Are Exact Exchange–Correlation Potentials Continuous at Atomic Nuclei in Molecules?

Abstract

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.