  We propose a novel partitioning of the Hilbert space, hierarchy configuration
interaction (hCI), where the excitation degree (with respect to a given
reference determinant) and the seniority number (i.e., the number of unpaired
electrons) are combined in a single hierarchy parameter. The key appealing
feature of hCI is that each hierarchy level accounts for all classes of
determinants whose number share the same scaling with system size. By surveying
the dissociation of multiple molecular systems, we found that the overall
performance of hCI usually exceeds or, at least, parallels that of
excitation-based CI. For higher orders of hCI and excitation-based CI, the
additional computational burden related to orbital optimization usually do not
compensate the marginal improvements compared with results obtained with
Hartree-Fock orbitals. The exception is orbital-optimized CI with single
excitations, a minimally correlated model displaying the qualitatively correct
description of single bond breaking, at a very modest computational cost.
