Cross-Comparisons between Experiment, TD-DFT, CC, and ADC for Transition Energies

Considering 41 electronic transitions in small- and medium-sized organic molecules, we benchmark the performances of 36 hybrid functionals within time-dependent density-functional theory (TD-DFT) and nine wave function theory (WFT) methods [CCSDT, CC3, CCSDT-3, CCSDR(3), CCSD, CC2, ADC(3), ADC(2), and SOS-ADC(2)]. Compared to highly accurate experimental 0-0 energies, it turns out that all coupled cluster (CC) approaches that include contributions from the triples [i.e., CCSDT, CC3, CCSDT-3 and CCSDR(3)] deliver a root-mean-square error (RMSE) smaller than or equal to 0.05 eV. The remaining WFT methods [i.e., CCSD, CC2, ADC(3), ADC(2), and SOS-ADC(2)] yield larger deviations with RMSE lying between 0.11 and 0.27 eV. Irrespective of the exchange-correlation functional, TD-DFT yields larger deviations (RMSE >= 0.30 eV). For vertical transitions without clear experimental equivalents (such as vertical absorption and fluorescence), a comparison between TD-DFT and CC3 provides a globally unchanged ranking of the various functionals. However, the errors on emission energies tend to be larger than on absorption energies, hinting that studying the latter property is not sufficient to gain a complete view of TD-DFT's performances. Finally, by cross-comparisons between TD-DFT and WFT, we observe that the WFT method selected as reference significantly impacts the conclusions regarding the overall accuracy of a given exchange-correlation functional. For example, for vertical absorption energies, the "best" functional is TPSSh (RMSE = 0.29 eV) based on CC3 reference energies, while LC-omega PBE (RMSE = 0.12 eV) is superior to the other functionals when one considers ADC(3) as the reference method.