Preexponential factor of the rate constant of low-temperature chemical reactions. Fluctuational width of tunneling channels and stability frequencies

The effect of transversal vibrations on the tunneling rate is studied for the two-dimensional potential in terms of the instanton technique, which allows to obtain the Gutzwiller-Miller formula expressing the tunneling probability via the stability parameters as well as the analogue of the fluctuational-dissipative theorem for the rms transversal vibration coordinate. The vibrational-adiabatic approximation corresponds to a slow variation of the transversal vibration frequency ω along the tunneling path. The opposite case of a step-like variation of ω is also examined. In general, the transition probability is the product of the tunneling rate in the vibrational-adiabatic potential and the geometric transmission factor which is less than unity owing to reflection. The role of dissipation in the two-dimensional model is also discussed.