A general determination of the energy averaged over spin-adapted atomic states

This paper describes the determination of the energy averaged over the atomic states, with a definite spin, derived from a general configuration composed of equivalent and nonequivalent electrons. Using a simpler approach, we extend previous determinations which were limited to the equivalent electron case. The procedure, which is based on our method for calculating traces of replacement operators over model spaces, leads to a formula which is appropriate for computer evaluations.