Time-dependent density functional theory investigation of the absorption, fluorescence, and phosphorescence spectra of solvated coumarins

Using time-dependent density functional theory (TD-DFT) and the polarizable continuum model, we have computed the electronic transitions of a large panel of coumarin dyes in their enol, keto, cationic, and anionic forms. Several processes have been studied: absorption, fluorescence, 0-0 phosphorescence, and triplet-triplet excitations. For each process, detailed comparison with experimental data has been carried out. Using the PBE 0 ∕ 6 - 31 + G ( d ) scheme, it turns out that for a given electronic transition the experimental shifts resulting from the substitution of the coumarin core are nicely reproduced. Indeed, once a simple statistical correction is applied, the mean absolute errors on the absorption and fluorescence wavelengths are limited to 8 nm ( 0.09 eV ) and 9 nm ( 0.07 eV ) , respectively. A valuable correlation between the experimental and theoretical phosphorescence auxochromic displacements has also been unravelled. The differences between the wavelengths of the various electronic processes of a given dye tend to be fairly predicted, especially for the fluorescence-phosphoresence shifts that are strongly overestimated by TD-DFT.