VALIDITY AND INTERPRETATION OF HUND'S MULTIPLICITY RULE FOR MOLECULES: A DENSITY FUNCTIONAL STUDY

Abstract

Validity and interpretation of Hund's multiplicity rule for one molecular system, boron hydride, is investigated from the density functional framework in the present work. Performance of a number of approximate exchange-correlaton energy denstiy functionals from LDA, GGA and hybrid models have been examined. It has been shown that all approximate functionals are able to predict the correct energy order, both adiabatically and vertically, for different spin states of the molecule, reproducing that a higher spin state from the same electronic configuration possesses a lower total energy. It is only the hybrid functionals, however, that render the picture derived for the exact density functionl theory of excited states and multiplets, that is, the validity of Hund's rule can be interpreted by the sole contribution from the outmost orbital (i.e. HOMO) of the spin states. Systematic discrepancy between the total and HOMO energy differences have been observed for both LDA and GGA forms, indicating that they are not as good in simulating the same-spin electron correlation effect as the Hartree–Fock method. We also show that it is the same as what we have found from the Hartree–Fock theory, and justification via either the nuclear-electron attraction or the exchange energy alone is not adequate to interpret the validity of the rule.