Theoretical Calculations on the Mechanism of Hydrogenation of Diphenylacetylene over Pdn (n = 1-4) Clusters

Diphenylacetylene (DPA) is a precursor of stilbene and benzil, and reduction of DPA or its derivatives with metallic reagents is both an old and contemporary topic of research. By means of density function theory (DFT) calculations, a detailed investigation of the mechanism of the hydrogenation of DPA over Pd clusters was carried out at the molecular level. The various species structures in the hydrogenation of DPA over Pd clusters were optimized and analyzed. The calculations indicate that the reactions over different Pd clusters share similar reaction mechanisms, and the entire reaction path could be divided into approximately two stages: stage 1: the hydrogenation of DPA to stilbene by the addition of one hydrogen molecule; and stage 2: the hydrogenation of stilbene to the final product diphenylethane (DPE) with the recovery of the catalyst. The Pd2and Pd3-catalyzed systems exhibit the smallest rate-determining step (RDS) energy barrier, and these systems might be the most active and effective catalytic species among the Pd clusters. Although the Pd clusters used in the current work are simple systems, these clusters could eventually provide insights into the specific structure of the Pd catalyst, since Pd and/or clusters and/or nanoparticles could be envisioned as active catalysts in experiments.


Introduction
The carbon-carbon triple bond of alkynes is one of the basic functional groups in chemistry, and its reaction belongs to the foundations of organic chemistry. [1][2][3] In recent years, the physical chemistry and theory of few organic molecules have been studied more deeply than those of acetylene. Acetylene chemistry has undergone a renaissance because acetylene not only is present in molecules on the frontiers of organic chemistry, such as pharmaceutical chemistry and biochemistry, but also serves as a building block or a general intermediate for the synthesis of large numbers of chemicals. [4][5][6] The development of new synthetic methodologies based on transition metal catalysis has provided impetus to alkyne chemistry. 7 The partial hydrogenation catalytic reduction of internal alkynes is an efficient method for preparing olefins and alkanes, and metal complex catalysts have been the most effective catalysts for achieving this transformation. 8,9 The methods for the hydrogenation of alkynes provide exciting strategies for the synthesis of complex organic building blocks and attract extensive attention in pharmaceuticals and other valuable chemicals. This type of hydrogenation reaction utilizes homogeneous Ni, Cr, Ru, Rh, Pd, Cu and borate organic catalysts and is known for the reduction of olefins, alkynes, nitriles and ketones. Although hydrogenation reagents are hydrogen activated by transition metal-based catalysts, Pd catalysts require the mildest of conditions and are the most widely used. [10][11][12][13][14] Diphenylacetylene (DPA) is particularly representative of the alkynes, and it can act as a Lewis acid and ligand in organometallic chemistry because of its symmetry and high planarity. Additionally, DPA is a precursor of stilbene and benzil and reduction of DPA or its derivatives with metallic reagents is old and contemporary topic of research; much attention has been focused on metal complexes, such as

Yan Chen, * ,a Yong Fang, b Jinglong Pan, c Hao Fu c and Wen Cao a
Pd, Ir, Ag, Rh complexes, etc., [15][16][17][18][19][20] as reductants. In the case of the hydrogenation reaction of diphenylacetylene, however, diphenylethylene is formed as a primary product, but 1,2-diphenylethane (DPE) is absent. In addition, with the development of chemistry, some different synthetic methods, such as the reduction of diphenylacetylene to 1,2-diphenylethane, have been discovered. Recent methods for the synthesis of 1,2-diphenylethane have concentrated on the direct reduction of diphenylacetylene, and most of the reported methods require metal complexes. For example, Cravotto and co-workers 21 reported that the Pd complex can act as a catalyst to generate 1,2-diphenylethane by the reduction of diphenylacetylene. Additionally, Webster and co-workers 22 reported that using the Fe II complex as a catalyst, in 1 equivalent of n BuNH 2 and HBpin, the triple bond was reduced, and the 1,2-diphenylethane was obtained. However, low yield and many byproducts affect the efficient utilization of catalysts in the hydrogenation of diphenylacetylene. A new hydrogenation reaction with complex metal catalysts was reported by Jackowski and co-workers. 20 When Cl 2 Pd(PPh 3 ) 2 /Me 2 Zn was used as the catalyst in the reduction of diphenylacetylene, 1,2-diphenylethane was the only product and was produced in 99% yield. Despite the use of a bimetallic complex in hydrogenation reactions, Cl 2 Pd(PPh 3 ) 2 as precatalyst and Me 2 Zn as a reducing agent, Me 2 Zn interacts with the Pd II precatalyst to deliver Cl 2 Pd(PPh 3 ) 2 , which is reduced to Pd 0 . 20 Therefore, Pd 0 is an efficient catalyst in the hydrogenation of diphenylacetylene to 1,2-diphenylethane. Although the authors deduced the reaction mechanism by experiments, the details of the transformations and, more importantly, the origins of the observed selectivity still need to be understood at the molecular level, without which the mechanism of the calculations is incomplete. In challenging situations, the preferred mechanism may depend on the reaction conditions and ligands. While experiments can provide sufficient insights, the interpretation of these results is often inconclusive. In such cases, moving to computational chemistry may attain a deeper understanding of specific chemical problems. In many cases, Pd catalysis has provided a new world of transformations and has made numerous structural parts more accessible. Although the role of Pd may be apparent, there are usually multiple pathways that need to be considered. 14,[23][24][25][26][27] With the progress of theoretical methods in recent years, the combination of quantum chemical computations and experiments has made great progress in the development of chemistry. Particularly, the density functional theory (DFT) method [28][29][30][31][32][33] has been widely used in the study of the mechanisms, molecular interactions, and origins of selectivity in the reactions.
Here, we have employed the DFT method to investigate the mechanism of the reduction reaction at a molecular level. The aim of the present paper is focused on the following aspects: (i) the most feasible step of the whole reaction, including the rate-determining step (RDS); (ii) the effect of the states of the palladium catalysts (Pd-Pd 4 ) on the hydrogenation reaction (Scheme 1); and (iii) the configuration of the stilbenes (semihydrogenation products). This computational study contributes to the understanding of these hydrogenation reactions at the molecular level and can also provide some important suggestions for new hydrogenation reactions.

Methodology
The previous computational literatures demonstrated that the density functional Minnesota 06 (M06) 34-37 and Becke, 3-parameter, Lee-Yang-Parr (B3LYP) 38,39 methods performed well for catalytic reactions based on the transition metal system. 33,[40][41][42][43][44][45] In the present investigations, the geometrical optimizations of all the intermediates (IM) and transition states (TS) were performed using the M06 and B3LYP methods, respectively. The palladium clusters were optimized before the coordination of DPA, the initial Pd−Pd distances of 1.5 and 3 Å were used in the optimization of Pd agglomerates and the coordinates of palladium atoms of the clusters were relaxed in following optimization. The electronic spin state of the considered Pd n clusters is the singlet state. The SDD basis set 46 was used for Pd atom and the 6-311+G(d,p) basis set 47 was employed for the rest atoms. The solvation effect was considered in the geometry optimization by a self-consistent reaction field (SCRF), in which the polarizable continuum model (PCM) implicit solvent model was employed with tetrahydrofuran (THF) as a solvent. [48][49][50] All geometries were optimized in vacuum by using PCM model. This model was used for single-point energy calculations based on all of the solventphase optimized geometries at a larger basis set (SDD for the Pd atom and 6-311+G(d,p) for other atoms). All DFT calculations were performed with the Gaussian 09 51 series of electronic structure programs. The vibrational frequencies were assessed at the same level of theory as that for the geometrical optimizations, to verify the stationary points as local minima (no imaginary frequencies) or transition states (unique imaginary frequency). Necessarily, using the intrinsic reaction coordinate (IRC) method, 52 the key transition states were confirmed to be the connection between the corresponding reactant and product. The total cartesian coordinates for all minima point and transition states in the gas-phase by B3LYP and M06 are provided in the Supplementary Information (SI) section.

Reaction mechanism
The DFT calculations predicted that the reactions over different Pd clusters share a reaction mechanism similar to that in Scheme 1, and the entire reaction path could be divided into approximately two successive stages: stage 1: the hydrogenation of DPA to stilbene by the addition of one hydrogen molecule; and stage 2: the hydrogenation of stilbene to the final product DPE with the recovery of the catalyst.
Additionally, M06 and B3LYP gave the comparable values with few discrepancies in the optimized geometries, which implies that the present calculation is reasonable for the titled reaction system. To give a concise expression, the following discussion will be based on the Pd 3 -catalyst system at the B3LYP(PCM)/6-311+G(d,p), SDD level unless otherwise specified. The detailed information about the optimized structures and energy profile of the hydrogenation of DPA over the Pd, Pd 2 and Pd 4 cluster systems is provided in the SI section. The energy profile and the optimized IMs and TSs at the B3LYP/6-311+G(d,p), SDD, are shown in Figure 1.
As shown in Figure 1, the reaction is triggered by the coordination of the alkyne moiety with the Pd atoms with the formation of the Pd 3 -DPA complex, and the palladium clusters were optimized before its approximation to DPA. In this complex, the Pd−C distances are calculated to be 1.99-2.14 Å, and the negative Laplacian of electronic densities ∇ 2 ρ at (3, -1) bonding critical points by atoms in molecule (AIM) analysis 53 in Figure 2 indicates the covalent interaction between Pd 3 and DPA, demonstrating that there is a strong interaction between the substrate and the Pd 3 cluster. This result could be enhanced by the lower relative free energy of 54.7 kcal mol -1 with respect to the separated substance and bare Pd 3 cluster.
Next, an external H 2 molecule gets close to one Pd-end of the Pd 3 -DPA complex and leads to the yield of Pd 3 -IM 1 Then, the cleavage of the H−H bond and the insertion of one hydrogen atom into the DPA takes place through the three-membered ring transition state (TS 1 ), leading to the formation of Pd 3 -IM 2 . In this species, the threemembered ring is characterized by an elongated C−H bond of 1.66 Å, Pd−C bond of 2.08 Å and Pd−H bond of 1.56 Å. For Pd 3 -IM 2 , the C−H distance is calculated to be 1.08 Å, indicating that the migration of hydrogen atom is complete, and the corresponding C−H bond has been formed. In addition, the rest of the alkyne coordinates with the two Pd ends of the Pd 3 cluster with the Pd−C distances of 2.09 Å. The calculations show that the above step has a moderate energy barrier of 26.2 kcal mol -1 .
From the Pd 3 -IM 2 , the next hydrogen atom transfers to another side of the alkyne moiety of the DPA via transition state TS 2 , which leads to the formation of Pd 3 -IM 3 . As shown in Figure 1 As a result, cis-and trans-IM 3 are identified at the end of stage 1 of the reaction mechanism. For each IM 3 , the C−H distance is calculated to be ca. 1.09 Å, indicating that the migration of the hydrogen atom is finished, and the corresponding C−H bond has been formed. In addition, the alkene that is generated coordinates with the Pd 3 cluster with the Pd−C distances in the range of 2.14-2.15 Å, demonstrating the interaction between the carbon of the phenyl ring and the Pd 3 cluster. As a result, the stilbene adsorbed on the Pd 3 cluster is generated at the end of this reaction state after TS 2 , and the energy barrier of the step via TS 2 is calculated to be 16.3 kcal mol -1 for the cis-path and 12.7 kcal mol -1 for the trans-path.
Here, it should be emphasized that the configuration of the stilbene intermediate is closely dependent on the step via the TS 2 , and therefore the TS 2 appears to be the stereo-controlling transition state in the reaction stage 1. The B3LYP calculation predicts the energy barrier via the trans-TS 2 is energy-favored by 3.6 kcal mol -1 over its competing transition state of cis-TS 2 . The trans-TS 2 links to the formation of stilbene in the Z-configuration and the cis-TS 2 to the formation of stilbene in the E-configuration, according to the absolute rate theory and the formula as follows: (1) where k is the rate constant, T is the absolute temperature, R is the gas constant, and DG ≠ is the activation Gibbs free energy.
The stereo-selectivity of stilbene is predicted to be Z / E > 1:99 at 298.15 K indicating that the generation of Z-stilbene might be advantageous in thermodynamics. However, considered the error generated from the DFT calculations, this reason may be not accurate enough to account for the selectivity of cis-and trans-IMs in the experiment.

Stage 2: hydrogenation of stilbene to DPE
In stage 2, the reaction must undergo the hydrogenation from stilbene to DPE over Pd-catalyst with the addition of another H 2 molecule after the reaction stage 1 has been completed. The results are shown in Figure 3.
In this stage, an external H 2 molecule coordinates to one Pd-end of two Pd 3 -IM 3 complexes and leads to the yield of cis-or trans-IM 4 intermediate. In each IM 4 , the H−H bond is slightly enlarged to ca. 0.85-0.86 Å, and the Pd−H distances are calculated to be ca. 1.70 Å. The formation of the cis-IM 4 is predicted to be energy-favored by 9.7 kcal mol -1 from the separated cis-IM 3 and H 2 , and the formation of the trans-IM 4 is calculated to be favored by 12.0 kcal mol -1 from the separated trans-IM 3 and H 2 in relative energy, indicating that the generation of IM 4 is spontaneous.
Next, the breakage of the H−H bond and the insertion of one hydrogen atom into the stilbene moiety occur through  5 , the calculations determine the optimized C−H distance to be 1.09 Å, which implies that the transfer of the hydrogen atom is completed with the formation of the corresponding sp 3 carbon. In addition, the rest of the alkene part coordinates the two Pd atom Pd 3 cluster with the Pd−C distances of ca. 2.09 Å. The calculations predict that the above step has a moderate energy barrier of 12.5 kcal mol -1 in relative energy.
Then, from the IM 5 , the reaction goes through the four-membered ring transition state (TS 5 ), leading to the formation of IM 6 . The three-membered ring is composed of a Pd−C bond of 2.13 Å, a C−H bond of 1.73 Å and a H−Pd bond of 1.61 Å. For IM 6 , the C−H distance is calculated to be 1.09 Å, indicating that the migration of the hydrogen atom is completed, and the corresponding C−H bond is formed. In addition, the rest of the alkyne coordinates with the three Pd atom Pd 3 cluster with the Pd−C distances of ca. 2.12 Å. The calculations indicate that the above step has a moderate energy barrier of 13.4 kcal mol -1 .
Finally, the release of DPE from IM 6 takes place with the recovery of the Pd 3 -cluster. This step is predicted to be endothermic by ca. 21.9 kcal mol -1 without any barrier. As shown in Figures 1 and 3, the entire reaction is clearly favored by 54.7 kcal mol -1 in Gibbs free energy, and the largest barrier of 26.2 kcal mol -1 corresponds to the step from the IM 1 → TS 1 , indicating that the first hydrogenation step should be the rate determining step (RDS).

Comparison of Pd-Pd 4 catalyzed reactions
The reaction mechanisms over the Pd-Pd 4 cluster are similar, but the properties of the energy profiles vary: for the Pd-Pd 3 systems, both the M06 and B3LYP calculations predict that the step of IM 1 → TS 1 is the RDS with the barrier of ca. 22-29 kcal mol -1 (see SI section), while the RDS of the Pd 4 system turns to the final hydrogen migration step in IM 5 → TS 5 with the giant barrier larger than 33 kcal mol -1 . It is found that B3LYP energies could be considerably underestimated, and this is in accordance with the literature. 54,55 The 3D models of various species and the energy profile are shown in Figures 4 and 5.

Analysis of turnover frequency (TOF) in the catalytic cycle
In addition, based on the transition state theory and energetic span model, 56 we evaluated the theoretical turnover frequency (TOF) of the catalytic cycle via the intermolecular and H-transfer mechanism catalyzed by the Pd n (n = 1-4) catalyst. In equations 2 and 3, 57-60 the δE (energy span) is the energy difference between the summit and the through of the catalytic cycle. GTDTS and GTDI are defined as the Gibbs free energy of the

Conclusions
The mechanism of the hydrogenation reaction of diphenylacetylene catalyzed by Pd-Pd 4 species was investigated by using DFT method. The entire reaction mechanism in the present investigation is predicted to be composed of two processes: stage 1: the hydrogenation of DPA to stilbene with the addition of one hydrogen molecule via TS 1 and TS 2 ; and stage 2: the hydrogenation of stilbene via TS 3 and TS 4 to the final product DPE with the recovery of the catalyst.
The calculation on the diphenylacetylene system indicates that the hydrogenation could take place in existence of four catalysis of Pd, Pd 2 , Pd 3 and Pd 4 . For the Pd-Pd 3 systems, both the M06 and B3LYP calculations predict that the step of IM 1 → TS 1 is the RDS with the barrier of the largest Gibbs energy, and the RDS of the Pd 4 system turns to the step of the final hydrogenmigration step in IM 5 → TS 5 with the giant barrier larger than 33.1 kcal mol -1 . The calculation reproduces the major product E-stilbene intermediate, and exhibits the smallest RDS energy barrier for the Pd 2 -and Pd 3 -catalyzed system. Therefore, Pd 2 -and Pd 3 -catalysts might be the most active and effective catalysis species among the four clusters. This computational study is expected to provide a full understanding of this hydrogenation reaction at the molecular level and can also provide some important suggestions for the rational design and synthesis of the new Pd-catalytic hydrogenation reactions.