An analysis of energy differences in atomic multiplets in connection with the inequality formulation of Hund's rules

Abstract

A detailed consideration is given of a recent reformulation of Hund's rules in terms of inequalities. The interpretation of Hund's rules is reconsidered assuming that each energy level is known exactly in the restricted Hartree-Fock approximation. Some general theorems and series expansions are derived for energy differences between atomic states. As is now well known, the state of lower energy in a multiplet has the higher expectation value for the electron-electron repulsion, especially in neutral systems. The behaviour of this repulsion is analysed in terms of the Fermi hole and the contraction of the wavefunction which one finds for the state of lowest energy. Numerical examples are given for the 1P and 3P states of the He isoelectronic series, the 1S, 1D and 3P states of the C and O series and the 2P, 2D and 4S states of the N series.