states of baryons, which can provide an unambiguous relationship between the in-medium reaction matrices for baryon-baryon scattering and the baryon self-energies. We solve the coupled, Bethe-Salpeter equations in the nuclear-matter rest frame by using the Bonn potentials. We assume that eight kinds of nonstrange and strange mesons ($\\sigma,\\,\\delta,\\,\\omega,\\,\\rho,\\,\\eta,\\,\\pi,\\,K,\\,K^{\\ast}$) take part in the interactions between two baryons. Then, we calculate the baryon self-energies, the energy density and pressure of matter. The present calculation provides a hard equation of state in neutron-star matter at high densities, which is generated by the effect of Pauli exclusion, the sho...
DBSR_HF: A B-spline Dirac-Hartree-Fock program
Zatsarinny, Oleg; Froese Fischer, Charlotte
2016-05-01
A B-spline version of a general Dirac-Hartree-Fock program is described. The usual differential equations are replaced by a set of generalized eigenvalue problems of the form (Ha -εa B) Pa = 0, where Ha and B are the Hamiltonian and overlap matrices, respectively, and Pa is the two-component relativistic orbit in the B-spline basis. A default universal grid allows for flexible adjustment to different nuclear models. When two orthogonal orbitals are both varied, the energy must also be stationary with respect to orthonormal transformations. At such a stationary point the off-diagonal Lagrange multipliers may be eliminated through projection operators. The self-consistent field procedure exhibits excellent convergence. Several atomic states can be considered simultaneously, including some configuration-interaction calculations. The program provides several options for the treatment of Breit interaction and QED corrections. The information about atoms up to Z = 104 is stored by the program. Along with a simple interface through command-line arguments, this information allows the user to run the program with minimal initial preparations.
$\\Delta$ (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...
Coordinate-Space Hartree-Fock-Bogoliubov Solvers for Super fluid Fermi Systems in Large Boxes
Pei, J. C.; Fann, G. I.; Harrison, R. J.; Nazarewicz, W.; Hill, J.; Galindo, D.; Jia, J.
2012-12-01
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.
Pairing gaps in Hartree-Fock Bogoliubov theory with the Gogny D1S interaction
Robledo, L M; Bertsch, G F
2012-01-01
As part of a program to study odd-A nuclei in the Hartree-Fock-Bogoliubov (HFB) theory, we have developed a new calculational tool to find the HFB minima of odd-A nuclei based on the gradient method and using interactions of Gogny's form. The HFB minimization includes both time-even and time-odd fields in the energy functional, avoiding the commonly used "filling approximation". Here we apply the method to calculate neutron pairing gaps in some representative isotope chains of spherical and deformed nuclei, namely the Z=8,50 and 82 spherical chains and the Z=62 and 92 deformed chains. We find that the gradient method is quite robust, permitting us to carry out systematic surveys involving many nuclei. We find that the time-odd field does not have large effect on the pairing gaps calculated with the Gogny D1S interaction. Typically, adding the T-odd field as a perturbation increases the pairing gap by ~100 keV, but the re-minimization brings the gap back down. This outcome is very similar to results reported f...
Basis set effects on the Hartree-Fock description of confined many-electron atoms
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) < TE(Bunge) < TE(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.
Haxton, Daniel J.; McCurdy, C. William
2015-01-01
The multiconfiguration time-dependent Hartree-Fock (MCTDHF) method has shown promise in calculating electronic dynamics in molecules driven by strong and high-energy lasers. It must incorporate restricted configuration spaces (meaning that a particular combination of Slater determinants is used, instead of full configuration interaction) to be applied to big systems. Two different Ansätze are used to determine the essential term in the equations. The first Ansatz is the Lagrangian variational principle. The explicit, complete MCTDHF equations of motion, satisfying that principle, for arbitrary configuration spaces, are given. The property that a restricted configuration list must satisfy in order for the Lagrangian and McLachlan variational principles to give different results is identified. The second Ansatz keeps the density matrix block diagonal among equivalent orbitals, in a generalization of the method of Worth [J. Chem. Phys. 112, 8322 (2000), 10.1063/1.481438]. The methods perform well in calculating the dynamics of Be and BC2 + subject to ultrafast, ultrastrong lasers in severely truncated Hilbert spaces, although they exhibit differing degrees of numerical stability as implemented.
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.)
Nuclear Tensor Force and Effective Pions in the Relativistic Hartree-Fock Formalism
Marcos S.
2014-03-01
Full Text Available In the framework of nonlinear nuclear models based on the relativistic Hartree-Fock approximation, we have isolated the contribution of the tensor force of pions in the effective NN interaction, by means of two different approximate methods, recently developed by us, in order to dilucidate its role in a variety of nuclear properties. Results show that a reduction of the contribution of this tensor force considerably influences the spin-orbit splittings and magic gaps in the spin-unsaturated midweight 56Ni nucleus as well as the behaviour of the total binding energies with A in heavy nuclei. Both methods give similar results. We also study the evolution of the splitting of the proton 1d spin-orbit doublet in the chain Z=14, from N=20 to N=28, and the neutron 2p − 1f shell in the chain N=28, from the 48Ca nucleus to the 42Si nucleus. Whereas, in the first case, the pion tensor force (PTF plays an important role and its reduction is needed to reproduce the corresponding experimental results; in the second case, the quenching of the neutron 2p3/2 − 1f7/2 gap in the mentioned isotonic chain N=28 is hardly affected by the PTF.
Miyatsu, Tsuyoshi; Saito, Koichi
2015-01-01
We construct the equation of state (EoS) for neutron stars explicitly including hyperons and quarks. Using the quark-meson coupling model with relativistic Hartree-Fock approximation, the EoS for hadronic matter is derived by taking into account the strange ($\\sigma^{\\ast}$ and $\\phi$) mesons as well as the light non-strange ($\\sigma$, $\\omega$, $\\vec{\\pi}$ and $\\vec{\\rho}$) mesons. Relevant coupling constants are determined to reproduce the experimental data of nuclear matter and hypernuclei in SU(3) flavor symmetry. For quark matter, we employ the MIT bag model with one-gluon-exchange interaction, and Gibbs criteria for chemical equilibrium in the phase transition from hadrons to quarks. We find that the strange vector ($\\phi$) meson and the Fock contribution make the hadronic EoS stiff, and that the maximum mass of a neutron star can be consistent with the observed mass of heavy neutron stars even if the coexistence of hadrons and quarks takes place in the core. However, in the present calculation the tran...
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...
Efficient method of evaluation for Gaussian Hartree-Fock exchange operator for Gau-PBE functional.
Song, Jong-Won; Hirao, Kimihiko
2015-07-14
We previously developed an efficient screened hybrid functional called Gaussian-Perdew-Burke-Ernzerhof (Gau-PBE) [Song et al., J. Chem. Phys. 135, 071103 (2011)] for large molecules and extended systems, which is characterized by the usage of a Gaussian function as a modified Coulomb potential for the Hartree-Fock (HF) exchange. We found that the adoption of a Gaussian HF exchange operator considerably decreases the calculation time cost of periodic systems while improving the reproducibility of the bandgaps of semiconductors. We present a distance-based screening scheme here that is tailored for the Gaussian HF exchange integral that utilizes multipole expansion for the Gaussian two-electron integrals. We found a new multipole screening scheme helps to save the time cost for the HF exchange integration by efficiently decreasing the number of integrals of, specifically, the near field region without incurring substantial changes in total energy. In our assessment on the periodic systems of seven semiconductors, the Gau-PBE hybrid functional with a new screening scheme has 1.56 times the time cost of a pure functional while the previous Gau-PBE was 1.84 times and HSE06 was 3.34 times. PMID:26178085
Coordinate-Space Hartree-Fock-Bogoliubov Solvers for Super fluid Fermi Systems in Large Boxes
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.
Efficient method of evaluation for Gaussian Hartree-Fock exchange operator for Gau-PBE functional
We previously developed an efficient screened hybrid functional called Gaussian-Perdew–Burke–Ernzerhof (Gau-PBE) [Song et al., J. Chem. Phys. 135, 071103 (2011)] for large molecules and extended systems, which is characterized by the usage of a Gaussian function as a modified Coulomb potential for the Hartree-Fock (HF) exchange. We found that the adoption of a Gaussian HF exchange operator considerably decreases the calculation time cost of periodic systems while improving the reproducibility of the bandgaps of semiconductors. We present a distance-based screening scheme here that is tailored for the Gaussian HF exchange integral that utilizes multipole expansion for the Gaussian two-electron integrals. We found a new multipole screening scheme helps to save the time cost for the HF exchange integration by efficiently decreasing the number of integrals of, specifically, the near field region without incurring substantial changes in total energy. In our assessment on the periodic systems of seven semiconductors, the Gau-PBE hybrid functional with a new screening scheme has 1.56 times the time cost of a pure functional while the previous Gau-PBE was 1.84 times and HSE06 was 3.34 times
Hartree-Fock and Density Functional Theory analysis of N-phenyl-1,2-naphthylamine
Şengül, Meryem Şenay; Cınaklı, Salih; Böyükata, Mustafa
2013-10-01
The energetic properties of N-phenyl-1,2-naphthylamine have been determined using a series of theoretical calculations and their geometries have been optimized using Hartree-Fock (HF) and Density Functional Theory (DFT). The structures have been examined to predict lower-lying energy structure of the title molecule within the considered potential conformations. Structural parameters and energetics, such as total energies with Zero-Point energy corrections, highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) energies, have been analyzed and compared between the structural isomers. 1-NPN is the most commonly used molecule for many purposes, mainly as the fluorescent probe in binding assays. When compared the two structures, we showed that 2-NPN isomers are energetically more stable than 1-NPN isomers. It is possible that 2-NPN may be favored in many applications with respect to 1-NPN, and thus its function may be understood in the light of its molecular and structural properties.
Coordinate-Space Hartree-Fock-Bogoliubov Solvers for Superfluid Fermi Systems in Large Boxes
Pei, J C; Harrison, R J; Nazarewicz, W; Hill, J; Galindo, D; Jia, J
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.
A simple version of the cranked Hartree Fock Bogoliubov (CHFB) scheme that has been applied in the present research work is viewed to understand the level systematics in several nuclei. However the transition rates, static quadrupole and magnetic moments are not feasible in this scheme as angular momentum is generated on average in CHFB approach. But the gyromagnetic ratio (g) that is the expectation value of the orbital and spin angular momentum vectors can be calculated within this scheme
We describe a method of solving the nuclear Skyrme-Hartree-Fock problem by using a deformed Cartesian harmonic oscillator basis. The complete list of expressions required to calculate local densities, total energy, and self-consistent fields is presented, and an implementation of the self-consistent symmetries is discussed. Formulas to calculate matrix elements in the Cartesian harmonic oscillator basis are derived for the nuclear and Coulomb interactions. (authors)
Hartree-Fock ground-state energy of anyons with no Coulomb interaction in the zero effective field
Sitko, P. (Inst. of Physics, Technical Univ. of Wroclaw (Poland))
1994-05-16
We find, in the Hartree-Fock approximation, the ground-state energy of anyons with no Coulomb interaction in the case when the external magnetic field precisely cancels the average statistical field. From the point of view of the fractional quantum Hall effect it is shown that statistics transmutations to superfermions at filling fractions [nu]=1/2p are not energetically favourable. (orig.)
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)
Hartree-Fock ground-state properties for the group 1 alkali metals and the group 11 noble metals
In order to use wavefunction-based correlation methods in solids it is necessary to have reliable Hartree-Fock results for the infinite system of interest. Therefore we performed Hartree-Fock calculations for the group 1 alkali metals (Li to Cs) and group 11 noble metals (Cu, Ag and Au). We optimized a basis set of valence-double-ζ quality for the periodic system. For the lighter atoms all-electron basis sets are applied, whereas for the heavier atoms small-core pseudopotentials with the corresponding basis sets were used to deal with the scalar-relativistic effects. We determine the cohesive energy, the lattice constant and the bulk modulus of the systems at the Hartree-Fock level. We use the counterpoise correction for the free atom to minimize the basis set superposition error occurring for finite basis sets. The effects due to the counterpoise correction not only for the cohesive energy but also for the lattice structure and bulk modulus are discussed in detail
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.
Full text: Interacting boson model has achieved a significant success in the phenomenological description of collective motion in medium and heavy nuclei at low excitation energies [1, 2]. However, there still remain some questions: why such a simple picture with s - and d - bosons works well, even in the deformed region, without the other higher bosons. On the other hand, the cranked Hartree-Fock-Bogoliubov (HFB) approximation gives a splendid rare-earth region from the microscopic point of view. The merits of the cranked HFB approximation are its ability to treat collective - and single - particle aspects of nuclear structure on the same footing, and to take into account in a consistent way shape and pairing changes as well as rotational alignment. The main aim of this paper is to explore the microscopic foundation of the Interacting Boson Model in the framework of the cranked HFB model, and to see the mechanism of backbending in terms of the boson picture. The numerical calculations are carried out for the structure of energy spectra and backbending phenomena of the isotope string of Er, Dy. Backbending of the moment of inertia of the yrast and β states can be reproduced reasonably. The gapless super-conductor effects, in which one of the quasiparticles starts to have negative energy, begins with the 10+ states. The calculated quadrupole moment does not change much as a function of the spin of state I, although there is a delicate change corresponding to backbending phenomena. (author) Reference: 1. Arima, F.Iachello, Ann. Phys., No111, 1978, p.201.; 2. K.Baktybayev, Iader. Phys., No42, 1978, p.1031.
In order to study the dynamics of a wide mass range of nuclides in addition to their ground state, the authors developed the canonical-basis expressed time-dependent Hartree-Fock-Bogoliubov theory (Cb-TDHFB) that can incorporate the pairing correlation with self-consistency. This paper directly derived Cb-TDHFB equation from the TDHFB equation of density matrix display, and introduced, as its application case, the linear response calculation and its systematic result, and the collision reaction calculation. In the example of linear response, it confirmed that the linear response due to real-time method and the random phase approximation that was calculated with self-consistency agreed to a large extent, by referring to the electric dipole excitation (E1) transition intensity distribution function of 24Mg. In addition, regarding the isoscalar quadrupole vibration mode of 34Mg with neutron-rich nuclei, the authors compared the result of quasi-particle random phase approximation as the small amplitude approximation of TDHFB and the result of the linear response of Cb-TDHFB, and obtained a very good match. As the example that Cb-TDHFB can be applied to heavily deformed nuclei, the authors examined the E1 excitation state of 172Yb. As the example of the study on systematic linear response, the authors also examined the low energy E1 excitation called pygmy resonance. As the example of application to non-linear phenomena, the authors also examined the results of the nuclear fusion reaction calculation of 52Ca + 22O due to TDHFB and Cb-TDHFB. (A.O.)
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)
Ab initio mass tensor molecular dynamics
Tsuchida, Eiji
2010-01-01
Mass tensor molecular dynamics was first introduced by Bennett [J. Comput. Phys. 19, 267 (1975)] for efficient sampling of phase space through the use of generalized atomic masses. Here, we show how to apply this method to ab initio molecular dynamics simulations with minimal computational overhead. Test calculations on liquid water show a threefold reduction in computational effort without making the fixed geometry approximation. We also present a simple recipe for estimating the optimal ato...
Discovering chemistry with an ab initio nanoreactor
Wang, Lee-Ping; Titov, Alexey; McGibbon, Robert; Liu, Fang; Pande, Vijay S.; Martínez, Todd J.
2014-01-01
Chemical understanding is driven by the experimental discovery of new compounds and reactivity, and is supported by theory and computation that provides detailed physical insight. While theoretical and computational studies have generally focused on specific processes or mechanistic hypotheses, recent methodological and computational advances harken the advent of their principal role in discovery. Here we report the development and application of the ab initio nanoreactor – a highly accelerat...
Thiessen, P. A.; Treder, H.-J.
Jedes initium wird durch experimenta crucis zum eventus. Jedes theoretisch interpretierbare ex-eventu-Resultat führt auf ein neues Initium. Gerade dies ist die gemeinsame Aussage von Atomistik, Quantenmechanik und Relativitätstheorie.Translated AbstractAb initio vel ex eventu. IIEvery initium becomes an eventus by experimenta crucis. Every theoretically interpretable ex-eventu result leads to a new initium. Right this is the joint assertion of atomism, quantum mechanics, and relativity.
Highly scalable Ab initio genomic motif identification
Marchand, Benoît
2011-01-01
We present results of scaling an ab initio motif family identification system, Dragon Motif Finder (DMF), to 65,536 processor cores of IBM Blue Gene/P. DMF seeks groups of mutually similar polynucleotide patterns within a set of genomic sequences and builds various motif families from them. Such information is of relevance to many problems in life sciences. Prior attempts to scale such ab initio motif-finding algorithms achieved limited success. We solve the scalability issues using a combination of mixed-mode MPI-OpenMP parallel programming, master-slave work assignment, multi-level workload distribution, multi-level MPI collectives, and serial optimizations. While the scalability of our algorithm was excellent (94% parallel efficiency on 65,536 cores relative to 256 cores on a modest-size problem), the final speedup with respect to the original serial code exceeded 250,000 when serial optimizations are included. This enabled us to carry out many large-scale ab initio motiffinding simulations in a few hours while the original serial code would have needed decades of execution time. Copyright 2011 ACM.
Suendo, Veinardi
2011-01-01
Chlorophyll a is one the most abundant pigment on Earth, which is responsible for trapping the light energy to perform the photosynthesis process in green plants. This molecule is a metal-complex compound that consists of a porphyrins ring with high symmetry that acts as ligands with magnesium as the central ion. Chlorophyll a has been studied for many years from different point of views for both experimental and theoretical interests. In this study, the restricted Hartree-Fock configuration interaction single (RHF/CIS), time-dependent density functional theory (TDDFT) and some semi-empirical methods (CNDO/s and ZINDO) calculations were carried out and compared to reconstruct the UV-Vis absorption spectra of chlorophyll a. In some extend, the calculation results based on a single molecule calculation were succeeded to reconstruct the absorption spectra but required to be scaling and broaden to match the experimental one. Different computational methods (ab initio and semi-empirical) exhibits the differences i...
New values of the indirect spin-spin coupling constants in CH4, SiH4 and GeH4, derived from experiment and ab initio calculations, are reported. The new experimental values of 1J(CH), 1J(SiH) and 1J(GeH) are obtained from gas-phase NMR spectra. The dependence of the measured one-bond coupling constants on the density is analysed and the results are extrapolated to zero-density point to eliminate the effects due to intermolecular forces. In the calculation of the coupling constants, at the nonrelativistic level coupled cluster singles and doubles (CCSD) perturbation theory is used and the basis set convergence of the results is discussed. The relativistic corrections are estimated from Dirac-Hartree-Fock (DHF) calculations. The final theoretical values are obtained adding available estimates of the vibrational and temperature corrections. The agreement of the calculated and experimental 1J(XH), X = C, Si, Ge, constants is very satisfying, the differences are approximately 1-3%
Veinardi Suendo
2012-07-01
Full Text Available Chlorophyll a is one the most abundant pigment on Earth that responsible for trapping the light energy to perform photosynthesis in green plants. This molecule has been studied for many years from different point of views in both experimental and theoretical interests. In this study, the restricted Hartree-Fock configuration interaction single (RHF/CIS, time-dependent density functional theory (TDDFT and several semi-empirical methods (CNDO/s and ZINDO calculations were carried out to reconstruct the UV-Vis absorption spectra of chlorophyll a. In some extend, the calculation results based on single molecule approach were succeeded to reconstruct the absorption spectra but required to be rescaled to fit the experimental one. In general, the semi-empirical methods provide better energy scaling factor that closer to unity. However, they lack of vertical transition fine features with respect to the spectrum obtained experimentally. Here, the ab initio calculations provide more complete features, especially the TDDFT at high level of basis sets that also has a good accuracy in the transition energies. The contribution of ground states and excited states orbitals in the main vertical transitions is discussed based on delocalization nature of the wavefunctions and the presence of solvent through polarizable continuum model (PCM.
Karakas, A.; Karakaya, M.; Ceylan, Y.; El Kouari, Y.; Taboukhat, S.; Boughaleb, Y.; Sofiani, Z.
2016-06-01
In this talk, after a short introduction on the methodologies used for computing dipole polarizability (α), second and third-order hyperpolarizability and susceptibility; the results of theoretical studies performed on density functional theory (DFT) and ab-initio quantum mechanical calculations of nonlinear optical (NLO) properties for a few selected organic compounds and polymers will be explained. The electric dipole moments (μ) and dispersion-free first hyperpolarizabilities (β) for a family of azo-azulenes and a styrylquinolinium dye have been determined by DFT at B3LYP level. To reveal the frequency-dependent NLO behavior, the dynamic α, second hyperpolarizabilities (γ), second (χ(2)) and third-order (χ(3)) susceptibilites have been evaluated using time-dependent HartreeFock (TDHF) procedure. To provide an insight into the third-order NLO phenomena of a series of pyrrolo-tetrathiafulvalene-based molecules and pushpull azobenzene polymers, two-photon absorption (TPA) characterizations have been also investigated by means of TDHF. All computed results of the examined compounds are compared with their previous experimental findings and the measured data for similar structures in the literature. The one-photon absorption (OPA) characterizations of the title molecules have been theoretically obtained by configuration interaction (CI) method. The highest occupied molecular orbitals (HOMO), the lowest unoccupied molecular orbitals (LUMO) and the HOMO-LUMO band gaps have been revealed by DFT at B3LYP level for azo-azulenes, styrylquinolinium dye, push-pull azobenzene polymers and by parametrization method 6 (PM6) for pyrrolo-tetrathiafulvalene-based molecules.
Four-faceted nanowires generated from densely-packed TiO2 rutile surfaces: Ab initio calculations
Evarestov, R. A.; Zhukovskii, Yu. F.
2013-02-01
Two-dimensional (2D) slabs and monoperiodic (1D) nanowires orthogonal to the slab surface of rutile-based TiO2 structure terminated by densely-packed surfaces and facets, respectively, have been simulated in the current study. The procedure of structural generation of nanowires (NWs) from titania slabs (2D → 1D) is described. We have simulated: (i) (110), (100), (101) and (001) slabs of different thicknesses as well as (ii) [001]- and [110]-oriented nanowires of different diameters terminated by either four types of related {110} facets or alternating {11¯0} and {001} facets, respectively. Nanowires have been described using both the Ti atom-centered rotation axes as well as the hollow site-centered axes passing through the interstitial sites between the Ti and O atoms closest to the axes. For simulations on TiO2 slabs and NWs, we have performed large-scale ab initio Density Functional Theory (DFT) and hybrid DFT-Hartree Fock (DFT-HF) calculations with the total geometry optimization within the Generalized Gradient Approximation (GGA) in the form of the Perdew-Becke-Ernzenhof exchange-correlation functionals (PBE and PBE0, respectively), using the formalism of linear combination of localized atomic functions (LCAO) implemented in CRYSTAL09 code. Both structural and electronic properties of enumerated rutile-based titania slabs and nanowires have been calculated. According to the results of our surface energy calculations, the most stable rutile-based titania slab is terminated by (110) surfaces whereas the energetically favorable [001]-oriented NWs are also terminated by {110} facets only, thus confirming results of previous studies.
Russ, Nicholas J.; Crawford, T. Daniel; Tschumper, Gregory S.
2004-04-01
We have examined the relative abilities of Hartree-Fock, density-functional theory (DFT), and coupled-cluster theory in describing second-order (pseudo) Jahn-Teller (SOJT) effects, perhaps the most commonly encountered form of symmetry breaking in polyatomic molecules. As test cases, we have considered two prototypical systems: the 2Σu+ states of D∞h BNB and C3+ for which interaction with a low-lying 2Σg+ excited state leads to symmetry breaking of the nuclear framework. We find that the Hartree-Fock and B3LYP methods correctly reproduce the pole structure of quadratic force constants expected from exact SOJT theory, but that both methods appear to underestimate the strength of the coupling between the electronic states. Although the Tamm-Dancoff (CIS) approximation gives excitation energies with no relationship to the SOJT interaction, the random-phase-approximation (RPA) approach to Hartree-Fock and time-dependent DFT excitation energies predicts state crossings coinciding nearly perfectly with the positions of the force constant poles. On the other hand, the RPA excited-state energies exhibit unphysical curvature near their crossings with the ground (reference) state, a problem arising directly from the mathematical structure of the RPA equations. Coupled-cluster methods appear to accurately predict the strength of the SOJT interactions between the 2Σu+ and 2Σg+ states, assuming that the inclusion of full triple excitations provides a suitable approximation to the exact wave function, and are the only methods examined here which predict symmetry breaking in BNB. However, coupled-cluster methods are plagued by artifactual force constant poles arising from the response of the underlying reference molecular orbitals to the geometric perturbation. Furthermore, the structure of the "true" SOJT force constant poles predicted by coupled-cluster methods, although correctly positioned, has the wrong structure.
Bierón, Jacek; Froese Fischer, Charlotte; 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 multiconfiguration Dirac-Hartree-Fock model has been employed to calculate the expectation values for the hyperfine splittings of the 5d96s22D3/2 and 5d96s22D5/2 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 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.
An exact treatment of the Coulomb interaction is performed within the Skyrme-Hartree-Fock/Bardeen-Cooper-Schrieffer approach for even-even nuclei ranging from light to superheavy nuclei. A test of the usual Slater approximation for the exchange part is carried out. The error made on the exchange term of the Coulomb interaction when using this approximation follows two schematic patterns. Beyond a decreasing behavior when increasing the mass number A, a more important structural effect has been found. The relative error ranges roughly from 0 to 8% being maximal for light closed proton (sub-)shell nuclei and minimal for open proton (sub-)shell nuclei.
Hartree-Fock approach to nuclear matter and finite nuclei with M3Y-type nucleon-nucleon interactions
Nakada, H
2003-01-01
By introducing a density-dependent contact term, M3Y-type interactions applicable to the Hartree-Fock calculations are developed. In order to view basic characters of the interactions, we carry out calculations on the uniform nuclear matter as well as on several doubly magic nuclei. It is shown that a parameter-set called M3Y-P2 describes various properties similarly well to the Skyrme SLy5 and/or the Gogny D1S interactions. A remarkable difference from the SLy5 and the D1S interactions is fo...
Yamagami, M; Yamagami, Masayuki; Matsuyanagi, Kenichi
2000-01-01
High-spin yrast structure of 32S is investigated by means of the cranked Skyrme-Hartree-Fock method in the three-dimensional Cartesian-mesh representation without imposing restrictions on spatial symmetries. The result suggests that 1) a crossover from the superdeformed to the hyperdeformed-like configurations takes place on the yrast line at angular momentum $I \\simeq 24$, which corresponds to the ``band termination'' point in the cranked harmonic-oscillator model, and 2) non-axial octupole deformations of the $Y_{31}$ type play an important role in the yrast states in the range $5\\leq I
Miyasita, Mitiyasu, E-mail: miyasita.mitiyasu@gmail.com [Graduate School of Science and Engineering, Shinshu University, Ueda 386-8567 (Japan); Higuchi, Katsuhiko [Graduate School of Advanced Science of Matter, Hiroshima University, Higashi-Hiroshima 739-8527 (Japan); Higuchi, Masahiko [Department of Physics, Faculty of Science, Shinshu University, Matsumoto 390-8621 (Japan)
2012-07-15
We present an alternative scheme for calculating the unrestricted Hartree-Fock (HF) equation. The scheme is based on the variational method utilizing the sophisticated basis functions that include no adjustable parameters. The validity of the present scheme is confirmed by actual calculations of the boron and neon atoms. The total energy of the present scheme is lower than that of the conventional restrictive HF equation, but higher than that of the CI method. Also, the resultant wave function satisfies the electron-nucleus cusp condition.
Gebremariam, B.; Bogner, S. K.; Duguet, T.
2009-01-01
We present the first of a two-part Mathematica notebook collection that implements a symbolic approach for the application of the density matrix expansion (DME) to the Hartree-Fock (HF) energy from a chiral effective field theory (EFT) three-nucleon interaction at N$^2$LO. The final output from the notebooks is a Skyrme-like energy density functional that provides a quasi-local approximation to the nonlocal HF energy. In this paper, we discuss the derivation of the HF energy and its simplific...
Heinemann, Dirk; Rosén, Arne; Fricke, Burkhard
1990-01-01
The finite element method (FEM) is now developed to solve two-dimensional Hartree-Fock (HF) equations for atoms and diatomic molecules. The method and its implementation is described and results are presented for the atoms Be, Ne and Ar as well as the diatomic molecules LiH, BH, N_2 and CO as examples. Total energies and eigenvalues calculated with the FEM on the HF-level are compared with results obtained with the numerical standard methods used for the solution of the one ...
Ab initio no core full configuration approach for light nuclei
Kim, Youngman; Shin, Ik Jae; Maris, Pieter; Vary, James P.; Forssén, Christian; Rotureau, Jimmy
2015-10-01
Comprehensive understanding of the structure and reactions of light nuclei poses theoretical and computational challenges. Still, a number of ab initio approaches have been developed to calculate the properties of atomic nuclei using fundamental interactions among nucleons. Among them, we work with the ab initio no core full configuration (NCFC) method and ab initio no core Gamow Shell Model (GSM). We first review these approaches and present some recent results.
Ruedenberg's well-known letter of 1951 contains two implications which still have been employed so far in numerical computations: (1) Whenever all types of attraction and repulsion integrals are subject to the Ruedenberg approximations in its simplest form partially known already from Mulliken, the attractive, the Coulomb, as well as the exchange part of the restricted Hartree-Fock-Roothaan equation can be led back to the calculation of corresponding diagonal elements, only. Using Ruedenberg's more elaborate concepts, which are invariant with respect to the rotation of local coordinate axes, the complete Fock-matrix representation can be constructed equivalently from only its own diagonal blocks, each belonging to one atom. Similar formulas are valid for the unrestricted Hartree-Fock theory of Pople and Nesbet. (2) If, however, one prefers to calculate all types of one- and two-center integrals exactly as suggested in Ruedenberg's headline, the original simplicity of both representations is lost. Instead, one is led to more complicated expressions, which arise from the fact that Ruedenberg's integral formulas, when applied to certain kinds of three-center repulsion integrals, imply considerable oversimplifications. In spite of this critical result, Ruedenberg's ideas offer an extension together with an interpretation of the semiempirical Wolfsberg and Helmholz recipe (better known from Hoffmann's extended Hueckel theory), on the one hand, and of the neglect of differential overlap schemes ZDO and NDDO, on the other, from a common point of view
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)
In this thesis in the framework of our model of the field-strength dependent coupling the properties of infinitely extended, homogeneous, static, spin- and isospin-saturated nuclear matter are studied. Thereby we use the Hartree-Mean-Field and the Hartree-Fock approximation, whereby the influence of the antiparticle states in the Fermi sea is neglected. In chapter 2 the Lagrangian density basing to our model is fixed. Starting from the Walecka model we modify in the Lagrangian density the Linear coupling of the scalar field to the scalar density as follows gSφanti ψψ→gSf(φ) anti ψψ. In chapter 3 we fix three different functions f(φ). For these three cases and for the Walecka model with f(φ)=φ nuclear-matter calculations are performed. In chapter 4 for the Hartree-Fock calculations, but also very especially regarding the molecular-dynamics calculations, the properties of the Dirac spinors in the plane-wave representation are intensively studied. (orig.)
Ab initio calculations of material strength
Šob, Mojmír; Friák, Martin; Vitek, V.
Tokyo : The Japan Society of Mechanical Engineers, 2003, s. 467-475. [International Symposium on Micro-Mechanical Engineering - Heat Transfer, Fluid Dynamics, Reliability and Mechanotronics.. Tsuchiura and Tsukuba (JP), 01.12.2003-03.12.2003] R&D Projects: GA AV ČR IAA1041302; GA ČR GA202/03/1351; GA MŠk OC 523.90 Institutional research plan: CEZ:AV0Z2041904 Keywords : ab initio calculations * electronic structure * theoretical tensile strength Subject RIV: BM - Solid Matter Physics ; Magnetism
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
Kopplung von Dichtefunktional- und ab-initio-Methoden
Goll, Erich
2008-01-01
Im Rahmen der Doktorarbeit wurde untersucht, inwieweit die Kopplung von Dichtefunktionalmethoden und ab-initio-Korrelationsmethoden der Quantenchemie eine Verbesserung bezüglich beider Grenzmethoden erbringt. Die Kopplung erfolgt durch eine Aufspaltung des interelektronischen Hamiltonoperators (abstoßende Coulombwechselwirkung). Die kurzreichweitige Wechselwirkung wird mit Dichtefunktionaltheorie behandelt, die langreichweitige mit Hilfe von ab-initio-Methoden. Diese Aufteilung soll dazu dien...
Several schemes to avoid the double counting of correlations in methods that merge multireference wavefunctions with density functional theory (DFT) are studied and here adapted to a combination of spin-projected Hartree-Fock (SUHF) and DFT. The advantages and limitations of the new method, denoted SUHF+fcDFT, are explored through calculations on benchmark sets in which the accounting of correlations is challenging for pure SUHF or DFT. It is shown that SUHF+fcDFT can greatly improve the description of certain molecular properties (e.g., singlet-triplet energy gaps) which are not improved by simple addition of DFT dynamical correlation to SUHF. However, SUHF+fcDFT is also shown to have difficulties dissociating certain types of bonds and describing highly charged ions with static correlation. Possible improvements to the current SUHF+fcDFT scheme are discussed in light of these results
Cui, Yao; Jimenez-Hoyos, Carlos A; Henderson, Thomas; Scuseria, Gustavo E
2013-01-01
We study the spectra of the molecular orbital Hessian (stability matrix) and random-phase approximation 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...
Garza, Alejandro J.; Jiménez-Hoyos, Carlos A. [Department of Chemistry, Rice University, Houston, Texas 77251-1892 (United States); Scuseria, Gustavo E. [Department of Chemistry and Department of Physics and Astronomy, Rice University, Houston, Texas 77251-1892, USA and Chemistry Department, Faculty of Science, King Abdulaziz University, Jeddah 21589 (Saudi Arabia)
2014-06-28
Several schemes to avoid the double counting of correlations in methods that merge multireference wavefunctions with density functional theory (DFT) are studied and here adapted to a combination of spin-projected Hartree-Fock (SUHF) and DFT. The advantages and limitations of the new method, denoted SUHF+f{sub c}DFT, are explored through calculations on benchmark sets in which the accounting of correlations is challenging for pure SUHF or DFT. It is shown that SUHF+f{sub c}DFT can greatly improve the description of certain molecular properties (e.g., singlet-triplet energy gaps) which are not improved by simple addition of DFT dynamical correlation to SUHF. However, SUHF+f{sub c}DFT is also shown to have difficulties dissociating certain types of bonds and describing highly charged ions with static correlation. Possible improvements to the current SUHF+f{sub c}DFT scheme are discussed in light of these results.
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.
Niembro, R., E-mail: niembror@unican.es; Marcos, S.; Lopez-Quelle, M. [Universidad de Cantabria (Spain); Savushkin, L. N. [St. Petersburg University for Telecommunications (Russian Federation)
2012-03-15
Relativistic nonlinear models based on the Hartree and Hartree-Fock approximations, including the {sigma}, {omega}, {pi}, and {rho} mesons, are worked out to explore the behavior of the nuclear charge radii and the binding energies of several isotopic chains. We find a correlation between the magnitude of the anomalous kink effect (KE) in the Pb isotopic family and the compressibility modulus (K) of nuclear matter. The KE appears to be sensitive, in particular, to the mechanisms which control the K value. The influence of the symmetry energy on the Ca isotopic chain is also studied. The behavior of the charge radii of single-particle states for some special cases and its repercussion on the nuclear charge radius is analyzed. The effect of pairing correlations on the models improves considerably the quality of the results in both binding energy and KE.
The ground state of the mid pf-shell nucleus 56Ni is described in the framework of a symmetry-projected complex mean-field theory in which the desired symmetry properties are exactly projected from the most general Hartree-Fock-Bogoliubov type determinants. This few determinant method is applied for the first time in a full 1p0f-shell model space. In the calculations the FPD6 effective interaction was used. It turns out that the use of only a few such generalized determinants is sufficient to give an excellent result. We compare the result with that of the quantum Monte Carlo approach, as well as with recently performed exact shell-model diagonalizations
Radziute, Laima; Jonsson, Per; Biero, Jacek
2013-01-01
The multiconfiguration Dirac-Hartree-Fock (MCDHF) method has been employed to calculate atomic electric dipole moments (EDM) of 225^Ra, 199^Hg, and 171^Yb. For the calculations of the matrix elements we extended the relativistic atomic structure package GRASP2K. The extension includes programs to evaluate matrix elements of (P, T)-odd e-N tensor-pseudotensor and pseudoscalar-scalar interactions, the atomic electric dipole interaction, the nuclear Schiff moment, and the interaction of the electron electric dipole moment with nuclear magnetic moments. The interelectronic interactions were accounted for through valence and core-valence electron correlation effects. The electron shell relaxation was included with separately optimised wave functions of opposite parities.
Xu, Ruirui; Zhang, Yue; Tian, Yuan; van Dalen, E N E; Müther, H
2016-01-01
The Microscopic Otical Model Potential is evaluated 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 reproduce the saturation properties of symmetric nuclear matter without any adjustable parameter. Its solution using the projection technique within the subtracted T-matrix (STM) representation provides a reliable extension to asymmetric nuclear matter, which is important to describe the features of the isospin asymmetric nuclei. Therefore, the present work aims to perform a global analysis of the isospin-dependent nucleon-nucleus MOP based on the DBHF calculation in symmetric and asymmetric nuclear matter. The DBHF is used to evaluate the relativistic structure of the nucleon self-energies in nuclear matter at various densities and asymmetries. The Schr\\"odi...
The finite element method (FEM) is now developed to solve two-dimensional Hartree-Fock (HF) equations for atoms and diatomic molecules. The method and its implementation is described and results are presented for the atoms Be, Ne and Ar as well as the diatomic molecules LiH, BH, N2 and CO as examples. Total energies and eigenvalues calculated with the FEM on the HF-level are compared with results obtained with the numerical standard methods used for the solution of the opne dimensional HF equations for atoms and for diatomic molecules with the traditional LCAO quantum chemical methods and the newly developed finite difference method on the HF-level. In general the accuracy increases from the LCAO - to the finite difference - to the finite element method. (orig.)
The thermal and the time-dependent versions of the Hartree-Fock-Bogoliubov approximation are used to describe the effects of the pairing interaction in a simple model. Similarities and differences between the two approaches are discussed. In the one-shell case analytic results are obtained which clearly show that as the degeneracy increases the exact energies tend to the limits provided by the approximate methods. A relation between the quasiparticle occupation probability and the seniority is established. In the two-shell case the time-dependent approach approximates all the families of exact states labeled by the shell seniority and gives information on the two different phase transitions present in the model. The finite-temperature method, instead, only approximates the exact energy for the lowest state of each family
The well-known 'augmented plane waves' method, for the calculation of electronic states in crystals, is first reviewed. A modification of this method in the case of insulators is then described, which treats exchange in the exact Hartree-Fock formulation, without use of the common free-electron approximation. The band structure of several rare gases (Ne, Ar) and ionic compounds (LiF, NaF, KF, LiCl, NaCl, KCl) has been calculated and discussed. The main point is the strong influence of correlation effects which must be taken into account before comparison between calculated and measured optical transitions. Such an improvement is obtained by including a local polarization potential in the one-electron Hamiltonian, leading to a good agreement of the theoretical transitions with the experimental ones. (author)
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.
Garza, Alejandro J; Jiménez-Hoyos, Carlos A; Scuseria, Gustavo E
2014-06-28
Several schemes to avoid the double counting of correlations in methods that merge multireference wavefunctions with density functional theory (DFT) are studied and here adapted to a combination of spin-projected Hartree-Fock (SUHF) and DFT. The advantages and limitations of the new method, denoted SUHF+fcDFT, are explored through calculations on benchmark sets in which the accounting of correlations is challenging for pure SUHF or DFT. It is shown that SUHF+fcDFT can greatly improve the description of certain molecular properties (e.g., singlet-triplet energy gaps) which are not improved by simple addition of DFT dynamical correlation to SUHF. However, SUHF+fcDFT is also shown to have difficulties dissociating certain types of bonds and describing highly charged ions with static correlation. Possible improvements to the current SUHF+fcDFT scheme are discussed in light of these results. PMID:24985613
Linker, G.J.; Broer, R.; Nieuwpoort, W.C.; Broer-Braam, H.B.
1996-01-01
We report spin-restricted and symmetry-restricted Hartree-Fock cluster calculations on the lower excited states of a Cu+ impurity in NaF in order to investigate their dependence on cluster size. In contrast to previous work on smaller clusters, we found all states arising from the configurations e(g
Combining linear polarization excitation and magnetic-field breaking of chiral symmetry of optical transitions in Group-III-V semiconductors, we use resonant degenerate four-wave mixing to observe effects beyond the time-dependent Hartree-Fock theory that are not seen by other techniques. (c) 2000 The American Physical Society
The Griffin-Hill-Wheeler-Hartree-Fock equations are applied to generate universal gaussian and Slater-type basis sets for the title atoms. The results for the energies compare competitively with atom-optimized calculations at a very low computational cost. (author)