The perfect quadruples model for electron correlation in a valence active space

A local approximation to the Schrödinger equation in a valence active space is suggested based on coupled cluster (CC) theory. Working in a pairing active space with one virtual orbital per occupied orbital, this perfect quadruples (PQ) model is defined such that electrons are strongly correlated up to “four-at-a-time” in up to two different (occupied-virtual) electron pairs. This is a truncation of the CC theory with up to quadruple substitutions (CCSDTQ) in the active space, such that the retained amplitudes in PQ are proportional to the fourth root of the number of CCSDTQ amplitudes. Despite the apparently drastic nature of the PQ truncation, in the cases examined this model is a very accurate approximation to complete active space self-consistent field. Examples include deformations of square $H4$⁠, dissociation of two single bonds (water), a double bond (ethene), and a triple bond (nitrogen). The computational scaling of the model (fourth order with molecule size) is less than integral transformation, so relatively large systems can be addressed with improved accuracy relative to earlier methods such as perfect and imperfect pairing, which are truncations of CCSD in an active space.