A correction for the Hartree-Fock Density of States for Jellium without Screening

TL;DR

This paper demonstrates that the Hartree-Fock approximation's failure to accurately predict the density of states in jellium is due to the nonlocal exchange operator, not the absence of screening, by using hyper-Hartree-Fock equations.

Contribution

The study shows that the divergence and zero in the density of states are artifacts of the nonlocal exchange operator, not screening deficiencies, shifting the problem away from the Fermi level.

Findings

Divergent derivative and zero in DOS are shifted away from the Fermi level.

The boundary of variationally optimized orbitals can be moved arbitrarily high.

Failure of HF is due to nonlocal exchange, not screening.

Abstract

We revisit the Hartree-Fock (HF) calculation for the uniform electron gas, or jellium model, whose predictions -- divergent derivative of the energy dispersion relation and vanishing density of states (DOS) at the Fermi level -- are in qualitative disagreement with experimental evidence for simple metals. Currently, this qualitative failure is attributed to the lack of screening in the HF equations. Employing Slater's hyper-Hartree-Fock (HHF) equations, derived variationally, to study the ground state and the excited states of jellium, we find that the divergent derivative of the energy dispersion relation and the zero in the DOS are still present, but shifted from the Fermi wavevector and energy of jellium to the boundary between the set of variationally optimised and unoptimised HHF orbitals. The location of this boundary is not fixed, but it can be chosen to lie at arbitrarily high values of wavevector and energy, well clear from the Fermi level of jellium. We conclude that, rather than the lack of screening in the HF equations, the well-known qualitative failure of the ground-state HF approximation is an artifact of its nonlocal exchange operator. Other similar artifacts of the HF nonlocal exchange operator, not associated with the lack of electronic correlation, are known in the literature.