Computational analysis of R–X oxidative addition to Pd nanoparticles

Oxidative addition (OA) is a necessary step in mechanisms of widely used synthetic methodologies such as the Heck reaction, cross-coupling reactions, and the Buchwald–Hartwig amination. This study pioneers the exploration of OA of aryl halide to palladium nanoparticles (NPs), a process previously unaddressed in contrast to the activity of well-studied Pd(0) complexes. Employing DFT modeling and semi-empirical metadynamics simulations, the oxidative addition of phenyl bromide to Pd nanoparticles was investigated in detail. Energy profiles of oxidative addition to Pd NPs were analyzed and compared to those involving Pd(0) complexes forming under both ligand-stabilized (phosphines) and ligandless (amine base) conditions. Metadynamics simulations highlighted the edges of the (1 1 1) facets of Pd NPs as the key element of oxidative addition activity. We demonstrate that OA to Pd NPs is not only kinetically facile at ambient temperatures but also thermodynamically favorable. This finding accentuates the necessity of incorporating OA to Pd NPs in future investigations, thus providing a more realistic view of the involved catalytic mechanisms. These results enhance the understanding of aryl halide (cross-)coupling reactions, reinforcing the concept of a catalytic “cocktail”. This concept posits dynamic interconversions between diverse active and inactive centers, collectively affecting the outcome of the reaction. High activity of Pd NPs in direct C–X activation paves the way for novel approaches in catalysis, potentially enhancing the field and offering new catalytic pathways to consider.


Introduction
Facile synthesis of functionalized organic molecules is of paramount importance for the development of personalized medicine, ne chemical synthesis, advancements in drug design, and innovative materials, among many other areas.[3] Activation of the C-X bond occurs through oxidative addition (OA), initiating a series of transformations in catalyst active centers.
Developing synthetic methodologies involving OA as an essential step in the reaction mechanism uncovered dynamic catalyst interconversions as a common phenomenon. 45][6][7] This dynamic behavior was exceptionally evident in one of the cornerstone classes of organic reactions, Pd-catalyzed (cross-) couplings. 8,91][12][13][14][15][16][17] The dynamic phenomena occur under homogeneous and heterogeneous catalysis conditions. 7It has been demonstrated that oxidative addition of aryl halides plays a central role in the formation of "cocktail"-type systems. 17,180][21][22][23][24][25][26][27][28] However, the high level of reaction mechanism complexity still drastically challenges our understanding of OA, even at the level of molecular complexes. 29d NPs have shown remarkable activity in cross-coupling reactions as versatile and practical catalysts.1][42][43][44][45] In the present study, for the rst time, we investigated the oxidative addition of an organic halide to the Pd surface at the nanoscale.The studied process is relevant to C-C and C-heteroatom bond formation in applied ne organic synthesis involving nanocatalysts.Comparison with regular Pd complexes, including various ligands, highlighted a critical difference in C-X bond activation at the molecular and nano-scale levels.

Results
We conducted metadynamics (MTD) modeling of oxidative addition (OA) to truncated octahedral Pd 79 and Pd 140 nanocrystallites, along with a smaller Pd 55 nanocrystallite, using the GFN1-xTB Hamiltonian (Pd 79 and Pd 55 : Fig. 1; Pd 140 : Fig. S2 †).We observed OAs in almost all Pd 55 and Pd 79 systems within tens of picoseconds (Fig. S1a † and 1a, respectively).A representative case of the PhBr OA to Pd 79 is depicted in Fig. 1a(1).PhBr dissociation occurred at the edge of the nanoparticle.Subsequently, the Br atom migrated to the (1 0 0) facet and remained bonded to it.Concurrently, the Ph group exhibited active migration along the edge between two (1 1 1) facets and the adjacent (1 0 0) facet, as illustrated in the snapshot structures at the top of Fig. 1a.
The OA mechanism and post-OA system evolution were similar across all cases examined.The majority of OA events occurred at nanoparticle edges.In a few cases involving Pd 55 , the OA occurred at the vertex of the nanoparticle, which is also a site comprised of a Pd atom with a low coordination number (see details below).Only one OA to Pd 140 was observed within 100 ps of sampling due to the increased conguration space size; this reaction also occurred on the edge (Fig. S2 †).In the Pd 55 and Pd 140 systems, Ph migrated along the NP edges similarly to the case of Pd 79 throughout all MTD simulations (Fig. 1a, b and S2a †).Aer the OA, Br similarly remained tightly bound to one of the (1 0 0) facets of Pd 140 .In contrast, some mobility of the adsorbed Br was observed on Pd 55 , with Br migrating along the (1 0 0) facet, which is larger in Pd 55 than in Pd 79 and Pd 140 (Fig. 1b).
Fig. 1c presents the free energy proles (FEPs) obtained from individual MTD runs involving Pd 79 .The movement of the dissociated Ph along the edge corresponds to a series of shallow minima on the right side of the obtained FEPs.Although these basins are deeper than the "thermal energy", RT, at 298.15 K (0.6 kcal mol −1 ), Ph migration occurs relatively easily.The corresponding FEP minima are signicantly higher than the lowest sharp minimum at approximately 1.9 Å, which corresponds to the undissociated state of PhBr.According to the obtained FEP, the OA activation free energy does not exceed approximately 11 kcal mol −1 , and OA is kinetically feasible at ambient temperature.OA can lead to the accumulation of tightly bound Br atoms on the Pd surface, with a preference for the (1 0 0) surface.This is accompanied by the chemisorption of Ph groups, which migrate easily near low-coordinate Pd atom sites such as edges, steps, vertices, etc.
MTD sampling of dissociation trajectories allowed us to identify transition states relevant to modeled nanoparticles.Upon examining the MTD trajectories, we determined two groups of OA processes in the Pd 79 system occurring at the edge of (1 1 1) facets, with variations in the positioning of the Ph group (Fig. 2a).In the rst group, the Ph group was situated on the (1 1 1) facet with the Ph-Br bond nearly perpendicular to the edge (Pd 79 fac-ed), whereas in the second group, the Ph moiety was positioned such that the Ph-Br bond nearly collinearized with the edge (Pd 79 ed-ed).The OA of PhBr to Pd 55 proceeded via two distinct pathways: in the rst, OA occurred on the edge (labeled Pd 55 ed in Fig. 2a), and in the second, the vertex Pd atom acted as the reactive center (labeled Pd 55 ver).The TS found during the MTD sampling of the PhBr-Pd 140 interaction (Pd 140 ed in Fig. 2a) was fully similar to that in the Pd 79 system.
In addition to the OA pathways identied in MTD simulations, we employed the DyNEB method 46 to explore several alternative active centers.Firstly, we examined OA to Pd-phosphine complexes: the electron-donating PMe 3 and the widely used relatively weakly electron-donating PPh 3 .Secondly, we included [Pd(NEt 3 ) 2 ] into the consideration to model a nitrogen base added in some coupling reactions conducted under "ligandless" conditions (the Heck reaction and others).Lastly, using the DyNEB method, we investigated a hypothetical pathway in which the reaction occurred on a facet of the Pd 79 nanoparticle (labeled Pd 55 ed in Fig. 2b).Although the latter pathway was not observed in the MTD simulations, it can be used a valuable reference to enhance our understanding of the effects of nanostructuring on OA to Pd catalysts.
The focal point of this study is the computed free energy proles of OA to Pd 79 and molecular complexes depicted in Fig. 3.The corresponding numerical values are given in Table S1.† The process begins with the formation of the pre-OA complex 1 0 .Pd 79 was selected to compare the adsorption affinity of PhBr towards Pd nanoparticles vs. the thermodynamic effect of 1 / 1 0 in the case of molecular complexes [PdL 2 ].The adsorption of PhBr onto Pd 79 is markedly exergonic, with DG 1/1 0 being lower than −46.9 kcal mol −1 .This result indicates a probable intensive coverage of Pd NP precatalysts by the aryl halide during coupling reactions.
The comparison of the DFT-calculated activation energies of oxidative addition is given in Table S1, † and the corresponding plot is given in Fig. 3. Since the transition 1 / 1 0 was exergonic in the cases of Pd 79 , [Pd(NEt 3 ) 2 ], and [Pd(PPh 3 ) 2 ], we regarded DG ‡ 1 0 /TS1 as the OA activation energy for these species.For [Pd(PMe 3 ) 2 ], however, DG ‡ 1 0 /TS1 was considered as the activation energy instead of DG ‡ 1 0 /TS1 due to the positive value of DG 1/1 0 .In all the molecular complexes, classic three-center Br-Pd-C transition states were identied (Fig. 2), characterized by imaginary  The calculated activation energies of PhBr OA to Pd 79 are comparable to or lower than those involving molecular Pd complexes, with DG ‡ 1 0 /TS1 being equal to 13.4, 11.4, and 6.0 kcal mol −1 for Pd 79 fac, Pd 79 fac-ed, and Pd 79 ed-ed, respectively.Evidently, the edge is a highly reactive site with the activation barrier for the Pd 79 ed-ed transition state well below those observed with the [PdL 2 ] complexes.Furthermore, the formation of the pre-reaction state 1 0 in pathway Pd 79 ed-ed is also the most exergonic among these three model reaction channels.Therefore, we may expect the preferable reactivity via the ed-ed channel.It should also be noted that the (1 1 1) facet exhibited the lowest activity in the model OA process, indicating that oxidative addition preferentially occurs at the edges of Pd nanoparticles.
Fig. 3 and the last columns of Table S1 † show that the transitions 1 0 / 2 and 1 / 2 with all the molecular complexes are highly exergonic.In the case of Pd 79 , the notable exergonicity of 1 / 2 is primarily due to the substantial exergonicity of PhBr adsorption (1 / 1 0 ).The DG 1 0 /2 values for the Pd 79 faced and fac channels are positive (1.9 and 3.2 kcal mol −1 , respectively), while DG 1 0 /2 for ed-ed is negative, being −3.8 kcal mol −1 .However, state 2 in the Pd 79 fac-ed and ed-ed channels does not correspond to the structures of the OA products observed in the MTD runs (see Fig. 1a).In particular, we can see that most structures of the post-OA complexes at the top of Fig. 1a have Br and Ph chemisorbed on two adjacent (1 0 0) facets.
Such a structure resulting from the facile migration of Br and Ph to the (1 0 0) facets is depicted in Fig. 1a as 3.The values of DG 1 0 /2 are negative for all three reaction channels.This suggests that the accumulation of chemisorbed Ph and Br (the products of 1 0 / 3) can be thermodynamically favorable when higher surface energy (1 0 0) facets are available on the NP surface along with edges between (1 1 1) facets.The availability of (1 0 0) surfaces was previously associated with a higher propensity for Pd leaching and activity in Suzuki crosscoupling. 34This nal product 3 differs signicantly from species 2 in molecular complexes; in the NP system, the Ph and Br groups are separated, whereas in the molecular complexes, they remain bonded to a single Pd center.
By comparing DG ‡ 1 0 /TS1 and DG 1 0 /2 in Pd 55 , Pd 79 , and Pd 140 systems, we can assess the effect of the nanoparticle size on the kinetic and thermodynamic feasibility of PhBr oxidative addition.The lowest DG ‡ 1 0 /TS1 values for each NP are presented in Table 1, while Table S1 † contains all the computed values.The DG ‡ 1 0 /TS1 values indicate that the activity of the edge sites increases with the increase of the nanoparticle size.The nonmonotonous behavior of DG 1 0 /2 with the increase of the nanoparticle's size is also evident, while all DG 1 0 /2 in Table 1 are negative.Given that the post-OA migration of Ph was observed in all MTD simulations (see Fig. 1, S1 and S2 †), and that process 1 0 / 3 was highly exergonic in the Pd 79 system, we may expect the high propensity of Pd NPs to undergo the OA of PhBr when there is a sufficient surface density of edge sites and presence of (1 0 0) surfaces.At the same time, the fraction of edge atoms is smaller in larger nanoparticles; hence, the density of active sites decreases with the increase in the size.
Although previous experimental studies associated OA of PhBr with the leaching of Pd into the solution, 11,18,47 within the context of this study, we can only hypothesize that Ph and Br on the surface may kinetically facilitate this process.Notably, our earlier analysis, which considered only thermodynamic factors, indicated that OA leads to negative (favorable) formation energies of molecular forms (metal complexes) of leached Pd in solution. 17Additionally, the spontaneous formation of Pd NPs is a common phenomenon in coupling reactions where the (pre) catalyst is initially introduced as a metal complex.Therefore, OA to Pd NPs should be recognized as a crucial mechanistic step.OA to Pd NPs is as kinetically feasible as the OA to Pd(0) complexes, reinforcing the concept of the catalytic "cocktail", in which a variety of potentially active and inactive interconverting centers contribute to the overall reaction outcome.

Discussion and conclusions
The conclusions of this study are schematically depicted in Fig. 4, which highlights the interplay of the elucidated transformations in the (cross-)coupling catalysis of reactions involving aryl halides.In our DFT modeling, we analyzed the activity of the nanoparticles ranging from ∼1.08 (Pd 55 ) to ∼1.56 nm (Pd 140 ).We focused primarily on the edges between their (1 1 1) facets that exhibit the highest thermodynamic stability; 48 however, we recognize that other centers containing low-valent Pd atoms (e.g., various vertices and kinks) could also be active in OA.
Pd nanoparticles featuring a sufficient surface concentration of low-coordinated atoms, such as facet edges, and atoms on higher-surface energy facets, such as (1 0 0), can undergo oxidative addition of aryl halides.The presented DFT modeling suggests that OA to Pd nanoparticles is well comparable to OA to Fig. 3 Reaction scheme and the free energy profile.Optimized structures of the intermediates are shown in Fig. 2. See Table S1 † for numerical data.
Pd(0) complexes by its activation barrier and also being thermodynamically favorable.(1 1 1) terraces on Pd nanoparticles also showed relatively high activity, though lower than that of the considered edge sites.OA to all nanoparticles was both kinetically facile at 25 °C and thermodynamically favorable.
For the rst time, the present study revealed the critical difference between the OA involving monometallic centers, i.e., molecular complexes, and metal nanoparticles.Classic OA to a monometallic Pd center proceeds as reversible coordination of Ph-Br followed by three-center interaction and breakage of C-Br bond with both Ph and Br groups remaining in close proximity.In contrast, OA to Pd NPs involves practically irreversible trapping of Ph-Br on the metal surface followed by facile C-Br bond breakage and separation of Ph and Br from each other via multicentered interactions on the surface.
The debate 49 about the occurrence of a (cross-)coupling process at the nanoparticle surface continues in recent literature, with works reporting the reaction at the metal surface, 50,51 exclusively in solution, 33,52 or in both modes, depending on the reaction conditions. 53Here, we show that the OA stage alone would not hamper (cross-)coupling at the nanoparticle surface, according to its calculated reaction (activation) free energies that are comparable with those related to Pd(0) complexes.5][56][57][58][59][60][61] Therefore, the relative activity of Pd complexes and nanoparticles in OA depends on the choice of reference ligand.The rate of the OA to Pd complexes bearing some designer ligands may surpass that to Pd NPs.In addition, mass transfer effects may be at play in the case of aryl halides OA to Pd NPs.A denitive answer to the question of the feasibility of truly heterogeneous (cross-)coupling on Pd(0) surface requires further investigation, particularly regarding the surface activity of Pd NPs in other coupling steps, such as transmetalation and reductive elimination.
The discussions in the present study highlight many significant phenomena related to coupling reactions involving Pd nanoparticles that require further elucidation.This nding emphasized that our understanding of oxidative addition is still evolving and incomplete.

Computational details
GFN1-xTB 62 was utilized for MTD simulations and thermochemical correction calculations in ASE. 63The GBSA solvation model parameterized for GFN1-xTB was employed to account for solvent effects. 64MTD simulations were conducted using DFTB+ 22.2 (ref.65) and PLUMED 2.8.2. 66,67DFT calculations were carried out using the revPBE functional 68 with the D3(BJ) correction 69,70 in VASP 6.3.2. 71Core electron density was modeled using PAW. 72The single-point Hessian (SPH) method 73 implemented in the xtb program 64 was used to perform thermochemical calculations.Additional computational details are provided in the ESI.† ChatGPT 4 was used for initial text proofreading.
modes representing the migration of Ph to Pd and the Ph-Br bond cleavage.The activation barriers of the OA to [Pd(PMe 3 ) 2 ] and [Pd(PPh 3 ) 2 ] did not surpass 12.6 kcal mol −1 , aligning well with the typically facile OA to complexes of Pd(0) with two non-overly sterically hindered phosphine ligands.The OA of PhBr to [Pd(PPh 3 ) 2 ] proceeded with DG ‡ 1 0 /TS1 equal to 9.7 kcal mol −1 .It is important to note the detachment of the second NEt 3 from the Pd center in the transition state, whereas both the initial and nal states, 1 0 and 2, featured NEt 3 attached to Pd.

Fig. 1
Fig. 1 (a) Collective variable (C-Br distance) evolution during the metadynamics simulations of the Pd 79 system; (b) selected case of the collective variable evolution in the Pd 55 system; (c) free energy profiles obtained from the metadynamics runs of PhBr OA to Pd 79 .The color scheme is as follows: Pddark cerulean; Brdark red; Cgrey; Hwhite.

Fig. 2
Fig. 2 (a) Optimized structures of the OA transition states along with pre-reaction and post-reaction states in the PhBr interactions with Pd 55 , Pd 79 , and Pd 140 nanoparticles, derived from metadynamics simulations.Intermediate 3, identified during the MTD sampling, is discussed in the text.(b) Optimized structures of the intermediates in the pathways involving Pd 79 (facet active site) and [PdL 2 ] (L = NEt 3 , PMe 3 , and PPh 3 ), elucidated in nudged elastic band calculations.The color scheme is as follows: Pddark cerulean; Brdark red; Porange; Nblue; Cgrey; Hwhite.Intermediate and transition states are numbered according to the scheme in Fig. 3.All optimizations were performed using DFT (see Section S1 † for details).