Revisiting the Performance of Time-Dependent Density Functional Theory for Electronic Excitations: Assessment of 43 Popular and Recently Developed Functionals from Rungs One to Four

In
this paper, the performance of more than 40 popular or recently
developed density functionals is assessed for the calculation of 463
vertical excitation energies against the large and accurate QuestDB
benchmark set. For this purpose, the Tamm–Dancoff approximation
offers a good balance between computational efficiency and accuracy.
The functionals ωB97X-D and BMK are found to offer the best
performance overall with a root-mean square error (RMSE) of around
0.27 eV, better than the computationally more demanding CIS­(D) wave
function method with a RMSE of 0.36 eV. The results also suggest that
Jacob’s ladder still holds for time-dependent density functional
theory excitation energies, though hybrid meta generalized-gradient
approximations (meta-GGAs) are not generally better than hybrid GGAs.
Effects of basis set convergence, gauge invariance correction to meta-GGAs,
and nonlocal correlation (VV10) are also studied, and practical basis
set recommendations are provided.