  Currently, there is a growing interest in the development of a new hierarchy
of methods based on the concept of seniority, which has been introduced quite
recently in quantum chemistry. Despite the enormous potential of these methods,
the accurate description of both dynamical and static correlation effects
within a single and in-principle-exact approach remains a challenge. In this
work, we propose an alternative formulation of reduced density-matrix
functional theory (RDMFT) where the (one-electron reduced) density matrix is
mapped onto an ab initio seniority-zero wave function. In this theory, the
exact natural orbitals and their occupancies are determined self-consistently
from an effective seniority-zero calculation. The latter involves a universal
higher-seniority density matrix functional for which an adiabatic connection
(AC) formula is derived and implemented under specific constraints that are
related to the density matrix. The pronounced curvature of the (constrained) AC
integrand, which is numerically observed in prototypical hydrogen chains and
the Helium dimer, indicates that a description of higher-seniority correlations
within second-order perturbation theory is inadequate in this context. Applying
multiple linear interpolations along the AC or connecting second-order
perturbation theory to a full-seniority treatment via Pad\'{e} approximants are
better strategies. Such information is expected to serve as a guide in the
future design of higher-seniority density-matrix functional approximations.
