Existence of minimizers for Kohn-Sham models in quantum chemistry

Arnaud Anantharaman; Eric Cancès

doi:10.1016/j.anihpc.2009.06.003

Existence of minimizers for Kohn-Sham models in quantum chemistry

Arnaud Anantharaman
, Eric Cancès

École des ponts

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	2425-2455
Number of pages	31
Journal	Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire
Volume	26
Issue number	6
DOIs	https://doi.org/10.1016/j.anihpc.2009.06.003
Publication status	Published - 1 Jan 2009

Keywords

Concentration-compactness
Density functional theory
Electronic structure
Kohn-Sham
Variational methods

Access to Document

10.1016/j.anihpc.2009.06.003

Cite this

@article{6640a13952dc454fae9b651cf933f453,

title = "Existence of minimizers for Kohn-Sham models in quantum chemistry",

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 Schr{\"o}dinger 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.",

keywords = "Concentration-compactness, Density functional theory, Electronic structure, Kohn-Sham, Variational methods",

author = "Arnaud Anantharaman and Eric Canc{\`e}s",

year = "2009",

month = jan,

day = "1",

doi = "10.1016/j.anihpc.2009.06.003",

language = "English",

volume = "26",

pages = "2425--2455",

journal = "Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire",

issn = "0294-1449",

number = "6",

}

TY - JOUR

T1 - Existence of minimizers for Kohn-Sham models in quantum chemistry

AU - Anantharaman, Arnaud

AU - Cancès, Eric

PY - 2009/1/1

Y1 - 2009/1/1

N2 - 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.

AB - 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.

KW - Concentration-compactness

KW - Density functional theory

KW - Electronic structure

KW - Kohn-Sham

KW - Variational methods

UR - https://www.scopus.com/pages/publications/71849118382

U2 - 10.1016/j.anihpc.2009.06.003

DO - 10.1016/j.anihpc.2009.06.003

M3 - Article

AN - SCOPUS:71849118382

SN - 0294-1449

VL - 26

SP - 2425

EP - 2455

JO - Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire

JF - Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire

IS - 6

ER -

Existence of minimizers for Kohn-Sham models in quantum chemistry

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this