EOMCCSDT

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... 

State Full Cf EOMCCSDP CC. f EOMCCSDT MMCC(2,3)/CP f MMCC(2,3)/PTf S CR-EOMCCSD(Tf CR-EOMCCSD(T)sf ... 

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. 

As shown in Table 2, the inexpensive MMCC(2,3)/PT approach is capable of providing the results which are practically as good as the excellent MMCC(2,3)/CI results. In the case of the 2 S+ and 1 states, which have a strong double excitation character, causing the EOMCCSD approach to fail, the MMCC(2,3)/PT corrections to CCSD/EOMCCSD energies produce the results of the EOMCCSDT quality, reducing the 0.560 and 0.924 eV errors in the EOMCCSD results to 0.102 and 0.090 eV, respectively. For these two states, the errors relative to full Cl obtained with the noniterative MMCC(2,3)/PT approach are 2-3 times smaller than the errors obtained with the much more expensive and iterative CC3 method. For states such as 2 n, which have a partially biexcited character, and for states dominated by single excitations (3 1 11), the MMCC(2,3)/PT results are as... 

Rc-h = Re = 2.13713 bohr with the CR-EOMCCSD(T) approach, with the analogous results obtained in the EOMCCSD, CC3, EOMCCSDT, and full Cl calculations reported in Refs. [39,44,103] is given in Table 2. As one can see, the relatively inexpensive CR-EOMCCSD(T) method, which has the ease-of-use of the standard ground-state CCSD(T) approach, pro-... 

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. 

Kowalski K, Piecuch P (2000) The active-space equation-of-motion coupled-cluster methods for excited states The EOMCCSDt approach. J Chem Phys 113 8490-8502. 

Although length of the many-body expansion of Hn,open is enormous, very few terms enter a particular approximate scheme. For example, the EOM-CCSD method needs one- and two-body components of H and certain types of the three-body H3 terms [33,34] (for further comments, see Ref. 60 cf., also, Sections 4 and 5). The situation gets complicated if we want to go beyond the EOMCCSD approximation and represent T as a sum of, for example, I), T2, and T3 components. For this reason, the only higher-than-two-body terms included in the current implementation of the EOM-CCSDT scheme are the three-body terms of the EOMCCSD method [46]. This approximation seems to work very well, even though the EOMCCSDT procedure defined in this way remains an n8 method. 

An interesting feature of the PE3 approximation, apart from its potential usefulness in the calculations (the T3-like terms analogous to T3 contributions to EOMCCSDT that enter the PE3 and PE3 approximations are the same see Section 6), is its clear relationship to the following decomposition of the similarity transformed Hamiltonian 77 >open,... 

The above relationship between the PE3 approximation and Eq. (201) allows us to better understand the general structure of the EOMXCCSD equations. We can clearly see, for example, which terms are responsible for the non-Hermitian nature of the EOMXCCSD approach and what is the effect of Hermitizing the standard EOMCCSD approach in terms of various contributions to equations characterizing the EOMXCCSD (PE3 ) scheme. As we are going to demonstrate in Section 6, the most important non-Hermitian terms of the EOMXCCSD(PE3) and EOMXCCSD(PE3 ) approaches are the H (T., Tj) components, since it is quite likely that these components allow us to calculate some T3 contributions of the EOMCCSDT scheme via the n6 computational procedure. 

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