Selective hydrogenation of organic compounds such as unsaturated hydrocarbons, α, β-unsaturated aldehydes (ketones), and aromatic nitro-compounds over catalysts is an interesting research area in heterogeneous catalysis and has been attracting increasing attention for a long time [1-9]. The current focus in this research area is to achieve high selectivity for relatively unstable intermediates; this requires that the hydrogenation only takes place for the proper bonds, and further hydrogenation should be prevented in some cases. The key aspect to solving this problem is to develop a proper catalyst exhibiting a high selectivity as well as high activity.

Selective hydrogenation of acetylene in ethylene feed is very important in the olefin industry, as acetylene acts as an impurity in the olefin feed that poisons the catalysts used subsequently for the polymerization of ethylene. The selective hydrogenation of acetylene will both remove this impurity and increase the amount of ethylene produced. The most effective catalyst for this reaction was found to be Pd-based owing to its relatively high selectivity and favorable activity. Previous investigations found that the presence of subsurface species such as carbon atoms formed from the dissociation of reactants and reaction intermediates could significantly promote the selective hydrogenation of acetylene over Pd [10, 11]. Our previous density functional theory (DFT) calculations revealed that subsurface species could promote the reaction through the electronic modification effect, and the adsorption energy of alkenes over Pd surfaces would be decreased, thereby inhibiting the possibility of over-hydrogenation reactions [12-16].

It was widely reported in the literature that the surface strain effect could influence the reactivity of metal surfaces and that the adsorption properties could be varied by changing the metal lattice size [9, 17-37]. Nørskov and co-workers found using DFT calculations that the surface reactivity of Ru(0001) towards the adsorption of carbon/oxygen and the dissociation of CO increased with lattice expansion. They further correlated the increased reactivity with the observed upshift in the metal d states during lattice expansion, and concluded that surface strain can be used to tailor the catalytic activities of metals [18]. Such a d-band-centric argument has been widely accepted by the catalysis community. A further study carried out by Mavrikakis' group demonstrated that such lattice strains could induce the formation of subsurface species in some cases [20]. The authors employed hydrogen adsorption at the subsurface sites of Ni(111) as an example, and found that subsurface hydrogen would form more readily in stretched regions than in the unstretched regions of the Ni surface.

Experimentally engineering the strain of catalyst surfaces has been attracting increased attention recently to tune the performance of these catalysts. However, the catalytic systems are far more complex, with many more variables to consider. One of the examples is that the surface of Pd during acetylene hydrogenation might be carbide-like, and therefore, the adsorption process could be influenced by both the surface strain and presence of subsurface species. Meanwhile, the direct relationship between the surface strain and the selectivity and activity for acetylene hydrogenation over Pd under the reaction conditions is still missing, which is the focus of the current work.

All the DFT calculations in this work were performed with the VASP [38-41] code in the slab models. The exchange-correlation functional PW91 [42] was used to calculate the electronic structure with generalized gradient approximation (GGA). The projector augmented wave (PAW) method was employed to describe the interactions between the atomic cores and electrons [43, 44]. For all the Pd-based surfaces, four-layer 2×2 slabs with the upmost two layers relaxed during optimization were used to model the adsorption and reaction processes. The optimized equilibrium lattice constant was 3.95 Å [12], which is close to the experimentally measured 3.89 Å . Then, we changed the lattice constant by minus or plus one, two, or four percent, which are designated as m1p, m2p, m4p, p1p, p2p and p4p. A 5×5×1 k-point sampling in the surface Brillouin zone was used in all the calculations. The vacuum height was set to be more than 12 Å to avoid any interactions between the slabs. An energy cutoff of 500 eV and a force threshold on each relaxed atom of 0.05 eV/Å were used in the current work. The transition states were located using the constrained minimization method [45-47], and only one imaginary frequency was found for the transition states obtained. The adsorption and binding energies are defined as follows:

where E_total is the energy of the system after adsorption, E_g denotes the energy of the gas-phase adsorbate, and E_slab is the energy of the slab. For the adsorption energy of the hydrogen atom, we used the energy of H₂ as the reference.

In this work, we used the simulation package CatMAP developed by Nørskov's group, which has been proven to be a powerful tool in predicting catalytic trends, to perform the microkinetic analyses of the hydrogenation activity [48, 49]. In our calculations, the reaction conditions were set as: T = 350 K, P_C2H2 = 1 bar, P_H2 = 10 bar, and P_C2H4 = 0.01 bar. We used the "fixed_entropy_gas" and "frozen_adsorbate" models to deal with the thermochemistry of the gases and adsorbates by assuming that the entropy of all gases is 0.002 eV/K, except that of H₂ (0.00135 eV/K).

The energies corresponding to the adsorption of C₂H₂, H, and C₂H₄ over pristine Pd(111) surfaces as a function of the variation in the lattice strain of Pd can be found in Fig. 1. It can be observed that the adsorption energies of all three species correlate linearly with the lattice strain, and a larger lattice results in stronger adsorption in all the cases; this is consistent with the d-band center theory and the results presented by Mavrikakis et al. [18]. The optimized adsorption configurations of C₂H₂, C₂H₃, and C₂H₄, as well as the transition state structures for the hydrogenation of these C₂ species over m1p Pd(111) are shown in Fig. S1 (Supporting Information, SI) as examples.

Based on the linear relationships between the adsorption energies and lattice strain, the scaling relationship between the adsorption energies can be established using the adsorption energy of C₂H₂ and H as descriptors; this is shown in Fig. 2. It is found that the transition state (TS) energies are also linearly correlated with the corresponding initial state (IS) energies for the elementary steps involved in the hydrogenation of C₂H₂ to C₂H₄ over Pd(111) surfaces with different strains. All the TS-IS scaling relations are also presented in Fig. 2. The corresponding activation barriers and reaction energies of the elementary reaction steps involved in the hydrogenation of acetylene to ethylene over the pristine Pd(111) surfaces with different lattice constants can be found in Table S1.

Combining all the scaling relationships in Fig. 2 and using the microkinetic modeling approach developed by Nørskov's group [48, 50, 51], a three-dimensional activity map can be obtained for the formation of ethylene, as shown in Fig. 3. It can be seen that although smaller lattice constants result in weaker adsorption of the reactants over the pristine Pd(111) surfaces, the activity for ethylene formation is increased. This may be due to the fact that the activity of Pd(111) for the hydrogenation of acetylene to ethylene corresponds to the strong adsorption side of the volcano curve, where, in general, the desorption of products from the surface is the rate-determining step [52]. On the other hand, weakening of the adsorption strength of the surface species will increase the turnover rate by facilitating the desorption process, which is similar to the case of Ni-catalyzed acetylene hydrogenation that we reported previously [53].

In order to further investigate the possible formation of subsurface species, we calculated the average adsorption energies of carbon and hydrogen atoms at the subsurface sites of Pd(111) surfaces with different lattice constants and subsurface coverages, and the corresponding trends are presented in Fig. 4. There are typically two possible sites for the adsorption of carbon and hydrogen at the subsurface site of Pd(111), namely, the subsurface octahedral and tetrahedral sites; the energies shown in Fig. 4 are those with lower energies at one site than the other. It is clearly demonstrated in this figure that the adsorption energies of both carbon and hydrogen become less negative with decreasing lattice constants, which is similar to the results reported by Greeley et al. [20]. However, the variation in the adsorption energies as a function of subsurface coverage is different between the carbon and hydrogen atoms. For carbon atoms, the adsorption becomes weaker with the increase in the subsurface coverages, while the adsorption strength of hydrogen does not vary much for different coverages. This observation is consistent with those that we reported recently for both Pd(111) and Pd(100) surfaces [12, 15]. It should be mentioned that when the lattice of Pd is expanded by 4% compared to the equilibrated Pd lattice (p4p), the adsorption of subsurface hydrogen at the octahedral/tetrahedral sites becomes unstable, and these hydrogen atoms diffuse to the corresponding surface fcc/hcp sites after structural optimization (Fig. S2); therefore the corresponding adsorption energies are not included in Fig. 4.

Here, we further consider Pd(111) surfaces with 0.25 monolayer (ML) subsurface carbon coverage, named Pd(111)-C, as an example to investigate the effect of the presence of subsurface atoms on the catalytic reactivity. The adsorption energies of C₂H₂, H, and C₂H₄ are calculated over Pd(111)-C and plotted as a function of the lattice strain in Fig. 1. In general, the adsorption of all the species over the Pd(111) surfaces become weaker upon the formation of subsurface carbon atoms. In our previous work, we found that the weakened adsorption over Pd(111)-C than over Pd(111) was due to the downshift of the metal d band upon the adsorption of carbon atoms at the subsurface sites [12]. We also find that the adsorption energies of H and C₂H₄ still linearly scale with the lattice strain, while the adsorption trend of C₂H₂ shows a peak at the equilibrium constant, indicating that changing the lattice constants of Pd(111)-C from those of the equilibrated lattice will always result in stronger acetylene adsorption over the surface. After carefully examining the adsorption energies of C₂H₂ over all the Pd(111)-C surfaces investigated, we found that the trend for larger lattice constants was the same as those observed for other species, while a smaller lattice would give rise to stronger adsorption, resulting in a stronger deviation from the linear trend. This is believed to result from the slightly deformed Pd(111)-C surface with smaller lattice constants due to the strong adsorption of C₂H₂, as shown in Fig. S3; such deformation will effectively release the stress within the lattice and lower the energy of the system. A similar deformation is not observed for the adsorption of C₂H₄ over Pd(111)-C surfaces, which involve weaker binding than C₂H₂. Nevertheless, it will be shown later that such unusual adsorption behavior of acetylene observed still supports our argument on the trend for the catalytic activity for ethylene formation.

Subsequently, the activity for ethylene formation is calculated based on all the activation energies and reaction energies obtained for all the surfaces studied, and the selectivity is also estimated by comparing the differences between the hydrogenation and desorption barriers of ethylene over the different catalyst surfaces, which is defined as ΔE_a = E_{a, hydr} - E_{a, des}. All of the energies are listed in the tables of the SI. According to our previous work [12, 15, 54-56], desorption barriers can be estimated based on the absolute value of the corresponding adsorption energies of ethylene, and therefore, higher ΔE_a values result in higher ethylene selectivity.

All the values of ΔE_a and log(TOF) are shown in Fig. 5, and the following trends can be readily observed.

(1) ΔE_a is always positive for both the pristine and subsurface carbon modified Pd(111) surfaces studied, indicating that the desorption of ethylene from the catalyst surface is preferred for all the surfaces studied;

(2) The activity and selectivity of ethylene over Pd(111)-C is always higher than those of the corresponding pristine Pd(111). It is found from the tables in the SI that the increased ethylene selectivity upon subsurface carbon modification is mainly due to the weakened adsorption of ethylene over these surfaces;

(3) Decreasing the lattice constant will improve the activity and selectivity, in general, for ethylene formation over pristine Pd(111);

(4) The m4p and m2p catalysts with subsurface carbon, which are the Pd(111)-C surfaces with four and two percent smaller lattice constants than the equilibrated Pd lattice, reveal higher selectivity and activity for ethylene formation from acetylene hydrogenation than the normal Pd(111) and other Pd(111)-C surfaces.

As revealed above, the adsorption of acetylene over pristine Pd(111) is on the strong adsorption side of the volcano curve for ethylene formation; the enhancement in the activity for ethylene formation can be rationalized by the weaker adsorption of the reactants over the Pd(111)-C surfaces. However, upon the formation of the subsurface carbon atoms, no clear trend can be observed in the activities of the Pd(111)-C surfaces with smaller lattice constants than the equilibrated value (i.e., m4p, m2p, and m1p Pd(111)-C surfaces) with the variation in the lattice constant. We ascribe this to the unusual scaling relation shown in Fig. 1, where a peak is observed in the trend of the acetylene adsorption energies over the subsurface carbon modified Pd(111) surfaces. Interestingly, we found that when the log(TOF) over Pd(111)-C surfaces were plotted as a function of the adsorption energy of C₂H₂+H, a linear relationship was obtained (Fig. S4); such a relationship further supports our argument that the adsorption energy of the reactants corresponds to the strong adsorption side of the volcano curve for ethylene formation.

It is clearly shown in the current work that the effects of lattice strain and subsurface promoters can improve the performance of catalysts in the case of Pd-catalyzed selective hydrogenation of acetylene. Although the activity of m2p Pd(111)-C is the highest, its selectivity for ethylene formation is slightly lower than the m4p Pd(111)-C catalyst, and we consider the latter as a good candidate for the selective acetylene hydrogenation reaction. Such shrinking of the lattice can be achieved experimentally through a number of catalyst preparation methods, as reported in the literature, including constructing core/shell type M/Pd structures, where M has a slightly smaller lattice constant than Pd, synthesizing Pd nanowires or octahedron nanoparticles with the first-shell Pd-Pd bond length possibly shorter than that of the Pd foil, or producing crystal twinning during the Pd catalyst synthesis process, wherein a lattice strain may result from the mismatch between the twinned structures [34-36, 57, 58].

We have thoroughly examined the effects of lattice strain and subsurface promoters, which are both important issues in heterogeneous catalysis, on the catalytic selectivity and activity of Pd by considering the selective hydrogenation of acetylene as an example. It is found that the adsorption energies of the reactants and products are, in general, linearly scaled with the lattice strain for both pristine and subsurface carbon atom modified Pd(111) surfaces, except for the adsorption of C₂H₂ over Pd(111)-C. The activity for ethylene formation corresponds to the strong reactant adsorption side of the volcano curve, and such lattice strain effects and presence of subsurface promoters can improve the activity of the catalyst through the weakening of the adsorption of reactants. The activity and selectivity of Pd(111)-C are always higher than those of the pristine Pd(111) surfaces for ethylene formation. These Pd-based catalysts are suggested as good candidates based on the framework that we have developed for the selective hydrogenation of acetylene, and a similar approach can be used to facilitate the future design of novel heterogeneous catalysts.

Acknowledgments

We thank the HPC Platform of ShanghaiTech University for computing time.