Assessment of n-Electron Valence State Perturbation Theory for Vertical Excitation Energies

The multireference n-electron Valence State Perturbation Theory is applied to a benchmark set of 28 organic molecules compiled by Schreiber et al. J. Chem. Phys. (2008) 128, 13. Different types of low-lying vertical excitation energies are computed using the same geometries and TZVP basis set as in the original work. The previously published coupled cluster CC3 results are used as a reference. The complete active space second order perturbation theory (CASPT2) results, as well as the results of second order N-electron valence perturbation theory (NEVPT2) (both in their single-state variants) are evaluated against this reference set, which includes 153 singlet and 72 triplet vertical transition energies. NEVPT2 calculations are carried out in two variants: the partially contracted (PC) and the strongly contracted (SC) scheme. The statistical evaluation with respect to CC3 is found to be similar for both: the mean unsigned deviations is 0.28 eV for singlets and 0.16 eV for triplets for PC-NEVPT2, while it is 0.23 and 0.17 eV for SC-NEVPT2, respectively. Further analysis has shown that deficiencies in the zeroth-order wave functions, in particular for the subset of π → π* singlet excitations, are responsible for the largest deviations from CC3. Those states have either a charge transfer or an ionic character. For the remaining singlet and all triplet excitations the general trend was established that NEVPT2 tends to slightly overestimate excitation energies while CASPT2 slightly underestimates them. However, overall, both methods are of very similar accuracy provided that the IPEA shift is used in the CASPT2 method. Interestingly, the conclusions reached in this study are independent of the orbital canonicalization scheme used in the NEVPT2 calculation.