Improved Lieb-Oxford exchange-correlation inequality with gradient correction
Abstract
We prove a Lieb-Oxford-type inequality on the indirect part of the Coulomb energy of a general many-particle quantum state, with a lower constant than the original statement but involving an additional gradient correction. The result is similar to a recent inequality of Benguria, Bley and Loss, except that the correction term is purely local, which is more usual in density functional theory. In an appendix, we discuss the connection between the indirect energy and the classical Jellium energy for constant densities. We show that they differ by an explicit shift due to the long range of the Coulomb potential.
Keywords
Cite
@article{arxiv.1408.3358,
title = {Improved Lieb-Oxford exchange-correlation inequality with gradient correction},
author = {Mathieu Lewin and Elliott H. Lieb},
journal= {arXiv preprint arXiv:1408.3358},
year = {2015}
}
Comments
Final version to appear in Physical Review A. Compared to the very first version, this one contains an appendix discussing the link with the Jellium problem