Valence states

Valence states are defined as the weighted average of all CSFs arising from an electronic configuration (occupation): (MO)ⁿ. This is identical to the average energy of all Slater determinants.

$${\frac{{2 n_{ir}(n-1)}}{{(2 n_{ir}-1)n}}}$$

This covers, e.g. the cases n = 1 and n = 2n_ir - 1: p¹, p⁵, d¹, d⁹, etc, since there is only a single CSF which is identical to the average of configurations.