Kinetic Isotope Effects: Interpretation and Prediction Using Degrees of Rate Control

Kinetic isotope effects (KIEs) have been used for decades in catalysis research as a tool for clarifying reaction mechanisms. Significant primary kinetic isotope effects have usually been interpreted as being a result of isotope substitution at a site of bond breaking (or forming) in the rate-determining step in the reaction mechanism. However, quantitative analysis of the magnitude of the KIE in complex multistep reaction mechanisms is seldom reported. We prove here that the logarithm of the rate ratio for two isotopes is the weighted average over all species in the mechanism of their standard-state free energy difference between the two isotopes, divided by RT. The weighting factor is the degree of rate control (DRC) for that species (e.g., transition state, intermediate, reactant) when the rate is measured separately for each isotope. It is instead the degree of selectivity ratio control (DSRC) when the KIE is measured as the product selectivity in a parallel competition between two isotopes within the same reactant molecule. Since only a few species have non-zero DRCs (or DSRCs) for most reactions, only these few contribute to this weighted average and the KIE. We show that this provides a simple way to interpret and quantitatively predict kinetic isotope effects that is powerful in the insights it provides, allowing one to evaluate directly which species contribute most to the KIE. By applying it to H/D KIEs in several example mechanisms, we further show that the traditional way of interpreting KIEs that focuses only on the rate-determining step can easily lead to misunderstanding of KIE and the reaction mechanism. Finally, this highlights the importance to consider the effect of isotope substitution on the energies of all species with large DRCs (i.e, those whose energies are kinetically relevant). This method also offers opportunities for quantitative validation of mechanism-based microkinetic models.