A tractable and accurate electronic structure method for static correlations: The perfect hextuples model

We present the next stage in a hierarchy of local approximations to complete active space self-consistent field (CASSCF) model in an active space of one active orbital per active electron based on the valence orbital-optimized coupled-cluster (VOO-CC) formalism. Following the perfect pairing (PP) model, which is exact for a single electron pair and extensive, and the perfect quadruples (PQ) model, which is exact for two pairs, we introduce the perfect hextuples (PH) model, which is exact for three pairs. PH is an approximation to the VOO-CC method truncated at hextuples containing all correlations between three electron pairs. While VOO-CCDTQ56 requires computational effort scaling with the 14th power of molecular size, PH requires only sixth power effort. Our implementation also introduces some techniques which reduce the scaling to fifth order and has been applied to active spaces roughly twice the size of the CASSCF limit without any symmetry. Because PH explicitly correlates up to six electrons at a time, it can faithfully model the static correlations of molecules with up to triple bonds in a size-consistent fashion and for organic reactions usually reproduces CASSCF with chemical accuracy. The convergence of the PP, PQ, and PH hierarchy is demonstrated on a variety of examples including symmetry breaking in benzene, the Cope rearrangement, the Bergman reaction, and the dissociation of fluorine.