Theoretical studies of hydrogen kinetic isotope effects

Abstract

__Theoretical studies of hydrogen kinetic isotope effects are carried out with particular emphasis on the development of methods of analysis for the interpretation of experimental kinetic-isotopeeffect data. Theoretical "exact" isotope-effect data are obtained by computer using a statistical-mechanical expression developed by Bigeleisen. __"Exact" model-reaction calcul11tions are used to determine the lower limit to the Arrhenius pre-exponential factors, AQ' for primary hydrogen kinetic isotope effects in the harmonic approximation and in the absence of quantum-mechanical tunneling. Attempts are made to force the AQ values as low as possible solely through adjustments in the force-constant changes, at the isotopic positions, between reactants and transition states. Values of AQ lower than- 0.7 could not be achieved without making the models so mechanistically unreasonable as to render the results meaningless. This result is in excellent agreement with a prediction made by Bell on the basis of a less rigorous theoretical treatment and lends support to the common practice of interpreting experimental values of AQ significantly lower than 0.5 as due to the operation of tunneling in the reactions. __A method of using Arrhenius pre-exponential factors for secondary hydrogen kinetic isotope effects as sources of information in the elucidation of mechanisms of chemical reactions is developed. The Arrhenius intercepts associated with the individual force-constant changes, from reactant to transition state at the isotopic position(s), occurring in a model reaction are found, under certain conditions, to be additive to give the intercept associated with the overall reaction. The same type of additivity is valid for the quantum-mechanical contribution to the kinetic isotope effect. These additivity relationships provide a basis for a systematic method of determining force fields for real reaction systems through a combination 'of experimental measurements . __It is shown theoretically that low-magnitude, primary, hydrogen kinetic isotope effects may be characterized by the same types of temperature-dependence irregularities that have been previously shown to be expected fairly commonly for secondary hydrogen isotope effects and primary heavy-atom isotope effects.