An Alternative Hierarchy of Electron Correlation beyond the Electron Pair Approximation†

Starting from the Nakatsuji theorem, a hierarchy of approximations is considered that begins with traditional coupled cluster theory with singles and doubles (CCSD) and proceeds via the ansatz of semigeneralized singles and doubles (CCSGSD), with operators of the types a(ab)(ic) and a(ka)(ij) included, to the generalized singles and doubles (CCGSD) ansatz with the full basis {a(pq)(rs); a(p)(q)}, and if necessary, beyond. The simplest realization of CCSGSD is the constrained coupled cluster ansatz with singles, doubles, and triples (CCCSDT). It is related to traditional coupled cluster with singles, doubles, and triples (CCSDT), but it requires (for sufficiently large n) a smaller number of parameters of O(nm3) vs O(n3m3) in CCSDT, n being the number of electrons and m the size of the basis. A linear system of equations for the CCCD[T] approximation is derived and strategies toward its solution are discussed.