Combining the Ensemble and Franck-Condon Approaches for Spectral Shapes of Molecules in Solution

Abstract

The correct treatment of vibronic effects is vital for the modeling of absorption spectra of solvated dyes, as many prominent spectral features can often be ascribed to vibronic transitions. Vibronic spectra can be computed within the Franck-Condon approximation for small dyes in solution using an implicit solvent model. However, implicit solvent models neglect specific solute-solvent interactions and provide only an approximate treatment of solvent polarization effects. Furthermore, temperature-dependent solvent broadening effects are often only accounted for using a broadening parameter chosen to match experimental spectra. On the other hand, ensemble approaches provide a straightforward way of accounting for solute-solvent interactions and temperature-dependent broadening effects by computing vertical excitation energies obtained from an ensemble of solute-solvent conformations. However, ensemble approaches do not explicitly account for vibronic effects and often produce spectral shapes in poor agreement with experiment. We address these shortcomings by combining the vibronic fine structure of an excitation obtained in the Franck-Condon picture at zero temperature with vertical excitations computed for a room-temperature ensemble of solute-solvent configurations. In this combined approach, all temperature-dependent broadening is therefore treated classically through the sampling of configurations, with vibronic contributions included as a zero-temperature correction to each vertical transition. We test the proposed method on Nile Red and the green fluorescent protein chromophore in polar and non-polar solvents. For systems with strong solute-solvent interaction, the approach yields a significant improvement over the ensemble approach, whereas for systems with weaker interactions, both the shape and the width of the spectra are in excellent agreement with experiment.