Effect of reaction path curvature and dimensionality on the accuracy of classical transition state theory

Abstract

Using a simple dynamical approximation based on the reaction path Hamiltonian of Miller, Handy, and Adams [J. Chem. Phys. 72, 99 (1980)], it is shown how reaction path curvature and dimensionality affect the accuracy of classical transition state theory. Specifically, an explicit expression is obtained for the critical energy up to which classical transition state theory is exact, and this critical energy is seen to vary inversely with the curvature of the reaction path. The model also shows that for energies above this critical energy transition, state theory deviates less from the correct result the larger the dimensionality (i.e.,the number of degrees of freedom) of the system. Finally, for the canonical (i.e.,thermally averaged) rate constant, as opposed to the microcanonical case, the fractional error in transition state theory (i.e.,the transmission coefficient) is found in certain cases to be independent of dimensionality.