Selective hydrogenation of acetylene over TiO₂-supported PdAg cluster: carbon species effect

Abstract

It is well known that the carbon species has a strong effect on the catalytic activity and selectivity of acetylene (C₂H₂) hydrogenation, and the previous theoretical work has mainly concentrated on the catalyst without the support, so it is important to investigate the carbon species effect on the behavior of selective hydrogenation over the metal oxide supported palladium (Pd)-based catalysts. In this work, the effect of the carbon atom on C₂H₂ hydrogenation is studied on the oxygen-defective anatase (TiO₂-A-Ov) and rutile (TiO₂-R-Ov) supported Pd₄ (Pd₂Ag₂) clusters using density functional theory calculations with a Hubbard U correction. The calculated results show that the carbon atom has a large effect on both catalytic and selectivity of C₂H₂ hydrogenation, and that such a promotion effect is strongly related to the properties of the support, i.e., the carbon species effect is different for anatase TiO₂ and rutile TiO₂. By analysing the hydrogenation reaction mechanism, it was found that: (i) the subsurface carbon atom can improve the selectivity of ethylene on the rutile supported PdAg metal cluster, but has little effect on its activity, (ii) in contrast to the rutile support, the presence of carbon species can enhance the activity of the anatase supported PdAg metal cluster, but has a little effect on its selectivity, (iii) the addition of Ag can further increase the selectivity, and (iv) the TiO₂ support can enhance the selectivity when compared to the catalyst without the TiO₂ support.

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1. Introduction

The selective hydrogenation of acetylene (C₂H₂) is important in industrial processes, because the C₂H₂ produced in the preparation of ethylene (C₂H₄) by oil cracking may generate catalyst poisoning.^1,2 The ideal catalyst which has good activity and high selectivity and which can remove the impurities to obtain a high purity C₂H₄ is the palladium (Pd) or Pd-based catalyst. Furthermore, to improve the selectivity towards the C₂H₄ formation, bimetallic systems that incorporate a second metal to palladium were widely used, such as silver (Ag),^3,4 gold,⁵ and so on. However, it was found that the addition of Ag enhanced the C₂H₄ selectivity but reduced the overall hydrogenation activity.⁶ The subsurface carbon can reduce the reaction barriers of C₂H_x hydrogenation and improve the reaction rate.^7,8 Nag⁹ studied the formation and stability of palladium hydride in a well characterized Pd-on-carbon catalyst and he found that the carbon atom, as a catalyst support, may come from the organic precursor used to prepare the catalyst or chemicals used during the investigation. Yang et al.¹⁰ discussed the effect of subsurface carbon on Pd(111) and Pd(221) and they found that the subsurface carbon species can increase the activity on Pd(111) slightly but decreases that of Pd(221) a little. Also, on Pd(111) the subsurface carbon atom can reduce the binding energy of C₂H₄ significantly because of the d-projected density of states of the surface Pd away from the Fermi level. Namely, the selectivity of C₂H₄ production on a Pd surface was found to be increased in the presence of subsurface carbon species.

Cinquini et al.¹¹ compared the carbon diffusion process in the near surface and in the bulk of nickel (Ni) and Ni₃Pd and discovered that the carbon atom is easy over the surface on the pure Ni but prefers to move to subsurface on the NiPd₃ alloy. Similarly, Studt et al.¹² studied the adsorption of carbon on a Pd(111) and a Pd(211) and in the subsurface octahedral sites, and found that the carbon species were unfavorable to diffuse from the surface into subsurface. Furthermore, it was found that the subsurface carbon atom was favored at the octahedral sites on Pd(111) and favored four-fold on Pd(221).^10,13,14 Stevanovic et al.¹⁵ and Qi et al.¹⁶ explored the effect of carbon adsorption on the isomer stability of tetrairidium (Ir₄) clusters and found that the tetrahedral Ir₄ cluster is the most stable configuration on the magnesium oxide [MgO(100)] with the single carbon atom and the carbon prefers to adsorb at the tetrahedral Ir₄ rather than the square one on MgO(100).

It is well known that titanium dioxide (TiO₂) has been used for C₂H₂ hydrogenation because of the strong metal support interaction. Kim et al.¹⁷ found that the TiO₂-modified Pd catalyst has a high selectivity for C₂H₂ hydrogenation. In previous work, the comparison between the perfect and defective anatase TiO₂(101) and the performance of different defective structures of TiO₂ supported Pd₄ cluster catalysts were studied.^18,19 It was found that the defective anatase catalyst has the highest selectivity of all. Concerning its effect on the subsurface carbon, there are many studies using pure Pd without support^10,12,20 but its influence on the anatase and rutile supported PdAg cluster is not ambiguous. Therefore, this study aimed to discuss the hydrogenation mechanisms on the anatase and rutile supported Pd and PdAg alloy in the presence of subsurface carbon atoms, and to compare it to that without subsurface carbon. The PdAg alloy has similar properties to the pure Pd according to the scanning tunneling microscopy images obtained by Khan et al.²¹ Zhang et al.²² indicated that the Pd cluster appeared to have a three-dimensional structure when the number of Pds reached four, and other studies also show that the Pd₄ cluster is a relatively stable configuration in both free and supported situations.^23,24 So the Pd₄ cluster was chosen to be used on the TiO₂ support in the previous studies by Yang et al.^18,19 In fact, the previous study of Yang et al. has also shown that the Pd₁₃ cluster shows similar catalytic properties as the Pd₄ cluster.¹⁹ For the effect of carbon species on the pure Pd–TiO₂ systems, the Pd₄ cluster model was chosen in the present work in order to compare the previous calculations more directly.^18,19 For the PdAg catalytic processes, the Pd₂Ag₂ system was chosen because it had the highest selectivity for C₂H₂ hydrogenation among the PdAg alloys based on the previous theoretical work of Mei et al.²⁵ and recent work by Meng and Wang.²⁶ Because the standard density functional theory (DFT) calculations based on the local density approximation (LDA) and generalized gradient approximation (GGA) significantly underestimate the band gap of TiO₂, the addition of U is important in such situation. This can express the repulsion between the electrons placed on the same Ti-3d orbital.^27–31 The present study results show that the carbon atom has a strong effect on both the catalytic and selectivity of C₂H₂ hydrogenation. More importantly, it was found that the carbon species has a significantly different action on anatase and rutile TiO₂, which will help to understand the effect of the subsurface carbon on the anatase and rutile supported-Pd(Ag) catalysts more easily.

2. Calculation method and models

The DFT+U calculations were performed using the Vienna ab initio simulation package (VASP).^32,33 The generalized gradient approximation (GGA-PW91) as the exchange–correlation functional is used to describe the electronic structures.^34–36 The projector augmented wave scheme was used to describe the inner cores^36,37 and the electronic wave functions were expended in a plane wave with the kinetic cut-off energy of 400 eV. To analyze electron correlations in transition metal oxides, conventional DFT calculations based on the LDA and GGA failed to predict the values of the band gap and band gap states. Therefore, the method described in this paper was the DFT+U method which was used to evaluate the on-site Coulomb interactions in the localized d orbital and exchange interactions, by adding an effective Hubbard-U parameter to express the repulsion between electrons on the same orbital. For the reduced Ti oxides, the existence of an oxygen vacancy leads to the electronic states being localized on the adjacent Ti atoms, and thus the addition of U becomes important in such situation. For example, titanium(III) oxide (Ti₂O₃) is an insulator with a band gap of 1 eV, but metallic characteristics were predicted using the conventional DFT calculation.^27–29 This means that the conventional DFT method cannot correctly describe the electronic properties of the reduced oxides.^30,31 The value of the U parameter was determined to be 4 eV for the Ti atom.^38,39 The detailed discussion on how to choose the magnitude of (U–J) can be found in the ESI (Table S1†). The transition state (TS) was employed in the following three steps: first, the nudged elastic band method was used to locate the likely TSs,^40–42 second, the likely TSs were relaxed using a quasi-Newton algorithm to make the forces on the atoms less than 0.035 eV Å⁻¹, and lastly, the frequency analysis was performed to confirm the TS structure.

In the calculation, a symmetric periodic slab model was selected for the anatase structure. The lattice constant was obtained by optimization from the reported experimental value. As a result, the lattice constant of bulk anatase TiO₂ structure (a = 3.80 Å, b = 9.60 Å, c/a = 2.53) is in agreement with the experimental value.⁴³ The 10.21 × 11.33 Å surface unit cell was obtained by cleaving the bulk in the (101̄ and 010) directions, and it has four Ti atomic layers and eight O atomic layers. For the rutile (110) surface, the lattice constant of the bulk rutile structure was calculated (a = 4.59 Å, c = 2.96 Å, c/a = 0.65), and the results were in agreement with the values (a = 4.58 Å, c = 2.95 Å, c/a = 0.64) found in the literature.⁴⁴ By cleaving the bulk in the (11̄0 and 100) directions, a p(2 × 2) unit cell is obtained. During the optimization, the three uppermost layers were allowed to fully relax. The slab was set at a vacuum region of 12–15 Å. The oxygen defective surfaces were made by removing one oxygen atom from the ‘bridging oxygen’ rows which protruded from the surface plane on relaxed anatase (101) surfaces (TiO₂-A-Ov for anatase and TiO₂-R-Ov for rutile). The k-point (2 × 2 × 1) was selected⁴⁵ and the stable structures of C₂H₂, C₂H₄, ethane, and possible intermediates are discussed. The adsorption energy (E_ad) and the activation energy (E_a) were calculated using the following two formulas: E_ad = E_A/M − E_A − E_M and E_a = E_TS − E_IS, respectively. Here, E_A, E_M, E_A/M, E_TS and E_IS are the calculated energy of the adsorbate, substrate, adsorption system, TS and initial state (IS), respectively. The relativistic effects on the stability of carbon species on Pd₂Ag₂/TiO₂-A-Ov were examined, and the calculated adsorption energy of the carbon atom was −6.40 eV, which was close to that of the non-relativistic calculation results (−6.53 eV).

3. Results and discussion

3.1 Pd₄ and Pd₂Ag₂ clusters adsorbed on TiO₂-A-Ov and TiO₂-R-Ov surfaces

Previous DFT calculations have shown that the oxygen-defective anatase supported the Pd₂Ag₂ system, and Pd₂Ag₂/TiO₂-A-Ov, has the highest selectivity for C₂H₄ formation, so the adsorption of Pd₄ and Pd₂Ag₂ clusters on to TiO₂-A-Ov and TiO₂-R-Ov surfaces were first calculated to obtain the most stable system. The adsorption configurations are listed in Fig. S1 in the ESI.† After the optimization of oxygen defective TiO₂ supported Pd₄ and Pd₂Ag₂ clusters, it was seen that the Pd₄ and Pd₂Ag₂ clusters move preferentially to the oxygen defective site to form distorted tetrahedral structures. For the Pd₂Ag₂ cluster, the two Pd atoms bind at the oxygen atom and the Ag atom exposed at the surface of the Pd–Ag bimetallic cluster. The adsorption energies of the Pd₄ cluster on the TiO₂-A-Ov and TiO₂-R-Ov surfaces are −4.53 and −2.92 eV, respectively. Similarly, for the Pd₂Ag₂ cluster, the adsorption energies on the TiO₂-A-Ov and TiO₂-R-Ov surfaces are −3.04 and −2.39 eV, respectively. Therefore, the rutile support and the Ag addition can reduce the interaction between the cluster and the support.

3.2 Adsorption properties of possible species on Pd₄(Pd₂Ag₂)C/TiO₂-A(R)-Ov surfaces

After obtaining the most stable adsorption configuration of the carbon atom on the Pd₄(Pd₂Ag₂)/TiO₂-A(R)-Ov systems (the detailed adsorption properties of carbon species on various supports can be found in the ESI in Fig. S2 and S3†), the adsorption natures of possible species such as C₂H₂, vinyl (C₂H₃), C₂H₄ and ethyl (C₂H₅) were studied on Pd₄/TiO₂-A-Ov, Pd₄C/TiO₂-A-Ov, Pd₄C/TiO₂-R-Ov, Pd₂Ag₂/TiO₂-A-Ov, Pd₂Ag₂C/TiO₂-A-Ov and Pd₂Ag₂C/TiO₂-R-Ov surfaces. The results of the calculations are shown in Table 1 and Fig. 1. In the presence of carbon species, the adsorption energies were generally reduced compared to the situation without carbon species, and the C₂ species preferred to adsorb at the top of the Pd/Ag atom for the π mode on these six surfaces. The bond lengths of C–Pd/Ag of C₂H₂ become longer in the presence of carbon atoms, which indicated that the C₂H₂ binding with catalysts may become weak. As seen from Table 1, the carbon atom could reduce the adsorption energy of C₂H₂ and C₂H₄ on the Pd₄ systems but it has little effect on the Pd₂Ag₂. However, for C₂H₃ and C₂H₅, the influence seems to be opposite in that the carbon atom could largely decrease the adsorption energy of C₂H₃ and C₂H₅ on the Pd₂Ag₂ surface but it had little effect on the Pd₄ system. Furthermore, it was found from the results shown in Table 1 that the presence of the carbon atom has a relatively large effect on the rutile TiO₂ compared to that of the anatase TiO₂. The rutile can also greatly stabilize the configuration with much higher adsorption energies and a shorter bond length of C–Pd in the presence of the carbon atom for the C₂H₃ and C₂H₅. Furthermore, after Ag addition the adsorption energies of the C₂ species were largely decreased both on the anatase and rutile supports. Using the previously described analysis, it could be believed that the carbon atom could reduce the adsorption energy of C₂H₄, thus it could improve the selectivity of the C₂H₄.

Table 1 Adsorption energies of C₂H₂, C₂H₃, C₂H₄ and C₂H₅ on Pd₄/TiO₂-A-Ov, Pd₄C/TiO₂-A-Ov, Pd₄C/TiO₂-R-Ov, Pd₂Ag₂/TiO₂-A-Ov, Pd₂Ag₂C/TiO₂-A-Ov and Pd₂Ag₂C/TiO₂-R-Ov surfaces (eV)

	Pd4-A	Pd4-R	Pd4C-A	Pd4C-R	Pd2Ag2-A	Pd2Ag2-R	Pd2Ag2C-A	Pd2Ag2C-R
C2H2	−1.37	−1.43	−1.14	−1.15	−0.44	−0.98	−0.48	−0.37
C2H3	−2.19	−2.33	−2.12	−2.38	−2.10	−1.93	−1.55	−1.92
C2H4	−1.49	−0.99	−1.26	−0.42	−0.51	−0.95	−0.58	−0.53
C2H5	−1.51	−1.81	−1.43	−2.49	−1.46	−1.35	−1.06	−1.43

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Fig. 1 Adsorption configurations of C₂H₂, C₂H₃, C₂H₄ and C₂H₅ on Pd₄/TiO₂-A-Ov, Pd₄C/TiO₂-A-Ov, Pd₄C/TiO₂-R-Ov, Pd₂Ag₂/TiO₂-A-Ov, Pd₂Ag₂C/TiO₂-A-Ov and Pd₂Ag₂C/TiO₂-R-Ov surfaces.

It is important to determine the effect of carbon species on the binding energy of C₂H₂/C₂H₄; here the energy decomposition scheme and the Bader charge analysis were employed. Usually the adsorption for a given species can be broken down into three parts: the deformation energy of the molecule , the deformation energy of the substrate E^Substrate_Def, and the interaction energy between these two parts . Using the energy decomposition figures shown in Table S2† and Fig. 2, it can be seen that there is a roughly proportional relation between the adsorption energy and the interaction energy. The interaction energy also has a larger contribution to the adsorption energy than the deformation energy. That is to say, the variations of the interaction of energy play an important role in the adsorption energy of C₂H₂ and C₂H₄. With the presence of the carbon atom the interaction energies are reduced, and thus the adsorption energies are also diminished.

Fig. 2 Energy decomposition of the adsorption energy of C₂H₂ and C₂H₄ on Pd₄/TiO₂-A-Ov, Pd₄C/TiO₂-A-Ov, Pd₄C/TiO₂-R-Ov, Pd₂Ag₂/TiO₂-A-Ov, Pd₂Ag₂C/TiO₂-A-Ov and Pd₂Ag₂C/TiO₂-R-Ov surfaces.

In addition to the previous energy analysis, the electronic structure analysis based on the Bader charge was also utilized (ESI, Table S3†) to study the effect of carbon species on the adsorption of C₂H₂/C₂H₄. In Table S3,† the Bader value (BV) was defined as the number of valence electrons of the ideal neutral atom in the gas minus the number of electrons on the atom that takes part in the bond formation. Using Table S3 (ESI†) it can be known that the BV of the metal cluster becomes less negative in the presence of carbon species, whereas the BV of carbon species is negative when it bonds to the PdAg cluster. Clearly, the electrons transferred from the metal cluster to the carbon atom on the Pd₄C/TiO₂-A-Ov, Pd₄C/TiO₂-R-Ov, Pd₂Ag₂C/TiO₂-A-Ov and Pd₂Ag₂C/TiO₂-R-Ov surfaces because the electronegativity of the carbon atom is larger than that of Pd(Ag). Because the adsorption of C₂H₂/C₂H₄ on the PdAg cluster requires the electron back donation from the metal cluster to its empty π* orbital to form π-back bonding, the fewer electrons on PdAg cluster in the presence of carbon species would reduce the adsorption of C₂H₂/C₂H₄. Additionally, it was found from the results given in Table S3 (ESI†) that the electron transferring from the metal cluster to the carbon species and/or the TiO₂ on rutile is more than that of anatase for Pd₄, and the addition of Ag makes the electron transfer to carbon and/or TiO₂ more than that of the pure Pd₄ cluster because the electronegativity of Ag is smaller than that of Pd.

3.3 C₂H₂ hydrogenation reaction mechanism

C₂H₂ hydrogenation is a complex process, and it is considered using the following four reaction steps: C₂H₂ + H → C₂H₃, C₂H₃ + H → C₂H₄, C₂H₄ + H → C₂H₅ and C₂H₅ + H → C₂H₆. The calculation results for the activation energy and reaction heat on the Pd₄(Pd₂Ag₂)C/TiO₂-A(R)-Ov catalyst surfaces are shown in Table 2. The corresponding TS configurations of every step and the free energy profiles of C₂H₂ hydrogenation are listed in Fig. 3 and 4, respectively. For comparison, results from previous studies on the Pd₄/TiO₂-A-Ov, Pd₄/TiO₂-R-Ov, Pd₂Ag₂/TiO₂-A-Ov^18,19,26 are also given in Table 2. Some side reaction steps such as C₂H₂ → CCH + H, C₂H₃ → CCH₂ + H, C₂H₃ + H → CHCH₃, 2C₂H₃ → C₄H₆, CHCH₃ + H → C₂H₅, C₂H₅ → CHCH₃ + H, and CHCH₃ → CH + CH₃, are ignored because of the relatively high reaction barrier compared to that of the main reaction according to previous theoretical studies.²⁶

Table 2 Reaction energy (eV) and C–H bond distance (Å) at TSs of whole C₂H₂ hydrogenation on Pd₄/TiO₂-A-Ov, Pd₄C/TiO₂-A-Ov, Pd₄C/TiO₂-R-Ov, Pd₂Ag₂/TiO₂-A-Ov, Pd₂Ag₂C/TiO₂-A-Ov and Pd₂Ag₂C/TiO₂-R-Ov surfaces

	C2H2 + H			C2H3 + H			C2H4 + H			C2H5 + H
	Ea	ΔH	d(C–H)	Ea	ΔH	d(C–H)	Ea	ΔH	d(C–H)	Ea	ΔH	d(C–H)
Pd4-A	1.04	−0.08	1.57	0.00	−1.62	2.01	0.93	0.71	1.60	0.18	−0.50	1.69
Pd4-R	0.71	0.03	1.58	0.27	−1.33	1.56	0.66	0.28	1.81	0.79	−0.22	1.57
Pd4C-A	1.02	−0.01	1.64	0.68	−1.12	2.05	1.02	0.69	1.60	0.73	−0.21	1.84
Pd4C-R	0.93	−0.27	1.68	0.95	−0.79	2.04	0.57	−0.05	1.81	0.66	−0.37	1.95
Pd2Ag2-A	1.23	−0.88	1.74	1.50	−1.10	2.00	1.23	−0.48	1.72	1.31	−0.62	1.94
Pd2Ag2-R	0.27	−0.75	1.23	0.23	−1.38	1.63	0.62	0.10	1.20	0.15	−0.61	1.71
Pd2Ag2C-A	1.04	−1.05	1.76	0.69	−1.61	2.23	1.24	0.19	1.72	0.55	−1.10	2.06
Pd2Ag2C-R	1.63	−0.58	1.77	1.24	−1.23	2.16	1.69	0.00	1.64	1.32	−0.93	2.15
Pd2Ag2/Pd(111)	0.43	−0.81	1.75	0.16	−1.14	1.74	0.55	−0.44	1.74	0.07	−1.14	1.91

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Fig. 3 Optimized TSs of C₂H₂ hydrogenation on Pd₄/TiO₂-A-Ov, Pd₄C/TiO₂-A-Ov, Pd₄C/TiO₂-R-Ov, Pd₂Ag₂/TiO₂-A-Ov, Pd₂Ag₂C/TiO₂-A-Ov and Pd₂Ag₂C/TiO₂-R-Ov surfaces.

Fig. 4 Energy profiles (eV) of C₂H₂ hydrogenation on Pd₄/TiO₂-A-Ov, Pd₄C/TiO₂-A-Ov, Pd₄C/TiO₂-R-Ov, Pd₂Ag₂/TiO₂-A-Ov, Pd₂Ag₂C/TiO₂-A-Ov and Pd₂Ag₂C/TiO₂-R-Ov surfaces. The entropy effect is considered for the adsorption and desorption process here.¹⁰ G^≠_ad is the TS energy of the adsorption of C₂H₂ on all the surfaces.

On Pd₄C/TiO₂-A-Ov and Pd₄C/TiO₂-R-Ov surfaces, the hydrogen atom initially adsorbs at the bridge of Pd–Pd with the C–H bond length of 3.04 and 3.07 Å, respectively. Then it moves to the C₂H₂ to form C₂H₃. The activation energy of first step is 1.02 and 0.93 eV, respectively, which is smaller than that on Pd₄/TiO₂-A-Ov surface (1.04 eV). Then the hydrogen atom approached to C₂H₃ to produce C₂H₄ and the activation energy is 0.68 and 0.95 eV on Pd₄C/TiO₂-A-Ov and Pd₄C/TiO₂-R-Ov surfaces, respectively. This is higher than that without the carbon species (0.00 eV). However, the adsorption energy of C₂H₄ is lower on Pd₄C/TiO₂-A-Ov and Pd₄C/TiO₂-R-Ov surfaces. The activation energy of C₂H₄ hydrogenation is 1.02 eV on Pd₄C/TiO₂-A-Ov surface and it is slightly higher than that on Pd₄/TiO₂-A-Ov surface (0.93 eV), indicating that on Pd₄C/TiO₂-A-Ov surface C₂H₄ further hydrogenation is more difficult. The last step goes ahead with the activation energy barrier of 0.73 and 0.66 eV, respectively, and the adsorption energy of ethane is small. This is regarded as a physical adsorption process and ethane is easy to desorb from the catalysts.

On Pd₂Ag₂C/TiO₂-A-Ov and Pd₂Ag₂C/TiO₂-R-Ov surfaces, the C₂H₂ adsorbs at the top of Ag atom and the adsorption energies are −0.48 and −0.37 eV, respectively. Then the hydrogen atom moves from the bridge of the Ag–Ag to the top of Ag with the C–H bond length of 1.76 Å at TS on the Pd₂Ag₂C/TiO₂-A-Ov surface. The corresponding activation energy is 1.04 eV, which is lower than that on the Pd₂Ag₂/TiO₂-A-Ov surface (1.23 eV). However, on the Pd₂Ag₂C/TiO₂-R-Ov surface the hydrogen atom initially stays at the bridge of the Pd–Ag and the corresponding activation energy is 1.63 eV. The activation barrier of the second step is 0.69 and 1.24 eV on Pd₂Ag₂C/TiO₂-A-Ov and Pd₂Ag₂C/TiO₂-R-Ov surfaces, respectively, and these are smaller than that without the carbon atom (1.50 eV). The generated C₂H₄ adsorbed at the Ag atom. The activation energy of the further hydrogenation is 1.24 and 1.69 eV, respectively, and this is largely higher than the desorption energy of the C₂H₄ (0.58 and 0.53 eV, respectively), which means that the C₂H₄ desorption is easier to achieve than its further hydrogenation. Therefore, this situation may result in high selectivity. The fourth step to form ethane proceeds with the energy barrier of 0.55 eV and the ethane adsorbs on the Pd₂Ag₂C/TiO₂-A-Ov surface with the adsorption energy of −0.14 eV. But on the Pd₂Ag₂C/TiO₂-A-Ov surface the activation energy is 1.32 eV, which is similar to that without carbon atoms. From the previous analysis it is believed that the activation barriers of C₂H₂ hydrogenation on the Pd₂Ag₂C/TiO₂-A-Ov system are generally smaller than that without carbon species, especially for the second step to form C₂H₄. Thus, it may increase its hydrogenation catalytic activity. However, the activation energy on the Pd₂Ag₂C/TiO₂-R-Ov system is higher than that without carbon atoms except for the second step.

Furthermore, in order to compare the Pd₂Ag₂/TiO₂-R-Ov system with that of Pd₂Ag₂C/TiO₂-R-Ov and determine the effect of carbon species on the selectivity of Pd₂Ag₂/TiO₂-R-Ov catalyst more directly, C₂H₂ selectivity hydrogenation on the Pd₂Ag₂/TiO₂-R-Ov is also considered in the present work (see Table 2 and Fig. 4). On the Pd₂Ag₂/TiO₂-R-Ov, the molecular C₂H₂ adsorbed at the Pd atom for the π mode and the bond length of the C–Pd is 2.08 Å. Then the hydrogen sitting at the bridge of Pd–Ag moved to the C₂H₂ to generate C₂H₃ with the activation energy of 0.27 eV. The activation barrier of the second step is 0.23 eV and the adsorption energy of C₂H₄ is −0.95 eV, whose absolute value is larger than the C₂H₄ further hydrogenation barrier (0.62 eV). This will lead to the low C₂H₄ selectivity. Lastly, the final step to produce ethane is easy with the activation energy of 0.15 eV and the adsorption energy of ethane is −0.04 eV, being considered as the spontaneous process.

The selectivity of the hydrogenation of C₂H₂ to C₂H₄ is discussed in this paper. It can be indicated by the difference between the hydrogenation activation energy and the desorption energy of C₂H₄. A good catalyst must have a low desorption energy of C₂H₄ and a high hydrogenation activation energy. The selectivity is defined by the formula: ΔE = E_a − |E_ad|. Here, E_a is the hydrogenation barrier of C₂H₄ and E_ad is the adsorption energy of C₂H₄. The adsorption energies of C₂H₄ and activation energies are listed in Table 3. It can be seen that on the Pd₄/TiO₂-A-Ov system the subsurface carbon atom not only enhances the hydrogenation activation barrier but also reduces the desorption energy of C₂H₄, which indicates that it can improve the selectivity of C₂H₄. This is in agreement with the previously reported results.^10,12 On the Pd₄C/TiO₂-A-Ov and Pd₄C/TiO₂-R-Ov surfaces, the desorption of C₂H₄ becomes easier so that the selectivity of C₂H₄ is largely increased compared to that on the Pd₄/TiO₂-A-Ov systems. However, this effect is not obvious on the Pd₂Ag₂C/TiO₂-A-Ov system. Namely, the subsurface carbon atom hardly affected the selectivity of C₂H₂ hydrogenation on the anatase support for the Pd₂Ag₂ system. But the selectivity of C₂H₂ hydrogenation is enhanced on the Pd₂Ag₂C/TiO₂-R-Ov system. Therefore, the rutile support with the subsurface carbon atom will increase the selectivity of C₂H₂ hydrogenation. This result is in agreement with the experimental conclusion that the selectivity for C₂H₄ formation is increased on the rutile supported PdAg catalyst and decreased on the anatase supported PdAg system.⁴⁶ Furthermore, the C₂H₄ selectivity is enhanced after Ag addition with the subsurface carbon atom both on the anatase support and on the rutile support.

Table 3 Hydrogenation barriers (E_a) and adsorption energies (E_ad) on Pd₄/TiO₂-A-Ov, Pd₄C/TiO₂-A-Ov, Pd₄C/TiO₂-R-Ov, Pd₂Ag₂/TiO₂-A-Ov, Pd₂Ag₂C/TiO₂-A-Ov and Pd₂Ag₂C/TiO₂-R-Ov surfaces (eV)

	Pd4-A	Pd4-R	Pd4C-A	Pd4C-R	Pd2Ag2-A	Pd2Ag2-R	Pd2Ag2C-A	Pd2Ag2C-R
Ead	−1.49	−0.99	−1.26	−0.42	−0.51	−0.95	−0.58	−0.53
Ea	0.93	0.66	1.02	0.57	1.23	0.62	1.24	1.69
ΔE	−0.56	−0.33	−0.24	0.15	0.72	−0.33	0.66	1.16

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3.4 Catalytic activity analysis based on the energetic span model

The desorption energy of C₂H₄ is an important measurement which can affect the catalytic selectivity of C₂H₂ hydrogenation, so it is important to analyze the factors which influence the C₂H₄ desorption. Because the DFT calculated total energy is obtained at 0 K, a temperature correction for the total energy is necessary, and this is done using Gibbs free energy to measure the catalytic activity. In the calculation of free energy, only the entropy change is considered for the processes of adsorption and desorption, and other elemental surface reaction steps are treated directly from the DFT determined energy. For example, when the entropy contribution is taken into account for the DFT calculated total energy, the C₂H₄ desorption energy would be reduced by 0.73 eV at the temperature of 350 K (here the entropy of chemisorbed C₂H₄ was ignored and it was assumed that the standard entropy of the gas phase of C₂H₄ was 219.5 J K⁻¹ mol⁻¹ (ref. 47)).

In order to compare the present calculation results with the more quantitative experimental results, the energetic span theory was used here to obtain the turnover frequencies (TOFs), which is the traditional measure to estimate the efficiency of a catalyst. The TOF can be expressed as the number of cycles performed per time unit and catalyst concentration. Based on an idea of Amatore and Jutand,⁴⁸ which was subsequently developed and implemented by Kozuch and Shaik,^49–52 this model included three assumptions: transition state theory is valid, a steady-state regime subsists, and the relaxation of the intermediates is fast. The calculation results based on the previous theory are shown in Fig. 5. It is indicated that the subsurface carbon atoms improve the reaction activity of C₂H₂ hydrogenation on the Pd₄/TiO₂-A-Ov, Pd₄/TiO₂-R-Ov, Pd₂Ag₂/TiO₂-A-Ov and Pd₂Ag₂/TiO₂-R-Ov surfaces. Furthermore, the anatase support has a higher activity than the rutile support with subsurface carbon atoms. It is general accepted that there is an inverse relationship between the activity and selectivity for a given catalysis reaction, namely high reactivity usually corresponds to the low selectivity. Because of the relatively high activity of C₂H₂ hydrogenation on an anatase supported PdAg system, a low selectivity on it is thus expected, being consistent with the previous selectivity analysis.

Fig. 5 The relationship between the adsorption energy of C₂H₂ and ln(TOF).

3.5 Physical original of the energy barrier for the C₂H₂ hydrogenation

In general, for the hydrogenation reactions, if the C₂H₂ or C₂H₄ binds to the catalysts weakly, its energy barrier would become relatively low. In order to understand the possible factors affecting the C₂H₂ hydrogenation reaction activation energy, the energy decomposition method was used to analyze the reaction barriers (the schematic diagram of reaction barrier (E_a) decomposition is given in Fig. S4, ESI†).⁴⁷ Because the selectivity towards the C₂H₄ formation was determined by the C₂H₄ hydrogenation barrier, so such a step was used in the following discussion. Also, considering that the Pd₂Ag₂C-R shows the highest selectivity among these models studied in this work, Pd₂Ag₂C-R was chosen as the example. The energy decomposition results of the C₂H₄ hydrogenation are shown in Table S4 (ESI†). After the addition of carbon species, the energy cost of reactants such as H and C₂H₄ moving from the initial state to the TS is generally reduced compared to the case without the carbon species, and this is clearly because of the relatively lower adsorption energy of H(C₂H₄) in the presence of carbon species (see Table 1). This may reduce the hydrogenation barrier to some extent. Additionally, with the carbon atom the interaction between C₂H₄ and H is significantly changed from attractive to repulsive (i.e., −1.19 versus 0.84 eV), which is because the bond length of the C–H becomes longer in the presence of carbon species compared to the situation without the carbon atom (i.e., 1.64 versus 1.20 Å, see Fig. 3 for more detail), and such interaction difference with and without carbon species is much larger than the sum of E_C2H4 and E_H, thus leading to the ultimate increase in the hydrogenation barrier after the introduction of carbon species.

3.6 C₂H₂ hydrogenation on Pd₂Ag₂/Pd(111)C

To further determine the effect of the support, C₂H₂ hydrogenation on Pd₂Ag₂/Pd(111)C, namely carbon species on the Pd₂Ag₂/Pd(111) was also investigated in this research. The calculation model is p(2 × 2) with four layers, in which the adsorbates as well as the first two layers are allowed to be relaxed during the calculation. A vacuum height was set to be 15 Å and k-points of 3 × 3 × 1 were used. The calculation results and the configurations are listed in the ESI (Fig. S5 and S6†). On Pd₂Ag₂/Pd(111)C, the carbon atom is located in the fcc site in the subsurface with the adsorption energy of −7.51 eV. The C₂H₂ adsorbs at the Pd–Pd bridge site for the di-σ mode with the C–H bond length of 2.10 Å. The responding adsorption energy is −0.89 eV, which is higher than that on Pd₂Ag₂C/TiO₂-A-Ov and Pd₂Ag₂C/TiO₂-R-Ov surfaces. The activation energy of the first step on the Pd₂Ag₂/Pd(111)C is 0.43 eV, lower than that with the TiO₂ support, and that will reduce the hydrogenation activity compared to that on Pd₂Ag₂C/TiO₂-A-Ov and Pd₂Ag₂C/TiO₂-R-Ov surfaces. Similarly, the activation energy to form C₂H₄ on Pd₂Ag₂/Pd(111)C is also the highest of the three catalysts and the adsorption energy of C₂H₄ on Pd₂Ag₂/Pd(111)C is −0.44 eV. The adsorption configurations of C₂H₄ are different in that it adsorbs at the Pd–Pd bridge site for the di-σ mode on Pd₂Ag₂/Pd(111)C but it stays at the top of the Ag atom for the π mode on the Pd₂Ag₂/TiO₂-A-Ov surface. Then the further hydrogenation of C₂H₄ is also considered on the three catalysts and the activation energies were 0.55, 1.24 and 1.69 eV, respectively. According to the formula to compare the selectivity of C₂H₄ (ΔE = E_a − |E_ad|), it has been seen that the Pd₂Ag₂/Pd(111)C has the lowest selectivity because the difference between the adsorption energy of C₂H₄ and the activation barrier of further hydrogenation is the least (0.11 eV), illustrating that the TiO₂ support can increase the selectivity of C₂H₄. The activation energy of the third step on Pd₂Ag₂/Pd (111)C is 0.55 eV. For the last step, the activation energy is the lowest on Pd₂Ag₂/Pd (111)C. Using the previous analysis, it has been shown that the TiO₂ support can decrease the adsorption energy of C₂H₂ and C₂H₄ which is in agreement with our previous work.²⁵ However, the hydrogenation activity will be suppressed because of the high activation energy on Pd₂Ag₂/TiO₂-A-Ov and Pd₂Ag₂/TiO₂-R-Ov surfaces.

4. Conclusions

In conclusion, the effect of the carbon atom on the C₂H₂ hydrogenation was explored on several TiO₂ (both anatase and rutile) supported-Pd(Ag) cluster model catalysts by using the DFT calculations with a Hubbard U correction. The DFT calculation results show that the carbon atom has a strong effect on both catalytic and selectivity of C₂H₂ hydrogenation. More importantly, it was found that the carbon species has a significantly different action on anatase TiO₂ and rutile TiO₂. The carbon atom prefers to move into the Pd₄ and Pd₂Ag₂ cluster and binds with more Pd atoms. The adsorption energies of the C₂H₂ and C₂H₄ are generally reduced in the presence of the carbon atom. The hydrogenation reaction mechanism indicates that the subsurface carbon atom can improve the selectivity of C₂H₄ on Pd₄/TiO₂-A-Ov, Pd₄/TiO₂-R-Ov, Pd₂Ag₂/TiO₂-R-Ov surfaces but have a little effect on the Pd₂Ag₂/TiO₂-A-Ov surface. The selectivity of C₂H₄ can also be enhanced with Ag addition in the presence of carbon atoms on the anatase and rutile supports. The energetic span model proves that the reaction activity can be enhanced on Pd₄C/TiO₂-A-Ov, Pd₄C/TiO₂-R-Ov, Pd₂Ag₂C/TiO₂-A-Ov and Pd₂Ag₂C/TiO₂-R-Ov surfaces compared to that without subsurface carbon atoms. Furthermore, the reaction activity on the anatase support is higher than that of the rutile support with the carbon atom, but the selectivity is reduced.

Acknowledgements

This work was supported by the State Key Program of Natural Science of Tianjin (Grant No. 13JCZDJC26800), the MOE Innovation Team (IRT13022) of China, the State Key Program of National Natural Science Foundation of China (Grant No. 21433008), the National Natural Science Foundation of China (Grant No. 91545106, 21503122), the Foundation of State Key Laboratory of Coal Conversion (Grant No. J15-16-908), the Shanxi Province Science Foundation for Youths (2014021016-2), the Scientific and Technological Programs in Shanxi Province (2015031017), and the foundation of Key Laboratory of Advanced Energy Materials Chemistry (Ministry of Education).

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Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c5ra23507c

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