Density functional characterization of methane metathesis with Cp* ₂MR (M = Sc, Y, Lu; R = Me, tBuCH ₂). Structural and kinetic consequences of alkyl steric bulk

The uni- and bimolecular C-H bond metathesis reactions of Cp* ₂ML (Cp≤ = pentamethylcyclopentadienide; L = CH ₃, CH ₂C(CH ₃) ₃; M = Sc, Y, Lu) were modeled with the MPW1K density functional and a relativistic effective-core-potential basis set. This level of theory, when combined with a one-dimensional tunneling model, provides enthalpies of activation that are in good agreement with experiment for known bimolecular reactions of methane with Cp* ₂ScCH ₂C(CH ₃) ₃ and Cp* ₂LuCH ₃. Analysis of theoretical trends as a function of metal and ligand indicates that bimolecular reactions dominate in every case under typical experimental conditions. However, unimolecular reactions proceeding through tuck-in complexes become increasingly competitive with increased steric bulk of the metal alkyl and also with metals having smaller ionic radii. For all of the C-H bond metatheses, quantum-mechanical tunneling is predicted to increase overall reaction rates by 1 to 3 orders of magnitude over the temperature range 284-323 K.