Abstract
Franck−Condon (FC) factors and the FC density associated with an electron transfer reaction are calculated for a betaine molecule, pyridinium-N-phenoxide betaine (4-(1-pyridinio)phenolate) in its S1 excited state. FC factors and density functions for harmonic vibrational modes are computed first by modifying the three level-fixed binary tree algorithm (Ruhoff, P. T.; Ratner, M. A. Int. J. Quant. Chem. 2000, 1, 383), a sum-over-states method based on recursion relations. This modified method allows the calculation of FC factors for 60 vibrational modes and avoids memory problems due to the large number of modes. The effects on the FC density of frequency shifts and mode mixing (Duschinky rotation) are included. For comparison, the more efficient time-dependent alternative is also employed for the calculation of the FC density function for the harmonic motion. In all cases, for a torsional motion which cannot be described by a harmonic potential, the FC density function is computed through the time-dependen...
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