Challenging the Lieb–Oxford bound in a systematic way. (17th April 2016)

• Record Type: Journal Article
• Authors: Seidl, Michael; Vuckovic, Stefan; Gori-Giorgi, Paola
• Is Part Of: Molecular physics. Volume 114:Number 7/8(2016)
• Page Start: 1076
• Page End: 1085
• Publication Date: 2016-04-17
• Subjects: Density functional theory -- Lieb–Oxford bound -- exchange-correlation functionals -- electronic correlation; Molecules -- Periodicals; Chemistry, Physical and theoretical -- Periodicals; Molécules -- Périodiques; Chimie physique et théorique -- Périodiques; 539.6.05
• DOI: 10.1080/00268976.2015.1136440
• Languages: English
• ISSNs: 0026-8976

Abstract

ABSTRACT: The Lieb–Oxford bound, a nontrivial inequality for the indirect part of the many-body Coulomb repulsion in an electronic system, plays an important role in the construction of approximations in density functional theory. Using the wave function for strictly correlated electrons of a given density, we turn the search over wave functions appearing in the original bound into a more manageable search over electron densities. This allows us to challenge the bound in a systematic way. We find that a maximising density for the bound, if it exists, must have compact support. We also find that, at least for particle numbers N ≤ 60, a uniform density profile is not the most challenging for the bound. With our construction, we improve the bound for N = 2 electrons that was originally found by Lieb and Oxford, we give a new lower bound to the constant appearing in the Lieb–Oxford inequality valid for any N, and we provide an improved upper bound for the low-density uniform electron gas indirect energy. GRAPHICAL ABSTRACT: