  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.
