Introductory lecture: when the density of the noninteracting reference system is not the density of the physical system in density functional theory.
Introductory lecture: when the density of the noninteracting reference system is not the density of the physical system in density functional theory.
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入门讲座：当非相互作用参考系统的密度不是密度功能理论中物理系统的密度时。
DOI：
10.1039/d0fd00102c
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发表时间：
2020-12-04
影响因子：
3.4
通讯作者：
Yang W
中科院分区：
文献类型：
--
作者：
Jin Y;Su NQ;Chen Z;Yang W
密度泛函理论(DFT)的一个主要挑战是发展密度泛函近似(DFA)来克服现有DFA中的错误，从而产生更复杂的泛函。对于这样的泛函，我们考虑了非相互作用的参照系的作用。具有局域电势的Kohn-Sham(KS)基准的电子密度传统上被定义为等于物理系统的电子密度。这一核心思想在两个方面得到了应用：从给定的密度反算参考的局域KS势，以及基于给定的DFA直接计算密度和能量。通过构造，逆计算可以产生具有等于物理系统的输入密度的密度的KS参考。然而，在DFT的应用中，由DFA直接计算密度和能量起着核心作用。对于直接计算，我们发现，当DFA依赖于外势时，由优化有效势(OEP)定义的KS参考的自洽密度不是物理系统的密度。当DFA依赖于外势时，这个不等式也适用于广义KS(GKS)或广义OEP参考的密度，它允许非局部势。相反，与给定的DFA一致的物理系统的密度是由总能量相对于外势变化的线性响应给出的。这是DFT在使用非相互作用参考方面的范式转变：非相互作用的KS或GKS参考代表了能量最小化的显式计算变量，而不是外部势相关DFA的物理系统密度。我们推导了一般DFA通过线性响应定义的电子密度的表达式，证明了轨道泛函和多体微扰理论在二阶和随机相近似下的结果，并探讨了它与密度泛函发展的关系。
A major challenge in density functional theory (DFT) is the development of density functional approximations (DFAs) to overcome errors in existing DFA, leading to more complex functionals. For such functionals, we consider roles of the noninteracting reference systems. The electron density of the Kohn-Sham (KS) reference with a local potential has been traditionally defined as being equal to the electron density of the physical system. This key idea has been applied in two ways: the inverse calculation of such a local KS potential for the reference from a given density and the direct calculation of density and energy based on given DFAs. By construction, the inverse calculation can yield a KS reference with the density equal to the input density of the physical system. In application of DFT, however, it is the direct calculation of density and energy from a DFA that plays a central role. For direct calculations, we find that the self-consistent density of the KS reference defined by the optimized effective potential (OEP), is not the density of the physical system, when the DFA is dependent on the external potential. This inequality holds also for the density of generalized KS (GKS) or generalized OEP reference, which allows a nonlocal potential, when the DFA is dependent on the external potential. Instead, the density of the physical system, consistent with a given DFA, is given by the linear response of the total energy with respect to the variation of the external potential. This is a paradigm shift in DFT on the use of noninteracting references: the noninteracting KS or GKS references represents the explicit computational variables for energy minimization, but not the density of the physical system for external potential-dependent DFAs. We develop the expressions for the electron density so defined through the linear response for general DFAs, demonstrate the results for orbital functionals and for many-body perturbation theory within the second-order and the random-phase approximation, and explore the its connections to developments in DFT.
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DOI：
10.1088/0953-4075/34/12/312
发表时间：
2001-06-28
影响因子：
1.6
作者：
Colle, R;Nesbet, RK
通讯作者：
Nesbet, RK
影响因子：
8.6
作者：
Dion, M;Rydberg, H;Lundqvist, BI
通讯作者：
Lundqvist, BI
DOI：
10.1007/978-3-642-14090-7
发表时间：
2011-01-01
期刊：
DENSITY FUNCTIONAL THEORY: AN ADVANCED COURSE
影响因子：
--
作者：
Engel, Eberhard;Dreizler, Reiner M.
通讯作者：
Dreizler, Reiner M.
影响因子：
4.4
作者：
Furche, Filipp
通讯作者：
Furche, Filipp
影响因子：
4.4
作者：
BECKE, AD
通讯作者：
BECKE, AD