A Simple Method for Calculating Quantum Effects on the Temperature Dependence of Bimolecular Reaction Rates: Application to H2 + H → H + H2 and CH4 + H → CH3 + H2

Abstract

The temperature dependence of thermal rate constants for hydrogen atom abstraction reactions is studied using transition-state theory with temperature-dependent effective potential energy functions derived from a quantum mechanical path integral analysis with a low-temperature correction. The theory uses temperature-dependent activation energies determined from Gaussian averages of an empirical potential. Simple analytic expressions are obtained for rate constants. To test the theory the rate constant for H2 + H is calculated, and the predicted curvature of the Arrhenius plot is shown to agree with results from accurate quantum scattering calculations. The predicted curvature for CH4 + H is compared with experimental results and shown to give better agreement with the observed temperature dependence than do commonly used empirical fits. The expression k(T) = aT exp[−(E0 + E1Teff-1 + E2Teff-3/2)/RT], with Teff = T + T0, is suggested for the rate constant for CH4 + H, with the parameters a, E0, E1, E2, and ...