Performance of the completely renormalized equation-of-motion coupled-cluster method in calculations of excited-state potential cuts of water

Benchmarking the completely renormalised equation-of-motion coupled-cluster approaches for vertical excitation energies

“…The aforementioned 1 1 B 3g (n 2 → π * 2 ) state of s-tetrazine, listed in Table I of [17], which could not be used in our overall statistical error analyses due to the absence of the reliable benchmark data to judge our δ-CR-EOMCC results, and 6 other states among the 54 states outside the set of 149 states listed in Table I of [17] are almost pure two-electron transitions, which many QC methods have problems with, but we have provided arguments, based on the successful track record involving various CR-EOMCC or δ-CR-EOMCC calculations, including quasi-degenerate excited states dominated by double excitations [63,70,71,[74][75][76]107,110,111,114,121,127,140,143] and the comparison of our best δ-CR-EOMCC (2,3),D excitation energies for the 1 1 B 3g (n 2 → π * 2 ) state of s-tetrazine with the recently published NEVPT2 data [23], that our δ-CR-EOMCC calculations for the doubly excited states found in this work and other additional states that have not been considered in the prior work [17][18][19][20][21][22][23][24][25] are accurate to within ∼0.2 − 0.3 eV. We have suggested full EOMCCSDT, active-space EOMCCSDt, or accurate MRCI calculations for all of the additional excited states found in our calculations to verify if our assessment of the accuracy of the δ-CR-EOMCC calculations for these extra states is correct.…”

“…The fact that the δ-CR-EOMCCSD(T),IA and δ-CR-EOMCC (2,3),A values are too high compared to the CASPT2 and TBE data is not surprising, since by relying on the Møller-Plesset rather than Epstein-Nesbet denominators in defining the corresponding triples corrections, as in Equation (9), these methods tend to overestimate excitation energies for doubly excited states [63,76]. A question arises though why there is a relatively large, ∼0.7-0.8 eV, discrepancy between the CASPT2/TBE and δ-CR-EOMCC (2,3),D data, given the excellent performance of the δ-CR-EOMCC (2,3),D approach, which uses the more robust Epstein-Nesbet-type denominator (Equation (8)) in the past applications involving doubly excited states [75,76,127,140,143]. We believe that our δ-CR-EOMCC(2,3),D result for the vertical excitation energy of the 1 1 B 3g (n 2 → π * 2 ) state, of 6.59 eV, when the MP2/6-31G * geometry of s-tetrazine is employed, or 6.55 eV, when the CR-CC(2,3),D/TZVP geometry is adopted, is more reliable than the previously reported CASPT2 and TBE values that range between 5.76 and 5.86 eV [17,21].…”

“…In the case of the EOMCCSD calculations, which place the excitation energy of the 1 1 B 3g (n 2 → π * 2 ) state of s-tetrazine at 13.19 eV, this is not surprising, since EOMCCSD fails when strongly multi-reference doubly excited states are considered. However, the discrepancy between the δ-CR-EOMCC and CASPT2/TBE results needs additional comments, since the δ-CR-EOMCC triples corrections, especially δ-CR-EOMCCSD(T),ID and δ-CR-EOMCC (2,3),D, have a successful track record in accurately describing excited states dominated by two-electron transitions (cf., e.g., [63,70,71,[74][75][76]107,110,111,114,121,127,140,143]). According to Table 1 (2,3),A, and δ-CR-EOMCC (2,3),D approaches lower the EOMCCSD excitation energy of the 1 1 B 3g (n 2 → π * 2 ) state, of 13.19 eV, to 8.46, 7.23, 7.97, and 6.59 eV, respectively.…”

“…As pointed out in Section 4.2, we have identified several additional states with significant contributions from double excitations, including, in addition to the above 1 1 B 3g (n 2 → π * 2 ) state of s-tetrazine, 6 other states with REL close to 2 that can be found among the 54 extra roots outside the set of 149 states listed in Table I of Schreiber et al [17] obtained in our EOMCC calculations, but none of these additional states can be considered in the overall error evaluation, since we do not have access to the appropriate high-level reference data which would allow us to assess performance of the δ-CR-EOMCC approaches in this case. On the basis of our past experiences with the δ-CR-EOMCC calculations [63,70,71,[74][75][76]107,111,127,140,143] and the previously discussed comparison of the δ-CR-EOMCC (2,3),D and NEVPT2 [23] results for the doubly excited 1 1 B 3g (n 2 → π * 2 ) state of s-tetrazine (cf. footnotes o and n to Tables 1 and 2, respectively), we may expect the results of our overall best δ-CR-EOMCC (2,3),D calculations for the excited states with REL close to 2 identified in this work to be accurate to within ∼0.2 − 0.3 eV, but we would need to perform additional high-level EOMCCSDT/EOMCCSDt or MRCI calculations, which are beyond the scope of the present study, to verify such a statement.…”

Accurate excited-state energetics by a combination of Monte Carlo sampling and equation-of-motion coupled-cluster computations

“…Indeed, when applied to excited-state potentials along bond breaking coordinates and excited states having significant double excitation contributions, the basic EOMCC method with singles and doubles (EOMCCSD), 3 where T and Rµ are truncated at T 2 and Rµ ,2 , respectively, and its LRCCSD analog, 9,10 which build the excited-state information on top of the ground-state CCSD calculation 18,19 and which are characterized by the relatively inexpensive computational steps that scale as n 2 o n 4 u [no (nu) is the number of occupied (unoccupied) correlated orbitals], produce errors in the excitation energies that usually exceed 1 eV, being frequently much larger. [20][21][22][23][24][25][26][27][28] Even when excited-state wave functions are dominated by one-electron transitions, EOMCCSD is not fully quantitative, giving errors on the order of 0.3-0.5 eV. 29 One can rectify these problems by turning to higher CC/EOMCC levels, such as the EOM extension of the CC approach with singles, doubles, and triples (CCSDT), 30,31 abbreviated as EOMCCSDT, where T and Rµ are truncated at T 3 and Rµ ,3 , 21,22,32 or the EOM counterpart of the CC method with singles, doubles, triples, and quadruples (CCSDTQ), [33][34][35][36] abbreviated as EOMCCSDTQ, where T and Rµ are truncated at T 4 and Rµ ,4 , 37,38 but methods of this type,…”