How Method-dependent Are Calculated Differences Between Vertical, Adiabatic, and 0-0 Excitation Energies?

Through a large number of benchmark studies, the performance of different quantum chemical methods in calculating vertical excitation energies is today quite well established. Furthermore, these efforts have in recent years been complemented by a few benchmarks focusing instead on adiabatic excitation energies. However, it is much less well established how calculated differences between vertical, adiabatic and 0-0 excitation energies vary between methods, which may be due to the cost of evaluating zero-point vibrational energy corrections for excited states. To fill this gap, we have calculated vertical, adiabatic, and 0-0 excitation energies for a benchmark set of molecules covering both organic and inorganic systems. Considering in total 96 excited states and using both TD-DFT with a variety of exchange-correlation functionals and the ab initio CIS and CC2 methods, it is found that while the vertical excitation energies obtained with the various methods show an average (over the 96 states) standard deviation of 0.39 eV, the corresponding standard deviations for the differences between vertical, adiabatic, and 0-0 excitation energies are much smaller: 0.10 (difference between adiabatic and vertical) and 0.02 eV (difference between 0-0 and adiabatic). These results provide a quantitative measure showing that the calculation of such quantities in photochemical modeling is well amenable to low-level methods. In addition, we also report on how these energy differences vary between chemical systems and assess the performance of TD-DFT, CIS, and CC2 in reproducing experimental 0-0 excitation energies.