Activation of H-H, C-H, C-C, and C-Cl bonds by Pd(0). Insight from the activation strain model

To achieve more insight into palladium-catalyzed H-H, C-H, C-C, and C-Cl bond activation and the mutual competition between these processes, several mechanistic pathways for oxidative addition of Pd(0) to H ₂ (H-H), CH ₄, (C-H), C ₂H ₆ (C-C and C-H), and CH ₃Cl (C-Cl) were studied uniformly at the ZORA-BP86/TZ(2)P level of relativistic nonlocal density functional theory (DFT). Oxidative addition is overall exothermic for all model reactions studied, with 298 K reaction enthalpies (ΔH _r,298) of -35.7 kcal/mol (C-Cl) through -9.7 kcal/mol (C-H in CH ₄). The lowest barrier pathway is the direct oxidative insertion of Pd into the C-X or H-H bond (X = H, CH ₃, Cl), with 298 K activation enthalpies (ΔH† ₂₉₈) that increase in the order H-H (-21.7 kcal/mol) < C-Cl (-6.0 kcal/mol) ≈ C-H (-5.0 and -4.1 kcal/mol for CH ₄ and C ₂H ₆) < C-C (9.6 kcal/mol). The "straight" S _N2 substitution resulting in PdCH ₃ ⁺ + X ^- or PdH ⁺ + H ^- is highly endothermic (144-237 kcal/mol) and thus not competitive. Only in the case of Pd + CH ₃Cl is a third pathway found in which S _N2 substitution occurs in concert with a rearrangement of the Cl ^- leaving group from C to Pd (S _N2/Cl-ra) leading, in one step, to CH ₃PdCl via an activation barrier ΔH† ₂₉₈ of 21.2 kcal/mol. The competition between the various bond activation processes is analyzed using the activation strain model in which activation energies (ΔE†) are decomposed into the activation strain (ΔE† _strain) of and the stabilizing transition state (TS) interaction (ΔE† _int) between the reactants in the activated complex: ΔE† = ΔE† _strain + ΔE† _int. Interestingly, the activation strain ΔE† _strain adopts characteristic values for each type of bond and reaction mechanism. The trend in TS interaction ΔE† _int turns out to be mainly determined by the donor-acceptor orbital interactions between occupied Pd 4d atomic orbitals and the empty σ*c-x (or σ*H-H) acceptor orbital associated with the bond to be activated in the substrate.