Excited States of the Uniform Electron Gas

TL;DR

This paper introduces excited-state uniform electron gases (UEGs) with a gap at the Fermi surface, providing analytical expressions for their energies and a new framework for state-specific density functional approximations.

Contribution

It extends the UEG concept to excited states, deriving analytical energy expressions and proposing a novel approach for excited-state density functional theory.

Findings

Closed-form kinetic and exchange energy expressions for excited UEGs.

Derived the leading correlation energy term in high-density limit.

Introduced a new variable for excitation degree in UEGs.

Abstract

The uniform electron gas (UEG) is a cornerstone of density-functional theory (DFT) and the foundation of the local-density approximation (LDA), one of the most successful approximations in DFT. In this work, we extend the concept of UEG by introducing excited-state UEGs, systems characterized by a gap at the Fermi surface created by the excitation of electrons near the Fermi level. We report closed-form expressions of the reduced kinetic and exchange energies of these excited-state UEGs as functions of the density and the gap. Additionally, we derive the leading term of the correlation energy in the high-density limit. By incorporating an additional variable representing the degree of excitation into the UEG paradigm, the present work introduces a new framework for constructing local and semi-local state-specific functionals for excited states.