Externally corrected MMCC

The purpose of the present paper is to review the most essential elements of the excited-state MMCC theory and various approximate methods that result from it, including the aforementioned CR-EOMCCSD(T) [49,51,52,59] and externally corrected MMCC ]47-50, 52] approaches. In the discussion of approximate methods, we focus on the MMCC corrections to EOMCCSD energies due to triple excitations, since these corrections lead to the most practical computational schemes. Although some of the excited-state MMCC methods have already been described in our earlier reviews [49, 50, 52], it is important that we update our earlier work by the highly promising new developments that have not been mentioned before. For example, since the last review ]52], we have successfully extended the CR-EOMCCSD(T) methods to excited states of radicals and other open-shell systems ]59]. We have also developed a new type of the externally cor-... 

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... 

EXTERNALLY CORRECTED MMCC(2,3) SCHEMES AND THE CR-EOMCCSD(T) APPROACH... 

An interesting alternative to the externally corrected MMCC methods, discussed in Section 3.1.1, is offered by the CR-EOMCCSD(T) approach [49, 51,52,59]. The CR-EOMCCSD(T) method can be viewed as an extension of the ground-state CR-CCSD(T) approach of Refs. [61,62], which overcomes the failures of the standard CCSD(T) approximations when diradicals [76,104,105] and potential energy surfaces involving single bond breaking and single bond insertion [49,50,52,60-62,65,67,69,70,72,73] are examined, to excited states. 

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