Vibration-assisted tunneling: a semiclassical instanton approach

A simple method to find the instanton trajectories is developed. This method does not employ any approximation and ‘exact’ instanton trajectories have been located for several collinear symmetric reactions. Underlying the method is the notion of stability of periodic trajectories and the behaviour of the action derivatives. Applications to thermal rate constants calculations are presented showing that the method is suitable for quantitative rate constant predictions. In the deep tunnelling regime, where a classical rate underestimation is about two orders of magnitude, the semiclassical instanton rate is within a few percent of the exact quantum mechanical value. Then, the consistent amount of tunnelling involved in the heavy particle transfer, as for the collinear H+BrH reaction, shows that ‘corner-cutting’ is not necessary for tunnelling to occur, even if it is a sufficient condition to detect a significant presence of tunnelling effects.