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Improved Lieb-Oxford bound on the indirect and exchange energies

Lewin, Mathieu; Lieb, Elliott H.; Seiringer, Robert (2022), Improved Lieb-Oxford bound on the indirect and exchange energies, Letters in Mathematical Physics, 112, p. 31. 10.1007/s11005-022-01584-5

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Article accepté pour publication ou publié
Date
2022
Journal name
Letters in Mathematical Physics
Number
112
Publisher
Springer
Pages
31
Publication identifier
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Author(s)
Lewin, Mathieu cc
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Lieb, Elliott H.
Department of Physics, Princeton University [DPPU]
Seiringer, Robert
Institute of Science and Technology [Klosterneuburg, Austria] [IST Austria]
Abstract (EN)
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.
Subjects / Keywords
Lieb–Oxford inequality; Density functional theory; Indirect energy; Exchange energy