Electron-pair densities of group 14, 15, and 16 atoms in their low-lying multiplet states

Abstract

Electron-pair intracule (relative motion) h(u) and extracule (center-of-mass motion) d(R) densities are studied for the 3P, 1D, and 1S multiplet states of five group 14 atoms with p2 configurations, the 4S, 2D, and 2P multiplets of five group 15 atoms with p3 configurations, and the 3P, 1D, and 1S multiplets of five group 16 atoms with p4 configurations. For all 15 atoms, it is confirmed that a lower total energy E in a high angular momentum state is always accompanied with the decrease of the electron–nucleus attraction energy Ven which is greater than the increase in the electron–electron repulsion energy Vee, as discussed in the literature for a few light atoms. In all the cases, the difference in the radial intracule densities 4πu2h(u) clarifies that for a multiplet with a higher angular momentum, the probability of finding a pair of electrons separated by a short/long distance is larger/smaller, leading to a greater Vee and a smaller average interelectronic distance 〈u〉. The Fermi hole effect is not important for the relative stability of the multiplets examined. For the multiplets arising from the pn electronic configurations, the differences in the radial extracule densities 4πR2d(R) are found to be almost isomorphic with the corresponding intracule ones: In a multiplet with a high angular momentum, the average center-of-mass radius 〈R〉 of an electron pair is always smaller, and two electrons are more likely to be at opposite positions with respect to the nucleus. Accordingly, the valence p orbital in a more stable multiplet is more tight, resulting in a lower electron–nucleus attraction energy Ven for all the 15 atoms.