密度泛函理论强相互作用极限下的胞内密度
Intracule densities in the strong-interaction limit of density functional theory
摘要：
密度泛函理论中的关联能可以精确地表示为当电子-电子相互作用乘以在0（Kohn-Sham系统）和1（物理系统）之间变化的实参数$λ$时，在给定距离$r_{12}$（胞内密度）处发现两个电子的概率的变化。在这个过程中，通常被称为绝热连接，单电子密度（理想情况下）保持固定的适当的局部单体势。虽然物理系统的精确的胞内密度只能从昂贵的基于波函数的计算中获得，但能够从Kohn-Sham成分开始构建良好的模型将大大提高密度泛函计算的准确性。为此，我们研究了绝热联系的$λ\to\infty$极限中的胞内密度。密度泛函理论的这种强相互作用极限，就像相反的无相互作用的科恩-沙姆极限一样，在数学上很简单，完全可以从单电子密度的知识中构造出来。我们在这里发展的理论框架，并使用精确的相关单电子密度，我们计算的强相互作用限制的几个原子的胞内密度。我们的结果与相应的Kohn-Sham和物理量的比较提供了有用的线索，建立近似的沿绝热连接的密度泛函理论的胞内密度。
英文摘要：
The correlation energy in density functional theory can be expressed exactly in terms of the change in the probability of finding two electrons at a given distance $r_{12}$ (intracule density) when the electron-electron interaction is multiplied by a real parameter $λ$ varying between 0 (Kohn-Sham system) and 1 (physical system). In this process, usually called adiabatic connection, the one-electron density is (ideally) kept fixed by a suitable local one-body potential. While an accurate intracule density of the physical system can only be obtained from expensive wavefunction-based calculations, being able to construct good models starting from Kohn-Sham ingredients would highly improve the accuracy of density functional calculations. To this purpose, we investigate the intracule density in the $λ\to\infty$ limit of the adiabatic connection. This strong-interaction limit of density functional theory turns out to be, like the opposite non-interacting Kohn-Sham limit, mathematically simple and can be entirely constructed from the knowledge of the one-electron density. We develop here the theoretical framework and, using accurate correlated one-electron densities, we calculate the intracule densities in the strong interaction limit for few atoms. Comparison of our results with the corresponding Kohn-Sham and physical quantities provides useful hints for building approximate intracule densities along the adiabatic connection of density functional theory.
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