A simple method for calculating quantum effects on the temperature dependence of bimolecular reaction rates: Application to H-2+H -> H+H-2 and CH4+H -> CH3+H-2

The temperature dependence of thermal rate constants for hydrogen atom abst raction reactions is studied using transition-state theory with temperature -dependent effective potential energy functions derived from a quantum mech anical path integral analysis with a low-temperature correction. The-theory uses temperature-dependent activation energies determined from Gaussian av erages of an empirical potential. Simple analytic expressions are obtained for rate constants. To test the theory the rate constant for H-2 + H is cal culated, and the predicted curvature of the Arrhenius plot is shown to agre e with results from accurate quantum scattering calculations. The predicted curvature for CH4 + H is compared with experimental results and shown to g ive better agreement with the observed temperature dependence than do commo nly used empirical fits. The expression k(T) = aT exp[-E-0 + E1Teff-1 + E2T eff-3/2)/RT], with T-eff = T + T-0, is suggested for the rate constant for CH4 + H, with the parameters a, E-0, E-1, E-2, and T-0 obtained from theory rather than by fitting to the experimental reaction rates.