The inequality formulation of Hund's rule and a reinterpretation of singlet-triplet energy differences, generalized for molecules at equilibrium geometry

An inequality formulation in the open-shell Hartree-Fock approximation for Hund's multiplicity rule for atoms has been generalized for the energy differences between a singlet and a triplet state of a molecule with different geometries for the two states. A numerical example is given for the lowest ¹Π_u and ³Π_u states of H₂. As in neutral atoms the energy difference is dominated by the difference in electron nuclear attraction and the interelectronic repulsion is higher for the triplet state than for the singlet state. The π orbital is more contracted in the triplet state than in the singlet state; the σ orbital gives a minor expansion in going from the ¹Π_u state to the ³Π_u state.