Ground-state MMCC theory

In the ground-state MMCC theory, we focus on the noniterative energy correction... 

The remaining issue is what do we do with the wave function F(,) in eqs (16) or (22), which in the exact MMCC theory represents the full Cl ground state. In the approximate MMCC methods considered in our earlier work, the wave functions Fo) were evaluated either by using the low-order MBPT... 

We are now equipped with all of the basic concepts of the CC/EOMCC theory which are necessary to explain the noniterative MMCC approaches to ground and excited electronic states. In this section, we focus on the exact MMCC theory. The approximate MMCC schemes for excited electronic states, including the externally corrected MMCC approaches and the CR-EOMCCSD(T) theory, and their most recent analog based on the left eigenstates of the similarity-transformed Hamiltonian, are discussed in Section 3. 

There are two issues that have to be addressed before one can use Eqs. (25) or (28) in practical calculations. First of all, the exact MMCC corrections SgA) and < qCCSD, Eqs. (25) and (28), respectively, have the form of long many-body expansions involving all n-tuply excited configurations with n == i/ia + I, ., /V, where N is the number of correlated electrons in a system. Thus, in order to propose the computationally inexpensive MMCC methods, we have to truncate the many-body expansions for SgA> or excitation level This leads to the so-called MMCC( i, mB) schemes [11-15,24,33,34,39,48,120,121], The CR-CCSD(T) and CR-CCSD(TQ) methods [11-14,24,33,34], reviewed and tested in this work, are the MMCC( u, mB) schemes with mA = 2 and mB = 3 (the CR-CCSD(T) case) or 4 (the CR-CCSD(TQ) case). Second of all, the wave function % that enters the exact Eqs. (25) or (28) is a full Cl ground state, which we usually do not know (if we knew the exact ko> state, we would not have to perform any calculations ). Thus, in order to propose the computationally tractable approaches based on the MMCC theory defined by Eqs. (25) and (28), we must approximate fi o) in some way as well. The CR-CCSD(T) and CR-CCSD(TQ) methods employ the low-order MBPT-like expressions to define fi o) [11-14,24,33,34],... 

It has recently been demonstrated that the applicability of the ground-state SRCC approaches, including the popular noniterative approximations, such as CCSD(T), can be extended to bond breaking and quasidegenerate states, if we switch to a new type of the SRCC theory, termed the method of moments of CC equations (MMCC) (7,16-18). It has further been demon-... 

In our view, the MMCC theory represents an interesting development in the area of new CC methods for molecular PESs. The MMCC-bas renormalized CCSD(T), CCSD(TQ), and CCSDT(Q) methods and the noniterative MMCC approaches to excited states provide highly accurate results for ground and excited-state PESs, while preserving the simplicity and the black-box character of the noniterative perturbative CC schemes. In this chapter, we review the MMCC theory and new CC i pnndmations that result firom it and show the examples of the MMCC and renormalized CC calculations for ground and excited state PESs of several benchmark molecules, including HF, F2, N2, and CH" ". The review of the previously published numerical results (7,16-20) is combined with the presentation of new results for the C2, N2, and H2O molecules. 

We begin our review of the MMCC theory with the ground-state formalism. The extension of the MMCC formalism to the EOMCC case is discussed in the next subsection. 

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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