Existence of minimizers for Kohn-Sham models in quantum chemistry

被引：48

作者：

Anantharaman, Arnaud ^{[1
]}

Cances, Eric ^{[1
]}

机构：

[1] Univ Paris Est, CERMICS, Project Team Micmac, INRIA,Ecole Ponts, F-77455 Marne La Vallee 2, France

来源：

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE | 2009年 / 26卷 / 06期

关键词：

Electronic structure; Density functional theory; Kohn-Sham; Variational methods; Concentration-compactness; CONCENTRATION-COMPACTNESS PRINCIPLE; GENERALIZED GRADIENT APPROXIMATION; COULOMB-SYSTEMS; EXCHANGE-ENERGY; ELECTRON-GAS; DENSITY; ACCURATE; PSEUDOPOTENTIALS; FUNCTIONALS; EQUATIONS;

D O I：

10.1016/j.anihpc.2009.06.003

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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 Schrodinger 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. (C) 2009 Elsevier Masson SAS. All rights reserved.

引用

页码：2425 / 2455

页数：31

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