CR-EOMCC methods

In a few numerical examples, we have demonstrated that all of the above MMCC and CR-EOMCC methods provide considerable improvements in the EOMCCSD results, particularly when the excited states of interest gain a significant double excitation or multi-reference character. The MMCC(2,3)/CI, MMCC(2,3)/PT, CR-EOMCCSD(T), and... 

As in the case of the ground-state MMCC and CR-CC methods [49,50,52,61-63,65-77], the key to a successful description of excited states by the CR-EOMCCSD(T) and other MMCC methods is the very good control of accuracy that all of these methods offer by directly addressing the quantity of interest, which is the difference between the exact, full Cl, and EOMCC (e.g., EOMCCSD) energies. The MMCC formalism provides us with precise information about the many-body structure of these differences, suggesting several useful types of noniterative corrections to EOMCCSD or other EOMCC energies. 

CR-EOMCCSD(T) methods can often compete with the much more expensive EOMCCSDT approach. In fact, there are cases, such as the lowest-energy state of the C2 molecule, where the MMCC(2,3)/CI and CR-EOMCCSD(T) methods balance the ground and excited state correlation effects better than full EOMCCSDT. Even if this particular case is a result of the fortuitous cancellation of errors, it is very encouraging to see that the low-cost and easy-to-use MMCC(2,3)/CI, MMCC(2,3)/PT, CR-EOMCCSD(T), and CR-EOMCCSD(T) sf methods can be as accurate as the high-level and very expensive EOMCC methods, such as EOMCCSDT. 

In particular, the one-, two-, and three-body components of enter the Epstein-Nesbet-like denominator for triple excitations which defines the amplitudes in the CR-EOMCC(2,3),D approach. In variant A of CR-EOMCC(2.3), abbreviated as CR-EOMCC(2,3),A and equivalent to the EOM-CC(2)PT(2) method of Ref. [90], one replaces the Epstein-Nesbet-like denominator defining the... 

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