Toward a Theoretical Quantitative Estimation of the λmax of Anthraquinones-Based Dyes

We have computed the absorption spectra of a large series of anthraquinone dyes by using the time-dependent density functional theory (TD-DFT) for the excited-state calculations and the polarizable continuum model (PCM) for evaluating bulk solvent effects. On one hand, we compare the results obtained with the B3LYP and the PBE0 hybrid functionals, combined with different atomic basis sets. On the other hand, using multiple linear regression, we take advantage of the λmax predicted by these two functionals in order to reach the best agreement between theoretical estimates and experimental measurements. It turns out that 1. PBE0 provides more accurate results than B3LYP; in addition the average errors provided by the former are less basis set dependent. 2. Multiple linear regression provides excited state spectra in better agreement with experiment than any simple linear fit that could be performed. 3. Using our best fitting procedure, we obtained a mean absolute error of 6 nm for a set of 66 anthraquinones, with no deviations exceeding 25 nm. The related standard deviation, useful for predictions, is only 8 nm, i.e.,[Formula: see text] =[Formula: see text] ± 8 nm (or ±0.05 eV) for unknown anthraquinone compounds.