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A Simple Method for Calculating Quantum Effects on the Temperature Dependence of Bimolecular Reaction Rates: An Application to $CH_4 + H \to CH_3 + H_2$

The temperature dependence of the rate of the reaction CH_4+H \to CH_3+H_2 is studied using classical collision theory with a temperature-dependent effective potential derived from a path integral analysis. Analytical expressions are obtained for the effective potential and for the rate constant. The rate constant expressions use a temperature-dependent activation energy. They give better agreement with the available experimental results than do previous empirical fits. Since all but one of the parameters in the present expressions are obtained from theory, rather than by fitting to experimental reaction rates, the expressions can be expected to be more dependable than purely empirical expressions at temperatures above 2000 K or below 350 K, where experimental results are not available.