The case of comparable donor and acceptor concentrations

When the concentrations of reagents have comparable values, it is necessary to pay attention to the correlation effect in the decay of different donors, i.e. to consider the fact that the spatial distribution of acceptors near the chosen donor can change as a result of the decay of the acceptors in the reactions with other donors neighbouring the chosen one. The rigorous derivation of kinetic equations with the consideration of such a correlation is, as far as we know, unavailable. The approximate description of the kinetics of a biomolecular electron tunneling reaction at n(t) = N t) can be given in terms of the pair density method with the help of eqn. (19) in which, however, N is not a constant quantity but depends on time in the same way as n(t), i.e. 

The method of conditional concentrations also leads to this system of equations. 

For the ratio of the concentration of the reagents at two different times t and tn, eqn. (28b) gives 

If only a small fraction of the reacting particles decays by the time t, so that the condition (7ia3/6)n(0)ln3v 1 is satisfied, then eqn. (29) yields 

Thus the reaction kinetics is characterized by the linear dependence of the concentration of the reagents on the logarithm of the observation time, similar to what was found for electron tunneling reactions in isolated pairs in the case of rectangular distribution of pairs over the distances [see eqn. (9)]. 

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