First-Principles Molecular Dynamics Analysis of Ligand-Free Suzuki

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First-Principles Molecular Dynamics Analysis of Ligand-Free SuzukiMiyaura Cross Coupling in Water Solvent: Oxidative Addition Step Teruo Hirakawa, Yuta Uramoto, Daisuke Mimura, Atsuya Takeda, Susumu Yanagisawa, Takashi Ikeda, Kouji Inagaki, and Yoshitada Morikawa J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.6b08644 • Publication Date (Web): 19 Dec 2016 Downloaded from http://pubs.acs.org on December 22, 2016

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The Journal of Physical Chemistry

First-Principles Molecular Dynamics Analysis of Ligand-Free Suzuki-Miyaura Cross Coupling in Water Solvent: Oxidative Addition Step Teruo Hirakawa,∗,† Yuta Uramoto,† Daisuke Mimura,† Atsuya Takeda,† Susumu Yanagisawa,‡ Takashi Ikeda,¶ Kouji Inagaki,†,§ and Yoshitada Morikawa∗,†,§,∥ Department of Precision Science and Technology, Graduate School of Engineering, Osaka University, 2-1, Yamada-oka, Suita, Osaka 565-0871, Japan , Department of Physics and Earth Sciences, Faculty of Science, University of the Ryukyus, 1 Senbaru, Nishihara, Okinawa 903-0213, Japan, Synchrotron Radiation Research Center, Quantum Beam Science Research Directorate, National Institutes for Quantum and Radiological Science and Technology (QST), 1-1-1 Kouto, Sayo, Hyogo 679-5148, Japan, Elements Strategy Initiative for Catalysts and Batteries (ESICB), Kyoto University, Katsura, Kyoto 615-8520, Japan, and Research Center for Ultra-Precision Science and Technology, Graduate School of Engineering, Osaka University, 2-1, Yamada-oka, Suita, Osaka 565-0871, Japan E-mail: [email protected]; [email protected] Phone: +81(0)6 68797288. Fax: +81(0)6 68797290

∗

To whom correspondence should be addressed Osaka University ‡ University of the Ryukyus ¶ QST § Kyoto University ∥ Research Center, Osaka University †

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Abstract We investigated the oxidative addition step of PhX (X=Cl, Br) to a single Pd(0) atom or a PdX− complex in water by using first-principles molecular dynamics simulations with solvent H2 O molecules explicitly included in calculation models to clarify the origin for the extremely high reactivity of a ligand-free Pd catalyst in an aqueous solution for the Suzuki-Miyaura reaction. The free energy profiles are estimated by using blue moon ensemble (BME) sampling to include the entropy effect in chemical reactions in a water solvent. The free energy barrier of the oxidative addition step is quite low especially for PhBr while the barrier for PhCl is sizable, indicating that the reaction can proceed at room temperature with a high rate for PhBr, but the rate is rather slow for PhCl. We also investigated the effect of the additional halogen anion to the Pd catalyst as a "supporting ligand". The activation barrier of the oxidative addition step is not affected by the supporting halogen ligands, but the stability of the final state is significantly destabilized, which should be important for the following transmetalation step. The solvent effect is also investigated and discussed.

Introduction The Suzuki-Miyaura reaction (SMR) is one of the most efficient palladium-catalyzed crosscoupling reactions for the formation of carbon-carbon bonds, in particular for the formation sp2 -sp2 carbon-carbon of biaryls in organic synthesis. 1–8 The SMR has been developed mainly with ligands, especially phosphine ligands to make the palladium catalyst stable and optimize its reactivity in an organic solvent. The catalytic cycle for the cross-coupling reaction consists of three main steps, i.e., oxidative addition, transmetalation, and reductive elimination (see Figure 1). The SMR without any ligands, that is "ligand free" in a water solvent, was suggested, and it has been attracting enormous interest recently. 9–12 In 2003, Smith and co-workers showed that palladium-containing perovskites are also quite reactive catalysts for the SMR in an aqueous solvent. 9 In 2005, Andrews and co-workers demonstrated that its 2 ACS Paragon Plus Environment

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turn-over number (TON) is over 399,000/Pd when PhBr is used as one of the reactants, 10 and Arisawa and co-workers reported higher TON up to 2,760,000 using sulfur-modified Ausupported Pd (SAPd), 13,14 which implies that the “ ligand-free ” SMR in water or ethanol solvents is much more efficient than that in organic solvents. Aryl bromide is still suitable as the reactant of the SMR in a water solvent, while aryl chloride cannot be used as aryl halide because of its low rate, which is similar to the ordinary SMR in an organic solvent. Although the ligand-free palladium is very promising and has been studied intensively, the active form of the catalyst is still in debate. Perovskite materials containing palladium were originally prepared as a heterogeneous catalyst, but it was shown that catalytically active Pd species are not on the perovskite surface but dissolved from the perovskite into the water solvent. 10 Reetz and co-workers and de Vries and co-workers proposed the leaching mechanism of the active Pd(0) catalyst from palladium nanoparticles by oxidative addition for the ligand-free Heck reaction, 15,16 and the leaching mechanism is also considered to be applicable for the SMR. 17–19 Leyva-Perez and co-workers observed the increase of the amount of small Pd clusters with a majority size of three or four atoms either by water or aryl bromide and concluded that they are active species as the homogeneous Pd catalyst for the SMR without any ligands in a water solvent. 20 Dhital and co-workers concluded that Pd20 nanoclusters are not so active for the oxidative addition of chlorobenzene using quantum chemical calculations. 21 de Vries and co-workers reported that a dipalladium intermediate has been observed in their experiment by using EXAFS. 22 The dipalladium intermediate can be obtained from the oxidative addition of aryl halide to the Pd catalyst or from the by-products, with some halogen anions (Cl− or I− ). In ligand-free systems, water or halogen anions in a solution may bond to the Pd catalyst and play some roles partly similar to phosphine ligands in conventional catalysts. 23 Since the seminal work by Amatore and Jutand, 24 a Pdhalogen anion complex has been investigated as an active species for cross-coupling reactions. The halogen anion can act as a "ligand" without any phosphine ligands in a water solvent. Moreover, the formation of the anion complex may inhibit the aggregation of Pd to form



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Pd black, extending the TON of catalysts. The oxidative addition with ligand systems has been studied by Kozuch and co-workers, and they reported that a tri-coordinated anionic Pd catalyst can still be reactive. 25 Surawatanawong and Hall suggested that the halogens can play roles similar to ligands to enhance the oxidative addition step under phosphine-free conditions for the Heck reaction. 26 The SMR without any ligands in a water solvent has the higher TON; therefore, the energy barriers for the reaction processes are expected to be lower than those of the conventional SMR with phosphine-ligands. However, as far as we know, the reaction mechanisms of the SMR in a water solvent have not been studied theoretically. In many cases, the oxidative addition is the rate determining step of the catalytic cycle. 27,28 Thus, in the present study we focus on the oxidative addition step of the SMR in a water solvent explicitly including solvent molecules in our calculation models and perform full quantum mechanical molecular dynamics (MD) simulations. Most theoretical studies for the SMR reported so far, used a simple solvent model to simulate the cross coupling mechanisms in an organic solvent. 21,25,26,29–64 In these studies, the solvent effect is approximately treated using a polarizable continuum model (PCM). Sikk and co-workers showed the importance of the solvent effect for oxidative addition steps, especially to the Pd-anion complex. 51 Only a few works used explicit solvent models. 57,61,62,65 However, solvent molecules may play important roles in ligand-free Pd cross coupling reactions. Vidossich and co-workers reported solvent coordination in the Pd-phosphine system by performing first-principles MD simulations explicitly including solvent molecules. 62 Furthermore, Besora and co-workers pointed out that a conformation search is important in cross-coupling reactions with bulky ligands. 48


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Methods All of the calculations are based on the density functional theory (DFT) within the generalized gradient approximation(GGA-PBE) as implemented in the STATE-Senri code. 66 We used ultrasoft pseudo potentials and a plane-wave basis set with cutoff energies of 25 Ry and 225 Ry for wave functions and charge densities, respectively. We performed first-principles MD simulations for the oxidative addition step of PhBr/PhCl over the ligand-free palladium catalyst with water solvent molecules explicitly included (see Figure 2). The supercell size used in our calculations is 12.38 Å × 12.38 Å × 12.38 Å and a single k-point was sampled for the Brillouin zone sampling. In the cell, 64 H2 O molecules are contained in the case of normal water (1.0 g/cm3 ). To simulate the oxidative addition step, one PhBr and one Pd atom or PdBr− anion were introduced into the cell and five H2 O molecules were instead removed from the cell to keep the water density constant. The catalyst model of Pd is still unknown, and here, we assumed Pd single atom or Pd-X− (X= Br or Cl) anion complexes. Constant temperature MD simulations were performed using the velocity Verlet integration scheme with a time-step of 0.75 fs per MD step. This time step is slightly longer than those typically used in classical MD simulations for water. Therefore, we actually used a deuteron mass rather a hydrogen mass for the H atoms in the water solvent. A Nosé-Hoover chain (NHC) with a chain length of eight was used, and the temperature target was set to 400K. Because the GGA-PBE tends to overestimate the hydrogen bond strength and accordingly the diffusion constant of water molecules is underestimated, the target temperature was set about 60 K higher than that in the actual experiments to mimic the real dynamics of the water solvent at experimental conditions. In order to accurately estimate the free energy barriers for the oxidative addition step in the water solvent, we used a blue moon ensemble (BME) method and a constrained MD to sample rare events, to calculate the mean force as a function of an arbitrary reaction coordinate ξ = ξ(r), and to construct the free energy profile. 67,68 In calculations of free energy profiles with the constrained MD by using the mean force, the error was estimated 5 ACS Paragon Plus Environment


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by the method of Jacucci and Rahman, using the concept of the correlation length between those samples. 69,70 We imposed a constraint on the distance between the Pd atom and the bond center between the C1 atom of the benzene ring and the halogen atom X (X = Br or Cl), and it is hereafter denoted by RPd−BC (see Figure 3). The accuracy of free-energy calculations with BME depends on the reaction coordinates, and RPd−BC seems to be reasonably good for a wide range of values from 0 Å to 7 Å. We noticed, however, a small jump of atomic geometries close to the transition states. Therefore, we used an angle between Pd-Br and Pd-C1 bonds (θBrPdC ), and the results are shown and discussed in the Results and Discussion section. We performed over 5000 MD simulations (time step: 0.75 fs, total time: 3.75 ps) for each point of constraint value along the reaction coordinate.

Results and Discussion Oxidative Addition Step In the oxidative addition reaction for the SMR in an organic solvent, two competitive pathways have been suggested. Senn and Ziegler found an SN 2 pathway, 29,30 while several other research groups supported a concerted pathway. 34,42,44,49 Other competitive pathways are proposed by Hartwig, namely oxidative addition and phosphine dissociation. 71–74 Recent studies concluded that favored pathways depend on both ligands and solvents, for example, Besora and co-workers reported that in the case of palladium bis-phosphine in polar solvent, the SN 2 mechanism is favored, while in the case of palladium mono-phosphine with a polar solvent, both of the two mechanisms become competitive. 49 Mollar and co-workers pointed out that the SN 2 pathway is preferred for the activation of C sp3 -Br bond, while the concerted pathway is preferred for the activation of C sp2 -Br bond. 45 Therefore, in the present study, we investigated the oxidative addition step of X-Ph in the concerted pathway. We use a single Pd(0) atom and PdX− anion complex in a water solvent as the simplest 6 ACS Paragon Plus Environment

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and most probable models for the ligand-free Pd catalyst in water and investigate the free energy profile for the concerted pathway of the oxidative addition to discuss the effects of the ligand and solvents. To observe the process of the oxidative addition step of the ligand-free SMR in the water solvent, we performed constrained MD with the BME sampling, starting with a Pd(0) atom and a PhX (X=Cl, Br) molecule separated and solvated in water, and ending in a Pd(II) XPh complex including a process of the isomerization from cis to trans. We used a single Pd atom as a basic model of a catalyst. Figure 4 shows the relative free energy profile as a function of RPd−BC (upper graph) along with the number of H2 O molecules connected to the Pd atom (coordination number, NC lower graph) and the atomic configurations of a PhX-Pd complex (top and bottom panels). The number of coordinated H2 O molecules to Pd is defined by the number of O-Pd bonds shorter than 2.4 Å. Before going into the details of the oxidative addition process of PhX to Pd in the water solvent, we check the accuracy of our calculations by comparing the present results with previously reported results. We calculated the free energy barrier for the oxidative addition of PhBr to mono-ligated PdPPh3 , and the free energy profile is shown with a green line in Figure 4. The free energy barrier for the oxidative addition of PhBr to monoligated PdPPh3 is calculated to be 2.4 kcal/mol, which is in good agreement with the value calculated for the same process by DFT with B3LYP hybrid functional. 41 Recently, the Maseras group reported a higher value of 9.6 kcal/mol as the activation energy for a similar oxidative addition by using a more sophisticated methodology, employing DFT with the M06 functional. 75 M06 includes dispersion correction, which increases the activation energies of the oxidative addition step systematically. However, the tendencies of the oxidative addition reaction are in good agreement between both functionals and we thus think that the main conclusion of our work is not affected by the inclusion of the van der Waals correction. In the initial state (RPd−BC = 7.0 Å), the Pd atom is solvated by two H2 O molecules, forming a bisligated Pd(H2 O)2 , as seen in Figures 2 and 4 (right upper panel). As the



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PhX molecule approaches the Pd atom, one of the two H2 O molecules bonded to the Pd atom is replaced with the PhX molecule, forming an η 2 coordinated PhX to the Pd atom (RPd−BC ∼ 4.5 Å). During the replacement, the free energy is downhill and the system is stabilized by ∼ 20 kcal/mol, indicating that the process is significantly exothermic. After forming the η 2 coordination of PhX to the Pd atom, the Pd atom moves along the benzene ring and comes to the C1 atom which is directly bonded to X (RPd−BC ∼ 2.5 Å). Then Pd is inserted in between C1 and X atoms, and at the same time, the number of coordinated H2 O molecules increases from one to two, forming a square planar cis-Pd(II) XPh(H2 O)2 complex. The activation free energy barriers in this process are 3.4 kcal/mol for PhBr and 8.5 kcal/mol for PhCl. The activation free energies of the oxidative addition of PhBr to H2 O ligated Pd (3.4 kcal/mol) is slightly larger than that to the mono-ligated PdPPh3 (2.4 kcal/mol) mentioned above. According to the report by Jover et al., the reactivity of the oxidative addition mainly depends on the σ-donation property. 43 It is known that the water ligand bonded to the palladium atom has a weaker σ-donation property than the phosphine ligand. 76 Therefore, the trend in the activation energies of the oxidative addition to H2 O ligated Pd and phosphine Pd follows the general rule. These activation energies are in reasonable agreement with previous results for oxidative addition of PhX (X=Cl, Br) in mono-phosphine pathway, and it was pointed out that the difference in the activation barriers between PhBr and PhCl can be ascribed to the difference in the bond strength of the C-X bonds in the PhX. 39 The cis-Pd(II) XPh(H2 O)2 complex is more stable than the η 2 complex by −15.2 kcal/mol for PhBr and −11.3 kcal/mol for PhCl (RPd−BC ∼ 1.5 Å). Finally, the cis-trans isomerization process is simulated, and the free energy barriers are estimated as about 26.0 kcal/mol for PhBr and 17.9 kcal/mol for PhCl (RPd−BC ∼ 0.6 Å). As discussed in the Introduction, the oxidative addition step is postulated to be the rate limiting step of the whole catalytic cycle. However, in the present study we show that the oxidative addition step of PhBr to ligand-free Pd in the water solvent has a small barrier of 3.4 kcal/mol, indicating that the process proceeds quite smoothly at room temperature or above.


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The low activation barrier should be the origin for the very high reactivity of the ligand-free Pd catalyst for the SMR. Furthermore, the large exothermic energy of the oxidative addition step suggests that if a ligand-free Pd atom exists in a solution, it immediately reacts with PhBr in the solution and forms a cis-Pd(II) XPh(H2 O)2 complex, inhibiting the aggregation of the Pd catalyst. This causes the long lifetime and the high TON of the catalyst. The activation barrier of the oxidative addition step for PhCl, however, is 8.5 kcal/mol and much higher than that for PhBr, slowing down the process. The higher barrier for the oxidative addition step leads to a longer lifetime of the η 2 complex, and this may cause the aggregation of the Pd catalyst as discussed by de Vries and co-workers. 16 In the isomerization from the cis-form to the trans-form of the Pd(II) XPh(H2 O)2 complex, there is a high energy barrier, namely, 26.0 kcal/mol for PhBr and 17.9 kcal/mol for PhCl; furthermore, the process is endothermic by 24.9 kcal/mol for PhBr and 15.1 kcal/mol for PhCl. Therefore, it is difficult to isomerize from the cis-form to the trans-form and even if it happens, the reverse reaction is easy to move back to the cis-form. Therefore, the product in the oxidative addition step of the ligand-free SMR in the water solvent is the cis-form of the Pd complex. This result is significantly different from that of Braga because Braga reported that the cis-trans isomerization happens easily due to the trans effect of PPh3 and H2 O. Thus, we think the transmetalation mechanism with bisligated Pd(H2 O)2 is rather different from that in the conventional SMR. This process is now under investigation and will be reported in our future work. Next, let us investigate the ligand effect of a halogen anion X− to Pd(0) on the oxidative addition reaction. Here, we investigated a single-atom Pd catalyst ligated by Br− or Cl− . In the ligand-free SMR, the Pd catalyst is solvated in a solution in which halogen anions exist and there is a possibility of forming PdX− anion complexes. We performed the BME sampling for the oxidative addition of PhX to PdX− (X=Cl, Br), and the results are shown in Figure 5 (right panel) along with the results without halogen anions. In the initial state, PhX is bonded to PdX− in η 2 coordination (see the lower right panel in Figure 5), while in the



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final state, Pd forms the square planar (PdPhX2 H2 O)− complex. (see the lower left panel in Figure 5). The free energy barriers for the oxidative addition step are 5.1 kcal/mol for PhBr to PdBr− and 8.4 kcal/mol for PhCl to PdCl− , and exothermic energies are 10.1 kcal/mol for (PdPhBr2 H2 O)− and 8.1 kcal/mol for (PdPhCl2 H2 O)− . The coordination number of H2 O changed from zero to one during the oxidative addition to form the square planar (PdPhX2 H2 O)− complex. Compared with the oxidative addition to halogen-free Pd(0) , the oxidative addition to PdBr− /PdCl− has almost the same free energy barriers. Conversely, the exothermic energies to form the (PdPhX2 H2 O)− complexes are significantly reduced from those to form the PdPhX(H2 O)2 complex. The destabilization of the products of the oxidative addition process may accelerate the following reaction step, i.e, the transmetalation step. After the oxidative addition to PdBr− /PdCl− , two halogen anions are connected to Pd in trans-position to each other and Ph is connected to Pd in cis-position to the halogen anions. We also checked the stability of the Ph connected to Pd in trans-position to one of the two halogen anions, but we could not identify the stable final state, indicating that the trans-form of the Pd(II) X2 PhH2 O complex is much less stable than the cis-form of the complex, which is similar to the Pd(II) XPh(H2 O)2 complex as discussed above. Therefore, the following transmetalation step may be different from the conventional SMR with phosphine ligated Pd catalysts. To clarify the solvent effect, we investigated the oxidative addition steps of PhX to a Pd(0) H2 O complex and to a PdX− anion complex in a vacuum. In the case of a Pd(0) H2 O complex, we included one H2 O molecule because during the oxidation step one H2 O molecule is always bonded to the central Pd metal, as seen in Figure 4. In these calculations, we did not perform finite-temperature MD simulations, but we carried out simpler static reaction path calculations using a climbing image nudged elastic band method proposed by Henkelman and co-workers 77 because without a solvent the entropy effect is expected to be small. The calculated energy profiles are shown in the upper left panel of Figure 5. As seen in Figure 5, the effect of X− on the activation barriers of the oxidative addition is small, namely, the


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barriers are slightly increased by about 3 kcal/mol in the present study, and the barriers are slightly decreased by ∼ 5 kcal/mol in previous studies on a CH3 X oxidative addition to Pd/PdCl− . 38,78 Conversely, the effect of the X− anion on the reaction energies is large, namely, the product of the oxidative addition step is stabilized by 8∼10 kcal/mol , which agrees with previous works. 38,78 We notice that the comparison with those previous studies on the CH3 X oxidative addition is valid for checking of the difference of solvent effects between the explicit solvent model and the continuum models. As for the solvent effect, the effect is small for the case of the oxidative addition step of PhX to a single Pd(0) H2 O complex. Conversely, for the oxidative addition step of PhX to the PdX− anion complex, the activation barriers do not depend on the inclusion of the solvent, but the exothermic energies do depend significantly on the inclusion of the solvent. This effect was observed previously using a continuous solvent model 38 but the effect seems to be larger in the present study using explicit solvent molecules. As seen in the right hand panel of Figure 5, by adding the halogen anion (X− ) to the Pd catalyst along with the solvent effect, the exothermic energy is reduced by about 5 kcal/mol for Br and by about 3 kcal/mol for Cl. The reduction of the exothermic energy will be important to enhance the following transmetalation step. Finally, we compare the solvent effects resulting from our explicit solvent model with that of the continuum model reported by Jong and Bickelhaupt. 38 In the case of the PhCl oxidative addition to Pd, the activation energy we calculated does not depend on the existence of the water solvent, and the final state energy is slightly more stabilized than that of the gas phase by about 3 kcal/mol, which is in good agreement with the case of the CH3 Cl oxidative addition to Pd using the continuum model. Whereas, in the case of the PhCl oxidative addition to PdCl− , the activation energy is 4.8 kcal/mol lower in solution than that in the gas phase; however, the activation barrier for the case of the CH3 Cl oxidative addition to PdCl− by using the continuum model is 4.9 kcal/mol higher in solution than that in the gas phase, having an opposite effect on the activation energy. The reaction energy is destabilized by 9.9 kcal/mol in solution more than that in the gas phase, which is in good agreement



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with the destabilization of 10.3 kcal/mol in solution calculated by the continuum model. Therefore, especially for the anionic catalyst, the explicit solvent model is important for the calculation of the activation energy.

Tendency of the Pd Aggregation To validate the single Pd catalyst model, we investigated the possibility of Pd aggregation, namely, the formation of a Pd2 dimer from two single Pd catalysts or from two single PdBr− catalysts. We performed first-principles MD simulations of two single Pd (or PdBr− ) catalysts located close to each other and monitored whether two Pd atoms form a Pd2 dimer or not. If a Pd2 dimer is formed, this suggests that the Pd single catalyst tends to aggregate to form large Pd clusters. For each single Pd catalyst, namely, Pd or PdBr− , we considered two possible cases, i.e., a dimer formation before and after the oxidative addition step. Before the oxidative addition step, one of the two reactants, PhBr, forms an η 2 complex with the Pd catalyst (see Figure 6). We assumed that two η 2 complexes would come close to each other in the water solvent and one of the two Pd (or PdBr− ) moved from one η 2 complex to the other one, forming two Pd (or PdBr− ) catalysts bonded to a single PhBr with a Pd-Pd distance of 2.68 Å. After the oxidative addition step, the Pd catalyst forms a square-shaped Pd complex, namely, PhPdBr(H2 O)2 in the case of the single Pd catalyst (Figure 4) and PhPdBr2 (H2 O)− in the case of the single PdBr− catalyst (Figure 5). We assumed that the two square-shaped Pd complexes would come close to each another in the water solvent. Starting from these four initial configurations, we performed first-principles MD simulations and investigated the tendency of the Pd catalyst aggregation. For these simulations, we used slightly different unit cell models from those used in the simulations of the oxidative addition step. Prior to the oxidation step for the Pd catalyst without Br− , two Pd atoms bonded to one PhBr are introduced together with 54 H2 O molecules in a cubic box of 12.38 Å× 12.38 Å× 12.38 Å, while for the PdBr− catalyst, two PdBr− anions are introduced together with 86 H2 O molecules in a cubic box of 14.21 Å× 14.21 Å× 14.21 Å. Following the oxidation 12 ACS Paragon Plus Environment

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step for the Pd catalyst without Br− (PdBr− catalyst), two PhPdBr (PhPdBr− 2 ) complexes are introduced together with 86 H2 O molecules in a cubic box of 14.21 Å× 14.21 Å× 14.21 Å. Figure 6 shows the time evolution of the Pd-Pd distances for the four cases. On the one hand, if two single Pd catalysts come close to each other before the oxidative addition, for both catalyst cases, namely, the single Pd catalyst (red dashed line) and the single PdBr− catalyst (black solid line), the Pd-Pd bond distances fluctuate between 2.5 and 3.0 Å, which is close to the metallic Pd-Pd distance of 2.75 Å, indicating the initial stage of the Pd aggregation. On the other hand, if two single Pd catalysts come close to each other after the oxidative addition, the Pd-Pd bond exceeds 3.0 Å for the case of the single Pd catalyst (blue dashed line), and it exceeds 3.5 Å for the case of the single PdBr− catalyst (green solid line); both bond lengths are much larger than the Pd-Pd metallic bond, suggesting that the Pd aggregation is unlikely. The results indicate that if the single Pd (or PdBr− ) catalysts come close to each other before the oxidative addition step, they easily form Pd-Pd metallic bonds and tend to aggregate, while if they meet each other after the oxidative addition step, they never form Pd-Pd metallic bonds and do not aggregate. Therefore, the lifetime of the η 2 complex is very important; namely, if the barrier of the oxidative addition step is large, and the lifetime of the η 2 complex is long, then the single Pd catalysts have a large probability to aggregate. Conversely, if the barrier of the oxidative addition step is small, and the lifetime of the η 2 complex is short, then the single Pd catalysts have a small probability to aggregate. The discussion is in accordance with the de Vries hypothesis. 16 Even after the oxidative addition, the Pd catalysts may form a Pd(Br2 )Pd complex as seen in Figure 6. In the case of the single PdBr− catalyst, however, the electrostatic repulsive interaction may significantly reduce the possibility of two PdBr− catalysts coming close to each other, making the aggregation more unlikely. Thus, we conclude that the Pd aggregation is unlikely especially for the case of the single PdBr− catalyst, provided that the free energy barrier for the oxidative addition step is reasonably low.



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Validity of the Constraint for the Free Energy Calculation The quality of the free energy difference calculated using the BME method depends on the choice of reaction coordinates. The reaction coordinate RPd−BC we chose in our simulations is reasonably good for a wide range of values from 0 Å to ∼7 Å. We noticed, however, a small gap in geometries near the transition steps of the oxidative addition steps. The right panel of Figure 7 shows the values for RPd−BC and the lengths of the C1 -Cl along the paths obtained using constraints on RPd−C or on θClPdC . As seen in the figure, the length of the C1 -Cl bond for BME with the constraint on RPd−BC changes suddenly at around RPd−BC ∼ 2.0 Å, indicating that the constraint on the RBd−BC is not adequate to describe the present reaction path. Conversely, both RPd−BC and RC1 −Cl for BME with the constraint on θClPdC1 are smooth, and there is no gap. Therefore, θClPdC seems to be a better reaction coordinate to describe the present path. Still, the right hand panel of Figure 7 shows that the relative free energies calculated by the two BME simulations agree rather well with each other, indicating that the relative free energies can be calculated by both of the constraints. Although θClPdC1 seems to be better for describing the present reaction path, especially near the transition state, the error in the free energies calculated by the constraint on θClPdC1 becomes large; therefore, θClPdC1 cannot describe the whole range of the reaction path we have investigated. Therefore, we used RPd−BC as the constraint in the present simulations.

Conclusion We performed first-principles MD simulations of the oxidative addition step in a SMR with a ligand-free Pd catalyst in a water solvent to clarify the origin for the extremely high catalytic activity. We used a single Pd atom solvated in water and solvent H2 O molecules are explicitly included in our calculation model. We precisely calculated the relative free energy profiles including the solvent entropy by using the BME method. The results show that the energy barrier on the oxidative addition step is quite low especially for PhBr, which


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is significantly different from the conventional SMR with ligands in organic solvents. This may be the reason why the SMR in water without any ligands can achieve a high TON and low-leaching of the Pd catalyst. Conversely, the barrier of the oxidative addition for PhCl is sizable, indicating that the reaction can proceed at room temperature or above, but the rate is rather slow compared with PhBr. Therefore, the lifetime of the η 2 complex of PhCl-Pd is elongated, causing the sintering of Pd to degrade the catalyst, which agrees with the de Vries idea for a ligand-free Heck reaction. 16 We also analyzed the by-product anion effect to the oxidative addition reaction of the ligand-free SMR in water. We observed that the activation barriers of the oxidative addition of PhX to the PdX− anion complex are similar to those of the oxidative addition of PhX to a single Pd(0) atom in a water solvent. The final state of the oxidative addition step, however, becomes significantly destabilized by the additional coordination of a halogen anion to the central Pd atom, and this should have an important effect for the following transmetalation step. The coordination of anions to the Pd atom should also prevent the aggregation of the Pd atom to form the Pd black. Therefore, the halogen anion can act as a "ligand" in a ligand-free system.

Acknowledgements We would like to thank Prof. Nobuaki Kambe, Prof. Takanori Iwasaki, Drs. Daiju Matsumura and Yasuo Nishihata for valuable discussions. The present study was partly supported by Grants- in Aid for Scientific Research on Innovative Areas 3D Active-Site Science (No. 26105010 and No. 26105011) and Scientific Research (C) (No. 26410014) from the Japan Society for the Promotion of Science (JSPS), the Elements Strategy Initiative for Catalysts and Batteries (ESICB) supported by the Ministry of Education, Culture, Sports, Science, and Technology, Japan (MEXT), and the JSPS Core-to-Core Program (Type A) "Advanced Research Networks: Computational Materials Design on Green Energy." The numerical calculations have been done with the facilities of the Supercomputer Center, In-



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stitute for Solid State Physics, the University of Tokyo, Nagoya University, and Tohoku University.

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Figures

Figure 1: Overall cycle of the Suzuki-Miyaura reaction. The red-circled PhBr and PhB(OH)2 are the two reactants. The blue-circled PhPh is the product. PhB(OH)2 becomes PhB(OH)− 3 in alkaline solutions.


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Figure 2: Model system of the simulation. The periodic boundary conditions are imposed on the system. PhX(X=Br or Cl) is placed in the center; halogen (X=Cl, Br) anions are shown in pink, carbon (C) atoms are shown in green, oxygen (O) atoms are shown in red, and hydrogen (H) atoms are shown in white. PhX is surrounded by H2 O molecules. Pd is represented in gold. The number of water molecules in a unit cell is 59. The cell size is 12.38 Å × 12.38 Å × 12.38 Å.

Figure 3: Constrained coordinate used in the BME simulations. The distance between Pd and the midpoint between the halogen atom and C in the ipso-position of the benzene ring is denoted by RPd−BC .



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Figure 4: Relative free energy profile and the number of coordinated H2 O to Pd for the oxidative addition step. The top and bottom panels show snapshots of the oxidative addition step, while the middle panel shows the free energy profile (upper graph) and the number of coordinated H2 O molecules to the Pd atom (lower graph). The solid red and blue lines in the upper graph represent the free energy profiles of the oxidative addition of PhBr and PhCl to Pd in the water solvent, respectively. The solid green line represents the free energy profile of the oxidative addition step of PhBr to mono-ligated PdPPh3 in a vacuum. The vertical bar is the standard deviation of the estimated free energies. The red dotted and blue dotted lines represent the number of coordinated H2 O molecules to the Pd atom during the oxidative addition of PhBr and PhCl, respectively.


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Figure 5: Energy profiles of the oxidative addition step. Upper left panel: static reaction path calculations using a climbing image nudged elastic band (CI-NEB) method for the oxidative addition of PhX (X=Cl, Br) to a PdX− anion complex or to a Pd(0) H2 O neutral complex in a vacuum. Upper right panel: free-energy profiles calculated on the basis of firstprinciples molecular dynamics simulations with BME sampling for the oxidative addition of PhX (X=Cl, Br) to the PdX− anion complex or to a Pd(0) neutral atom in water. Lower panels: Snap shot of the oxidative addition step of PhCl to the PdX− anion complex in water.



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Figure 6: Trajectories of the distance between one Pd and another Pd during finite temperature MD for over 8 ps (upper-right panel) and final configurations. The black (red) line shows the Pd-Pd distances in case of PdBr− (Pd) before the oxidative addition (O.A.). The green (blue) line shows the Pd-Pd distances in case of PdBr− (Pd) after the oxidative addition. The black (red) framed panel represents the final structure in case of PdBr− (Pd) before the oxidative addition. The green (blue) framed panel represents the final structure in case of PdBr− (Pd) after the oxidative addition.

Figure 7: Relative free energy for the oxidative addition step of PhCl to Pd in the water solvent calculated using two reaction coordinates, namely the distance between Pd and the bond center of C1 of the phenyl ring and a Cl atom (RPd−BC ) and the angle between Pd-Cl and Pd-C1 bonds (θClPdC ) (left panel). Profiles of the reaction coordinate RPd−BC and the length of the Cl-C1 bond (right panel)


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First-Principles Molecular Dynamics Analysis of Ligand-Free Suzuki

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