Applications of electrostatic interpretation of components of effective Kohn–Sham potential in atoms

Abstract

The fundamental significance of the components of the electronic Kohn–Sham potential evaluated at the nucleus is highlighted via the numerical studies on atoms He–Lu which suggest their formally similar power-law relationship in expressing the associated components of total electronic energy. Similar studies on the isoelectronic series of closed shell atoms lead to the linear correlations. The proposed static exchange–correlation charge density concept [S. Liu, P. A. Ayers, and R. G. Parr, J. Chem. Phys. 111, 6197 (1999)] is used to interpret these relationships. The maxima in the static integrated radial exchange–correlation charge density function, Qxc(r), in atoms are shown to reflect the shell boundaries. The quantum Monte Carlo density derived exchange–correlation potentials for Be and Ne are used to obtain Qxc(r) that can be used as standards to directly assess the quality of approximate exchange–correlation potentials. For the negative ions, Qxc(r) displays a characterstic outer minimum as a consequence of the Sen–Politzer theorem [K. D. Sen and P. Politzer, J. Chem. Phys. 90, 4370 (1989)]. This minimum is found to be related with the stability of negative ions.