Palladium-catalyzed activation of H_nA–AH_n bonds (AH_n = CH₃, NH₂, OH, F)

Introduction

Catalysis is intertwined with synthetic chemistry and is of central importance to the chemical industry, as approximately 90 % of all industrial processes make use of a catalyst [1]. One of the most prominent catalytic transformations is the palladium-catalyzed cross-coupling reaction, where activated molecular fragments are reacting to form a new bond, typically, between carbon or other main group elements, such as C, N, O, yielding C–C, C–N or C–O bonds, respectively (Scheme 1) [2]. The catalytic cycle of the palladium-catalyzed cross-coupling begins with the activation of the bond between two cojoined main group elements (H_nA–AH_n, AH_n = CH₃, NH₂, OH, F) by oxidative addition to the palladium center. The insertion of Pd into the H_nA–AH_n bond is commonly observed as the rate-determining step [3] and has been subjected to extensive experimental [4] and theoretical studies [5, 6]. The next step involves transmetalation where one of the AH_n groups bound to the palladium center is replaced by a hydrocarbon R. In the last step, the original palladium catalyst is regenerated by a reductive elimination step (the reverse of oxidative addition), resulting in a new H_nA–R bond. To enable the design of better performing catalysts in terms of rate and selectivity, a detailed physical understanding of the oxidative addition step is required related to the difference of the electronic and steric properties of the catalyst as well as the H_nA–AH_n bond.

Scheme 1:

Schematic catalytic cycle of a palladium-catalyzed cross-coupling reaction.

To delineate the effect of varying the nature of the H_nA–AH_n bond on the bond activation process, we have quantum chemically explored the potential energy surface (PES) of the oxidative insertion of PdL_n, with L_n = no ligand, PH₃, (PH₃)₂, into the H_nA–AH_n bond (AH_n = CH₃, NH₂, OH, F), using relativistic density functional theory at ZORA-BLYP/TZ2P (Scheme 2). The activation strain model (ASM) [7] in combination with quantitative Kohn–Sham molecular orbital (KS-MO) theory [8] and a matching energy decomposition analysis (EDA) scheme [9] were employed to unravel the trends in reactivity and provide quantitative insights into the effect of varying AH_n on the H_nA–AH_n bond activation. This computational methodology provides deep physical insight into the factors controlling reactivity and has proven useful for the understanding of, among others, related oxidative addition reactions [6].

Scheme 2:

Model oxidative addition reaction between PdL_n and H_nA–AH_n, where L_n = no ligand, PH_3, (PH₃)₂; and AH_n = CH₃, NH₂, OH, F.

Computational methods

Results and discussion

We have analyzed the single C–C, N–N, O–O and F–F bonds in the series H_nA–AH_n (AH_n = CH₃, NH₂, OH, and F). First, we compare the lengths and strengths of these bonds in the different substrates, which are important factors for the overall bond activation (vide infra). Table 1 contains the computed bond lengths and bond dissociation enthalpies at ZORA-(U)BLYP/TZ2P. We find that the H_nA–AH_n bond becomes systematically weaker and shorter following the trend from A = C to N to O to F, namely, from 83.2 kcal mol⁻¹ and 1.539 Å for H₃C–CH₃ to 47.8 kcal mol⁻¹ and 1.440 Å for F–F. There is one exception, however, namely, the fact that the bond length does not become shorter from H₂N–NH₂ (1.457 Å) to HO–OH (1.495 Å), but longer. This is in line with a previous report where this anomaly in bond length is ascribed to the differing degrees of hyperconjugative stabilization between H₂N–NH₂ and HO–OH [24].

The results of our ZORA-BLYP/TZ2P exploration are collected in Table 2 and Fig. 1. Full details and additional data can be found in Tables S1 and S2 and Figs. S1–S3. Note that the overall activation energy ΔE ^‡, that is, the energy difference between the TS and the infinitely separated reactants (PdL_n and H_nA–AH_n), can be negative if a substantially stabilized reactant complex is formed. For a more detailed discussion on the various types of reaction potential energy surfaces, see Reference [25]. The oxidative addition reactions of Pd + H_nA–AH_n (AH_n = CH₃, NH₂, OH, F) generally proceeds via a reactant complex (RC) and a transition state (TS) towards the product complex (PC). Three reactivity trends can be discerned from the computed reaction profiles. First, the corresponding overall activation energy decreases from +18.7 kcal mol⁻¹ for H₃C–CH₃ to +7.7 kcal mol⁻¹ for H₂N–NH₂ to −8.5 kcal mol⁻¹ for HO–OH to barrierless for F–F. This latter barrierless process has been previously studied in detail by our group [26]. Second, the coordination of one phosphine ligand to the palladium metal center, i.e., going from Pd to PdPH₃, raises the oxidative-addition barrier of the H_nA–AH_n bonds that are more sterically shielded by A–H bonds (i.e., H₃C–CH₃ and H₂N–NH₂), but it does not affect the reactivity trends along the various bonds compared to the situation for the bare model Pd catalyst. Thus, the highest activation energy is still found for the activation of H₃C–CH₃ (+26.4 kcal mol⁻¹), then consistently lowers upon going to HO–OH (−10.1 kcal mol⁻¹) and remains barrierless for the activation of F–F. Third, coordinating two phosphine ligands to the Pd catalyst, i.e., Pd(PH₃)₂, further raises the oxidative-addition barrier for the H₃C–CH₃ and H₂N–NH₂ bonds. Along H₃C–CH₃ and H₂N–NH₂, the barrier continues to decrease, just as for the model catalysts PdPH₃ and Pd. For the activation of the other two substrates, that is, HO–OH and F–F, Pd(PH₃)₂ has a major influence on the reaction mode, because (i) it changes the reaction mode of the former towards a stepwise process in which the phosphine ligands play an active role (Fig. S3); and (ii) the latter substrate reacts via a concerted pathway with an activation energy of −37.0 kcal mol⁻¹.

Fig. 1:

Stationary point structures (in Å) for the oxidative addition of Pd + H_nA–AH_n (AH_n = CH₃, NH₂, OH, F) computed in the gas phase at ZORA-BLYP/TZ2P. [a] = Non-existent: oxidative addition into F–F is a barrierless process, see Reference [26]. Atom colors: H = white, C = gray, N = blue, O = red, F = green, Pd = orange.

The computed trends in reactivity are also recovered for bulk solvation computed in THF and water, simulated using COSMO(THF)-ZORA-BLYP/TZ2P and COSMO(water)-ZORA-BLYP/TZ2P. Tables S1 and S2 report the effect of solvation on the reaction profile of the studied systems. The activation barriers for Pd + H_nA–AH_n (AH_n = CH₃, NH₂, OH, F) are all stabilized by solvation, whereas the activation barriers for both PdPH₃ + H_nA–AH_n and Pd(PH₃)₂ + H_nA–AH_n are all slightly destabilized. Note that, in solution, the activation of the F–F bond is a barrierless process for all studied catalysts, including Pd(PH₃)₂.

To gain quantitative insight into the physical factors governing the oxidative addition reactivity trend, we applied the activation strain model (ASM) of reactivity [7]. Fig. 2 displays the activation strain diagrams (ASDs) of the H_nA–AH_n bond activation (AH_n = CH₃, NH₂, OH) by the model bare Pd catalyst along the IRC projected on the H_nA⋯AH_n bond stretch. The activation of F–F follows a barrierless process due to the crossing of the singlet and triplet potential energy surfaces. The underlying physics thereof has previously been studied by our group; we refer the interested reader to Reference [26] for complete details. The bare Pd catalyst is chosen for this detailed analysis, because the simplicity of this model catalyst allows for a lucid picture to emerge from the analyses and because, already for this model catalyst, the universal trend (only Pd(PH₃)₂ + HO–OH and F–F constitute exceptions, vide supra) of a decreasing activation energy occurs. As shown in Table 2, the activation energy goes down from H₃C–CH₃ to H₂N–NH₂ to HO–OH (Fig. 2a), which can be traced back to both the strain and interaction energy (Fig. 2b and 2c). The high activation energy of H₃C–CH₃ is the result of the highly destabilizing strain energy for a twofold reason: (i) The H₃C–CH₃ is the strongest bond along the investigated series (see Table 1): the stronger the bond, i.e., larger ΔH _BDE, the harder it is to break, i.e., the more activation strain it generates during the oxidative addition reaction; (ii) the methyl C–H bonds shield the H₃C–CH₃ bond, which requires the methyl groups to tilt away from the incoming Pd catalyst [6]. The lowering of the activation energy upon going from H₂N–NH₂ to HO–OH is exclusively the result of the more stabilizing interaction energy, since the strain energies around the transition state for these two substrates are nearly identical. Based on the bond dissociation energies discussed earlier (Table 1), one would expect that the stronger H₂N–NH₂ bond experiences a more destabilizing strain energy than the HO–OH during the oxidative addition reaction. This is, however, not the case, because the latter experiences additional deformation of the strong O–H bonds, which, in turn, are stronger than N–H bonds [27], resulting in similar strain energies around the transition states for HO–OH and H₂N–NH₂ bond activation.

Fig. 2:

Activation strain analyses: a) total energy, b) strain energy, c) interaction energy; and energy decomposition analyses: d) electrostatic interaction, e) Pauli repulsion, and f) orbital interactions, for the oxidative addition reactions of Pd + H_nA–AH_n (AH_n = CH₃, NH₂, OH), where the transition states are indicated with a dot and the energy terms along the IRC are projected on the H_nA⋯AH_n bond stretch. Computed at ZORA-BLYP/TZ2P.

Next, we turn to the energy decomposition analysis (EDA) [9] to obtain a better understanding of why the interaction energy becomes more stabilizing when the substrate changes from H₂N–NH₂ to HO–OH. The energy decomposition analysis diagrams reveal that the enhanced interaction energy upon going from H₂N–NH₂ to HO–OH is a result of two factors, namely, (i) a less destabilizing Pauli repulsion (Fig. 2e); and (ii) more stabilizing orbital interactions (Fig. 2f). The electrostatic interactions (Fig. 2d), on the other hand, are not responsible for the trend in reactivity, because they run counter to the observed reactivity trend.

The origin of the less destabilizing Pauli repulsion for the oxidative addition reaction between Pd and HO–OH compared to H₂N–NH₂ was further investigated by performing a Kohn-Sham molecular orbital (KS-MO) [8] analysis (Fig. 3). The overlap between occupied orbitals of Pd, H₂N–NH₂, and HO–OH that engage in a repulsive closed-shell–closed-shell orbital interaction was quantified at consistent geometries obtained from the IRC with a H_nA⋯AH_n bond stretch of 0.441 Å. Performing this analysis at a consistent point along the reaction coordinate (near all transition state structures), rather than on the individual transition state structures alone, ensures that the results are not skewed by the position, earlier or later, of the transition state [7b]. For the model bare palladium catalyst, we consider all five occupied 4d atomic orbitals (HOMO_Pd). The participating occupied orbitals of H₂N–NH₂ and HO–OH are the π*-HOMO_HnA–AHn, where there is a nodal plane between the two AH_n fragments. The closed-shell–closed-shell orbital overlap between the 4d AOs of Pd and H_nA–AH_n is the largest for H₂N–NH₂ (S = 0.19) and the smallest and, therefore, less destabilizing for HO–OH (S = 0.07) (Fig. 3a).

Fig. 3:

Origin into the trends in Pauli repulsive interactions. a) Schematic molecular orbital diagram of the most important occupied-occupied orbital overlaps, and b) the key occupied molecular orbitals of H_nA–AH_n (isovalue = 0.03 Bohr^−3/2) of the oxidative addition reaction between Pd and H_nA–AH_n (AH_n = NH₂, OH). Computed at ZORA-BLYP/TZ2P along the IRC projected with a H_nA⋯AH_n bond stretch of 0.441 Å.

The differences in Pauli-orbital overlap originate from the difference in orientation between Pd and H_nA–AH_n (Fig. 1), which, in turn, is a direct consequence of the degree of steric shielding of the H_nA–AH_n bond by the A–H bonds. The NH₂ groups of H₂N–NH₂ have a conformation that shields the direct attack of the Pd catalyst. This differs from the OH groups of HO–OH and hence allows the direct attack of the Pd catalyst for this molecular species. Thus, upon bond activation, the NH₂ groups need to rotate to accommodate the Pd catalyst, thereby forcing the Pd + H₂N–NH₂ structure to be symmetric, such that both newly formed Pd⋯NH₂ bonds are identical in length. Consequently, there are two contact points between the occupied orbitals of Pd and H₂N–NH₂, at both NH₂ sides, yielding a large closed-shell–closed-shell orbital overlap and hence Pauli repulsion. For HO–OH, on the other hand, the Pd catalyst can approach the HO–OH bond directly without any need for the OH groups to rotate, due to the absence of steric shielding of the O–H bonds. This gives rise to an asymmetric structure where one newly formed Pd⋯OH bond is shorter than the other. As a result, the number of contact points between the occupied orbitals of Pd and HO–OH is reduced, leading to a less destabilizing closed-shell–closed-shell orbital overlap and thus a lower Pauli repulsion.

Finally, we examine why the oxidative addition reaction involving HO–OH proceeds with more stabilizing orbital interactions than H₂N–NH₂. Changing the substrate from H₂N–NH₂ to HO–OH results in a strengthening of the HOMO_Pd–LUMO_HnA–AHn backbonding interaction, whereas the LUMO_Pd–HOMO_HnA–AHn bonding interaction remains nearly constant, as explained in the following (Fig. 4). By performing a Kohn–Sham molecular orbital (KS-MO) analysis on consistent geometries obtained from the IRC with a H_nA⋯AH_n bond stretch of 0.441 Å, we found that the LUMO_HnA–AHn drops in energy from −2.4 eV for H₂N–NH₂ to −6.0 eV for HO–OH, thereby reducing the HOMO_Pd–LUMO_HnA–AHn orbital energy gap (Fig. 4a). The reduction in orbital energy gap, together with the enhanced HOMO_Pd–LUMO_HnA–AHn orbital overlap due to the previously discussed difference in orientation between Pd and H_nA–AH_n, results in a more stabilizing backbonding interaction for HO–OH compared to H₂N–NH₂.

Fig. 4:

Schematic molecular orbital diagram with the key orbital energies and overlaps of a) the HOMO_Pd–LUMO_HnA–AHn backbonding interaction and c) the LUMO_Pd–HOMO_HnA–AHn bonding interaction of the oxidative addition reaction between Pd and H_nA–AH_n (AH_n = NH₂, OH). The key molecular orbitals of H_nA–AH_n contributing to b) the backbonding interaction and d) bonding interaction (isovalue = 0.03 Bohr^−3/2). Computed at ZORA-BLYP/TZ2P along the IRC projected with a H_nA⋯AH_n bond stretch of 0.441 Å.

The LUMO_Pd–HOMO_HnA–AHn bonding interaction, on the other hand, remains nearly constant when going from H₂N–NH₂ to HO–OH, even though the σ-HOMO_HO–OH is lower in energy than HOMO_H2N–NH2, resulting in a larger, less stabilizing, orbital energy gap for the former. HO–OH, however, benefits, due to the approach of the reactants, from an additional stabilizing bonding interaction between LUMO_Pd–π^*-HOMO_HO–OH, thereby recovering the bonding orbital interactions (Fig. 4c).

Conclusions

The activation barrier for palladium-mediated H_nA–AH_n bond activation decreases systematically along the series H₃C–CH₃ to H₂N–NH₂ to HO–OH to F–F. The activation of the F–F bond is even barrierless. This follows from our quantum chemical exploration of the A–A oxidative addition to palladium in the model reactions of PdL_n + H_nA–AH_n (L_n = no ligand, PH₃, (PH₃)₂; AH_n = CH₃, NH₂, OH, F), using relativistic density functional theory.

Our detailed activation strain and Kohn-Sham molecular orbital analyses reveal that the decreased oxidative addition reaction barrier upon going from H₃C–CH₃ to H₂N–NH₂ to HO–OH to F–F mainly originates from the difference in bond strength along this series which decreases along this series. The H₃C–CH₃ bond is the strongest bond along the investigated series. The stronger the bond, the more energy it costs to break, and hence the more activation strain it generates during the oxidative addition reaction. Furthermore, the methyl C–H bonds shield the H₃C–CH₃ bond, which requires the methyl groups to bend away from the incoming Pd catalyst, generating additional activation strain.

The activation barrier lowers further from H₂N–NH₂ to HO–OH due to two additional barrier lowering phenomena, namely, (i) a less destabilizing steric (Pauli) repulsion; and (ii) more stabilizing orbital interactions. The former effect is a result of the difference in steric shielding of the H_nA–AH_n bond by the AH_n groups. The NH₂ groups of H₂N–NH₂ have a conformation that shields the N–N bond, forcing the Pd catalyst to attack the bond more side-on and hence yields a large closed-shell–closed-shell orbital overlap and Pauli repulsion. In the case of HO–OH, the absence of steric shielding of the OH groups allows the direct attack of the Pd catalyst, resulting in less contact points between the occupied orbitals of the reactants and hence decreased Pauli repulsion. The more stabilizing orbital interactions, on the other hand, originate from the energetically lower-lying σ* acceptor orbital of HO–OH compared to H₂N–NH₂ that can engage in a strong backbonding interaction with the occupied 4d atomic orbitals of the palladium catalyst. Finally, the activation of the F–F bond is a barrierless process due to the crossing of the singlet and triplet potential energy surfaces, as has been described in detail by de Jong et al. [26].