Size-extensive seniority-zero energy functionals derived from configuration interaction with double excitations

The doubly occupied configuration interaction (DOCI) approach can provide an accurate black-box description of nondynamic electron correlation at a computational cost that increases combinatorially with the system size. Remarkably, a pair coupled-cluster doubles (pCCD) approach (also known as the antisymmetrized product of one-reference orbital geminals) can reproduce DOCI energies with only a quadratic number of wave function parameters, and, when neglecting the cost associated with any two-electron integral transformations, these parameters can be determined at a cubic computational cost. Other simpler seniority-zero approaches derived from size-extensive modified configuration interaction doubles functionals can also provide approximations to DOCI energies at similar computational costs. We develop seniority-zero formulations of the coupled-electron pair approximation, the averaged coupled-pair functional, averaged quadratic coupled-cluster, and the parametric two-electron reduced density matrix (p2RDM) approach. These methods are Hermitian and thus offer several potential advantages over pCCD theory, including a reduction in the number of variable parameters and simplified definitions of reduced density matrices. Of the methods investigated, only the pair p2RDM (pp2RDM) approach yields energies that are comparable in quality to pCCD and DOCI. For the molecular systems investigated, pp2RDM-derived RDMs are found to be better approximations to DOCI ones than those obtained from pCCD.