Isotope Effect in Transition State Theory

Discussion of Isotope Effect in Transition State Theory 

The transition state theory proceeds on the assumption that there is a single potential energy surface along which the reaction takes place. For the usual reaction there will be a barrier between the part of coordinate space corresponding to reactants and the part of space corresponding to products. The reaction will then take place over the path corresponding to the lowest barrier. 

The transition state is located at the top of the barrier along the path Of decomposition. Thus the transition state lies in a trough and in general will be stable along all degrees of freedom except along the path of decomposition. The transition state theory leads to the following well-known expression for the rate equation constant k, 

The initial assumption is made — xa. This assumption will be discussed further subsequently. The problems of calculating ratios of rate constants become then a matter of calculation of ratios of isotopic partition functions. The latter is simplified by the fact that the potential energy surfaces for isotopic molecules are the same to a very high degree of approximation. 

The theory of calculation of ratios of isotopic partition functions has been developed in detail for exchange equilibria in gases. The formulation of Bigeleisen and Goeppert-Mayer,10 which writes everything in terms of the vibrational frequencies of the molecules, will be reviewed. Classically QAJQAx is where the tn/s are 

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B. Discussion of Isotope Effect in Transition State Theory... 

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