Completely renormalized CCSDT approach

Finally, in two variants of the completely renormalized CCSDT(Q) approach, referred to as the CR-CCSDT(Q),a and CR-CCSDT(Q),b schemes, which are examples of the MMCC(3,4) approximation, we add the renormalized energy corrections due to to the CCSDT energy. Thus, if Ti, T2, and Tz are cluster operators obtained by solving the CCSDT equations, then the energy expressions defining the CR-CCSDT(Q),a and CR-CCSDT(Q),b approaches are (7,16,20)... 

Further improvements in the CR-CCSD(TQ),b results for N2 can be obtained by applying the completely renormalized versions of the CCSDT(Qf) approach (see Refs. [11,30] for the description of these methods). For example, variant b of the CR-CCSDT(Q) method [11,30], in which the completely renormalized corrections due to T4 clusters are added to the full CCSDT energies, provides a curve for N2 which is characterized by errors relative to full Cl that do not exceed 7.6 millihartree in the entire R = 0.75 — 2.25i e region and that are as small as 0.719 millihartree at R = Re and 1.161 millihartree a.t R = 2Re [12,34] (cf. Table 2). The question is if we can obtain similar or better improvements by adding noniterative corrections to the CCSD (rather than CCSDT) energies. 

Different types of the MMCC(2,3), MMCC(2,4), and MMCC(3,4) approximations are obtained by making different choices for o) in eqs (35)-(37) (7,16-18). The most intriguing results are obtained when wave functions o) are defined by the low-order MBPT. The MBPT-like forms of o) lead to the renormcdized and completely renormalized CCSD[T], CCSD(T), CCSD(TQ), and CCSDT(Q) schemes (7,16-18). As demonstrated below, these new methods represent powerful computational tools that remove the failing of the standard CCSD[T], CCSD(T), CCSD(TQ), and CCSDT(Q) approximations at large internuclefu separations, while preserving the simplicity and black-box character of the noniterative perturbative CC approaches. 

We have overviewed the new approach to the many-electron correlation problem in atoms and molecules, termed the method of moments of coupled-cluster equations (MMCC). The main idea of the MMCC theory is that of the noniterative energy corrections which, when added to the ground- and excited-state energies obtained in approximate CC calculations, recover the exeict energies. We have demonstrated that the MMCC formalism leads to a number of useful approximations, including the renormalized and completely renormalized CCSD(T), CCSD(TQ), and CCSDT(Q) methods for... 

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