Gradient-dependent upper bound for the exchange-correlation energy and application to density functional theory

TL;DR

This paper introduces a new gradient-dependent bound for exchange-correlation energy in density functional theory, which is tighter for slowly-varying densities and improves functional performance.

Contribution

A novel gradient-dependent bound (sLL) for exchange-correlation energy is proposed, enhancing the construction of functionals with better accuracy.

Findings

sLL is equivalent to Lieb-Oxford bound in rapidly-varying densities

sLL is tighter for slowly-varying densities

Improved results in functional applications using sLL

Abstract

We propose a simple gradient-dependent bound for the exchange-correlation energy (sLL), based on the recent non-local bound derived by Lewin and Lieb. We show that sLL is equivalent to the original Lieb-Oxford bound in rapidly-varying density cases but it is tighter for slowly-varying density systems. To show the utility of the sLL bound we apply it to the construction of simple semilocal and non-local exchange and correlation functionals. In both cases improved results, with respect to the use of Lieb-Oxford bound, are obtained showing the power of the sLL bound.