Improved Lieb-Oxford bound on the indirect and exchange energies
Abstract
The Lieb-Oxford inequality provides a lower bound on the Coulomb energy of a classical system of identical charges only in terms of their one-particle density. We prove here a new estimate on the best constant in this inequality. Numerical evaluation provides the value 1.58, which is a significant improvement to the previously known value 1.64. The best constant has recently been shown to be larger than 1.44. In a second part, we prove that the constant can be reduced to 1.25 when the inequality is restricted to Hartree-Fock states. This is the first proof that the exchange term is always much lower than the full indirect Coulomb energy.
Keywords
Cite
@article{arxiv.2203.12473,
title = {Improved Lieb-Oxford bound on the indirect and exchange energies},
author = {Mathieu Lewin and Elliott H. Lieb and Robert Seiringer},
journal= {arXiv preprint arXiv:2203.12473},
year = {2024}
}
Comments
Final version to appear in Lett. Math. Phys. This article belongs to the themed collection: "Mathematical Physics and Numerical Simulation of Many-Particle Systems"; V. Bach and L. Delle Site (eds.)