EOMCC method

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. 

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... 

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. 

As in the ordinary EOMCC theory, in the EOMXCC method we solve the electronic Schrodinger equation (1) assuming that the excited states are represented by Eq. (7). We use the exponential representation of the ground-state wave function I S o), Eq. (8), but no longer assume that the cluster components Tn result from standard SRCC calculations (see below). The many-body expansions of the excitation operator Rk have the same form as in the ordinary EOMCC formalism. In particular, the three different forms of Rk discussed in the previous section [fi -E, R A, and REqs. (28), (30), and (26), respectively] are used to define the EE-EOMXCC, EA-EOMXCC, and IP-EOMXCC methods. As in the standard EOMCC method, by making suitable choices for the operators Qa, which define Rk, we can always extend the EOMXCC theory to other sectors of the Fock space. 

As mentioned in the Introduction, one of our purposes is reduction of the non-Hermitian character of the ordinary EOMCC formalism (or, in some variants of the new theory, its complete elimination). Unlike the original Hamiltonian Hk, the transformed Hamiltonian H used in the EOMCC method is no longer Hermitian and the non-Hermiticity of H measured by a difference H — (H) shows up already in the first-order of MBPT, i.e. 

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),... 

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