Moore Conrad C, Staroverov Viktor N
Department of Chemistry, The University of Western Ontario, London, Ontario N6A 5B7, Canada.
J Chem Theory Comput. 2024 Oct 22;20(20):8934-8939. doi: 10.1021/acs.jctc.4c00904. Epub 2024 Oct 1.
The Kohn-Sham exchange-correlation potential of a given system can be written exactly in terms of several quantities including the interacting and noninteracting kinetic energy densities of the electrons. Electronic kinetic energy densities are sharply discontinuous at the atomic nuclei in molecules, which implies that exact exchange-correlation potentials of molecules might also be discontinuous at the nuclear positions. This surprising possibility is made even more likely by the fact that molecular exchange-correlation potentials derived from wave functions within Slater-type basis sets do have jump discontinuities. We deduce analytically the exact behavior of the relevant quantities near atomic nuclei and conclude that, in the basis-set limit, all jump discontinuities cancel out nontrivially so that exact exchange-correlation potentials are continuous after all.
给定系统的科恩-沈（Kohn-Sham）交换关联势可以精确地用几个量来表示，这些量包括电子的相互作用动能密度和非相互作用动能密度。电子动能密度在分子中的原子核处有急剧的不连续性，这意味着分子的精确交换关联势在核位置处也可能是不连续的。斯莱特型基组内的波函数导出的分子交换关联势确实存在跳跃不连续性，这一事实使得这种令人惊讶的可能性变得更加可能。我们通过解析推导得出了原子核附近相关量的精确行为，并得出结论：在基组极限下，所有跳跃不连续性以非平凡的方式相互抵消，因此精确的交换关联势终究是连续的。
