Koopmans' theorem in statistical Hartree-Fock theory

TL;DR

This paper investigates the applicability of Koopmans' theorem within statistical Hartree-Fock theory at non-zero temperature, revealing its limitations in grand-canonical and canonical ensembles due to missing interaction contributions.

Contribution

It demonstrates that Koopmans' theorem does not generally hold in statistical Hartree-Fock theory, providing modified conditions under which a restricted version applies.

Findings

Koopmans' theorem fails in the grand-canonical ensemble due to missing interaction terms.

In the canonical ensemble, a restricted version of Koopmans' theorem can be derived.

The study clarifies the limitations of Koopmans' theorem in finite-temperature Hartree-Fock models.

Abstract

In this short paper, the validity of Koopmans' theorem in the Hartree-Fock theory at non-zero temperature (Hartree-Fock statistical theory) is investigated. It is shown that Koopmans' theorem does not apply in the grand-canonical ensemble, due to a missing contribution to the energy proportional to the interaction between two electrons belonging to the same orbital. Hartree-Fock statistical theory has also been applied in the canonical ensemble [Blenski et al., Phys. Rev. E 55, R4889 (1997)] for the purpose of photo-absorption calculations. In that case, the Hartree-Fock self-consistent-field equations are derived in the super-configuration approximation. It is shown that Koopmans' theorem does not hold in the canonical ensemble, but that a restricted version of the theorem can be obtained, by assuming that a particular quantity multiplying the interaction matrix element in the expression of the energy does not change during the removal of an electron.