The Local Density Approximation in Density Functional Theory
Lewin, Mathieu; Lieb, Elliott H.; Seiringer, Robert (2020), The Local Density Approximation in Density Functional Theory, Pure and Applied Analysis, 2, 1, p. 35-73. 10.2140/paa.2020.2.35
TypeArticle accepté pour publication ou publié
Journal namePure and Applied Analysis
Mathematical Sciences Publishers
MetadataShow full item record
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Lieb, Elliott H.
Departments of Physics and Mathematics
Abstract (EN)We give the first mathematically rigorous justification of the local density approximation in density functional theory. We provide a quantitative estimate on the difference between the grand-canonical Levy–Lieb energy of a given density (the lowest possible energy of all quantum states having this density) and the integral over the uniform electron gas energy of this density. The error involves gradient terms and justifies the use of the local density approximation in the situation where the density is very flat on sufficiently large regions in space.
Subjects / KeywordsSchrödinger operators; statistical mechanics; density functional theory; uniform electron gas
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