Evaluation of using the time-dependent density functional theory in studying the fluorescence properties of coumarin derivatives

In this study, the performance of predicting fluorescence properties using 11 density functional theory (DFT) functionals was evaluated through a comparison with experimental results of 30 coumarin derivatives. The results revealed that there was no significant difference in the predictive performance of maximum emission wavelengths (MEWs) when using the optimized geometries obtained with the PBE0 functional compared to the other studied functionals. The global hybrid functionals with a small constant fraction of HF exchange (B3LYP, PBE0, M06), double-hybrid functionals (APDF and PW6B9D3), global hybrid functionals with a large constant fraction of HF exchange (M06-2X), and long-range correction functionals (CAM-B3LYP and ωB97X-D) exhibited good predictive ability. The linear relationship coefficient (R) values, between the experimental and calculated MEWs, ranked in the strong linear correlation group. Among them, the functionals B3LYP, PBE0, M06, APDF, and PW6B9D3 yielded the best mean signed error (MSE), mean absolute error (MAE), and root mean square error (RMSE) values. The values (MSE, MAE, RMSE) for the B3LYP, PBE0, M06, APDF, and PW6B9D3 functionals in nanometers (nm) were as follows: (−47, 53, 58), (−59, 61, 66), (−56, 58, 63), (−55, 59, 64), and (−58, 59, 65), respectively. In electronvolts (eV), the values were: (0.34, 0.37, 0.41), (0.44, 0.45, 0.49), (0.41, 0.42, 0.46), (0.41, 0.42, 0.46), and (0.43, 0.43, 0.47), respectively. The pure density functionals (PBE and BP86) and LC-ωPBE exhibited poor predictive ability, with a linear relationship coefficient (R) only ranking in the medium linear correlation group. To enhance prediction accuracy, the corrected calculated MEWs, based on the linear correlation between the calculated and experimental MEWs, were determined. This correction resulted in substantially reduced values for the corrected statistical parameters (MSEcor, MAEcor, and RMSEcor) when compared to the uncorrected values. Importantly, this correction also minimized the variation in prediction performance among different DFT functionals, providing users with greater flexibility in selecting the most suitable DFT functional for their specific needs.