Richardson–Gaudin states of non-zero seniority: Matrix elements

Seniority-zero wave functions describe bond-breaking processes qualitatively. As eigenvectors of a model Hamiltonian, Richardson-Gaudin states provide a clear physical picture and allow for systematic improvement via standard single reference approaches. Until now, this treatment has been performed in the seniority-zero sector. In this paper, the corresponding states with higher seniorities are identified, and their couplings through the Coulomb Hamiltonian are computed. In every case, the couplings between the states are computed from the cofactors of their effective overlap matrix. Proof-of-principle calculations demonstrate that a single reference configuration interaction is comparable to seniority-based configuration interaction computations at a substantially reduced cost. The next paper in this series will identify the corresponding Slater-Condon rules and make the computations feasible.