Local spins: An improved treatment for correlated wave functions

The expectation value 〈 S ^ 2 〉 of the total spin operator for general (correlated) wave functions is transformed to a form in which it appears a physically reasonable sum of atomic and diatomic contributions. The general formula obtained reduces to that given previously in the single determinant case, thus is able to describe in a physically correct manner both limiting cases—the closed shell RHF one which is lacking any spins and the strongly correlated case in which the spins may be considered localized on individual atoms.