Hund?s multiplicity rule: a unified interpretation

Abstract

Hund’s multiplicity rule, stating that a higher spin state has a lower energy within the same electron configuration, is empirical but has shown to be valid for both atoms and molecules. Several theoretical interpretations for its validity, including explanations in terms of the lower interelectron repulsion and the greater electron–nuclear attraction in the higher spin state, are available. None of them, however, are satisfactory. Here we show that Hund’s rule can be explained by the Janak theorem in density functional theory, extended to excited states and multiplets. In the exact density functional theory theory, it leads to ΔE ST=E S−E T=ΔeHOMO, with E S and E T the singlet and triplet state energies and eHOMO the highest occupied molecular orbital energies of the spin states. This relationship was previously obtained by M. Levy [(1995) Physical Review A 52:R4313]. In this paper, numerical results within the Hartree–Fock framework for both atoms and molecules confirm the previously mentioned justification. Good results of the Hartree–Fock method come from the accurate description of the exchange effect from where Hund’s multiplicity rule originated.