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The Local Density Approximation in Density Functional Theory

Lewin, Mathieu; Lieb, Elliott H.; Seiringer, Robert (2019-03), The Local Density Approximation in Density Functional Theory. https://basepub.dauphine.fr/handle/123456789/19372

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Type
Document de travail / Working paper
External document link
https://hal.archives-ouvertes.fr/hal-02143071
Date
2019-03
Publisher
Cahier de recherche CEREMADE, Université Paris-Dauphine
Series title
Cahier de recherche CEREMADE, Université Paris-Dauphine
Published in
Paris
Pages
41
Metadata
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Author(s)
Lewin, Mathieu cc
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Lieb, Elliott H.

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
Local Density Approximation; Density Functional Theory