Transition state theory the rate of barrier crossing

1 Transition state theory the rate of barrier crossing 

Transition state theory is a method for predicting the rate of chemical reactions. Technically, what the theory provides is the rate of crossing of a barrier. If there is only one barrier between reactants and products, then transition state theory specifies how to compute the reaction rate constant. Transition state theory assumes the vahdity of only one condition, but a cardinal one, namely that on one side of the barrier, the states of the system are in equilibrium. If there is only one barrier between reactants and products, then it is the reactants that should be kept at equihbrium. The simplicity of transition state theory is lost if the reactants are state-selected.  

The equihbrium condition required by the theory makes one sometimes think that transition state theory is a theory like that described in Section 6.2 where there is a collision complex. This impression is categoricaUy false. If anything, transition state theory is atthe opposite extreme. It is a theory of direct crossing. In one and only one go, the system is to cross the barrier. The statistical assumption made by transition state theory is not about the dynamics of the reaction instead, it is about the equihbrium nature of the reactants that are located to one side of the barrier. A very important implication of this assumption is that it allows the theory to be cast in structural terms, terms that are familiar to chemists. 

The statistical assumption made by transition state theory is a specification of the reactants to which the theory can be apphed. It is not an approximation. Either the reactants that you are interested in are in equihbrium and the theory is applicable or the reactants are not in equihbrium and you should look for another way to compute the reaction rate. Transition state theory does make one simple and physicaUy clear approximation to which we now turn. 

The e q)iession for the rate of barrier crossing, as obtained by transition state theory, can also be iisefiil applied when there is a well, with barriers on either side, separating reactants and products. Under such circumstances, the theory can be applied but it is plied to the crossing of each barrier separately, as discussed in detail in Section 6.2. Such an implication requires that the motion of the system rattles many times in the well region between the two barriers, see Section 5.3.3. Transition state theory itself conmutes the rate of barrier crossing, and this rate equals the reaction rate only for direct reactions. 

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