Parallel and Low-Order Scaling Implementation of Hartree–Fock Exchange Using Local Density Fitting

We consider N fermions in a two-dimensional harmonic oscillator potential interacting with a very short-range repulsive pair-wise potential. The ground-state energy of this system is obtained by performing a Thomas-Fermi as well as a self-consistent Hartree-Fock calculation. The two results are shown to agree even for a small number of particles. We next use the finite-temperature Thomas-Fermi method to demonstrate that in the local density approximation, these interacting fermions are equivalent to a system of noninteracting particles obeying the Haldane-Wu fractional exclusion statistics. It is also shown that mapping onto a system of N noninteracting quasiparticles enables us to predict the energies of the ground and excited states of the N-body system. PACS Nos.: 05.30-d, 73.20Dx

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A new mixing of Hartree–Fock and local density‐functional theories

The Journal of Chemical Physics ◽

10.1063/1.464304 ◽

1993 ◽

Vol 98 (2) ◽

pp. 1372-1377 ◽

Cited By ~ 9666

Author(s):

Axel D. Becke

Keyword(s):

Density Functional ◽

Local Density ◽

Hartree Fock ◽

Local Density Functional

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Quadrupole polarizabilities and Sternheimer antishielding factors in the density functional theory

Canadian Journal of Physics ◽

10.1139/p82-027 ◽

1982 ◽

Vol 60 (2) ◽

pp. 210-221 ◽

Cited By ~ 11

Author(s):

M. J. Stott ◽

E. Zaremba ◽

D. Zobin

Keyword(s):

Density Functional Theory ◽

Density Functional ◽

Correlation Energy ◽

Local Density ◽

Closed Shell ◽

Energy Functional ◽

Functional Theory ◽

Hartree Fock ◽

Shielding Factor ◽

The Density Functional Theory

The quadrupole polarizability and Sternheimer antishielding factor have been calculated for selected closed-shell atoms and ions using the density functional theory. In most cases, the results agree favourably with coupled Hartree–Fock calculations. However, for atoms with valence (d-shells the local density approximation used in the calculations is found to be inadequate. Our results suggest that refinements to the exchange-correlation energy functional are required in order to obtain accurate values for the polarizability and shielding factor of (d-shell atoms within a density functional approach.

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

10.20944/preprints201803.0056.v1 ◽

2018 ◽

Author(s):

Thomas Gomez ◽

Taisuke Nagayama ◽

Dave Kilcrease ◽

Stephanie Hansen ◽

Mike Montgomery ◽

...

Keyword(s):

Differential Equation ◽

Atomic Structure ◽

Shooting Method ◽

Local Density ◽

Line Broadening ◽

Matrix Methods ◽

Hartree Fock ◽

Spectral Line Broadening ◽

Atomic Structure Calculations ◽

Structure Calculations

Atomic structure of N-electron atoms is often determined using the Hartree-Fock method, which is an integro-differential equation. The exchange term of the Hartree-Fock equations is usually treated as an inhomogeneous term of a differential equation, or with a local density approximation. This work uses matrix methods to solve for the Hartree-Fock equations, rather than the more commonly-used shooting method to integrate an inhomogeneous differential equation. It is well known that a derivative operator can be expressed as a matrix made of finite-difference coefficients; energy eigenvalues and eigenvectors can be obtained by using computer linear-algebra packages. We extend the same technique to integro-differential equations, where a discretized integral can be written as a sum in matrix form. This method is compared against experiment and standard atomic structure calculations. We also can use this method for free-electron wavefunctions. This technique is important for spectral line broadening in two ways: improving the atomic structure calculations, and improving the motion of the plasma electrons that collide with the atom.

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Quantum mechanics II–many body systems

10.1093/oso/9780198708636.003.0023 ◽

2018 ◽

Author(s):

Joseph F. Boudreau ◽

Eric S. Swanson

Keyword(s):

Local Density Approximation ◽

Density Functional ◽

Local Density ◽

Slater Determinant ◽

Density Approximation ◽

Many Body ◽

Hartree Fock ◽

Separation Of Scales ◽

Many Body Systems ◽

Molecular Computations

Chapter 23 develops formalism relevant to atomic and molecular electronic structure. A review of the product Ansatz, the Slater determinant, and atomic configurations is followed by applications to small atoms. Then the self-consistent Hartree-Fock method is introduced and applied to larger atoms. Molecular structure is addressed by introducing an adiabatic separation of scales and the construction of molecular orbitals. The use of specialized bases for molecular computations is also discussed. Density functional theory and its application to complicated molecules is introduced and the local density approximation and the Kohn-Sham procedure for solving the functional equations are explained. Techniques for moving beyond the local density approximation are briefly reviewed.

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FISSION OF METAL CLUSTERS

International Journal of Modern Physics E ◽

10.1142/s0218301306003990 ◽

2006 ◽

Vol 15 (01) ◽

pp. 153-195 ◽

Cited By ~ 9

Author(s):

A. LYALIN ◽

O. I. OBOLENSKY ◽

A. V. SOLOV'YOV ◽

W. GREINER

Keyword(s):

Ab Initio ◽

Energy Surface ◽

Metal Clusters ◽

Local Density ◽

Correction Method ◽

Shell Correction ◽

Fission Process ◽

Hartree Fock ◽

Oscillator Shell ◽

Dynamics Simulations

Advances achieved during recent years in model and ab initio descriptions of fission of metal clusters are reviewed. We focus on developments in ab initio treatment of the electronic subsystem within the jellium background model, as well as on applications of potential energy surface analysis to determining the characteristics of the fission process. We reiterate the main results obtained with the implementation of the Hartree–Fock and local density schemes for the two-center deformed jellium model. We overview the influences of the geometrical and statistical factors on the parameters of the fission process revealed recently. Also, we overview concisely the classical liquid drop model, the shell correction method, the asymmetric two-center-oscillator shell model, and the main approaches to the molecular dynamics simulations of the fission process.

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SIZE AND DENSITY DEPENDENCES OF THE SCREENING EFFECT IN METAL CLUSTERS

Surface Review and Letters ◽

10.1142/s0218625x96000607 ◽

1996 ◽

Vol 03 (01) ◽

pp. 329-334 ◽

Cited By ~ 1

Author(s):

KOHJI SONODA ◽

FUYUKI SHIMOJO ◽

KOZO HOSHINO ◽

MITSUO WATABE

Keyword(s):

Charge Density ◽

Local Density ◽

Metal Cluster ◽

The Self ◽

Local Spin Density Approximation ◽

Density Approximation ◽

Screening Effect ◽

Hartree Fock ◽

Charge Distributions ◽

Induced Charge Density

We employ a jellium sphere as a model for a metal cluster and calculate the change in the electronic states when an extra positive point charge is introduced at its center, by solving the Kohn–Sham equation in the local-density approximation and in the local-spin-density approximation with the self-interaction correction, and by solving the Hartree–Fock equation. The screening charge density around the extra charge is estimated by subtracting the charge induced near the cluster surface from the total induced charge density. It is found that, even for small clusters with the number of atoms N=20, 40, and 58, the screening effect is similar to that in the bulk jellium and that the screening charge distributions for larger clusters with N=92 almost coincide with that in the bulk. The density dependence of the screening charge is also investigated by calculating the screening charge for rs=3.0, 4.0, and 5.0. It is shown that the period of oscillation of these screening charge distributions can almost be scaled by rs and it is close to that of the Friedel oscillation. The results obtained by three methods are compared with special attention to the effect of the self-interaction.

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