Transient Uniform Electron Gases

TL;DR

This paper introduces the concept of transient uniform electron gases (TUEGs), a new class of systems where electron density is temporarily homogeneous, expanding the understanding of uniform electron gases beyond traditional models.

Contribution

It proposes the classification of certain excited states on spherical electron systems as TUEGs, highlighting their transient homogeneity and providing concrete examples with two-electron systems.

Findings

Some excited states on spherical electron systems exhibit transient uniform electron gas behavior.

These TUEGs occur at specific sphere radii with homogeneous electron density.

The study provides explicit examples with two-electron systems.

Abstract

The uniform electron gas (UEG), a hypothetical system with finite homogenous electron density composed by an infinite number of electrons in a box of infinite volume, is the practical pillar of density-functional theory (DFT) and the foundation of the most acclaimed approximation of DFT, the local-density approximation (LDA). In the last thirty years, the knowledge of analytical parametrizations of the infinite UEG (IUEG) exchange-correlation energy has allowed researchers to perform a countless number of approximate electronic structure calculations for atoms, molecules, and solids. Recently, it has been shown that the traditional concept of the IUEG is not the unique example of UEGs, and systems, in their lowest-energy state, consisting of electrons that are confined to the surface of a sphere provide a new family of UEGs with more customizable properties. Here, we show that, some of the excited states associated with these systems can be classified as transient UEGs (TUEGs) as their electron density is only homogenous for very specific values of the radius of the sphere even though the electronic wave function is not rotationally invariant. Concrete examples are provided in the case of two-electron systems.