Temperature Dependences of Kinetic Isotope Effects

Abstract

Model-reaction calculations are used to investigate the expected incidence of temperature-dependence anomalies produced by the harmonic-vibrational contributions to kinetic isotope effects. These “anomalies” are defined as deviations from a smooth-monotonic log–log plot of isotopic rate-constant ratio vs temperature. Such deviations include inflections, extrema, and crossovers (inversions in direction with respect to the infinite-temperature, classical limit). The model systems studied represent a variety of mechanisms ranging from simple bond break to simultaneous rupture or formation of four bonds. The effects on the temperature-dependence-curve shapes of off-diagonal force-constant changes, variations in potential-barrier curvature, and tunneling corrections are examined. The major emphasis is on carbon and hydrogen isotope effects although some nitrogen and oxygen effects are also considered. Out of the 476 isotopic reaction pairs investigated, approximately 25% were found to be anomalous. Several examples of corresponding deuterium and tritium isotope effects exhibiting different types of temperature-dependence anomalies were found. Situations most likely to lead to anomalous temperature behavior are discussed. It is concluded that kinetic-isotope-effect temperature-dependence anomalies should occur fairly commonly although, at least for monosubstitution with carbon and hydrogen isotopes, probably less frequently than in equilibrium isotope effects. However, the anomalous region of a temperature-dependence curve might not fall within the range of experimental accessibility. No method of detecting an anomaly from observation of a portion of the temperature-dependence curve removed from the anomalous region has been found. It is shown that the quality of data fitting with the gamma-bar approximation cannot be used as a reliable criterion of nonanomalous temperature behavior. The significance of kinetic-isotope-effect temperature-dependence anomalies to investigations of reaction mechanisms is discussed with respect to both approximation methods and model-calculation force-field-fitting procedures.