Exchange functionals based on finite uniform electron gases

TL;DR

This paper introduces a new exchange functional based on finite uniform electron gases, extending LDA to incorporate the Fermi hole curvature, and demonstrates its integration with GGA and MGGA functionals for improved atomic and molecular calculations.

Contribution

The paper presents a novel generalized local-density approximation (GLDA) functional using only density and Fermi hole curvature, and introduces factorizable MGGAs (FMGGAs) by coupling with GGA functionals.

Findings

The new functional performs well for atoms and molecules.

It can be combined with GGA to form advanced meta-GGA functionals.

Comparisons show competitive accuracy with existing functionals.

Abstract

We show how one can construct \alert{a simple} exchange functional by extending the well-know local-density approximation (LDA) to finite uniform electron gases. This new generalized local-density approximation (GLDA) functional uses only two quantities: the electron density $\rho$ and the curvature of the Fermi hole $\alpha$. This alternative "rung 2" functional can be easily coupled with generalized-gradient approximation (GGA) functionals to form a new family of "rung 3" meta-GGA (MGGA) functionals that we have named factorizable MGGAs (FMGGAs). Comparisons are made with various LDA, GGA and MGGA functionals for atoms and molecules.