Calculating Absorption and Fluorescence Spectra for Chromophores in Solution with Ensemble Franck-Condon Methods

Accurately modeling absorption and fluorescence spectra for molecules in solution poses a challenge due to the need to incorporate both vibronic and environmental effects, as well as the necessity of accurate excited state electronic structure calculations. Nuclear ensemble approaches capture explicit environmental effects, Franck-Condon methods capture vibronic effects, and recently introduced ensemble-Franck-Condon approaches combine the advantages of both methods. In this study, we present and analyze simulated absorption and fluorescence spectra generated with combined ensemble-Franck-Condon approaches for three chromophore-solvent systems and compare them to standard ensemble and Franck-Condon spectra, as well as to experiment. Employing configurations obtained from ground and excited state ab initio molecular dynamics, three combined ensemble-Franck-Condon approaches are directly compared to each other to assess the accuracy and relative computational time. We find that the approach employing an average finite-temperature Franck-Condon lineshape generates spectra nearly identical to the direct summation of an ensemble of Franck-Condon spectra at one-fourth of the computational cost. We analyze how the spectral simulation method, as well as the level of electronic structure theory, affects spectral lineshapes and associated Stokes shifts for 7-nitrobenz-2-oxa-1,3-diazol-4-yl (NBD) and Nile Red in dimethyl sulfoxide (DMSO), and 7-methoxy coumarin-4-acetic acid (7MC) in methanol. For the first time, our studies showcase the capability of combined ensemble-Franck-Condon methods for both absorption and fluorescence spectroscopy and provide a powerful tool for simulating linear optical spectra.