具有LDA和GGA交换相关泛函的Kohn-Sham模型
On Kohn-Sham models with LDA and GGA exchange-correlation functionals
摘要：
本文在局部密度近似（LDA）和广义梯度近似（GGA）框架下对Kohn-Sham模型和扩展Kohn-Sham模型进行了数学分析。在回顾了Kohn-Sham和扩展的Kohn-Sham LDA和GGA模型从薛定谔方程的数学推导之后，我们证明了扩展的Kohn-Sham LDA模型对中性和正电荷系统都有解.然后，我们证明了一个类似的结果，自旋非极化的Kohn-Sham GGA模型的两电子系统，通过一个集中的紧凑性参数。
英文摘要：
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 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.
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