Electronic decoherence and nonadiabatic chemical dynamics in betaine dye molecules

The effect of electronic decoherence on nonadiabatic (NA) transition rate is investigated with nuclear overlap/phase function (NOPF) and mixed quantum/classical molecular dynamics (MQC-MD) simulations are performed to obtain the NA transition rate on betaine dye molecules. First of all, spinboson model with ohmic spectral density is used to explore electronic decoherence. We obtain a decoherence function by comparing two solutions for the canonical NOPF based on quantum mechanical and mixed quantum/classical methods, respectively. We provide an electronic decoherence time under short time and high temperature limits. Secondly, electronic decoherence only induced by intramolecular vibrational motions is studied with the NOPF in the simplest betaine molecule, pyridinium-N-phenoxide betaine [4-(1-pyridinio)phenolate]. Decoherence times from several approximations are obtained, including the role of frequency shifts and Duschinsky rotation. We find that the low frequency torsional motion does not make any significant contribution to the decay of the NOPF. Frequency shifts have more effect on the decay of the NOPF, than Duschinsky rotation does, but the simplest spinboson model alone describes coherence decay quite well. At longer times, we observe an exponential decay modulated by phase recurrence, but the contribution of the exponential decay to the relaxation is small. Calculated ultrafast decoherence time scales from intramolecular vibrational motions indicate that nuclear motions in solute can have more influence on the total electronic decoherence than does solvent. Thirdly, Frank-Condon (FC) density function in the simplest betaine molecule is calculated, combining the sum-over-states method and the time-dependent method. The FC density function for harmonic vibrational modes is computed by a modified three level-fixed binary tree algorithm including the role of frequency shifts and Duschinsky rotation. For the torsional mode, FC density is computed with the time-dependent method. We find that frequency shifts affect FC density function more than Duschinsky rotation does. The lack of a strong exponential decay in the high frequency region of the FC density function implies that the vibrational motions in the simplest betaine fall onto the strong coupling limit. Finally, Nuclear NA coupling matrix elements by intramolecular vibrational motions are analytically calculated with the spin-boson model. Limitations and applications of the calculation are discussed.