On the relation between the Hartree-Fock and Kohn-Sham approaches

TL;DR

This paper demonstrates that Hartree-Fock and Kohn-Sham methods are fundamentally incompatible for finite systems because their resulting densities are not mutually representable, clarifying the limitations of Kohn-Sham theory.

Contribution

It establishes that Hartree-Fock densities are not v-representable within Kohn-Sham theory, explaining why KS can overestimate ground state energies compared to HF.

Findings

HF densities are not v-representable in KS theory

KS theory can overestimate ground state energies

No contradictions in density functional theory are implied

Abstract

We show that the Hartree-Fock (HF) results cannot be reproduced within the framework of Kohn-Sham (KS) theory because the single-particle densities of finite systems obtained within the HF calculations are not $v$-representable, i.e., do not correspond to any ground state of a $N$ non-interacting electron systems in a local external potential. For this reason, the KS theory, which finds a minimum on a different subset of all densities, can overestimate the ground state energy, as compared to the HF result. The discrepancy between the two approaches provides no grounds to assume that either the KS theory or the density functional theory suffers from internal contradictions.