An efficient way to include connected quadruple contributions into the coupled cluster method

The general inclusion of the T4 operator into the coupled cluster equations requires an n10 computational procedure, and even n9 in the lowest order, as in the CCSDTQ-1 (coupled cluster singles, doubles, triples and lowest-order quadruples) method. That level of n-dependence makes it difficult to apply the method to larger systems. In this paper we circumvent this difficulty by a factorization approximation that requires only an n7 procedure, but that provides results nearly identical to those obtained with the CCSDTQ-1 method. This observation offers a practical and accurate method to go beyond the CCSDT (coupled cluster singles, doubles and triples) approach. We also consider noniterative CCSDT(Qf) (coupled cluster singles, doubles, triples and noniterative quadruples) and CCSD(TQf) (coupled cluster singles and doubles with noniterative triples and quadruples) methods.