Quantum chemical characterization of methane metathesis in L₂MCH₃ (L = H, Cl, Cp, Cp*; M = Sc, Y, Lu)

The dimerization, unimolecular methane ejection, and bimolecular methane metathesis reactions of L₂MCH₃ species where L = H, Cl, Cp, and Cp* and M = Sc, Y, and Lu are modeled at the density functional level (B3LYP) using a relativistic effective core potential basis set. Results for cases with H or Cl ligands are in poor quantitative agreement with analogous results for cases with Cp* ligands; in some instances, Cp ligands provide results in good agreement with those for Cp*, but in the case of methane metathesis, activation enthalpies are underestimated by 3-4 kcal mol^-1 with the unmethylated ligand. Unimolecular methane ejection via formation of a tuck-in complex versus bimolecular methane metathesis is predicted potentially to be a competitive process for Sc, but to be comparatively too high in energy for Y and Lu to be thermodynamically significant under typical sets of reaction conditions. The difference is ascribable to the shorter metal-ligand distances observed for Sc. For (Cp*)₂LuCH₃, quantum mechanical tunneling is predicted to increase the overall rate of methane metathesis by factors of 4-93 over the temperature range 300-400 K. When tunneling is accounted for in the experimentally measured rate constants, a semiclassical enthalpy of activation of 19.2 kcal mol^-1 is predicted for the methane metathesis reaction, in good agreement with a direct prediction from density functional theory of 20.3 kcal mol^-1.