Transition state and recombination rate theories

There are two classes of reactions for which Eq. (2.10) is not suitable. Recombination reactions and low activation energy free-radical reactions in which the temperature dependence in the pre-exponential term assumes more importance. In this low-activation, free-radical case the approach known as 

FIGURE 2.2 Arrhenius plot of the specific reaction rate constant as a function of the reciprocal temperature. 

The concentration of the activated complex may be calculated by statistical thermodynamics in terms of the reactant concentrations and an equilibrium constant [1, 6], If the reaction scheme is written as 

However, one of the terms in the vibrational partition function part of Q is different in character from the rest because it corresponds to a very loose vibration that allows the complex to dissociate into products. The complete vibrational partition function is written as 

If species A is only a diatomic molecule, the reaction scheme can be represented by 

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