Quantum effects in the calculation of the transmission coefficient as applied to reaction rate constants

Quantum effects in the calculation of the transmission coefficient on the basis of the collision theory were found to be important when specific potential energy models were assumed. The fraction of collisions that are effective in reaction as obtained from a consideration of quantum results was typically about one half the fraction obtained classically. Results obtained from each of the potential models could not be considered classical except over an extremely limited temperature range. Over most of the temperature range either effective penetration or reflection was important for each of the potential models used. Effective penetration represents collisions that are effective in reaction with energy less than the activation energy; reflection represents collisions that are ineffective in reaction at an energy exceeding the activation energy. The results of this study could be applied to several different kinds of rate processes including those which are often described by the absolute reaction rate theory. This theory was applied with moderate success to rate processes such as reaction rates, molecular diffusion rates, momentum transport rates in viscous flow for both Newtonian and nonNewtonian fluids, and in other similar rate processes. Transport properties predicted by the absolute reaction rate theory when quantum effects aremore » neglected are generally higher than those measured experimentally. A correction on the order of magnitude of that found could give good agreement between predicted and experimental transport properties. The prediction of transport properties is not restricted to non- metallic substances but can with minor modification be used for liquid metals. The experimental temperature dependence of the rate constants was found to agree well with the temperature dependence calculated from the addition of quantum results. Experimental data showed many of the qualitative effects that were predicted by calculation. The method by which the quantum results were included allows a great deal of flexibility. Any arbitrary one dimensional potential model may be used. In addition any arbitrary normalized energy distribution can be employed. A finite-width potential model gave fair agreement with experimental results. The use of this model in general gives better resulis than classical results and should perhaps be used when a more exact potential model is unavailable. The effect of the energy distributions was found to be unimportant. The simple energy distribution model, which restricts effective collisions to those which occur along the line of centers for the reactant molecules, could be used exclusively. A program for the numerical solution of the transmission coefficient from the Schro--dinger wave equation was developed. The time necessary to obtain fifty energy points by use of an IBM-7074 would average about ten to fifteen minutes depending upon the spacing used. The integration of the energy distribution weighted with the transmission coefficient generally takes less than five minutes to evaluate the complete temperature dependence. (auth)« less