What is the Key for Accurate Absorption and Emission Calculations, Energy or Geometry?

Using a hierarchy of wave function methods, namely ADC(2), CC2, CCSD, CCSDR(3), and CC3, we investigate the absorption and emission energies in a set of 24 organic compounds. For all molecules, reference values are determined at the CC3//CC3 or CCSDR(3)//CCSDR(3) levels and the energetic and geometric effects are decomposed considering all possible methodological combinations between the five considered methods. For absorption, it is found that the errors are mainly energy-driven for ADC(2), CC2, and CCSDR(3), but not for CCSD. There is also an error compensation between the errors made on the geometries and transition energies for the two former approaches. For emission, the total errors are significantly larger than for absorption due to the significant increase of the structural component of the error. Therefore, the selection of a very refined method to compute the fluorescence energy will not systematically provide high accuracy if the excited-state geometry is not also optimized at a suitable level of theory. This is further demonstrated using results obtained from TD-DFT and hybrid TD-DFT/wave function protocols. We also found that, compared to full CC3, only CCSDR(3) is able to deliver errors below the 0.1 eV threshold, a statement holding for both absorption (mean absolute error of 0.033 eV) and emission (mean absolute error of 0.066 eV).