Uniform electron gases

TL;DR

This paper challenges the traditional uniform electron gas model by introducing a two-parameter characterization, including a new two-electron parameter, and proposes a strategy for a more comprehensive density functional.

Contribution

It introduces a two-parameter model for the uniform electron gas, extending beyond the traditional density-only description, and outlines a method to develop corresponding density functionals.

Findings

Traditional UEG concept is inadequate for finite systems.

A new two-electron parameter is necessary to characterize UEGs.

A systematic approach to determine $E( ho, ext{eta})$ is proposed.

Abstract

We show that the traditional concept of the uniform electron gas (UEG) --- a homogeneous system of finite density, consisting of an infinite number of electrons in an infinite volume --- is inadequate to model the UEGs that arise in finite systems. We argue that, in general, a UEG is characterized by at least two parameters, \textit{viz.} the usual one-electron density parameter $\rho$ and a new two-electron parameter $\eta$. We outline a systematic strategy to determine a new density functional $E(\rho,\eta)$ across the spectrum of possible $\rho$ and $\eta$ values.