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

2008/09/30 by Arnaud Anantharaman, Anantharaman, Arnaud, Éric Cancès +1
Physics and Astronomy · #Advanced Condensed Matter Physics #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Physics of Superconductivity and Magnetism #Quantum Physics (quant-ph) #Spectral Theory (math.SP) #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.0809.5139

openalex publication_date 2008/09/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Projector augmented-wave method
• Generalized Gradient Approximation Made Simple
• Accurate spin-dependent electron liquid correlation energies for local spin density calculations: a critical analysis
• Self-interaction correction to density-functional approximations for many-electron systems
• Soft self-consistent pseudopotentials in a generalized eigenvalue formalism

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