Valence states

Valence states are defined as the weighted average of all CSFs arising from an electronic configuration (occupation): (MO)$^n$ mathend000#. This is identical to the average energy of all Slater determinants.

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

This covers, e.g. the cases $n=1$ mathend000# and $n=2n_{ir}-1$ mathend000#: $p^1$ mathend000#, $p^5$ mathend000#, $d^1$ mathend000#, $d^9$ mathend000#, etc, since there is only a single CSF which is identical to the average of configurations.