Error analysis and improvements of coupled-cluster theory

Summary The error in the energy of the traditional coupled-cluster (TCC) approach and of several variants is analyzed in terms of the error of the cluster operatorS. A key feature of this analysis is that TCC can be based on an energy functional (asymmetric inS andS ) that is made stationary with respect to variation ofS . The error of TCC scales with the particle numbern, but it is not quadratic in . An improved coupled-cluster method (ICC) is presented that is the next step in a hierarchy from TCC to an exact variational theory. An alternative hierarchy is possible that leads to the extended coupled-cluster (ECC) method of Arponen. Variational (VCC) and unitary (UCC) coupled cluster theories and their stationary conditions and errors are analyzed along similar lines and practicable VCC or UCC approaches are presented. An infinite summation of certain terms in the VCC expectation value is shown to lead to a coupled-pair functional of the type proposed by Ahlrichs. The various CC schemes discussed here are compared on the CC-D, CC-SD and CC-SDT levels and beyond this. Special aspects referring to properties are also discussed.