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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.

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

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.