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arXiv 2605.02492cond-mat.mtrl-scicond-mat.otherphysics.comp-ph
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基于势设计电荷密度的显式泛函

Designing explicit functionals for the charge density in terms of a potential

École Polytechnique, Institut Polytechnique de Paris(巴黎综合理工学院,巴黎理工学院);European Theoretical Spectroscopy Facility (ETSF)(欧洲理论光谱设施);Ruhr University Bochum(波鸿鲁尔大学);Synchrotron SOLEIL(SOLEIL同步辐射中心)

Muhammed H. Güneş, Ayoub Aouina, Vitaly Gorelov, Matteo Gatti, Lucia Reining

AI总结:

本研究以均匀电子气的Lindhard密度-密度响应函数为核心,设计无需求解Kohn-Sham方程的电荷密度显式泛函,经立方氦、硅、铝测试,结果随近似等级提升而改善,为获取易计算分析的可观测量泛函提供了有前景的路径。

摘要:

解决真实多体系统性质的最有效策略之一是整合模型数据,例如利用均匀电子气的数据构建Kohn-Sham交换关联势的局域密度近似。本研究探究可在多大程度上借助模型数据直接设计材料可观测量的泛函,具体以均匀电子气的Lindhard密度-密度响应函数为核心构建块,研究真实非均匀材料电荷密度的不同近似,将其表示为给定Kohn-Sham势的简单显式泛函。该近似集合的现实性逐步提升,包含与Thomas-Fermi近似等价的完全近程表达式、泛函泰勒展开,以及对[Aouina等人,npj Computational Materials {\bf 11}, 242 (2025)]提出的Connector Theory的不同近似。所有情形下,电荷密度的获取无需求解Kohn-Sham薛定谔方程。针对立方氦(典型强非均匀材料)、共价半导体硅和金属铝的结果,随近似等级提升而系统改善。现阶段,所得结果可用于定性讨论,或作为自洽Kohn-Sham循环的优化起点;更广泛而言,其质量表明这是获取可观测量泛函表达式的有前景途径,此类表达式计算与分析相对简便。

英文摘要:

One of the most powerful strategies to address properties of real many-body systems is to incorporate data obtained for models, for example, to use data of the homogeneous electron gas in order to build the Local Density Approximation for the Kohn-Sham exchange-correlation potential. In the present work, we examine to what extent we can use model data to design functionals directly for observables of materials. In particular, we study different approximations for the charge density of real inhomogeneous materials expressed as a simple, explicit functional of a given Kohn-Sham potential, using as central building block the Lindhard density-density response function of the homogeneous electron gas. Our increasingly realistic set of approximations includes a fully nearsighted expression equivalent to the Thomas-Fermi approximation, functional Taylor expansions, and different approximations to the Connector Theory developed in [Aouina \textit{et al.}, npj Computational Materials {\bf 11}, 242 (2025)]. In all cases, the charge density is obtained without ever solving the Kohn-Sham Schrödinger equation. Results for cubic helium, a prototypical strongly inhomogeneous material, as well as the covalent semiconductor silicon and metallic aluminum, systematically improve with higher levels of approximation. At the present stage, the results may be used for qualitative discussions or as optimized starting point for a self-consistent Kohn-Sham cycle. More generally, their quality indicates that this is a promising route to obtain functional expressions for observables that are relatively simple to calculate and to analyze.

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。

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