Coupled cluster singles and doubles polarisation propagator accurate through the third order of Møller–Plesset theory

Abstract

A non-iterative low-cost correction for the polarisation propagator of coupled cluster theory limited to single and double excitations (CCSD) has been developed. The proposed expression accounts for the most important terms resulting from triple excitation operators, which are missing in the CCSD formula. These contributions have been identified and analysed for both existing theories of coupled cluster response functions, i.e. for the time-dependent and expectation-value approaches. It has been demonstrated on the operator level that–by an appropriate rearrangement of these terms and an elimination of long energy denominators–the total third-order contribution can be recast into the form, which does not contain triple excitation operators, but is still correct through the third order of Møller–Plesset theory. The computational cost of the proposed correction scales with the sixth power of the molecular size, and is therefore at least one order of magnitude smaller than in the case of an explicit inclusion of triple excitation operators into the propagator formula.