Exact MMCC theory

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],... 

---