Extended Hartree-Fock method based on pair density functional theory

TL;DR

This paper introduces an extended Hartree-Fock method utilizing pair density functional theory, which improves correlation energy calculations by avoiding divergence issues and aligning with the high-density limit of the homogeneous electron gas.

Contribution

It develops a practical pair density functional approach based on Hartree-Fock theory that accurately accounts for correlation energies without divergence problems.

Findings

Functional avoids divergence under homogeneous scaling

Accurate correlation energies for atomic systems

Based on high-density limit of electron gas

Abstract

A practical electronic structure method in which a two-body functional is the fundamental variable is constructed. The basic formalism of our method is equivalent to Hartree-Fock density matrix functional theory [M. Levy in {\it Density Matrices and Density Functionals}, Ed. R. Erdahl and V. H. Smith Jr., D. Reidel, (1987)]. The implementation of the method consists of solving Hartree-Fock equations and using the resulting orbitals to calculate two-body corrections to account for correlation. The correction terms are constructed so that the energy of the system in the absence of external potentials can be made to correspond to approximate expressions for the energy of the homogeneous electron gas. In this work the approximate expressions we use are based on the high-density limit of the homogeneous electron gas. Self-interaction is excluded from the two-body functional itself. It is shown that our pair density based functional does not suffer from the divergence present in many density functionals when homogeneous scaling is applied. Calculations based on our pair density functional lead to quantitative results for the correlation energies of atomic test cases.