TD-DFT benchmark for UV-Vis spectra of coumarin derivatives

The predictive performances for maximum absorption wavelength of the PBE, BP86, PBE0, B3LYP, M06, M06-2X, CAM-B3LYP, LC-wPBE, APDF, wB97XD, and PW6B9D3 functionals have been benchmarked through comparison of maximum absorption wavelength values between calculation and experiment of 21 coumarin derivatives. For the results obtained from direct calculation by these functionals, the predictive performance decreases gradually in the following order: B3LYP > APDF > M06 > PW6B9D3 > PBE0 > BP86 > PBE > M06-2X > CAM-B3LYP > wB97XD > LC-wPBE. B3LYP functional gives the best predictive performance, with the smallest value of the mean absolute error (MAE = 15 nm) and the root mean square deviation (RMSD=19 nm). When using the results obtained through correction based on the linear correlation, the predictive performance decreases gradually in the following order: M06-2X > PBE0, M06, PW6B9D3 > B3LYP, APDF > CAM-B3LYP, LC-wPBE, wB97XD > PBE and BP86. M06-2X functional gives the best predictive performance, with the smallest values of MAE(fix) (7 nm) and RMSDfix (9nm). The correction is very necessary because the values of the corrected maximum absorption wavelengths are closer to the experimental maximum absorption wavelengths. The values of MAE(fix) and RMSDfix are much smaller than those of MAE and RMSD.