The non-monotonic behavior of the electron repulsion energy and the inter-electronic distance, as a function of the internuclear separation, in the³Π_uexcited state of the hydrogen molecule has been assessed by explicit calculation and analysis of the electron-pair density distribution functions from high level ab initio full configuration interaction wave functions, for both the³Π_uand the¹Π_ustates. Additionally, 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.