BNPd single-atom catalysts for selective hydrogenation of acetylene to ethylene: a density functional theory study

The mechanisms of selective hydrogenation of acetylene to ethylene on B11N12Pd single-atom catalyst were investigated through the density functional theory by using the 6-31++G** basis set. We studied the adsorption characteristics of H2 and C2H2, and simulated the reaction mechanism. We discovered that H2 underwent absolute dissociative chemisorption on single-atom Pd, forming the B11N12Pd(2H) dihydride complex, and then the hydrogenation reaction with C2H2 proceeded. The hydrogenation reaction of acetylene on the B11N12Pd complex complies with the Horiuti–Polanyi mechanism, and the energy barrier was as low as 26.55 kcal mol−1. Meanwhile, it also has a higher selectivity than many bimetallic alloy single-atom catalysts.


Introduction
Ethylene is an important polymerization monomer and industrial reaction intermediate, and it is predominantly produced by the pyrolysis of hydrocarbons. The thermal cracking production process always contains on the order of 1% of acetylene; however, ethylene used in the production of polymers needs to contain less than a few parts per million of acetylene in order not to affect the polymerization process [1,2]. The most suitable way to remove a small amount of acetylene in ethylene is to catalyse the hydrogenation of acetylene to produce ethylene.
Pd catalysts have a good conversion rate for hydrogenation reactions and are used as a catalyst for the selective hydrogenation reaction [3][4][5]. However, the high price assumes far-reaching significance for the research and development of catalysts with high reactivity and selectivity [6,7]. The main reason for the 2018 The Authors. Published by the Royal Society under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/4.0/, which permits unrestricted use, provided the original author and source are credited.

Calculation method and models
All density functional calculations were executed using the GAUSSIAN09 program package [40]. The hybrid density functionals of Lee, Yang and Parr (B3LYP) with the 6-31++G** basis set were applied for all structures. The nonlocal correlation functional of B3LYP [41] with the 6-31++G** basis set was used for H, C, B and N atoms, and the B3LYP functional was combined with the LANL2DZ basis set for the Pd atoms. No symmetry constraints were imposed on the geometry optimization. All relative energies in this study were zero-point-energy. All stationary points were characterized as the minima (no imaginary frequency) or transition state (TS; one imaginary frequency) by Hessian calculation. Intrinsic reaction coordinate (IRC) calculations [42,43] were performed to determine if each TS links the correct product with the reactant. Transition-state structures were characterized using frequency calculations and by analysing the vibrational modes. In all instances, only one imaginary frequency corresponding with the reaction coordinate was obtained.
An essential reference point for this calculation is the adsorption energy for C 2 H 2 and H 2 absorbed on the B 11 N 12 Pd nanocage. In this paper, we used the following definitions for adsorption energy.
When H 2 or C 2 H 2 is absorbed on B 11 N 12 Pd-SAC, the adsorption energy calculated was defined by the following equation.
When H 2 is absorbed on BNPd-C 2 H 2 , the adsorption energy is calculated as the following equation: When C 2 H 2 is absorbed on HCl, the adsorption energy is calculated as the following equation: When H 2 and C 2 H 2 are co-absorbed on B 11 N 12 Pd SAC, the co-adsorption energy is calculated as the following equation. The optimized structures of the pristine B 12 N 12 and B 11 N 12 Pd are depicted in figure 1. As expected, the calculated result shows that the charges uniformly distribute among all B(N) atoms in B 12 N 12 , with a Mulliken value of 0.57 e for B, and −0.57 e for N, which is consistent with previous calculations [36]. While one of the B-N bonds was shared between two six-membered rings with a length of about 1.44 Å, the other was shared between a four-and a six-membered ring with length of 1.48 Å. By substituting one Pd atom for a B site in the B 12 N 12 nanocage, the charges redistribute on the B 12 N 12 cage, and the electrons are found to accumulate around the Pd atom in B 11 N 12 Pd. The Mulliken charge for Pd is about 2.22 e, while the charge of the replaced B was 0.57 e, which means that the electron transfer is 1.65 e from the Pd atom to the B 12 N 12 nanocage. The Pd-N bond which was shared between the two six-membered rings had a length of about 2.10 Å, while the other was shared between a four-and a six-membered ring with a length of 2.04 Å. The adjacent three N atoms have a Mulliken charge of −0.37, −0.37 and −0.38 e. This means that the Pd atom and BN nanocage had a strong interaction.
In table 1, we list the HOMO and LUMO distributions and frontier molecular orbital (FMO) energies of the B 12 N 12 and B 11 N 12 Pd nanocages, respectively. One can see that after Pd doping, the orbital energy of HOMO was reduced, which means the stability of the B 11 N 12 Pd SAC is enhanced; the band gap ( E g ) between HOMO and LUMO also decreases, which facilitates the interaction between adsorbates and the surfaces.

Adsorption of reactants
The molecular orbital calculations and electron density analysis can be used to determine the adsorption position of C 2 H 2 and H 2 molecules on B 11 N 12 Pd SAC. According to the FMO analysis of the B 11 N 12 Pd SAC, the Pd atom may be the only active site (figure 1). In order to fully consider the possible adsorption sites, we put C 2 H 2 and H 2 on different sites both around the Pd atom and the BN nanocage structure, and obtained the most stable adsorption structures, which are shown in figure 2. Figure 3 shows that an H 2 molecule was initially absorbed on the Pd atom of the B 11 N 12 Pd SAC with an adsorption of about 6.28 kcal mol −1 ; the length between Pd and H 2 was about 1.94 Å, the bond length of H 2 was 0.78 Å, and it increased by 0.04 Å compared with the free H 2 molecule, indicating that there was interaction between H 2 and B 11 N 12 Pd SAC. Subsequently, a TS was formed when the H-H bond length was about 1.01 Å, which increased by 0.27 Å compared with the free H 2 molecule. From the vibrational analysis, we obtained only one imaginary frequency (−1426.63 cm −1 ), as the two H atoms of H 2 gradually separate approaching the B and Pd atoms. Then the two H atoms finally settled and formed the B 11 N 12 Pd(2H) dihydride complex, with a 2.72 Å distance for H-H, and the system gains a stabilization energy of −18.83 kcal mol −1 , indicating H 2 absolutely dissociative chemisorption.
To investigate the kinetic issue in the process of the hydrogenation on the B 11 N 12 Pd SAC, we calculated the activation barrier for one H 2 fully chemisorbed on the B 11 N 12 Pd SAC. Figure 3 shows the calculated reaction diagram for the H 2 adsorption on B 11 N 12 Pd SAC. The corresponding activation barrier (energy difference between TS and initial state (IS)) for the hydrogenation reaction is found to be 12.56 kcal mol −1 , indicating that H 2 dissociative chemisorption on the B 11 N 12 Pd SAC and the diffusion process of H atoms are facile.
In table 2, the Mulliken charge of absorbed C 2 H 2 is 0.47 e, indicating that an electron transfer of 0.47 e occurred from C 2 H 2 to B 11 N 12 Pd SAC; the length between Pd and C 2 H 2 is 2.30 Å, meaning that the C 2 H 2 molecules were absorbed only on the single Pd atom. The optimal adsorption energy of C 2 H 2 is −14.95 kcal mol −1 , which can be seen in table 2.       TS1  TS2  FS  FS  R2 TS1  TS2  TS3  IMS1  IMS2  IMS3  IMS1  reaction coordinate  reaction coordinate   IMS2   FS   R2  IMS1  IMS1  IMS2 IMS2 IMS3   forms an ethane molecule on the B 11 N 12 Pd SAC. Then C 2 H 4 is desorbed and achieves the final state (FS); the C 2 H 4 only needs 16.55 kcal mol −1 energy to move away, and the low desorption energy can ensure the selectivity of ethylene. From the energy diagrams of the R1, the step from IMS1 to TS2 is the rate-limiting step. We calculated the activation energy of hydrogenation of acetylene to ethylene action as 26.22 kcal mol −1 (the activation energy is the biggest energy difference in the energy diagram, as shown in figure 4), which is similar to the Pd 5 cluster (the lowest activation energy is 25.72 kcal mol −1 ) [44]. This indicates that the B 11 N 12 Pd SAC has a similar activation energy for hydrogenation of acetylene to ethylene; moreover, it can make full use of the noble metal and decrease the price of the catalyst.

3.3.2.
Vinylidene adsorbed onto the B 11 N 12 Pd(2H) dihydride complex As figure 4 (R2) shows, there is another pathway from vinylidene (C=CH 2 ) to C 2 H 4 , in which the H atom adsorbed on the Pd atom of R2 can move to the vinylidene to form ethenyl-B 11 N 12 Pd(H), with only 4.16 kcal mol −1 difference of free energies. Then the remaining H atom which linked to the B atom of IMS1 is transferred to the ethenyl group to obtain ethylidene via TS2, whose free energy is −36.96 kcal/mol. In the complicated pathways of acetylene hydrogenation, ethylidene can obtain the C 2 H 4 by proton translocation (TS3). The free energies of the TS for the IMS2 and IMS3 are −39.12 kcal mol −1 . The final step was the C 2 H 4 molecule desorption from the B 11 N 12 Pd, and the desorption energy was 16.55 kcal mol −1 . From the vibrational analysis of the TS, we obtained only one imaginary frequency for each TS (−1099.77, −1167.07, −923.56 cm −1 ). To gain a better understanding of the reaction, series IRC calculation testified that the TS connected the co-adsorption and IMS, and showed that no further intermediates are involved in the reaction.
From the potential energy change of catalytic hydrogenation of acetylene to ethylene in figure 4 (R2), the activation energy is 39.12 kcal mol −1 , and the rate-controlling step is also from IMS2 to TS3. Considering the complex hydrogenation pathways, it is found that the semi-hydrogenation of acetylene on the B 11 N 12 Pd cluster is easy to achieve.

H 2 adsorbed onto the B 11 N 12 Pd-C 2 H 2 complex
We also investigated the non-Horiuti-Polanyi mechanism of selective hydrogenation of acetylene on the B 11 N 12 Pd, as shown in the electronic supplementary material, figure S1-S3; the activation energy of hydrogenation of acetylene to ethylene action is 57.79, 53.26 and 55.84 kcal mol −1 . This means that selective hydrogenation of acetylene on the B 11 N 12 Pd complies with the Horiuti-Polanyi mechanism. Therefore, the lowest activation energy of hydrogenation of acetylene to ethylene is 26.22 kcal mol −1 .

C 2 H 4 adsorbed onto the B 11 N 12 Pd(2H) dihydride complex
In order to clearly research the selectivity of the catalyst, we studied the reaction of ethylene to produce ethane. As figure 5 shows, C 2 H 4 was first adsorbed onto the B 11 N 12 Pd(2H) dihydride complex to form the co-adsorption configuration (R3); according to equation (2.3) the adsorption energy is −12.67 kcal mol −1 , indicating that the complex also has a high adsorption to C 2 H 4 compared with C 2 H 2 . R3 passes through a small energy barrier to obtain TS1. From the vibrational analysis of TS1, we obtained only one imaginary frequency (−639.02 cm −1 ), which was associated with the stretching motion of the H atom that is linked to the Pd atom. We can observe that the H atom adjacent to Pd is active in TS1. Then the H atom approaches to form an ethyl-B 11 N 12 Pd(H) intermediate (IMS1); the length of C=C double bonds of C 2 H 4 is 1.37 Å, which is raised 0.03 Å compared with the TS1. The IMS1 through a 29.35 kcal mol −1 energy can proceed to the TS2.
IRC calculation testified that TS1 connected the co-adsorption and IMS1 and showed that no further intermediates are involved in the reaction. The length of C=C double bonds is 1.34 Å, which is close to the C=C bond length of free C 2 H 4 . The H atom which is linked with the N atom has a nearly neutral charge, which denotes the weak binding of intermediates. The IMS1 through a 26.22 kcal mol −1 energy can proceed to the TS2; from the vibrational analysis of TS2, we obtained only one imaginary frequency (−1597.33 cm −1 ), which was associated with the stretching motion of the H atom linked to the B atom. IMS2 approaches the vinyl-B 11 N 12 Pd and forms an ethane molecule on the B 11 N 12 Pd SAC. Then C 2 H 6 is desorbed and the FS is obtained; the dissociation energy of C 2 H 6 is about 2.83 kcal mol −1 .
From the energy diagrams of R3, the step from IMS1 to TS2 is the rate-limiting step. We calculated the activation energy of hydrogenation of ethylene to ethane action as 29  than that of the acetylene to ethylene action. This indicates that the B 11 N 12 Pd SAC has a high selectivity of acetylene hydrogenation to ethylene.

H 2 adsorbed onto the B 11 N 12 Pd-C 2 H 4 complex
We also investigated the hydrogenation of ethylene to ethane action onto the B 11 N 12 Pd in non-Horiuti-Polanyi mechanism (electronic supplementary material, figure S4); the activation energy is 53.11 kcal mol −1 . This means that hydrogenation of ethylene onto the B 11 N 12 Pd complies with the Horiuti-Polanyi mechanism. Therefore, the lowest activation energy of hydrogenation of acetylene to ethylene is 29.35 kcal mol −1 .

Selectivity of the acetylene hydrogenation to ethylene on B 11 N 12 Pd SAC
The factor influencing the selectivity of acetylene hydrogenation to ethylene is considered to be the difference between the desorption barriers and the hydrogenation barrier of ethylene [8,45]; we defined the difference as E a . The desorption barriers are estimated with the absolute value of the adsorption energies according to the approximation made in previous studies [8,16,[46][47][48][49][50]. Namely, we define E a = E a − |E ad |, (3.1) where E a and E ad are the hydrogenation and desorption barriers of ethylene, respectively. This equation indicates that the more positive the E a , the more selective the catalyst will be for the production of ethylene compared with ethane formation. As table 1 shows, B 11 N 12 Pd has a better selectivity than most bimetallic alloys [13,16,17,26]. A high selectivity also can be judged from the following two aspects. One is a low desorption energy of ethylene, which can effectively inhibit the hydrogenation of ethylene to produce ethane. In this work, the desorption energy of ethylene (16.55 kcal mol −1 ) is less than the activation energy of ethylene (29.35 kcal mol −1 ), which can ensure a high selectivity. The other is a high ethylene hydrogenation activation energy. In this work, the acetylene hydrogenation activation energy is 26.55 kcal mol −1 , which is less than the ethylene hydrogenation activation energy. Therefore, we can draw the conclusion that the B 11 N 12 Pd SAC has a high selectivity for the acetylene hydrogenation to ethylene.

Conclusion
This work uses DFT to study the catalytic process of selective hydrogenation on B 11 N 12 Pd SAC. The results show that a Pd single atom can effectively dissociate an H 2 molecule and form the B 11 N 12 Pd(2H) dihydride complex, with the hydrogenation of acetylene to ethylene following the Horiuti-Polanyi mechanism. The activation energy for hydrogenation of acetylene is similar to that with Pd clusters, which is beneficial to reduce the cost of the catalyst. Besides, the low desorption energy of ethylene and high ethylene hydrogenation activation energy can ensure that the B 11 N 12 Pd SAC has a high selectivity. From the selectivity formula, we conclude that the selectivity of the B 11 N 12 Pd SAC is higher than that of the majority of the binary metal monatomic catalysts. This work provides a theoretical basis for the development of catalysts with novel high catalytic performance and selectivity for hydrogenation.
Data accessibility. All original data can be accessed at the Dryad Digital Repository [51].