DFT studies of the methyl exchange reaction between Cp2M-CH3 or Cp*2M-CH3 (Cp = C5H5, Cp* = C5Me5, M = Y, Sc, Ln) and CH4. Does M ionic radius control the reaction?

The activation energies for the methyl exchange reactions between Cp2M-CH3 and H-CH3 have been calculated for M = Sc, Y and representative metals of the lanthanide family (La, Ce, Sm, Ho, Yb and Lu) with DFT(B3PW91) calculations with large-core pseudopotentials for M. The sigma-bond metathesis reactions are calculated to have lower activation energies for early lanthanides than for late lanthanides and any of group 3 metals. The relative activation barriers are analyzed using the NBO charge distributions in the reactant and in the transition states. It is shown that the methane needs to be polarized in the transition state as H((+delta))-CH3((-delta)) by the reactant, because this sigma-bond metathesis is best viewed as heterolytic cleavage of methane, leading to a proton transfer between two methyl groups in the field of an electropositive M metal. Early lanthanides, which are involved in strongly ionic metal-ligands bonds are thus associated with the lowest activation energies. The ionic radius and the steric effects influence the relative rates of reaction for the complexes of Sc, Y and Lu. In agreement with earlier works of Sherer et al., the experimental reactivity trends found by Tilley are reproduced best with Cp2M-CH3 (Cp = C5Me5) rather than Cp2M-CH3 (Cp = C5H5) because the steric bulk of C5Me5 deactivates most the complex where the metal has the smallest ionic radius (Sc). While the steric effects and the influence of the metal ionic radius cannot be neglected, these factors are not the only ones involved in determining the activation barriers of the sigma-bond metathesis reaction.