MMCC approaches left eigenstates

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. 

Eqs. (50) and (53) are the full Cl states. Thus, we must approximate wave functions T ) in some way. A few different methods of approximating T ) in Eq. (53), leading to the aforementioned externally corrected MMCC(2,3) approaches and CR-EOMCCSD(T) schemes, and their analogs exploiting the left eigenstates of, and the performance of all of these methods... 

THE MMCC SCHEMES EXPLOITING THE LEFT EIGENSTATES OF THE SIMILARITY-TRANSFORMED HAMILTONIAN THE CR-EOMCCSD(T) APPROACH... 

In addition to discussing specific renormalized CC methods, we have reviewed the MMCC formalism, which is the key concept behind all renormalized CC approaches. In this discussion, we have included the most recent biorthogonal formulation of the MMCC theory employing the left eigenstates of the similarity-transformed Hamiltonian which leads to the CR-CC(2,3) and other CR-CC(ma, / / ) approaches. We have discussed the similarities and differences between the original MMCC theory of Piecuch and Kowalski, introduced in Refs. [11,24,34], and the biorthogonal MMCC formalism of Piecuch and Wloch, introduced in Ref. [45] and further elaborated on in Ref. [46]. In particular, we have pointed out how the biorthogonal formulation of the MMCC theory enables one to eliminate the overlap denominators, which are... 

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