On the violation of a local form of the Lieb-Oxford bound

TL;DR

This paper demonstrates that the local form of the Lieb-Oxford bound is frequently violated in density-functional theory calculations, highlighting limitations in current functional development and suggesting alternative approaches for more accurate exchange energy functionals.

Contribution

The study reveals violations of the local Lieb-Oxford bound in practical calculations, challenging its use in functional design and proposing new directions for constructing density functionals.

Findings

Local Lieb-Oxford bound is violated in many cases.

Violations occur across various electron densities and gradients.

Results indicate need for alternative functional construction methods.

Abstract

In the framework of density-functional theory, several popular density functionals for exchange and correlation have been constructed to satisfy a local form of the Lieb-Oxford bound. In its original global expression, the bound represents a rigorous lower limit for the indirect Coulomb interaction energy. Here we employ exact-exchange calculations for the G2 test set to show that the local form of the bound is violated in an extensive range of both the dimensionless gradient and the average electron density. Hence, the results demonstrate the severity in the usage of the local form of the bound in functional development. On the other hand, our results suggest alternative ways to construct accurate density functionals for the exchange energy.