The equilibrium geometries and bond-dissociation energies for loss of one CO and loss of six CO from TM(CO)6 q (TMq = Hf2-, Ta-, W, Re+, Os2+, Ir3+) have been calculated at the BP86 level using Slater type basis sets. The bonding interactions between TM(CO)5 and one CO and between TMq in the t 2 g 6 valence state and the ligand cage (CO)6 were analyzed in the framework of Kohn-Sham MO theory with the use of the quantitative ETS energy-partitioning scheme. The BDEs exhibit a U-shaped curve from Hf(CO)6 2- to Ir(CO)6 3+, with W(CO)6 having the lowest BDE for loss of one CO while Re(CO)6 + has the lowest BDE for loss of 6 CO. The stabilizing orbital interaction term, ΔE orb, and the electrostatic attraction term, ΔE elstat, have comparable contributions to the (CO)5TMqCO bond strength. The largest orbital contributions relative to the electrostatic attraction are found for the highest charged complexes, Hf(CO)6 2- and Ir(CO)6 3+. The contribution of the (CO)5TMq←CO σ donation continuously increases from Hf(CO)6 2- to Ir(CO)6 3+ and eventually becomes the dominant orbital interaction term in the carbonyl cations, while the (CO)5TMq→CO π-back-donation decreases in the same direction. The breakdown of the contributions of the d, s, and p valence orbitals of the metals to the energy and charge terms of the TMq←(CO)6 donation shows for a single AO the order d ≫ s > p, but the contributions of the three p orbitals of TMq are larger than the contribution of the s orbital.

To understand the mechanism of anion assistance in palladium-catalyzed H-H, C-H, C-C and C-Cl bond activation, several mechanistic pathways for oxidative addition of Pd and PdCl(-) to H2 (H-H), CH4 (C-H), C2H6 (C-C and C-H) and CH3Cl (C-Cl) were studied uniformly at the ZORA-BP86/TZ(2)P level of relativistic nonlocal density functional theory (DFT). Oxidative addition of the neutral, uncoordinated Pd atom proceeds, as reported earlier, via direct oxidative insertion (ΔH(⧧)298 is -22 to 10 kcal/mol), whereas straight SN2 substitution (yielding, e.g., PdCH3(+) + X(-)) is highly endothermic (144-237 kcal/mol) and thus not competitive. Anion assistance (i.e., going from Pd to PdCl(-)) lowers all activation barriers and increases the exothermicity of all model reactions studied. The effect is however selective:  it favors the highly endothermic SN2 mechanism over direct oxidative insertion (OxIn). Activation enthalpies ΔH(⧧)298 for oxidative insertion of PdCl(-) increase along C-H (-14.0 and -13.5 kcal/mol for CH4 and C2H6) ≈ C-Cl (-11.2 kcal/mol) < C-C (6.4 kcal/mol), i.e., essentially in the same order as for neutral Pd. Interestingly, in case of PdCl(-) + CH3Cl, the two-step mechanism of SN2 substitution followed by leaving-group rearrangement becomes the preferred mechanism for oxidative addition. The highest overall barrier of this pathway (-20.2 kcal/mol) drops below the barrier for direct oxidative insertion (-11.2 kcal/mol). The effect of anion assistance 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. For each type of activated bond and reaction mechanism, the activation strain ΔE(⧧)strain adopts characteristic values which differ only moderately, within a relatively narrow range, between corresponding reactions of Pd and PdCl(-). The lowering of activation barriers through anion assistance is caused by the TS interaction ΔE(⧧)int becoming more stabilizing.

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 CH 4 , C 2 H 6 and CH 3 Cl with Pd-d 10 using nonrelativistic ͑NR͒, quasirelativistic ͑QR͒, and zeroth-order regularly approximated ͑ZORA͒ relativistic density functional theory ͑DFT͒ at the BP86/TZ͑2͒P 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 ⌬H 298 of Ϫ5.0 ͑C-H͒, 9.6 ͑C-C͒ and Ϫ6.0 kcal/mol ͑C-Cl͒ relative to the separate reactants at ZORA-BP86/TZ͑2͒P. 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 CH 4 ͒ at Ϫ11.4 ͑CH 4 ͒, Ϫ11.6 ͑C 2 H 6 ͒ and Ϫ15.6 kcal/mol ͑CH 3 Cl͒ relative to separated reactants ͓ZORA-BP86/TZ͑2͒P͔. Furthermore, we analyze the height of and the relativistic effects on the activation energies ⌬E in terms of the activation strain ⌬E strain of and the transition-state interaction ⌬E int between the reactants in the activated complex, with ⌬E ϭ⌬E strain ϩ⌬E int .

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We have computed a state-of-the-art benchmark potential energy surface (PES) for the archetypal oxidative addition of the ethane C-C bond to the palladium atom and have used this to evaluate the performance of 24 popular density functionals, covering LDA, GGA, meta-GGA, and hybrid density functionals, for describing this reaction. The ab initio benchmark is obtained by exploring the PES using a hierarchical series of ab initio methods [HF, MP2, CCSD, CCSD(T)] in combination with a hierarchical series of five Gaussian-type basis sets, up to g polarization. Relativistic effects are taken into account either through a relativistic effective core potential for palladium or through a full four-component all-electron approach. Our best estimate of kinetic and thermodynamic parameters is -10.8 (-11.3) kcal/mol for the formation of the reactant complex, 19.4 (17.1) kcal/mol for the activation energy relative to the separate reactants, and -4.5 (-6.8) kcal/mol for the reaction energy (zero-point vibrational energy-corrected values in parentheses). Our work highlights the importance of sufficient higher angular momentum polarization functions for correctly describing metal-d-electron correlation. Best overall agreement with our ab initio benchmark is obtained by functionals from all three categories, GGA, meta-GGA, and hybrid DFT, with mean absolute errors of 1.5 to 2.5 kcal/mol and errors in activation energies ranging from -0.2 to -3.2 kcal/mol. Interestingly, the well-known BLYP functional compares very reasonably with a slight underestimation of the overall barrier by -0.9 kcal/mol. For comparison, with B3LYP we arrive at an overestimation of the overall barrier by 5.8 kcal/mol. On the other hand, B3LYP performs excellently for the central barrier (i.e., relative to the reactant complex) which it underestimates by only -0.1 kcal/mol.