Extensive Time-Dependent Density Functional Theory (TD-DFT) calculations have been carried out in order to obtain a statistically meaningful analysis of the merits of a large number of functionals. To reach this goal, a very extended set of molecules (∼500 compounds, >700 excited states) covering a broad range of (bio)organic molecules and dyes have been investigated. Likewise, 29 functionals including LDA, GGA, meta-GGA, global hybrids, and long-range-corrected hybrids have been considered. Comparisons with both theoretical references and experimental measurements have been carried out. On average, the functionals providing the best match with reference data are, one the one hand, global hybrids containing between 22% and 25% of exact exchange (X3LYP, B98, PBE0, and mPW1PW91) and, on the other hand, a long-range-corrected hybrid with a less-rapidly increasing HF ratio, namely LC-ωPBE(20). Pure functionals tend to be less consistent, whereas functionals incorporating a larger fraction of exact exchange tend to underestimate significantly the transition energies. For most treated cases, the M05 and CAM-B3LYP schemes deliver fairly small deviations but do not outperform standard hybrids such as X3LYP or PBE0, at least within the vertical approximation. With the optimal functionals, one obtains mean absolute deviations smaller than 0.25 eV, though the errors significantly depend on the subset of molecules or states considered. As an illustration, PBE0 and LC-ωPBE(20) provide a mean absolute error of only 0.14 eV for the 228 states related to neutral organic dyes but are completely off target for cyanine-like derivatives. On the basis of comparisons with theoretical estimates, it also turned out that CC2 and TD-DFT errors are of the same order of magnitude, once the above-mentioned hybrids are selected.

The structure and visible spectra of a large panel of thioindigo dyes and derivatives have been evaluated using a TD-PBE0/6-311+G(2d,p)//PBE0/6-311G(d,p) approach explicitly taking bulk solvent effects into account by means of the polarizable continuum model. The influence of the solvent characteristics, the trans-cis isomerization, and the chemical substitution on the benzene rings have been investigated. In addition, hemi-thioindigo dyes, thiazine-indigo, chromophore-like molecules, and selenoindigo have been considered. Though the relative oscillator strengths of the two allowed visible transitions in the nonplanar cis isomers are not always correctly reproduced by theory, the agreement between theoretical and experimental results is far above expectations. For the 170 cases studied, we obtained a mean unsigned error on the predicted lambda(max) limited to 6.9 nm or 0.03 eV, with only 6 (4) cases for which the difference exceeds 20 nm (0.10 eV). These errors are 1 order of magnitude smaller than what has previously been reported for indigoids. A linear correlation between the central double bond length and the lambda(max) has been established, while the bond length and vibrational frequency of the carbonyl groups do not correlate with the thioindigo color. The higher excitation energies of the cis conformers, compared to the trans structures, result from a less stabilized LUMO in the former case. Indeed, for cis thioindigo, the two electron-rich (in the excited state) carbonyl units lie close to each other.

The UV/visible spectra of a series of indigo derivatives have been evaluated by using ab initio methods. The combination of the Polarizable continuum model for estimating bulk solvent effects with the TD-B3LYP6-311 + G(2d,p)B3LYP6-311G(d,p) level of approximation, leads to an accurate description of the wavelength of maximum absorption of indigoids compounds. Using this procedure, we have assessed the effects of both the surroundings (solvent and solid state) and the substitution pattern. For the latter, we obtained a mean absolute deviation of only 7 nm (0.02 eV) compared to experiment, for a set of 86 molecules/solvents.