Jump discontinuities of finite-basis-set exchange-correlation potentials at atomic nuclei

The kinetic energy density of electrons and the gradient of the electron density have pronounced jump discontinuities at the positions of the atomic nuclei in molecules. Certain exact relations then imply that molecular Kohn-Sham exchange-correlation potentials may also be discontinuous at atomic nuclei. Here, we confirm that exchange-correlation potentials derived from Hartree-Fock and correlated wavefunctions within Slater-type basis sets do exhibit such discontinuities. Despite their persistence even in large basis sets, these discontinuities are almost certainly artifacts of basis set finiteness and are expected to disappear in the basis-set limit. The findings imply that imposing electron-nucleus cusp conditions in spherically averaged form may not always be appropriate.