Absorption and Emission Spectral Shapes of a Prototype Dye in Water by Combining Classical/Dynamical and Quantum/Static Approaches

We study the absorption and emission electronic spectra in an aqueous solution of N-methyl-6-oxyquinolinium betaine (MQ), an interesting dye characterized by a large change of polarity and H-bond ability between the ground (S0) and the excited (S1) states. To that end we compare alternative approaches based either on explicit solvent models and density functional theory (DFT)/molecular-mechanics (MM) calculations or on DFT calculations on clusters models embedded in a polarizable continuum (PCM). In the first approach (ClMD), the spectrum is computed according to the classical Franck-Condon principle, from the dispersion of the time-dependent (TD)-DFT vertical transitions at selected snapshots of molecular dynamics (MD) on the initial state. In the cluster model (Qst) the spectrum is simulated by computing the quantum vibronic structure, estimating the inhomogeneous broadening from state-specific TD-DFT/PCM solvent reorganization energies. While both approaches provide absorption and emission spectral shapes in nice agreement with experiment, the Stokes shift is perfectly reproduced by Qst calculations if S0 and S1 clusters are selected on the grounds of the MD trajectory. Furthermore, Qst spectra better fit the experimental line shape, mostly in absorption. Comparison of the predictions of the two approaches is very instructive: the positions of Qst and ClMD spectra are shifted due to the different solvent models and the ClMD spectra are narrower than the Qst ones, because MD underestimates the width of the vibrational density of states of the high-frequency modes coupled to the electronic transition. On the other hand, both Qst and ClMD approaches highlight that the solvent has multiple and potentially opposite effects on the spectral width, so that the broadening due to solute-solvent vibrations and electrostatic interaction with bulk solvent is (partially) counterbalanced by a narrowing of the contribution due to the solute vibrational modes. Qst analysis evidences a pure quantum broadening effect of the spectra in water due to vibronic progressions along the solute/solvent H-bonds.