Examination of the viability of the Collins-Kimball model and numerical calculation of the time-dependent energy gap law of photoinduced charge separation in polar solution Original Research Article

Viability of the analysis using the Collins-Kimball model for the rate constant of photoinduced charge separation reactions in polar solutions is investigated. In the Collins-Kimball model, it is assumed that the reaction occurs only at a specified distance in the encounter between donor and acceptor molecules under mutual diffusional motion while in real systems the reaction can occur over a range of distances. By comparing the fluorescence decay curve obtained by the Collins-Kimball model with the decay curve calculated numerically using the model incorporating a suitable distance dependence of the reaction rate, we found that the Collins-Kimball model is viable with some reservation. Using the numerically calculated distance distribution function of donor and acceptor molecules, we calculated time-dependent energy gap laws of photoinduced charge separation reactions. The calculated energy gap law for t = 0 fits well the experimental data obtained by a transient effect analysis of the fluorescence decay curve (S. Nishikawa, T. Asahi, T. Okada, N. Mataga and T. Kakitani, Chem. Phys. Letters 185 (1991) 237). The calculated energy gap law for t → ∞ fits very well the experimental data obtained by the stationary state fluorescence quenching measurements (D. Rehm and A. Weller, Israel J. Chem. 8 (1970) 259).