Dielectric Continuum Representation of the Environment

For a dielectric continuum environment, the probability flux correlation function is given by  

AG is the reaction free energy defined as the difference in the equilibrium free energies for the reactant and product surfaces  

The R mode reduced mass M and frequency Q are related to the reactant surface ej, Zp, Ze through the second derivative at the minimum  

These terms reflect the dynamical correlations between the R mode and the non-adiabatic coupling fluctuations. 

The rate expression in Eq. (16.15) can be simplifled signiflcantly under a series of well-deflned approximations. In the short-time high-temperature approximation for a Debye solvent, the solvent dynamics is negligible on the time scale of the probability flux correlation function, leading to the following simpliflcation  

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