School of Science, Huzhou University, Zhejiang 10083, China.
J Chem Phys. 2010 May 28;132(20):204102. doi: 10.1063/1.3429608.
The Coulomb hole does not have its largest depth around an electron in or near the bond midplane. It splits into two parts, localized on both nuclear sites forming the bond. Even counterintuitive positive values of the "hole" around such a position may be observed. This happens when the Fermi hole is deeper than the total exchange-correlation hole at the reference electron position. This Coulomb "heap" is shown to arise from correlation effects on the one-electron density rather than correlation effects in the pair density. Left-right correlation tends to enhance the effect of the nuclear attraction, contracting the electron density around the nuclear positions and depleting the bond center region. Possible alternative definitions of the Coulomb hole are discussed, including one based on the exact Kohn-Sham exchange hole. Approximate density functional theory methods (generalized gradient approximation) are not accurate enough to realize the advantages of this definition.
库仑空穴不在键的中面内或附近的电子处达到最大深度。它分裂为两部分，定域在两个核位点上，形成键。即使在这种位置周围观察到反直觉的正的“空穴”值也是可能的。当费米空穴比参考电子位置处的总交换相关空穴更深时，就会发生这种情况。这种库仑“堆积”是由单电子密度上的相关效应引起的，而不是在对密度上的相关效应。左右相关倾向于增强核吸引的效果，收缩核位置周围的电子密度，并耗尽键中心区域。讨论了库仑空穴的可能替代定义，包括基于精确的 Kohn-Sham 交换空穴的定义。近似密度泛函理论方法（广义梯度近似）不够准确，无法实现此定义的优势。
