Analysis of kinetic isotope effects for nonadiabatic reactions

Factors influencing the rates of quantum mechanical particle transfer reactions in many-body systems are discussed. The investigations are carried out on a simple model for a proton transfer reaction that captures generic features seen in more realistic models of condensed phase systems. The model involves a bistable quantum oscillator coupled to a one-dimensional double-well reaction coordinate, which is in turn coupled to a bath of harmonic oscillators. Reactive-flux correlation functions that involve quantum-classical Liouville dynamics for chemical species operators and quantum equilibrium sampling are used to estimate the reaction rates. Approximate analytical expressions for the quantum equilibrium structure are derived. Reaction rates are shown to be influenced significantly by both the quantum equilibrium structure and nonadiabatic dynamics. Nonadiabatic dynamical effects are found to play the major role in determining the magnitude of the kinetic isotope effect for the model transfer reaction.