Kinetic Modeling for Unimolecular Β-Scission of the Methoxymethyl Radical from Quantum Chemical and RRKM Analyses

Unimolecular β-scission of the methoxymethyl (CH3OCH2) radical has been considered to be the crucial chain-propagating step in both oxidation and pyrolysis of dimethyl ether. The present work employs hybrid density functionals M06-2X, BB1K, B3LYP, and MPW1K with the MG3S basis set as well as double-hybrid density functional B2PLYP and Moller-Plesset perturbation theory MP2 with the TZVP basis set to study the detailed mechanism of unimolecular decomposition of CH3OCH2. Energies of all stationary points are refined with the CCSD(T), QCISD(T), CBS-QB3, and G4 calculations. The minimum energy path was computed at the CCSD(T)/aug-cc-PVTZ//M062X/MG3S level. Kinetic calculations are performed by means of high-pressure multi-structural canonical variational transition state (MS-CVT) theory and pressure-dependent Rice–Ramsperger–Kassel–Marcus (RRKM) theory to clarify the available experimental observations and previous theoretical results. A kinetic model for the low and the high-pressure limiting, and falloff region was extracted. For high pressure limit, k∞ = 2.08 × 1012 (T/300)1.002 exp(–11097.64/T) s−1 at temperatures of 200–2600 K based on the MS-CVT/SCT method. Furthermore, the intermediate falloff curve was found to be best represented by k/k∞=[x/(1+x)]Fcent1/[1+(a+logx)2/(N±ΔN)2] with x = k0/k∞, a = 0.263, N = 1.208, ΔN = 0.096, (+ΔN for (a + logx) < 0 and –ΔN for (a + logx) > 0), and Fcent(DME) = 0.348 independent of temperature. The low and high pressure limiting rate constants have been extracted by extrapolation of the fall-off curves: k0 = [DME] 2.49 × 1016 (T/300)0.053 exp(–9067.58/T) cm3 mol–1 s–1 and k∞ = 1.88 × 1012 (T/300)1.05 exp(–11061.79/T) s−1 at temperatures of 450–800 K, which agree well with the reported experimental low and high pressure limit results.