  Postulated by Pauli to explain the electronic structure of atoms and
molecules, the exclusion principle establishes an upper bound of 1 for the
fermionic natural occupation numbers $\{n_i\}$. A recent analysis of the pure
$N$-representability problem provides a wide set of inequalities for the
$\{n_i\}$, leading to constraints on these numbers. This has a strong potential
impact on reduced density matrix functional theory as we know it. In this work
we continue our study the nature of these inequalities for some atomic and
molecular systems. The results indicate that (quasi)saturation of some of them
leads to selection rules for the dominant configurations in configuration
interaction expansions, in favorable cases providing means for significantly
reducing their computational requirements.
