Testing and Using the Lewin-Lieb Bound in Density Functional Theory

TL;DR

This paper evaluates recent bounds on exchange-correlation energy in density functional theory across various systems, revealing they are generally less restrictive than existing bounds but imply new constraints for GGA functionals.

Contribution

It tests new theoretical bounds on exchange-correlation energy and explores their implications for the design of GGA functionals in DFT.

Findings

New bounds are usually less strict than Lieb-Oxford bound.

Satisfaction of bounds imposes restrictions on GGA enhancement factors.

Bounds are tested on atoms, gases, and Hooke's atom.

Abstract

Lewin and Lieb have recently proven several new bounds on the exchange-correlation energy that complement the Lieb-Oxford bound. We test these bounds for atoms, for slowly-varying gases, and for Hooke's atom, finding them usually less strict than the Lieb-Oxford bound. However, we also show that, if a generalized gradient approximation (GGA) is to guarantee satisfaction of the new bounds for all densities, new restrictions on the the exchange-correlation enhancement factor are implied.