密度泛函理论的Kohn-Sham计算和二元视图

Paul E Lammert
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引用次数: 0

摘要

摘要通过对Kohn-Sham计算的抽象,即KS机,在密度泛函理论的数学方面发展了一个泛函分析的观点。机器的自然语义是二元的,由与地面密度配对的电位序列组成。虽然这里没有解决KS机器何时收敛到解决方案(潜在组件与指定目标匹配)的问题,但有许多相关的问题。例如:机器能找到解决方案吗?除非可能的特殊情况,在能量意义上是的,但使用电位混合方案而不是通常的密度混合品种。接近解的能量和功能空间距离概念是否相称?是的,在很大程度上。如果一系列地对的潜在分量收敛于目标密度,密度分量是否聚集在其地密度上?是的,除非粒子数漂移到无穷大。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Kohn-Sham computation and the bivariate view of density functional theory
Abstract Informed by an abstraction of Kohn-Sham computation called a KS machine, a functional analytic perspective is developed on mathematical aspects of density functional theory. A natural semantics for the machine is bivariate, consisting of a sequence of potentials paired with a ground density. Although the question of when the KS machine can converge to a solution (where the potential component matches a designated target) is not resolved here, a number of related ones are. For instance: Can the machine progress toward a solution? Barring presumably exceptional circumstances, yes in an energetic sense, but using a potential-mixing scheme rather than the usual density-mixing variety. Are energetic and function space distance notions of proximity-to-solution commensurate? Yes, to a significant degree. If the potential components of a sequence of ground pairs converges to a target density, do the density components cluster on ground densities thereof? Yes, barring particle number drifting to infinity.
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