Understanding the optical band shape: Coumarin-153 steady-state spectroscopy

We have developed a band-shape analysis of optical transitions in polarizable chromophores characterized by large magnitudes of the transition dipole (intense transitions). The model is tested on steady-state spectra of the coumarin-153 optical dye, employing an explicit solvent description accounting for dipole moment, quadrupole moment, and polarizability of the solvent molecules. The calculations are performed for solvents ranging from nondipolar to strongly dipolar. The solvent dependence of both the experimental Stokes shift and the spectral width is satisfactorily reproduced over the whole polarity range. The optical width is shown to demonstrate a qualitatively different solvent dependence for absorption and emission. The solvent-induced absorption width increases with solvent polarity, whereas the solvent-induced emission width passes through a maximum. This is a result of non-Gaussian statistics of the energy gap fluctuations in polarizable/electronically delocalized chromophores. The total (i.e., solvent and vibrational) emission width tends to pass through a broad maximum at low solvent polarities, decreasing with solvent polarity for highly polar solvents. This results from the combined influence of a solvent-induced mixing of the vacuum adiabatic states and a decrease of the vibrational reorganization energy with increasing solvent polarity. The latter effect arises as a result of a coupling of the vibrational and solvent nuclear modes due to the electronic state occupation number difference, making the vibrational reorganization energy solvent-dependent. The study revels a breakdown of the linear relation between the solvent-induced width and Stokes shift. The model suggests that the Franck-Condon factor of intense optical lines should significantly depend on the magnitude of the transition dipole.