Asymptotic Behavior of the Exchange‐Correlation Energy Density and the Kohn‐Sham Potential in Density Functional Theory: Exact Results and Strategy for Approximations,Israel Journal of Chemistry

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Asymptotic Behavior of the Exchange‐Correlation Energy Density and the Kohn‐Sham Potential in Density Functional Theory: Exact Results and Strategy for Approximations
Israel Journal of Chemistry ( IF 2.3 ) Pub Date : 2020-01-21 , DOI: 10.1002/ijch.201900103
Eli Kraisler ₁

Affiliation

Density functional theory (DFT) is nowadays the leading theoretical framework for quantum description of materials from first principles. Being an exact theory on one hand and computationally efficient on the other hand, DFT allows to address large and complex many‐electron systems and accurately predict their properties. The predictive power of DFT critically depends though on an accurate approximation to the generally unknown exchange‐correlation (xc) energy functional. Approximations can be constructed from first principles by satisfying known properties of the exact functional. In this work I review two such exact properties: the asymptotic behavior of the xc energy density per particle and the asymptotic behavior of the Kohn‐Sham potential, in finite many‐electron systems. The derivation of the asymptotic forms for both quantities is reviewed, employing the concepts of the adiabatic connection and of the xc hole with relation to the first quantity and the exact electron factorization approach for the second one. Furthermore, it is shown that the correct asymptotic behavior of one of the aforementioned quantities does not guarantee a correct behavior of the other. These quantities are related via the xc hole response function, which is defined, examined and its exact exchange part is analytically derived. The extent to which existing xc approximations satisfy the named exact properties is reviewed and the relationship between correct asymptotics and freedom from one‐electron self‐interaction in DFT is discussed. Finally, a strategy for development of advanced approximations for exchange and correlation with a correct asymptotic behavior is suggested.

中文翻译：

密度泛函理论中交换相关能量密度和Kohn-Sham势的渐近行为：精确的结果和近似策略

如今，密度泛函理论（DFT）是从第一原理对材料进行量子描述的领先理论框架。DFT一方面是一种精确的理论，而另一方面却在计算上很有效，它可以解决大型复杂的多电子系统并准确预测其特性。DFT的预测能力主要取决于准确地近似于通常未知的交换相关（xc）能量函数。可以通过满足确切功能的已知属性，从第一原理构造近似值。在这项工作中，我回顾了两个这样的确切性质：在有限的多电子系统中，每个粒子的xc能量密度的渐近行为和Kohn-Sham势的渐近行为。回顾了两个量的渐近形式的推导，采用与第一个量有关的绝热连接和xc孔的概念，对第二个量采用精确的电子分解方法。此外，已经表明，上述量之一的正确渐近行为不能保证另一个量的正确渐近行为。这些数量通过定义，检查的xc空穴响应函数相关联，并通过分析得出其精确交换部分。审查了现有xc逼近满足命名精确性能的程度，并讨论了正确渐近性与DFT中不受单电子自相互作用影响的关系。最后，提出了一种开发具有近似渐近行为的交换和相关性高级逼近的策略。

更新日期：2020-01-21

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