A new estimate on the indirect Coulomb Energy

TL;DR

This paper introduces a new, tighter lower bound on the indirect Coulomb energy in quantum mechanics, improving upon classical bounds by incorporating an additive kinetic energy term related to the single particle density.

Contribution

It provides a novel lower bound on Coulomb energy that is more accurate and involves kinetic energy, offering an alternative to the Lieb--Oxford bound.

Findings

New lower bound with a smaller constant (1.45 vs 1.68)

Involves an additive kinetic energy term

Offers an improved estimate on Coulomb energy

Abstract

We prove a new lower bound on the indirect Coulomb energy in quantum mechanics in terms of the single particle density of the system. The new universal lower bound is an alternative to the classical Lieb--Oxford bound (with a smaller constant, 1.45 < 1.68) but involving an additive kinetic energy term of the single particle density.