On Pair Functions for Strong Correlations.

The UHF wave function may be written as a spin-contaminated pair wave function of the APSG form, and the overlap of the α and β corresponding orbitals of the UHF solution can be taken as a proxy for the strength of the correlation captured by breaking symmetry. We demonstrate this with calculations on one- and two-dimensional hydrogen clusters and make contact with the well studied Hubbard model. The UHF corresponding orbitals pair in a manner that allows a smooth evolution from doubly occupied orbitals at small distance to one in which wave function breaks symmetry, segregating the α and β electrons onto distinct sublattices at large distances. By performing spin projection on these UHF solutions, we address strong correlations that are difficult to capture at intermediate distances using a single determinant.