Title: 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.