Pairwise distribution of reagents

When the reagents are located in the form of isolated pairs, so that it is possible to neglect the reactions between the particles from different pairs, the total kinetics of an electron tunneling reaction can be obtained by averaging the kinetics for the separate pairs. Let the distribution of pairs of donors and acceptors over the distance between them, R, at the initial instant of time (t = 0) be described by the function f(jR) normalized accord- 

The simplest type of pairwise distribution is a rectangular distribution. It has the form 

Substituting eqns. (2) and (4) into eqn. (3), we obtain the following result for times of observation t, satisfying the condition R, g(a/2)ln vt R2 

This relation corresponds to the so-called stepwise approximation of the exponential term under the integral of eqn. (3) since it has been obtained under the assumption that this term is equal to 1 for the reagent pairs with the distances R Rt and to 0 for those with R Rt where 

The tunneling distance R, which appears in the right-hand side of eqn. (8) is such that, for the pairs with R Rt, the probability of decay by the time t is close to 1 while, for the pairs with R Rt, it is practically equal to zero. Thus, both the right- and the left-hand sides of eqn. (8) represent the fraction of pairs which avoided the decay by the time t. 

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With a pairwise distribution of reagents it is impossible to find separately the parameters ve and ae from the kinetic curves in the majority of practically important situations. Only combinations of these parameters can be found. This is, first of all, connected with the fact that, for real systems, the form of the pair-wise distribution function is, as a rule, unknown. In addition, with the pair-wise distribution it is usually also impossible to determine the initial concentration n(0). 

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