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 (S<inf>0</inf>) and the excited (S<inf>1</inf>) 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 (Cl<inf>MD</inf>), 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 (Q<inf>st</inf>) 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 Q<inf>st</inf> calculations if S<inf>0</inf> and S<inf>1</inf> clusters are selected on the grounds of the MD trajectory. Furthermore, Q<inf>st</inf> spectra better fit the experimental line shape, mostly in absorption. Comparison of the predictions of the two approaches is very instructive: the positions of Q<inf>st</inf> and Cl<inf>MD</inf> spectra are shifted due to the different solvent models and the Cl<inf>MD</inf> spectra are narrower than the Q<inf>st</inf> 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 Q<inf>st</inf> and Cl<inf>MD</inf> 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. Q<inf>st</inf> analysis evidences a pure quantum broadening effect of the spectra in water due to vibronic progressions along the solute/solvent H-bonds.