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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

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Type
Article accepté pour publication ou publié
Date
2020
Journal name
Pure and Applied Analysis
Volume
2
Number
1
Publisher
Mathematical Sciences Publishers
Pages
35-73
Publication identifier
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Author(s)
Lewin, Mathieu cc
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Lieb, Elliott H.
Departments of Physics and Mathematics
Seiringer, Robert
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 / Keywords
Schrödinger operators; statistical mechanics; density functional theory; uniform electron gas