Ground-state MMCC schemes

The Ground-State MMCC(m, ma) Methods and the Renormalized CCSD(T), CCSD(TQ), and CCSDT(Q) Schemes... 

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],... 

Three choices of (m4,mB) are particularly useful in the ground-state case, namely, (m>i,mB) = (2,3), (2,4), and (3,4). These three choices lead to the MMCC(2,3), MMCC(2,4), and MMCC(3,4) schemes. In the MMCC(2,3) and MMCC(2,4) ground-state methods, we add correction ( o to the CCSD energy, JS csD whereas in the MMCC(3,4) approach we correct the CCSDT energy, CCSDT obtain (7,16,17),... 

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. 

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