Quantum mechanical calculations coupled with a dynamical continuum model for the description of dielectric relaxation; Time dependent Stokes shift of coumarin C153 in polar solvents

We present here a study of the time dependent Stokes shift, performing quantum-mechanical calculations on coumarin C153 in polar solvents. The electrostatic interaction between the solute and the solvent is treated within the Polarizable Continuum Model, which allows us to use a molecular shaped cavity for the solute. In order to take into account that the sudden change in the solute electronic density after the S0 → S1 excitation can be accompanied by a non instantaneous rearrangement of a component of the solvent polarization, we use a non-equilibrium representation of the solvent response. We have implemented a procedure to calculate the solvation time correlation function (the theoretical counterpart of the Stokes shift), including experimental data of the complex dielectric permittivity ge(ω). The results that we have obtained are in good agreement with the experimental measurements. We will report the calculations for water, methanol, acetonitrile and dimethyl sulfoxide as solvents, showing that a correct treatment of dielectric relaxation generally needs a more detailed description of the solvent response than diffusive models.