Assessing the Performances of CASPT2 and NEVPT2 for Vertical Excitation Energies

Abstract: Methods able to simultaneously account for both static and dynamic electron correlations have often been employed, not only to model photochemical events, but also to provide reference values for vertical transition energies, hence allowing to benchmark lower-order models. In this category, both CASPT2 and NEVPT2 are certainly popular, the latter presenting the advantage of not requiring the application of the empirical ionization-potential-electron-affinity (IPEA) and level shifts. However, the actual accuracy of these multiconfigurational approaches is not settled yet. In this context, to assess the performances of these approaches the present work relies on highly-accurate ($\pm 0.03$ eV) \emph{aug}-cc-pVTZ vertical transition energies for 284 excited states of diverse character (174 singlet, 110 triplet, 206 valence, 78 Rydberg, 78 $n \to \pi^*$, 119 $\pi \to \pi^*$, and 9 double excitations) determined in 35 small- to medium-sized organic molecules containing from three to six non-hydrogen atoms. The CASPT2 calculations are performed with and without IPEA shift and compared to the partially-contracted (PC) and strongly-contracted (SC) variants of NEVPT2. We find that both CASPT2 with IPEA shift and PC-NEVPT2 provide fairly reliable vertical transition energy estimates, with slight overestimations and mean absolute errors of $0.11$ and $0.13$ eV, respectively. These values are found to be rather uniform for the various subgroups of transitions. The present work completes our previous benchmarks focussed on single-reference wave function methods (\textit{J.~Chem. Theory Comput.} \textbf{14}, 4360 (2018); \emph{ibid.}, \textbf{16}, 1711 (2020)), hence allowing for a fair comparison between various families of electronic structure methods. In particular, we show that ADC(2), CCSD, and CASPT2 deliver similar accuracies for excited states with a dominant single-excitation character.