Spectral approximation scheme for a hybrid, spin-density Kohn–Sham density-functional theory in an external (nonuniform) magnetic field and a collinear exchange-correlation energy

IF 1.7 3区化学 Q3 CHEMISTRY, MULTIDISCIPLINARY Journal of Mathematical Chemistry Pub Date : 2024-01-08 DOI:10.1007/s10910-023-01557-6

引用次数: 0

Abstract

We provide a mathematical justification of a spectral approximation scheme known as spectral binning for the Kohn–Sham spin density-functional theory in the presence of an external (nonuniform) magnetic field and a collinear exchange-correlation energy term. We use an extended density-only formulation for modeling the magnetic system. No current densities enter the description in this formulation, but the particle density is split into different spin components. By restricting the exchange-correlation energy functional to be of a collinear LSDA form, we prove a series of results which enable us to mathematically justify the spectral binning scheme using the method of Gamma-convergence, in conjunction with auxiliary steps involving recasting the electrostatic potentials, justifying the spectral approximation by making a spectral decomposition of the Hamiltonian and “linearizing" the latter Hamiltonian.

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外部（非均匀）磁场和共线交换相关能下的混合自旋密度 Kohn-Sham 密度泛函理论的谱近似方案

摘要我们为存在外部（非均匀）磁场和共线交换相关能量项的 Kohn-Sham 自旋密度函数理论提供了一种称为光谱分选的光谱近似方案的数学理由。我们使用扩展的纯密度公式来模拟磁性系统。在这个公式中，没有电流密度的描述，但粒子密度被分成不同的自旋成分。通过将交换相关能函数限制为共线 LSDA 形式，我们证明了一系列结果，这些结果使我们能够利用伽马收敛法，结合静电势重铸、通过对哈密尔顿进行谱分解和对后一个哈密尔顿进行 "线性化"等辅助步骤，从数学上证明谱分选方案的合理性。

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来源期刊

Journal of Mathematical Chemistry 化学-化学综合

CiteScore

3.70

自引率

17.60%

发文量

105

审稿时长

6 months

期刊介绍： The Journal of Mathematical Chemistry (JOMC) publishes original, chemically important mathematical results which use non-routine mathematical methodologies often unfamiliar to the usual audience of mainstream experimental and theoretical chemistry journals. Furthermore JOMC publishes papers on novel applications of more familiar mathematical techniques and analyses of chemical problems which indicate the need for new mathematical approaches. Mathematical chemistry is a truly interdisciplinary subject, a field of rapidly growing importance. As chemistry becomes more and more amenable to mathematically rigorous study, it is likely that chemistry will also become an alert and demanding consumer of new mathematical results. The level of complexity of chemical problems is often very high, and modeling molecular behaviour and chemical reactions does require new mathematical approaches. Chemistry is witnessing an important shift in emphasis: simplistic models are no longer satisfactory, and more detailed mathematical understanding of complex chemical properties and phenomena are required. From theoretical chemistry and quantum chemistry to applied fields such as molecular modeling, drug design, molecular engineering, and the development of supramolecular structures, mathematical chemistry is an important discipline providing both explanations and predictions. JOMC has an important role in advancing chemistry to an era of detailed understanding of molecules and reactions.