Frequency Factor in the Transition Probability

The value of the frequency factor (the pre-exponential factor), A, in the expression for the average transition probability 

For entirely nonadiabatic transitions, the transition probabilities are so small that the reaction does not disturb the equilibrium distribution in the nuclear subsystems (q9 Q, s), and the calculation of the mean transition probability is reduced to averaging the corresponding local transition probability over the equilibrium distribution of the coordinates q, Q, s  

In this case, A is independent of the frequency characteristics of the nuclear subsystems. 

As for the adiabatic transitions, various situations are possible when the system involves several subsystems (e.g., r, s, and q). 

The frequency factor As for the transition probability Wlf(q) in subsystem (s) depends on the values of the probabilities Wlf(q, s) and Wfi(q,s). If the latter are sufficiently small, then we have 

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Thus, in this case the pre-exponential factor (the frequency factor) in the transition probability depends on the relaxation time rq. Various refinements of this simple model were made in many papers by considering the change of the intramolecular structure of the reactants,79,80 cases of several relaxation times,88 etc. 

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