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

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

2008-09-30

arxiv.org/abs/0809.5139v1

Physics

Quantum Physics

Scientific paper

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\"odinger 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.

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