The Transition State Theory of Isotope Effects

We begin with the transition state theory result for the rate constant, Equation A 1.40. We shall need to consider bimolecular processes, A + B—+ C, for which the proper adaptation of Equation A1.40 is Equation A2.1. The quantity A El is 

The transition state sum omits the reaction coordinate degree of freedom since it is not a bound vibration and does not contribute to the zero-point energy in the transition state. E% and Er are respectively the energy of the potential energy surface at transition state and reactants. Then, 

The isotope effect is now found by taking the ratio of rate constants for the two isotopic systems (Equation A2.9). 

The energy difference AE is independent of isotopic substitution and cancels. We have assumed that the isotopic substitution is in A, so QB cancels also. 

We now refer to Appendix 1 to write the partition functions in terms of their translational, rotational, and vibrational components. Of the quantities appearing in the expressions for these components, only the molecular mass M, the moments of inertia /, the vibrational frequencies uu and the symmetry numbers a are different for the isotopic molecules all other factors cancel, leaving Equation A2.10. 

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Appendix 2 THE TRANSITION STATE THEORY OF ISOTOPE EFFECTS... 

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