Effects of frequency variation in modes orthogonal to the reaction path on condensed phase rate constants

We examine the effects of frequency variation along the reaction path in intramolecular or lattice modes on the rate constant for light atom transfer in the condensed phase. Accurate quantum mechanical calculations using the quasi-adiabatic propagator path integral representation of the flux-flux auto-correlation function reveal significant variations in the reaction rate compared with the constant frequency case. The vibrationally adiabatic approximation captures these effects rather faithfully if the frequency of these modes is high, relative to that of the reaction coordinate. Significant deviations from the predictions of the adiabatic approximation are observed when low variable frequency modes are involved. In such cases, the competition between the decrease in the reactive flux accompanying a tightening or dilation of the reaction path valley and corner-cutting effects arising from sharp curvature of the reaction path leads to positive or negative corrections to the predictions of the adiabatic model.