Using TD-DFT, we performed simulations of the adiabatic energies of 40 fluorescent molecules for which the experimental 0-0 energies in condensed phase are available. We used six hybrid functionals (B3LYP, PBE0, M06, M06-2X, CAM-B3LYP, and LC-PBE) that have been shown to provide accurate transition energies in previous TD-DFT assessments, selected two diffuse-containing basis sets, and applied the most recent models for estimating bulk solvation effects. In each case, the correction arising from the difference of zero-point vibrational energies between the ground and the excited states has been consistently determined. Basis set effects have also been carefully studied. It turned out that PBE0 and M06 are the most effective functionals in terms of average deviation (mean absolute error of 0.22-0.23 eV). However, both the M06-2X global hybrid that contains more exact exchange and the CAM-B3LYP range-separated hybrid significantly improve the consistency of the prediction for a relatively negligible degradation of the average error. In addition, we assessed (1) the cross-structure/spectra relationships, (2) the importance of solvent effects, and (3) the differences between adiabatic and vertical energies.

The band shapes corresponding to both the absorption and emission spectra of a set of 20 representative conjugated molecules, including recently synthesized structures, have been simulated with a Time-Dependent Density Functional Theory model including diffuse atomic orbitals and accounting for bulk solvent effects. Six hybrid functionals, including two range-separated hybrids (B3LYP, PBE0, M06, M06-2X, CAM-B3LYP, and LC-PBE) have been assessed in light of the experimental band shapes obtained for these conjugated compounds. Basis set and integration grid effects have also been evaluated. It turned out that all tested functionals but LC-PBE reproduce the main experimental features for both absorption and fluorescence, though the average errors are significantly larger for the latter phenomena. No single functional stands out as the most accurate for all aspects, but B3LYP yields the smallest mean absolute deviation. On the other hand, M06-2X could be a valuable compromise for excited-states as it reproduces the 0-0 energies and also gives reasonable band shapes. The typical mean absolute deviations between the relative positions of the experimental and theoretical peaks in the vibrationally resolved spectra are ca. 100 cm(-1) for absorption and 250 cm(-1) for emission. In the same time, the relative intensities of the different maxima are reproduced by TD-DFT with a ca. 10-15% accuracy.

Using a set of 40 conjugated molecules, we assess the performance of an "optimally tuned" range-separated hybrid functional in reproducing the experimental 0-0 energies. The selected protocol accounts for the impact of solvation using a corrected linear-response continuum approach and vibrational corrections through calculations of the zero-point energies of both ground and excited-states and provides basis set converged data thanks to the systematic use of diffuse-containing atomic basis sets at all computational steps. It turns out that an optimally tuned long-range corrected hybrid form of the Perdew-Burke-Ernzerhof functional, LC-PBE*, delivers both the smallest mean absolute error (0.20 eV) and standard deviation (0.15 eV) of all tested approaches, while the obtained correlation (0.93) is large but remains slightly smaller than its M06-2X counterpart (0.95). In addition, the efficiency of two other recently developed exchange-correlation functionals, namely SOGGA11-X and ωB97X-D, has been determined in order to allow more complete comparisons with previously published data.