EOMCC method EOMCCSDT

As shown in Table 2, the inexpensive MMCC(2,3)/CI approach is capable of providing the results of full EOMCCSDT quality. Indeed, the errors in the vertical excitation energies for the 2 S+, 1 A, 2 A, and 2 states of CH+ that have large double excitation components, obtained with the noniterative MMCC(2,3)/CI approximation, are 0.006-0.105 eV. This should be compared to the 0.327-0.924 eV errors in the EOMCCSD results, the 0.219-0.318 eV errors obtained with the CC3 method, and the 0.504-0.882 eV errors obtained with the CISDt approach used to construct wave functions T ) for the MMCC(2,3)/CI calculations [47,48]. For the remaining states shown in Table 2 (the third and fourth states and the lowest-energy state), the errors in the CISDt-corrected MMCC(2,3) results, relative to full Cl, are 0.000-0.015 eV. Again, the only standard EOMCC method that can compete with the MMCC(2,3)/CI approach is the expensive full EOMCCSDT approximation. 

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. 

The active-space SRCC methods and their EOMCC extensions are very promising and we will continue to develop them. They are relatively easy to use, although, in analogy to multireference approaches, they require choosing active orbitals, which in some cases may be a difficult thing to do. From this point of view, the active-space CC methods are not as easy-to-use as the noniterative perturbative methods, such as CCSD(T) or CCSD(TQf), or their response CC or EOMCC extensions. Undoubtedly, it would be desirable to have an approach that combines the simplicity of the noniterative CC schemes with the effectiveness with which the iterative active-space CC and EOMCC methods, such as CCSDt and EOMCCSDt, describe ground-and excited-state PESs. 

In Table II, our MMCC(2,3) results are compared with the EOMCCSD and CC3 excitation energies reported in ref 37 and with the EOMCCSDt excitation energies reported in ref 41. The EOMCCSDt approach is the EOMCC method, in which relatively small subsets of triexcited components of cluster operator T and excitation operator R are selected through active orbitals 40,41)- manifold of triexcited configurations used in the EOMCCSDt method is identical to that us in the CISDt calculations. This remark is important, since the CISDt wave functions eq (63),... 

In consequence, the most expensive steps of the ground- and excited-state calculations using methods based on the MMCC(2,3) approximation are essentially identical to the n nf noniterative steps of the ground-state CCSD(T) calculations uo and are the numbers of occupied and unoccupied correlated orbitals, respectively). Similar remarks apply to the memory and disk-space requirements. Clearly, these are great simplifications in the computer effort, compared to the higher-level EOMCC approaches, such as EOMCCSDT [43,44,55,56], particularly if we realize that we only have to use the Ti and T2 clusters, obtained in the CCSD calculations, to construct matrix elements of that enter 9Jt (2), Eqs. (58) and (59). In... 

The CISDt approach, used to generate wave functions x) for the MMCC(2,3) calculations, can be regarded as a Cl analog of the recently developed EOMCCSDt method ( 0, The noniterative character of the MMCC(2,3) method and the fact that the CISDt calculations are less expensive than the EOMCCSDt calculations means that the CISDt-based MMCC(2,3) approximation represents a useful and inexpensive alternative to the already relatively inexpensive EOMCCSDt method. The MMCC(2,3) approach is an alternative to the perturbative triples approaches, such as EOMCCSD(T) (51), EOMCCSD(T) (55), EOMCCSD(r) (55), and CCSDR(3) (55,57), and their iterative EOMCCSDT-n (51,55) and CC3 (34 -37) analogs. The perturbative triples EOMCC or response CC approximations provide erroneous description of excited-state PESs (38) and fail to describe more compUcated excited states, such as the lowest A state of the C2 molecule (57). As demonstrated below, the CISDt-based MMCC(2,3) method has no such problems. 

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