Richardson–Gaudin states of non-zero seniority. III. The perfect-pairing limit

Strongly correlated electrons can be treated with a configuration interaction of Slater determinants grouped by their number of unpaired electrons with exponential cost. Papers I and II [P. A. Johnson, J. Chem. Phys. 162, 134106 (2025) and P. A. Johnson, J. Chem. Phys. 163, 081101 (2025)] demonstrated that single reference methods built from Richardson–Gaudin states gave results of similar quality at polynomial cost. In this contribution, the states are simplified substantially, yielding the perfect-pairing state as a reference along with its low-lying excitations. The states are much simpler; the computational cost is substantially reduced; and there is no sacrifice in numerical accuracy. Second-order Epstein–Nesbet perturbative corrections for the valence electrons are similar in quality to the complete active space self-consistent field.