A quantum mechanical explanation for Hund's multiplicity rule

Abstract

Hund's multiplicity rule, according to which a high spin state has a lower energy than any other state of lower spin arising from the same configuration, was deduced from atomic spectra immediately before the advent of modern quantum mechanics. Since then, the lower energy of the state of higher multiplicity has generally been explained by assuming greater electron repulsion in the lower spin states. Numerous calculations1–13 have shown, however, that the traditional explanation of Hund's rule is invalid. In every neutral species for which the requisite calculations have been carried out, the electron–electron repulsion, Vee, is greater in the high spin state, and the lower energy of the high spin state is due to its greater electron–nucleus attraction, Ven. I show here that Hund's rule is a consequence of the Fermi correlation between electrons with parallel spin which leads to less screening of the nucleus in the high spin state.