Reanalysis of Rate Data for the Reaction CH₃ + CH₃ → C₂H₆ Using Revised Cross Sections and a Linearized Second-Order Master Equation

Rate coefficients for the CH₃ + CH₃ reaction, over the temperature range 300–900 K, have been corrected for errors in the absorption coefficients used in the original publication (Slagle et al., J. Phys. Chem. 1988, 92, 2455−2462). These corrections necessitated the development of a detailed model of the B̃²A₁′ (3s)–X̃²A₂″ transition in CH₃ and its validation against both low temperature and high temperature experimental absorption cross sections. A master equation (ME) model was developed, using a local linearization of the second-order decay, which allows the use of standard matrix diagonalization methods for the determination of the rate coefficients for CH₃ + CH₃. The ME model utilized inverse Laplace transformation to link the microcanonical rate constants for dissociation of C₂H₆ to the limiting high pressure rate coefficient for association, <i>k</i>_∞(<i>T</i>); it was used to fit the experimental rate coefficients using the Levenberg–Marquardt algorithm to minimize χ² calculated from the differences between experimental and calculated rate coefficients. Parameters for both <i>k</i>_∞(<i>T</i>) and for energy transfer ⟨Δ<i>E</i>⟩_down(<i>T</i>) were varied and optimized in the fitting procedure. A wide range of experimental data were fitted, covering the temperature range 300–2000 K. A high pressure limit of <i>k</i>_∞(<i>T</i>) = 5.76 × 10^–11(<i>T</i>/298 K)^−0.34 cm³ molecule^–1 s^–1 was obtained, which agrees well with the best available theoretical expression.