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.

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

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