Improved Lieb-Oxford exchange-correlation inequality with a gradient correction

Mathieu Lewin, Elliott H. Lieb

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33 Scopus citations


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 et al. [Int. J. Quantum Chem. 112, 1579 (2012)IJQCB20020-760810.1002/qua.23148], 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.

Original languageEnglish (US)
Article number022507
JournalPhysical Review A - Atomic, Molecular, and Optical Physics
Issue number2
StatePublished - Feb 11 2015

All Science Journal Classification (ASJC) codes

  • Atomic and Molecular Physics, and Optics


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