A unified framework for quantum activated rate processes .1. General theory

It is shown that several existing quantum reaction rate theories can be unified around a single mathematical framework. These theories include the high temperature parabolic barrier approximation, the instanton approach, and the path integral quantum transition state theory. In particular, it is shown that the quantum reactive flux can be approximated as a product of a simple frequency factor times the imaginary part of the barrier partition function. The latter term arises from the steepest descent solution to the partition function in the barrier region, while the prefactor can he interpreted as the frequency of the stationary barrier trajectory. Importantly, the analysis introduces the imaginary time Feynman path centroid variable into the expression for the quantum activated rate constant in an a priori way. The present theoretical framework also allows for an analytical treatment of the quantum activated rate problem in the vicinity of the crossover temperature, and for a generalization of the saddle point analysis in an extended-dimensional quantum mechanical space of the Fourier path modes. (C) 1996 American Institute of Physics.