Improved Lieb-Oxford exchange-correlation inequality with gradient correction

TL;DR

This paper establishes a refined Lieb-Oxford inequality incorporating a local gradient correction, improving the lower bound on Coulomb energy for quantum states, with implications for density functional theory.

Contribution

It introduces a Lieb-Oxford inequality with a local gradient correction, providing a tighter lower bound on Coulomb energy compared to previous results.

Findings

Lower constant in Lieb-Oxford inequality with gradient correction

Correction term is purely local, aligning with density functional theory

Explicit connection between indirect energy and classical Jellium energy

Abstract

We prove a Lieb-Oxford-type inequality on the indirect part of the Coulomb energy of a general many-particle quantum state, with a lower constant than the original statement but involving an additional gradient correction. The result is similar to a recent inequality of Benguria, Bley and Loss, except that the correction term is purely local, which is more usual in density functional theory. In an appendix, we discuss the connection between the indirect energy and the classical Jellium energy for constant densities. We show that they differ by an explicit shift due to the long range of the Coulomb potential.