轨道自由与Kohn-Sham模型的平面波离散化数值分析第一部分：Thomas-Fermi-von Weizsäcker模型
Numerical analysis of the planewave discretization of orbital-free and Kohn-Sham models Part I: The Thomas-Fermi-von Weizacker model
AI总结：
针对周期Thomas-Fermi-von Weizsäcker模型和Kohn-Sham模型在局域密度近似下的谱与伪谱Fourier（平面波）离散化，推导先验误差估计。
摘要：
我们为周期Thomas-Fermi-von Weizsäcker（TFW）模型和Kohn-Sham模型在局域密度近似（LDA）下的谱与伪谱Fourier（也称为平面波）离散化提供了先验误差估计。这些模型允许计算凝聚相分子系统的基态能量和密度的近似值。TFW模型关于电子密度是严格凸的，并且允许进行全面的分析（第一部分）。Kohn-Sham LDA模型则不然，其基态电子密度的唯一性无法保证。在二阶最优性条件的强制性假设下，我们在第二部分中证明，对于足够大的能量截断，离散化的Kohn-Sham LDA问题在任何Kohn-Sham基态附近都有一个极小化子，并且该极小化子在酉变换下是唯一的。然后，我们为谱离散化和伪谱离散化方法推导出最优的先验误差估计。
英文摘要：
We provide {\it a priori} error estimates for the spectral and pseudospectral Fourier (also called planewave) discretizations of the periodic Thomas-Fermi-von Weizsäcker (TFW) model and of the Kohn-Sham model, within the local density approximation (LDA). These models allow to compute approximations of the ground state energy and density of molecular systems in the condensed phase. The TFW model is stricly convex with respect to the electronic density, and allows for a comprehensive analysis (Part I). This is not the case for the Kohn-Sham LDA model, for which the uniqueness of the ground state electronic density is not guaranteed. Under a coercivity assumption on the second order optimality condition, we prove in Part II that for large enough energy cut-offs, the discretized Kohn-Sham LDA problem has a minimizer in the vicinity of any Kohn-Sham ground state, and that this minimizer is unique up to unitary transform. We then derive optimal {\it a priori} error estimates for both the spectral and the pseudospectral discretization methods.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
