Empirical analysis of the Lieb-Oxford bound in ions and molecules

TL;DR

This paper empirically investigates the Lieb-Oxford bound across various ions and molecules, demonstrating that it can be tightened, which may improve the accuracy of density functional approximations.

Contribution

It extends previous analyses by examining a broader set of systems, showing the Lieb-Oxford bound can be empirically tightened for ions and molecules.

Findings

The Lieb-Oxford bound can be empirically tightened for ions and molecules.

Tightening the bound has potential implications for exchange-correlation functional accuracy.

The analysis confirms previous observations made for atoms and electron liquids.

Abstract

Universal properties of the Coulomb interaction energy apply to all many-electron systems. Bounds on the exchange-correlation energy, inparticular, are important for the construction of improved density functionals. Here we investigate one such universal property -- the Lieb-Oxford lower bound -- for ionic and molecular systems. In recent work [J. Chem. Phys. 127, 054106 (2007)], we observed that for atoms and electron liquids this bound may be substantially tightened. Calculations for a few ions and molecules suggested the same tendency, but were not conclusive due to the small number of systems considered. Here we extend that analysis to many different families of ions and molecules, and find that for these, too, the bound can be empirically tightened by a similar margin as for atoms and electron liquids. Tightening the Lieb-Oxford bound will have consequences for the performance of various approximate exchange-correlation functionals.