The Electron-pair Density Distribution of the ${^{1,3}\Pi_u}$ Excited States of H$_2$

Abstract

The non-monotonic behavior of the electron repulsion energy and the interelectronic distance, as a function of the internuclear separation, in the $^{3}\Pi_{u}$ excited state of the hydrogen molecule has been assessed by explicitly calculation and analysis of the electron-pair density distribution functions from high level ab initio Full Configuration Interaction wave functions, for both the $^{3}\Pi_{u}$ and the $^{1}\Pi_{u}$ states. Additionally, the Hund's rule as applied to these two states has been accounted for in terms of simple electronic shielding effects induced by wave function antisymmetrization.