Effects of Excited State Vibrational Coherence on Photo-Induced Electron Transfer Rates in Dye-Sensitized Nanocrystalline TiO<sub>2</sub>

Based on the expression for the electron occupation probability of the excited state, and the empirical formula of the Franck-Condon factor, theoretical investigations of the effects of excited state vibrational coherence on photo-induced electron transfer rates of a nanocrystalline TiO2 semiconductor were carried out. The calculations were performed at different values of reorganization energy, various energetic positions for the injecting level and several initial vibrational wave packets, using a single vibrational spacing mode of 0.2 eV and a conductor bandwidth of 1.4 eV. Comparing the results to the published literature confirmed that the empirical formula should be rationalized with modified parameters of A=16, B=0.4735, and C=0.1. This work will provide a theoretical basis and guidance for future experimental work concerning photo-induced electron transfer rates as well as research into applications of dyesensitized solar cells.