Oxidative addition of Pd to C–H, C–C and C–Cl bonds: Importance of relativistic effects in DFT calculations

To assess the importance of relativistic effects for the quantum chemical description of oxidative addition reactions of palladium to C–H, C–C and C–Cl bonds, we have carried out a systematic study of the corresponding reactions of CH4, C2H6 and CH3Cl with Pd-d10 using nonrelativistic (NR), quasirelativistic (QR), and zeroth-order regularly approximated (ZORA) relativistic density functional theory (DFT) at the BP86/TZ(2)P level. Relativistic effects are important according to both QR and ZORA, the former yielding similar but somewhat more pronounced effects than the latter, more reliable method: activation barriers are reduced by 6–14 kcal/mol and reaction enthalpies become 15–20 kcal/mol more exothermic if one goes from NR to ZORA. This yields, for example, 298 K activation enthalpies ΔH298≠ of −5.0 (C–H), 9.6 (C–C) and −6.0 kcal/mol (C–Cl) relative to the separate reactants at ZORA-BP86/TZ(2)P. In accordance with gas-phase experiments on reactions of Pd with alkanes, we find reaction profiles with pronounced potential wells for reactant complexes (collisionally stabilized and observed in experiments for alkanes larger than CH4) at −11.4 (CH4), −11.6 (C2H6) and −15.6 kcal/mol (CH3Cl) relative to separated reactants ZORA-BP86/TZ(2)P. Furthermore, we analyze the height of and the relativistic effects on the activation energies ΔE≠ in terms of the activation strain ΔEstrain≠ of and the transition-state interaction ΔEint≠ between the reactants in the activated complex, with ΔE≠=ΔEstrain≠+ΔEint≠.