Equilibrium Theory of Reaction Rates The Transition-state Method

In the preceding sections we have shown that at sufficiently high concentrations or for molecules sufficiently complex, unimolecular reactions may proceed in such a manner that the disturbance of the equilibrium distribution of reactive molecules does not significantly affect the rate of reaction. Under such conditions it is permissible to approximate the rate of a unimolecular reaction by its high-pressure rate. But such a pseudoequilibrium invites still another approach to the formulation of the theory of reactions. This approach, known as the transition-state method, was first outlined by Marcellin, was developed further by Rodebush and Rice and Gershinowitz, and was put in its present form by Eyring and Evans and Polanyi. -  

The method proposes that every molecule A that reacts does so by being excited to some state of energy E PJ, the critical energy for the reaction, and having the configuration that corresponds to a maximum in its 

We see that the results of this approach are identical in form with the result obtained by an application of the detailed theory to a quantum-mechanical model for the reaction [Eq. (XI.6.10)]. 

If now it is assumed that the rupture of the molecule that leads to reaction corresponds to the motion of one of the normal coordinates of the complex of frequency v = Vc and further that Vc kT/hy then the individual vibrational partition function for this coordinate is 9 = (1 — = 

In the case that the vibrations of complex and normal species are all high viy I t kT/h) or identical and that k = 1 and the dimensions of the molecule are not changed by activation so that Q%t = Qrot we have 

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