Interpretation of Hund's multiplicity rule for the carbon atom
  Hund's multiplicity rule is investigated for the carbon atom using quantum Monte Carlo methods. Our calculations give an accurate account of electronic correlation and obey the virial theorem to high accuracy. This allows us to obtain accurate values for each of the energy terms and therefore to give a convincing explanation of the mechanism by which Hund's rule operates in carbon. We find that the energy gain in the triplet with respect to the singlet state is due to the greater electron-nucleus attraction in the higher spin state, in accordance with Hartree-Fock calculations and studies including correlation. The method used here can easily be extended to heavier atoms. 
Kenta Hongo, Ryo Maezono, Yoshiyuki Kawazoe, Hiroshi Yasuhara, M. D.   Towler, and R. J. Needs