Improved Lieb-Oxford exchange-correlation inequality with gradient correction

Lewin, Mathieu; Lieb, Elliott H.

Lewin, Mathieu; Lieb, Elliott H. (2015), Improved Lieb-Oxford exchange-correlation inequality with gradient correction, Physical Review. A, Atomic, Molecular and Optical Physics, 91, p. n°022507. 10.1103/PhysRevA.91.022507

Type

Article accepté pour publication ou publié

External document link

https://arxiv.org/abs/1408.3358v5

Date

2015

Journal name

Physical Review. A, Atomic, Molecular and Optical Physics

Volume

Publisher

Published by the American Physical Society through the American Institute of Physics

Published in

Paris

Pages

n°022507

Abstract (EN)

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)], 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.

Subjects / Keywords

Lieb-Oxford-type inequality