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 2 H 6 (C−C and C−H), and CH 3 Cl (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 (Δ H 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 (Δ H ⧧ 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 2 H 6 ) < C−C (9.6 kcal/mol). The “straight” S N 2 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 3 Cl is a third pathway found in which S N 2 substitution occurs in concert with a rearrangement of the Cl - leaving group from C to Pd (S N 2/Cl-ra) leading, in one step, to CH 3 PdCl via an activation barrier Δ H ⧧ 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 (Δ E ⧧ ) are decomposed into the activation strain (Δ E ⧧ strain ) of and the stabilizing transition state (TS) interaction (Δ E ⧧ int ) between the reactants in the activated complex: Δ E ⧧ = Δ E ⧧ strain + Δ E ⧧ int . Interestingly, the activation strain Δ E ⧧ strain adopts characteristic values for each type of bond and reaction mechanism. The trend in TS interaction Δ E ⧧ 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.