EOMCC method EOMCCSD

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. 

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),... 

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. 

CC/EOMCC equations corresponding to the approximate method A, as defined by Eq. (48). In particular, if we want to recover the full Cl energies E from the CCSD/EOMCCSD energies (the niA = 2 case), we... 

Examples of truncated EOMCC schemes are the IP-EOMCCSD [9] (cf., also, Ref. 38), EE-EOMCCSD [32-34], and EA-EOMCCSD [38] methods, where... 

The standard formulation of the EE-EOMCCSD theory is based on Eqs. (61) and (63) (in general, the standard truncation scheme for the EE-EOMCCSD method is characterized by the condition Mr = Mt)- However, in the truncated IP-EOMCC and EA-EOMCC approaches, it is customary to assume that Mr = Mt — 1. Therefore, the standard EA-EOMCCSD method is in fact equivalent to what we would call here the... 

First of all, it should be emphasized that Eq. (201) has an interesting mathematical structure. It explicitly shows that the leading terms of the similarity transformed Hamiltonian of the EOMXCC theory are obtained by symmetrizing (Hermitizing) the H Hamiltonian of the standard EOMCC formalism. In particular, Eq. (202) represents the similarity transformed Hamiltonian of the EOMCCSD method, when projected on a manifold of singly and doubly excited configurations. In this case, the first three terms in Eq. (201) correspond to Hermitized EOMCCSD method. The departure from Hermiticity of H is described by Eq. (203), which contains second-and higher-order components of H. 

The EOMCCSD method uses up to three-body terms of H. The EOMXCCSD approach needs certain types of three- and four-body components of H as well as all one- and two-body terms. Although the presence of four-body terms in the EOMXCCSD approach makes this approach slightly more complicated compared to EOMCCSD, the four-body terms of H that enter the EOMXCCSD eigenvalue problem are inexpensive (they scale as or less) and we may also think of eliminating them altogether, since they do not bring any information about T3 components of EOMCC. 

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