Communication: Existence of the doubly excited state that mediates the photoionization of azulene

Abstract

A state-selective multireference coupled-cluster theory employing the single-reference formalism

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.…”

“…It is also possible that states with REL close to 2 have to be fitted to a different functional representation than that represented by Equation (A1). Nevertheless, in order to see if Equation (A1) (or similar equations relating δ μ to REL that we may propose in the future) can be used in practice to generate the δ-CR-EOMCC-level information on the basis of EOMCCSD calculations for organic species outside the set of 28 molecules examined in this work, which may have a mixture of singly and doubly excited states in their electronic spectra, we have used it to determine the vertical excitation spectrum of azulene, examined by us in [140], where we have discovered the previously unknown doubly excited state in the higher energy part of the spectrum near the ionisation threshold. The results are shown in Table A2.…”

“…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.…”