On Kohn-Sham models with LDA and GGA exchange-correlation functionals

Arnaud Anantharaman; Eric Cancès

inria-00325660, version 1

On Kohn-Sham models with LDA and GGA exchange-correlation functionals

Arnaud Anantharaman () ^1, 2, Eric Cancès ^1, 2

(2008)

Abstract: This article is concerned with the mathematical analysis of the Kohn-Sham and extended Kohn-Sham models, in the local density approximation (LDA) and generalized gradient approximation (GGA) frameworks. After recalling the mathematical derivation of the Kohn-Sham and extended Kohn-Sham LDA and GGA models from the Schrödinger equation, we prove that the extended Kohn-Sham LDA model has a solution for neutral and positively charged systems. We then prove a similar result for the spin-unpolarized Kohn-Sham GGA model for two-electron systems, by means of a concentration-compactness argument.

1: Centre d'Enseignement et de Recherche en Mathématiques, Informatique et Calcul Scientifique (CERMICS)
INRIA – Ecole des Ponts ParisTech
2: MICMAC (INRIA Paris - Rocquencourt)
Ecole des Ponts ParisTech – INRIA

inria-00325660, version 1
http://hal.inria.fr/inria-00325660
oai:hal.inria.fr:inria-00325660
From: Arnaud Anantharaman <>
Submitted on: Monday, 29 September 2008 19:19:43
Updated on: Tuesday, 30 September 2008 11:06:12

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arXiv: 0809.5139

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