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Dynamical effects in electron transfer reactions. II. Numerical solution

Nadler, Walter and Marcus, R. A. (1987) Dynamical effects in electron transfer reactions. II. Numerical solution. Journal of Chemical Physics, 86 (7). pp. 3906-3924. ISSN 0021-9606.

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In part I a reaction–diffusion equation was introduced for the description of electron transfer reactions which are induced by fluctuations in both the solvent polarization and in the intramolecular vibrational coordinates. We analyze the model employing a generalized moment expansion for the time behavior of the survival probability Q(t), i.e., for the fraction of molecules that have not transferred their electron at time t. Numerical and, in the narrow reaction window limit, analytical solutions are given for the average survival times τ. When the contribution of the intramolecular coordinates is appreciable an approximate power‐law behavior τ∝τ^α_L, with 0<α≤1, is found for the dependence of τ on the solvent dielectric relaxation time τ_L, in the large τ_L regime. Within the framework of the generalized moment description Q(t) is approximated as a superposition of several optimized exponential functions. In the small and intermediate τ_L regimes it is found that a single‐ or bi‐exponential description, respectively, is sufficient. Simple formulas for such approximations in terms of the average survival times are given. Furthermore it is demonstrated that in the large τ_L regime a truly multiexponential time behavior for the survival probability is encountered which, over a certain range of time, can appear to be algebraic, i.e., Q(t) ∝t^(−γ). The relation of these results to experimental data is discussed.

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Additional Information:© 1987 American Institute of Physics. Received 24 October 1986; accepted 23 December 1986. We gratefully acknowledge the support of this research by an Office of Naval Research contract and a grant from the National Science Foundation. W. N. is pleased also to acknowledge support by a grant from the Deutsche Forschungsgemeinschaft (Schu 523/1-1) during a period where some of the concepts used in this paper were developed.
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Office of Naval Research (ONR)UNSPECIFIED
Deutsche Forschungsgemeinschaft (DFG)Schu 523/1-1
Classification Code:PACS: 82.20.Pm, 77.22.Gm, 31.70.Dk
Record Number:CaltechAUTHORS:20120626-123353890
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Official Citation:Dynamical effects in electron transfer reactions. II. Numerical solution Walter Nadler and R. A. Marcus J. Chem. Phys. 86, 3906 (1987);
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:32098
Deposited By: Ruth Sustaita
Deposited On:26 Jun 2012 21:43
Last Modified:26 Dec 2012 15:23

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