Richardson-Gaudin states of non-zero seniority I: matrix elements

TL;DR

This paper extends Richardson-Gaudin states to higher seniorities, computes their couplings, and demonstrates that single reference configuration interaction can be a cost-effective alternative to seniority-based methods.

Contribution

It introduces higher seniority Richardson-Gaudin states and their couplings, enabling more efficient electronic structure calculations beyond seniority-zero.

Findings

Couplings between higher seniority states are computed from cofactors of overlap matrices.

Single reference configuration interaction achieves comparable results to seniority-based methods.

Proof of principle calculations validate the approach.

Abstract

Seniority-zero wavefunctions 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 done in the seniority-zero channel. In this manuscript, 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 with seniority-based configuration interaction computations at a substantially reduced cost. The next manuscript in this series will identify the corresponding Slater-Condon rules and make the computations feasible.