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Mathematical Physics
Title: Improved Lieb-Oxford bound on the indirect and exchange energies
(Submitted on 23 Mar 2022 (v1), last revised 13 Sep 2022 (this version, v3))
Abstract: The Lieb-Oxford inequality provides a lower bound on the Coulomb energy of a classical system of $N$ 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.
Submission history
From: Mathieu Lewin [view email][v1] Wed, 23 Mar 2022 15:10:16 GMT (50kb,D)
[v2] Tue, 6 Sep 2022 15:04:04 GMT (54kb,D)
[v3] Tue, 13 Sep 2022 08:43:54 GMT (54kb,D)
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