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The Local Density Approximation in Density Functional Theory

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1903.04046.pdf (392.4Kb)
Date
2019-03
Publisher city
Paris
Publisher
Cahier de recherche CEREMADE, Université Paris-Dauphine
Publishing date
03-2019
Collection title
Cahier de recherche CEREMADE, Université Paris-Dauphine
Link to item file
https://hal.archives-ouvertes.fr/hal-02143071
Dewey
Sciences connexes (physique, astrophysique)
Sujet
Local Density Approximation; Density Functional Theory
URI
https://basepub.dauphine.fr/handle/123456789/19372
Collections
  • CEREMADE : Publications
Metadata
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Author
Lewin, Mathieu
60 CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Lieb, Elliott H.
Seiringer, Robert
224226 Institute of Science and Technology Austria
Type
Document de travail / Working paper
Item number of pages
41
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.

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