The modulation mechanism of geometric and electronic structures of bimetallic catalysts: Pd_13−mAg_m (m=0–13) clusters for acetylene semi-hydrogenation

Abstract

The modulating mechanism of the second metal in bimetallic catalysts for the catalytic properties has always been a hot topic. Pd_13−mAg_m (m=0–13) clusters are used as the model catalysts to explore the influence of Ag-induced configurational and electronic evolution of the PdAg phase on the catalytic performance of acetylene semi-hydrogenation by theoretical calculations. From the results obtained, it can be found that the activity/selectivity to ethylene dramatically depends on the geometric and electronic structures of 13-atom bimetallic clusters in the subnanometer size regime. The adsorption configuration of the C₂ species is determined by the structure of bimetallic clusters, which can be attributed to the reasonable matching with the highest occupied molecular orbital (HOMO). A metastable composition Pd₆Ag₇ cluster, exhibiting the biggest difference in electrons supplied from the clusters to acetylene and ethylene, promotes the reaction path of the target product in the semi-hydrogenation of acetylene. The modulating mechanism of silver has been deeply explored in this paper, which will provide important theoretical guidance for the rational design and development of bimetallic catalysts.

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Introduction

Bimetals are high-profile catalytic materials due to their superior catalytic properties which are strongly associated with their intrinsic geometric/electronic structures.^1–3 The exploration of the modulation mechanism opens new perspectives for precise synthetic control of bimetallic active sites.^4–6

Palladium–silver catalysts have found successful applications in the acetylene semi-hydrogenation industry that requires the conversion of trace amounts of acetylene (∼0.1–1%) produced by steam cracking furnaces into ethylene and its reduction to below 1 ppmv.^7–9 Currently, the major issues are the complete hydrogenation of acetylene to ethane and the oligomerization of unsaturated hydrocarbons.⁸ Therefore, enhancing the palladium–silver catalyst selectivity to ethylene has been the focus of research on the acetylene semi-hydrogenation process.

The existence of d holes makes the Pd d orbital possess high-energy electrons in consecutive ensembles, which can activate acetylene and ethylene to achieve sp³ hybridization and result in tetra-σ and di-σ adsorption modes, respectively, favoring complete hydrogenation to ethane.^10–12 The widely accepted strategy is to tune the geometric and electronic structures of the metal active phase of Pd-based catalysts by doping promoter metals to reduce the d-electron energy and break large Pd ensembles.^13–15 Ag alloying of Pd may dilute the Pd atoms, which can inhibit the generation of the non-selective PdH_x phase as the main cause of over-hydrogenation to C₂H₆.^8,16,17 An electron transfer from Ag to Pd, increasing the electron density of the Pd d-band in a bimetallic system, can weaken the adsorption of hydrogen, acetylene, ethylene and other C₂ intermediates on the PdAg catalyst, which is beneficial for improving the ethylene selectivity.^13,18,19 Theoretical study results suggested that Ag atoms tend to be exposed to the surface of a silver-rich system, which is conducive to the formation of isolated Pd atoms.^16,20–22 They also confirmed that Ag donates electrons to Pd, weakening the adsorption strength of related C₂ species on the Pd site, which is consistent with the results of experiments.

For the fabrication of catalysts with adequate activity and stability, the active species of dispersed metal catalysts are often small clusters.^4,23–25 Constructing appropriate spatial structures and electronic properties is a long-term goal for the design of metal cluster catalysts.^4,26,27 The dopant of heteroatoms may drastically transform the structural and electronic properties of the bimetallic phase because of the different nucleation and growth modes of metals, which was also confirmed by our previous study.^28–30 However, limited by the analysis tools available, few research studies have been able to achieve sensitivity of the catalytic performance to the second metal-induced spatially geometric and electronic structures of bimetallic species in the subnanometer size regime. This is still unclear despite it being crucial for optimizing the catalytic performance of bimetallic catalysts.

PdAg clusters can be used as high-performance and cost-effective catalytic materials for acetylene semi-hydrogenation.^31,32 The change of just one atom in clusters may cause a variation of the ensembled morphologies, local coordination environments, electronic properties and so on.^26,33 The evolution of the structure (geometric/electronic) may affect the chemisorption configurations of relevant molecules, which play an important role in the catalysis.^9,10 For acetylene hydrogenation, a catalyst with specific well-defined geometric and electronic structures is expected to efficiently adjust and catalyze the rate-determining step (RDS) and provide excellent reactivity to ethylene.³⁴ One of the challenges is that the similar atomic scattering factors of Pd and Ag cause the experimental studies to provide ensemble-average information and to be unable to identify the crucial active metal component favoring the conversion of acetylene to ethylene.^19,35 The explicit structural and electronic information correlates with catalytic properties can be provided by density functional theory (DFT) calculations.

In the present work, we carried out DFT calculations combined with Monte Carlo simulation to systematically investigate the modulating mechanism of silver on the activity/selectivity of acetylene semi-hydrogenation over Pd_13−mAg_m (m=0–13) clusters. This is pivotal to disentangling the modulation mechanism of the second metal in bimetallic catalysts, and it has allowed us to comprehend in-depth the effect of Ag-induced configurational evolution and the resulting electronic structure of bimetallic clusters on the activity and selectivity in harsh reaction conditions. The RDS of acetylene hydrogenation varies with the evolution of the cluster structure. With these central insights, we notice that a metastable Pd₆Ag₇ cluster having a unique geometric and electronic structure seems to exhibit extraordinary acetylene hydrogenation activity and poor ethylene adsorption capacity, showing optimal activity and selectivity.

Computational details

The calculations were carried out with the density-functional theory (DFT) method, as performed using the Cambridge Serial Total Energy Package (CASTEP) plane-wave code in the Materials Studio 5.5 software package, Accelyrs.³⁶ The generalized gradient approximation (GGA) and the Perdew-Wang 91 generalized gradient approximation (GGA-PW91) functional were selected and used the formal spin as initial (the initial value for the number of unpaired electrons for each atom will be taken from the formal spin specified for each atom and subsequently optimized during the calculation) to calculate the character of the base state.³⁷ The available 13-atom palladium–silver clusters and the corresponding pure cluster structures mentioned in our previous work were used for the growth method considering simulated annealing.²⁹ All calculations were performed in a 15 Å cubic lattice with a Gamma k-point and a cutoff energy of 450 eV. The force threshold and self-consistent tolerance were set to 0.03 eV Å⁻¹ and 10⁻⁶ eV per atom, respectively. Double numerical plus polarization (DNP) was employed with a smearing of 0.05 eV. The parameters in our calculations were carefully tested, with the change of the calculated energy being smaller than 2%. A complete LST (linear synchronous transit)/QST (quadratic synchronous transit) method was used to search for the transition state (TS) of every elementary reaction and all transition states had only one imaginary frequency.

The adsorption free energy (ΔG_ads) of adsorbates on clusters, the activation free energy (G_a) and the reaction free energy (ΔG) were calculated using

ΔG_ads = E_Ads/Cluster + G_Ads/Cluster − (E_Ads + G_ads + E_Cluster + G_Cluster) (1)

G_a = E_TS + G_TS − (E_R + G_R) (2)

ΔG = E_P + G_P − (E_R + G_R) (3)

where E_Ads/Cluster, E_Ads, E_Cluster, E_TS, E_R and E_P are the energy of clusters with adsorbates, gas-phase adsorbates, bare clusters, transition states, reactants and products, respectively. G_Ads/Cluster, G_Ads, G_Cluster, G_TS, G_R and G_P are the corresponding standard free energies at a finite temperature.

The d-band center (ε_d) is defined as the following:^38,39

where ε and Δε are the DOS and weighted DOS, respectively.

Results and discussion

Structural evolution of Pd_13−mAg_m–C₂H_x (x=2, 4) systems

The multiple low-energy adsorption sites of acetylene on Pd_13−mAg_m (m = 0–13) clusters were found using Adsorption Locator (based on Monte Carlo simulation with the CAMPASS force field) with 10 cycles and 100 000 steps per cycle;^40,41 only the most favorable adsorption configurations with the lowest energy are presented in Fig. 1. For acetylene adsorption on the Pd-based catalyst, four adsorption modes are proposed: tetra-σ mode, with each carbon atom of acetylene binding to two substrate atoms respectively; di-σ mode, with two carbon atoms of acetylene binding to two substrate atoms; π mode, with two carbon ends of acetylene binding to one substrate atom; and di-σ/π mode, with two carbon ends of acetylene not only binding to two substrate atoms, but also jointly binding to the third substrate atom (via two σ-bonds and one π-bond).^{9,10,22,42,43}

Fig. 1 The most stable adsorption configurations, adsorption free energies (ΔG_ads, kJ mol⁻¹, 425 K) and adsorption modes of Pd_13−mAg_m–C₂H_x (top, C₂H₂; and bottom, C₂H₄). Dark green, Pd; light blue, Ag; gray, C; and white, H.

The contributions of various translations, vibrations and rotations of the systems are reflected by G (T). The adsorption free energies (ΔG_ads) of C₂H₂ and C₂H₄ at 425 K were calculated,⁴⁴ as shown in Table 1. Acetylene preferentially adsorbs on the Pd₁₃ cluster in the tetra-σ mode, yielding an adsorption free energy of −264.70 kJ mol⁻¹ (Fig. 1 and Table 1). The adsorbed C₂H₂ is activated and the C–C bond is stretched from 1.21 (gas phase) to 1.39 Å. The adsorption mode of acetylene on Pd₁₂Ag is similar to that on Pd₁₃. The ΔG_ads, −246.07 kJ mol⁻¹, is larger than that of Pd₁₃, but the deformation of C₂H₂ and the Pd₁₂Ag cluster is more serious because of the evolution of the cluster configuration caused by the doping of Ag atoms (Table S1†). Acetylene adsorption on the Pd₁₁Ag₂ cluster via the tetra-σ-bound mode is close to that on Pd₁₂Ag that has a ΔG_ads of −221.30 kJ mol⁻¹.

Table 1 Adsorption modes, adsorption free energies (ΔG_ads, 425 K, kJ mol⁻¹) and carbon–carbon bond distances (d_C–C) of C₂H₂ and C₂H₄ and the d-band center of Pd_13−mAg_m (m = 0–13) clusters

M (Ag atom)	Mode		ε d (eV)	ΔGads (kJ mol^−1)		d C–C (Å)
	C2H2	C2H4		C2H2	C2H4	C2H2	C2H4
a The calculated values of dC–C of gas-phase C2H2, C2H4 and C2H6 in the gas phase are 1.21, 1.33, and 1.53 Å, respectively.
0	Tetra-σ	Di-σ	−1.96	−264.70	−152.36	1.39	1.43
1	Tetra-σ	Di-σ	−2.04	−246.07	−126.09	1.40	1.42
2	Tetra-σ	Di-σ	−2.09	−221.30	−119.16	1.40	1.43
3	Di-σ/π	Di-σ	−2.14	−231.80	−122.39	1.35	1.44
4	Di-σ/π	Di-σ	−2.23	−193.70	−82.87	1.35	1.44
5	Di-σ/π	Di-σ	−2.29	−212.40	−108.95	1.34	1.44
6	Di-σ/π	Di-σ	−2.46	−197.00	−100.12	1.35	1.43
7	Di-σ/π	π	−2.52	−124.31	−41.64	1.32	1.39
8	Di-σ	π	−2.63	−99.05	−69.54	1.29	1.39
9	π	π	−3.53	−99.16	−83.29	1.26	1.39
10	π	π	−2.99	−79.49	−57.44	1.25	1.39
11	π	π	−3.52	−62.65	−67.67	1.25	1.38
12	π	π	−3.44	−63.04	−49.31	1.22	1.36
13	π	π	−3.96	−36.70	−29.66	1.22	1.36

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Acetylene adsorption on Pd₁₀Ag₃ is the di-σ/π mode, yielding a ΔG_ads of −231.80 kJ mol⁻¹, suggesting that with the increase of doped Ag atoms, the adsorption configuration of acetylene transforms with the evolution of the cluster structure and the adsorption strength decreases. For Pd₉Ag₄, acetylene adsorption prefers the di-σ/π-bound state, which accounts for a ΔG_ads of −193.70 kJ mol⁻¹. Interestingly, in the geometry optimization of acetylene adsorption on the Pd₈Ag₅ cluster, the adsorption mode is the same as that of Pd₉Ag₄, but the adsorption free energy is −212.40 kJ mol⁻¹, being lower than that of Pd₉Ag₄. This may be attributed to the difference in cluster structures, that is, the Ag-induced structural evolutions affect the adsorption of acetylene.

Acetylene interacts with the Pd₆Ag₇ cluster via σ-bonding to two Pd atoms and an unusual π-mode interaction with an Ag atom; the most favorable adsorption configuration is shown in Fig. 1. The corresponding adsorption free energy is −124.31 kJ mol⁻¹. With the increase of Ag atom content from 7 to 8 in the bimetallic cluster, the most favorable adsorption configuration of acetylene is the di-σ state rather than the di-σ/π mode with a ΔG_ads of −99.05 kJ mol⁻¹. The energetically preferred adsorption configurations of acetylene on Pd₄Ag₉ ∼ Ag₁₃ clusters are shown in Fig. 1, via the π-bound mode. The calculations yield values of ΔG_ads of −99.16 kJ mol⁻¹ (Pd₄Ag₉), −79.49 kJ mol⁻¹ (Pd₃Ag₁₀), −62.65 kJ mol⁻¹ (Pd₂Ag₁₁), −63.04 kJ mol⁻¹ (PdAg₁₂) and −36.70 kJ mol⁻¹ (Ag₁₃).

Our results show that the low-energy adsorption configurations of ethylene on Pd_13−mAg_m clusters only two modes are presented: di-σ mode and π mode, in line with what has been reported.^9,10,20,45 The most stable adsorption configuration of ethylene on the Pd₁₃ cluster via the di-σ-bound mode is presented in Fig. 1. This di-σ structure yields a ΔG_ads of −152.36 kJ mol⁻¹, which is 112.34 kJ mol⁻¹ higher than that of acetylene adsorption (Table 1). Ethylene adsorption on Pd₁₂Ag∼ Pd₉Ag₄ clusters also via the di-σ-bound mode is shown in Fig. 1. These di-σ structures yield values of ΔG_ads of −126.09 kJ mol⁻¹ (Pd₁₂Ag), −119.16 kJ mol⁻¹ (Pd₁₁Ag₂), −122.39 kJ mol⁻¹ (Pd₁₀Ag₃) and −82.87 kJ mol⁻¹ (Pd₉Ag₄), which increase with the increase of Ag atom content. For ethylene adsorption on Pd₈Ag₅ (−108.95 kJ mol⁻¹), the calculations found identical di-σ-bound state energy minimum structures but it was more stable than Pd₉Ag₄. Geometry optimization of ethylene adsorption on the Pd₇Ag₆ cluster yielded the di-σ-bound mode with a ΔG_ads of −100.12 kJ mol⁻¹.

Ethylene adsorption on both Pd₆Ag₇ and Pd₅Ag₈ prefers the π-bound state, which separately accounts for values of ΔG_ads of −41.64 and −68.54 kJ mol⁻¹. The Pd₄Ag₉ cluster has an anomaly with a ΔG_ads of −83.29 kJ mol⁻¹, which is 13.78 kJ mol⁻¹ lower than the ethylene adsorption on Pd₅Ag₈ with a similar adsorption mode (Fig. 1 and Table 1). For ethylene adsorption on Pd₃Ag₁₀∼Ag₁₃ clusters, the adsorption modes are all the π-bound state, possessing values of ΔG_ads of −57.44, −67.67, −49.31 and −29.66 kJ mol⁻¹, respectively.

To interpret the adsorption behaviors in more detail, ΔE_ads is divided into three contributions according to ΔE_ads = E_def(C₂H_x) + E_def (Pd_13−mAg_m) + E_int. According to the data summarized in Table S1,† we can see that the acetylene deformation energies (E_def) for the tetra-σ, di-σ/π, di-σ and π structures are within the ranges of 258.99–274.54, 172.66–200.66, 129.57 and 3.49–46.11 kJ mol⁻¹, respectively. The E_def of acetylene increases with the extension of the C–C bond activated by the clusters (Tables 1 and S1†). The tetra-σ-bound mode always induces a greater extension (with regard to the gas phase) than the others in our studies. The C–C bond distance (d_C–C) in the tetra-σ, di-σ/π, di-σ and π modes enlarged to ∼1.40, 1.34, 1.29 and 1.24 Å from 1.21 Å in the gas phase, while the π-bound structures of acetylene on PdAg₁₂ and Ag₁₃ show only a slight and almost negligible elongation (∼1.22 Å).

Further analysis shows that the ethylene deformation energies for the di-σ and π structures are within the energy ranges of 71.99–89.99 and 4.19–22.94 kJ mol⁻¹, respectively. The E_def of ethylene increases with the extension of the C–C bond too. The di-σ structures always induced a greater extension than the π modes compared with the gas phase. The d_C–C in the di-σ-bound mode enlarged to ∼1.43 Å from 1.33 Å (gas-phase), while the π-bound structures caused a smaller C–C bond elongation (∼1.38 Å).

An in-depth study of E_def shows that the deformation of adsorbates is much stronger than that of the adsorbents. As the largest deformation energies of the adsorbed acetylene and ethylene are 274.54 and 89.99 kJ mol⁻¹, the deformation energies of Pd_13−mAg_m clusters are rather small, below 53.30 and 15.99 kJ mol⁻¹, respectively. The energy consumption for the deformation can be compensated for by the interaction between the adsorbates and the clusters. Despite the Pd_13−mAg_m–C₂H_x interaction in various modes, E_int could compensate for the energy cost of deformation between the adsorbates and the bimetallic clusters.

It can be seen that the interaction between clusters and C₂H_x is affected not only by the content of Ag around Pd, but also the geometric structure of Pd_13−mAg_m clusters is a factor that cannot be underestimated. Our calculation shows that the ΔG_ads (425 K) of C₂H₂ adsorption is always greater than that of C₂H₄ on the 13-atom bimetallic clusters (except for Pd₂Ag₁₁). Meanwhile, for C₂H_x adsorption on Pd₂Ag₁₁, PdAg₁₂ and Ag₁₃ clusters, there are small differences in the values of ΔG_ads (425 K) between the two adsorbates (Fig. 1). In summary, the stability of acetylene adsorption on the Pd_13−mAg_m clusters is better than that of ethylene, excluding Pd₂Ag₁₁ at 425 K. However, the acetylene semi-hydrogenation process is used to remove trace (∼0.1–1%) acetylene in ethylene, so m ≥ 11 is not conducive.

Electron interaction in Pd_13−mAg_m–C₂H_x systems

The partial densities of states (PDOSs) for Pd_13−mAg_m clusters before and after C₂H_x adsorption are shown in Fig. 2 and S1–S7.† In general, the adsorption stability is mainly determined by the bond strength of adsorbed molecules, increasing in the order tetra-σ > di-σ/π > di-σ > π (for acetylene) and di-σ > π (for ethylene) (Fig. 1). For C₂H_x adsorption, the d band states of Pd resonate with the p band states of carbon in Pd_13−mAg_m–C₂H_x systems, forming the π^*_pd orbital. The p orbitals of carbon atoms strongly mixed with the low-energy (typically below the Fermi level) d states of Pd atoms, while for the d states, the distribution is wider and more delocalized but still localize at the metal cluster. The d states of Pd show a finite density of states at the Fermi level.

Fig. 2 Partial densities of states (PDOSs) for Pd₁₃, Pd₁₀Ag₃, Pd₆Ag₇, Pd₅Ag₈ and Pd₄Ag₉ clusters (different adsorption modes) projected on the bonded Pd atoms and C atoms in acetylene (a) and ethylene (b) before and after adsorption. Dotted lines, before adsorption, and solid lines, after adsorption.

The p states of carbon from acetylene are more delocalized than those of carbon from ethylene, indicating that the interactions between acetylene and Pd_13−mAg_m are stronger. There are also significant differences in the resonances of p states near the Fermi level, and that of p states of carbon in acetylene is stronger. We note that both the d-band state of Pd and the p states of C are moving towards the lower energy region after C₂H_x adsorption, compared with the bare clusters and C₂H_x. This means that the adsorption of C₂H_x induces charge redistribution. The d-band center can be used as a “descriptor” to describe the adsorption of the adsorbent.^38,39,46 As shown in Table 1, an electron transfer from Ag to Pd effectively reduces the d-band center of Pd_13−mAg_m, possibly weakening the adsorption of Pd on hydrogen and related C₂ hydrocarbon, which inhibits over-hydrogenation.

The variation of electronic density spatial distribution (electronic density difference) is shown in Fig. 3 and S9.† The positive (green) and negative (yellow) areas indicate where the electron density is enriched or depleted, respectively. C₂H_x are adsorbed on Pd_13−mAg_m and an electron transfer apparently occurs in the Pd_13−mAg_m–C₂H_x systems. Electronic interactions between C₂H_x and the bimetallic clusters with the tetra-σ mode are the strongest and the weakest are π-interactions. The carbon atoms in C₂H_x obtain electrons from the clusters through the Pd/Ag atoms bonded to them. The Pd/Ag atoms lose electrons in d_z²-like orbitals, which is associated with the charge redistribution of the formed C–Pd/C–Ag bonds. At the same time, the bonded metal atoms also obtain electrons from other Pd/Ag atoms in the clusters to compensate for the loss. The increase of electronic density (the green areas) is embodied on C₂H_x with a π*-like distribution, and in d_xz and d_yz combinations on Pd atoms. As an increase in the content of Ag atoms in the clusters leads to the evolution of adsorption configuration, the electrons contributed by the cluster to C₂H_x decrease. Thus, the interactions between bimetallic clusters and C₂H_x weaken. The interaction of C₂H₂ with the Ag in Pd₆Ag₇ is also evidenced by Ag donating electrons to C and the overlap of the orbital from the PDOS (see Fig. 3 and S8†).

Fig. 3 Electron density difference for acetylene (upper) and ethylene (bottom) adsorbed on Pd₁₃, Pd₁₀Ag₃, Pd₆Ag₇, Pd₅Ag₈ and Pd₄Ag₉ clusters. The green and yellow areas indicate where the electron density is enriched or depleted; the color scheme is identical to that in Fig. 1.

In the Pd_13−mAg_m–C₂H_x systems, Ag transfers electrons to Pd, which in turn transfers electrons to C atoms, following the order of electronegativity: C > Pd > Ag. The Hirshfeld charge of Pd atoms interacting with C₂H_x was analyzed, aiming at further clarifying the effect of electron interaction on the adsorption behavior of C₂H_x over Pd_13−mAg_m clusters (Fig. 4). Among the Pd_13−mAg_m, the discrepancy between the electron lost by Pd after acetylene adsorption and that lost after ethylene adsorption is the largest in Pd₆Ag₇, which may be beneficial for the removal of trace acetylene in ethylene.

Fig. 4 The Hirshfeld charge of the bonded Pd atoms in Pd_13−mAg_m–C₂H_x (m = 0–10) systems.

The frontier molecular orbital analysis was performed according to the differential charge density result, from which the lowest unoccupied molecular orbital (LUMO) of C₂H_x and the highest occupied molecular orbital (HOMO) of Pd_13−mAg_m clusters are obtained (see Fig. 5 and S10†). The doping of Ag atoms causes the evolution of the HOMO structure of the bimetallic clusters, whose principle is the transformation of metal–metal interaction. To achieve the maximum orbital overlap, the LUMOs of acetylene and ethylene are matched with the HOMOs of Pd_13−mAg_m clusters to form different adsorption configurations.

Fig. 5 The lowest unoccupied molecular orbitals (LUMOs) of acetylene and ethylene molecules and the highest occupied molecular orbitals (HOMOs) of Pd₆Ag₇ and Pd₅Ag₈ clusters (the red numbers indicate the bond length, Å). The color scheme is identical to that in Fig. 1.

In particular, the π^*_p-shaped LUMO of acetylene, formed by the p orbitals of two carbon atoms, interacts with the HOMO of Pd₆Ag₇ (two Pd atoms with d_xz-shaped orbitals) to form the π^*_pd molecular orbital, as shown in Fig. 5. The acetylene molecule (with an sp hybrid orbital) rotates to maximize the overlap with the d_xz-shaped HOMO orbitals (inclined to the corresponding Pd–Pd–Ag plane, view A in Fig. 5), forming two σ chemical bonds (C–Pd) that are inclined to the corresponding plane. This results in the acetylene molecule approaching the corresponding Ag atom and interacting with the Ag atom with the π-mode, forming the di-σ/π mode adsorption configuration on the Pd₆Ag₇ cluster. For the ethylene molecule, with an sp² hybrid orbital, it can only interact with one d_xz-shaped orbital to form the π-mode adsorption configuration. In addition, the two d_xz-shaped orbitals, forming bonds with acetylene, have exactly the same interaction with the two carbon atoms, so the lengths of the two C–Pd bonds in the Pd₆Ag₇–C₂H₂ system are also the same (both are 2.022 Å, Fig. 5). However, due to the metal–metal interaction in the cluster, the d_xz-shaped orbital loses its original centrosymmetric type, so the interaction with the two carbon atoms in ethylene is different and the C–Pd bond formed is also different, which are 2.180 and 2.166 Å, respectively.

The HOMO of Pd₅Ag₈ is also a d_xz-shaped orbital, just suitable for acetylene to bind in a configuration where the C–C bond is directly above the corresponding Pd–Pd bond to achieve the maximum orbital overlap (view A1 in Fig. 5). Therefore, acetylene preferentially adsorbs on the Pd₅Ag₈ cluster in the di-σ mode with the same C–Pd bonds, while ethylene has a π mode adsorption configuration with different C–Pd bonds. From the above analysis, it can be seen that the intra-cluster metal–metal interaction changes the HOMO of the clusters, thereby transforming the adsorption configuration of acetylene and ethylene.

Acetylene hydrogenation process on Pd_13−mAg_m

There are three possible reaction paths for acetylene hydrogenation, as shown in Scheme 1; one is acetylene gradually hydrogenated to ethylene and desorbed from the catalyst to form a gas [CH₂CH₂ (g)] and the second and third correspond to the hydrogenation of adsorbed ethylene [CH₂CH₂ (ad)] and ethylidene (CHCH₃) to C₂H₅ (ad), respectively, indicating the occurrence of over-hydrogenation.^10,11,47 Therefore, in order to improve the selectivity of ethylene, the latter two paths should be inhibited.

Scheme 1 Possible reaction pathways of C₂H₂ hydrogenation. * The adsorption state and (g) the gas-phase state, respectively.

Ag is doped with the Pd cluster, aiming at regulating the reaction path of acetylene hydrogenation along path I. According to this, there are two key steps in the hydrogenation of acetylene on the catalysts, which are the hydrogenation of C₂H₃ species to CHCH₃ or CH₂CH₂ (ad) and the generated CH₂CH₂ (ad) preferring desorption or further hydrogenation. First, the activation free energy (G_a) of generating CH₂CH₂ (ad) and CHCH₃ from C₂H₃ is differentiated, judging whether the path associated with CH₂CH₂ (ad) is superior to CHCH₃. Subsequently, the free energy differences between CH₂CH₂ (ad) desorption and its hydrogenation should be distinguished, which elaborates whether CH₂CH₂ (ad) prefers desorption rather than further hydrogenation (as mentioned above, Pd₂Ag₁₁, PdAg₁₂ and Ag₁₃ clusters are not considered).

For m ≤ 2, the activation free energy of C₂H₂ hydrogenation to C₂H₃ increased with the increase of Ag incorporation (Table 2). Pd₁₃, Pd₁₂Ag and Pd₁₁Ag₂ contribute the activation free energies of 11.98, 77.25 and 104.29 kJ mol⁻¹, respectively. G_a decreases slightly, 94.99 kJ mol⁻¹ for Pd₁₀Ag₃, which is assumed to be due to the structural evolution of the bimetallic cluster (from a hexagonal bi-layer to a distorted icosahedral structure). Subsequently, it still shows a downward trend (51.51 kJ mol⁻¹ for Pd₉Ag₄). When the content of Ag atoms in Pd_13−mAg_m clusters further increases to m=5, the G_a (C₂H₂ + H) gradually decreases (20.76 kJ mol⁻¹ for Pd₈Ag₅), and then it increases again (100.31 kJ mol⁻¹ for Pd₃Ag₁₀). That is to say, doping an appropriate amount of Ag in the clusters makes the interaction of Pd_13−mAg_m–C₂H₂ moderate and conducive to the reaction. By the way, the geometric structure of the bimetallic clusters is also an important factor.

Table 2 The activation free energy (G_a, kJ mol⁻¹) of acetylene hydrogenation related steps, adsorption free energies (G_co–ads, kJ mol⁻¹) of acetylene and ethylene co-adsorption with the H atom, ethylene selectivity ΔG_sel (kJ mol⁻¹) and the reaction rate of ethylene formation (r per s site) on Pd_13−mAg_m (m = 0–10) clusters at 425 K

Clusters	G a (kJ mol^−1)				G co-ads (kJ mol^−1)		ΔGsel (kJ mol^−1)	r (per s per site)
	C2H2 + H → CHCH2	CH2CH + H → CH2CH2	CHCH2 + H → CHCH3	CH2CH2 + H → CH2CH3	C2H2	C2H4
Pd13	11.98	157.31	20.64	30.23	−184.49	−108.00	−77.77	0.46
Pd12Ag	77.25	145.32	32.72	123.71	−179.02	−119.28	4.43	1.90 × 10^−2
Pd11Ag2	104.29	77.33	4.29	19.06	−220.66	−88.03	−68.97	1.32 × 10^2
Pd10Ag3	94.99	63.26	67.14	101.28	−226.39	−104.48	−3.20	1.25
Pd9Ag4	51.51	61.21	88.01	54.78	−204.12	−102.94	−48.16	1.94
Pd8Ag5	20.76	52.69	25.53	80.91	−236.90	−85.15	−4.24	2.99 × 10^2
Pd7Ag6	29.05	59.62	125.25	44.96	−186.75	−84.27	−39.31	3.83 × 10^2
Pd6Ag7	65.59	21.02	—	46.06	−119.15	−23.18	22.88	1.25 × 10^10
Pd5Ag8	47.30	52.47	—	49.16	−127.94	−74.98	−25.82	5.32 × 10^3
Pd4Ag9	66.41	13.45	—	80.65	−67.21	−60.59	20.06	3.13 × 10^5
Pd3Ag10	100.31	46.86	—	52.85	−102.61	−59.31	−6.46	4.50 × 10^5

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Doping Ag atoms significantly changes the hydrogenation path of acetylene on the clusters (Fig. 6 and Fig. S11 and S12†). For the co-adsorption configuration of the H atom and the C₂H₃ species on Pd₁₃, the hydrogen atom near the carbon atom bonded with two H atoms in C₂H₃[(CHCH₂ + H)*] (where * denotes the adsorption state) is superior to the hydrogen atom near the carbon atom bonded with one H atom [(CH₂CH + H)*], and the values of G_a of CHCH₂ + H and CH₂CH + H are 20.64 and 157.31 kJ mol⁻¹, respectively. Namely, C₂H₂ prefers the CHCH₃ hydrogenation path on Pd₁₃ (path III in Scheme 1 and see Fig. 6). In the case of Pd₁₂Ag and Pd₁₁Ag₂, there is only a slight difference in stability between (CHCH₂ + H)* and (CH₂CH + H)*, and the G_a of CHCH₂ + H is lower than that of CH₂CH + H (32.72 vs. 145.32 kJ mol⁻¹ for Pd₁₂Ag and 4.29 vs. 77.33 kJ mol⁻¹ for Pd₁₁Ag₂) (in Table 2). C₂H₂ hydrogenates in favor of path III on Pd₁₂Ag and Pd₁₁Ag₂ too.

Fig. 6 Potential energy diagram for preferred pathways and the rate-determining step (RDS) involving in acetylene hydrogenation on Pd₁₃, Pd₆Ag₇ and Pd₅Ag₈ clusters (paths I, II and III, respectively) at 425 K (* denotes the adsorption site).

Pd₁₀Ag₃ prefers the (CH₂CH + H)* co-adsorption configuration and CH₂CH + H hydrogenation path (I or II, 63.26 vs. 67.14 kJ mol⁻¹ for CHCH₂ + H, Fig. S11†). Subsequently, there is only a slight difference between the desorption of CH₂CH₂ (ad) from Pd₁₀Ag₃ (104.48 kJ mol⁻¹) and further hydrogenation to C₂H₅ (101.28 kJ mol⁻¹). That is, both path I and path II can occur at the same time on Pd₁₀Ag₃, and the latter may be a priority.

For Pd₉Ag₄ and Pd₈Ag₅ clusters, the (CHCH₂ + H)* configuration is slightly more stable than the (CH₂CH + H)* configuration, so they may coexist on Pd₉Ag₄ and Pd₈Ag₅ (Fig. S12†). Path III is unlikely to occur because the barrier of CHCH₃ formation from the C₂H₃ + H species on Pd₉Ag₄ (88.01 kJ mol⁻¹) is greater than that of CH₂CH₂ (ad) (61.21kJ mol⁻¹), but that on Pd₈Ag₅ is just the opposite (25.53 vs. 52.69 kJ mol⁻¹), preferring path III. Even if they form CH₂CH₂ (ad), they hydrogenate further to C₂H₅ instead of desorption on Pd₉Ag₄ (54.78 vs. 102.94 kJ mol⁻¹) and Pd₈Ag₅ (80.91 vs. 85.15 kJ mol⁻¹) (Table 2). The CHCH₃ hydrogenation path is dominant on Pd₇Ag₆, even though the larger barrier of CHCH₃ formation (125.25 kJ mol⁻¹) than CH₂CH₂ (ad) formation (59.62 kJ mol⁻¹) starting from C₂H₃ + H species, as shown in Table 2 and Fig. S12†, (CHCH₂ + H)* is more stable. Even if CH₂CH₂ (ad) is formed, it prefers further hydrogenation to C₂H₅ rather than its desorption over Pd₇Ag₆ (44.96 vs. 84.27 kJ mol⁻¹).

When (C₂H₃ + H) adsorbs on Pd₆Ag₇, the carbon atom bonded with two H atoms in C₂H₃ is suspended and far away from the cluster, and only the carbon atom bonded to one H atom is attached to the cluster, as shown in Fig. 6. The adsorption configuration of (C₂H₃ + H) is only (CH₂CH + H)*, that is, the CHCH₃ hydrogenation path (path III) is inhibited. For Pd_13−mAg_m (8≤m≤10), the adsorption configuration of (C₂H₃ + H) is similar to that of Pd₆Ag₇ (except for Pd₅Ag₈, where the carbon atom bonded with one hydrogen atom in C₂H₃ is bridged with two Pd atoms of Pd₅Ag₈), and path III is inhibited on these clusters (see Fig. 6 and S11†). Then, it is just necessary to confirm whether CH₂CH₂ (ad) prefers desorption rather than its further hydrogenation on Pd_13−mAg_m (7≤m≤10). For Pd₆Ag₇, the G_a for the hydrogenation of CH₂CH₂ (ad) to C₂H₅ is 46.06 kJ mol⁻¹, compared with 23.18 kJ mol⁻¹ for desorption. CH₂CH₂ (ad) preferentially desorbs from Pd₆Ag₇ rather than its further hydrogenation to C₂H₅. However, on Pd₅Ag₈, CH₂CH₂ (ad) is more likely to undergo further hydrogenation than desorption (49.16 vs. 74.98 kJ mol⁻¹, Fig. 6, S11† and Table 2), which can be interpreted as a stronger adsorption capacity of Pd₅Ag₈ to CH₂CH₂ (ad) (see Fig. 1 and Table 1). CH₂CH₂ (ad) preferentially desorbs from Pd₄Ag₉ rather than its further hydrogenation to C₂H₅ (60.59 vs. 80.65 kJ mol⁻¹). For Pd₃Ag₁₀, the hydrogenation of CH₂CH₂ (ad) to C₂H₅ is slightly advantageous over or competitive with desorption (52.85 vs. 59.31 kJ mol⁻¹, Table 2).

As presented in Table 2 and Fig. 6, the doping of Ag atoms also changes the progress of acetylene hydrogenation, that is, the RDS (with larger G_a) of two-step hydrogenation is transferred. Ag atoms cause the evolution of bimetallic cluster structures, which tunes the catalytic performance for acetylene semi-hydrogenation. Pd₆Ag₇ and Pd₄Ag₉ are favorable for acetylene hydrogenation to CH₂CH₂ (ad), and subsequently desorption from the catalyst rather than further hydrogenation (path I).

Effect of Ag doping on the activity and selectivity of CH₂CH₂ formation

The catalytic activity of the corresponding Pd_13−mAg_m clusters toward the formation of CH₂CH₂ is estimated from the reaction rate calculated through a two-step model according to the following eqn (5), which has been systematically reported by Hu et al. and others.^48–51where k_B, T, h, R are the Boltzmann constant, temperature, Planck constant and universal gas constant, respectively; P_R and P_P represent the partial pressure of the reactant and product, respectively and ΔG, G^ad_R, G^de_R and G^de_P are the reaction free energy of C₂H₂ hydrogenation to CH₂CH₂, and the effective free barriers of reactant adsorption, reactant desorption and product desorption, respectively. With the purpose of reflecting the catalytic performance of the clusters under real reaction conditions, the relevant parameters in the calculations of the reaction rate are selected as follows: the ratio of H₂ and C₂H₂ is 10, and the CH₂CH₂, C₂H₂ and H₂ species correspond to the partial pressures of 0.89, 0.01 and 0.1 atm, respectively. Thus, P_R and P_P are 0.11 and 0.89 atm, respectively.

The reaction rates for the hydrogenation of acetylene to ethylene on Pd_13−mAg_m clusters calculated using eqn (5) are shown in Table 2. The reaction rate of acetylene hydrogenation to ethylene on Pd₆Ag₇ is 1.25 × 10¹⁰ per s site, compared with 3.13 × 10⁵ per s site on Pd₄Ag₉. Pd₁₃, Pd₁₁Ag₂, Pd₉Ag₄, Pd₇Ag₆ and Pd₅Ag₈ still exhibit poor CH₂CH₂ selectivity, which is shown in the results of Table 2.⁵² The selectivity of CH₂CH₂ is 4.43, −3.20, −4.24 and −6.46 kJ mol⁻¹ on Pd₁₂Ag, Pd₁₀Ag₃, Pd₈Ag₅ and Pd₃Ag₁₀, respectively, indicating that further hydrogenation of CH₂CH₂ is competitive with desorption. For Pd₆Ag₇ and Pd₄Ag₉, the selectivity of CH₂CH₂ is 22.88 and 20.06 kJ mol⁻¹, respectively. However, the adsorption free energy of CH₂CH₂ on Pd₆Ag₇ (co-adsorption with the H atom) is only −23.18 kJ mol⁻¹, desorption of which is easy. This shows that Pd₆Ag₇ is more conducive to the semi-hydrogenation of acetylene to ethylene.

The most stable cluster may not necessarily exhibit the best catalytic performance; instead clusters with unique electronic structures and accessible low-energy metastable structures may contribute to the excellent adsorption/transformation of reactants.^53,54 The structural properties of Pd_13−mAg_m clusters, which are central to comprehending their catalytic performance for acetylene semi-hydrogenation, have been studied in detail in our previous work.²⁹ With the variation of Ag atom content in Pd_13−mAg_m clusters, the metal–metal interaction in the clusters has changed, affecting the stability of clusters. Regardless of the perspective of energy or electrons, Pd₅Ag₈ has the most stable composition among the 13-atom bimetallic clusters. As discussed above, however, the catalytic performance of Pd₅Ag₈ for acetylene semi-hydrogenation is not good. Opposition between stability and catalytic activity is often encountered in research on catalysis, namely, the stability of catalysts is not always positively correlated with their reactivity. Sure enough, the low-energy metastable composition of Pd₆Ag₇ exhibits the best activity and selectivity for ethylene formation. The unique distribution of palladium and silver in Pd₆Ag₇ promotes the adsorption and activation of acetylene and the desorption of ethylene, which is more conducive to the semi-hydrogenation of acetylene to ethylene under the reaction conditions. The most stable composition for the Pd_13−mAg_m clusters is Pd₅Ag₈ associated with stronger interaction between ethylene molecules, and hence shows poor ethylene selectivity. The most stable bimetallic cluster is not the best composition for acetylene semi-hydrogenation. Instead, the metastable bimetallic cluster with diverse compositions contributes to the high activities and selectivity for ethylene formation.

4. Conclusions

We explore the effect of a dizzying variety of Ag-induced structural and electronic properties of Pd_13−mAg_m clusters on their catalytic performance of acetylene semi-hydrogenation by computation chemistry. The adsorption configurations of acetylene and ethylene on a series of bimetallic clusters are identified, which are closely related to the structural evolution induced by Ag. With an increase in the content of Ag, a transformation of acetylene adsorption configurations from a tetra-σ mode (Pd₁₃∼Pd₁₁Ag₂) to a di-σ/π mode (Pd₁₀Ag₃∼Pd₆Ag₇), then to a di-σ mode (Pd₅Ag₈) and finally to a π mode (Pd₄Ag₉∼Ag₁₃) was observed. However, ethylene has only two adsorption modes, di-σ (Pd₁₃∼Pd₇Ag₆) and π mode (Pd₆Ag₇∼Ag₁₃). Electronic structural analysis reveals that the adsorption configuration is governed by the HOMO structures of the clusters dominated by intra-cluster metal–metal interactions.

Acetylene hydrogenation on Pd_13−mAg_m clusters was systematically investigated. The doping of Ag atoms can effectively tune the hydrogenation path of acetylene, and the RDS of the reaction is also transferred. Excessive hydrogenation of acetylene could not be prevented by too much or too little Ag doping. The activity and selectivity of acetylene semi-hydrogenation on the Pd₅Ag₈ cluster, which is the most stable composition, are not good. Instead, the low-energy metastable Pd₆Ag₇ exhibits optimal ethylene formation activity and selectivity, attributed to its unique geometric and electronic structure, which can effectively activate acetylene and weaken the adsorption strength of ethylene. The proposed mechanism is generally applicable, providing an interesting opportunity for the design and development of novel sub-nanometric bimetallic catalysts.

Author contributions

Panpeng Wei: conceptualization, methodology, investigation, writing – original draft, and writing – review and editing. Jian Zheng and Qing Li: methodology and software. Yucai Qin: writing – review and editing. Huimin Guan and Duping Tan: writing – review and editing. Lijuan Song: methodology, software, supervision, project administration, and funding acquisition.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

This work was supported by the National Natural Science Foundation of China (U1908203) and the Natural Science Foundation of Liaoning Province (2020-MS-284).

Notes and references

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Footnote

† Electronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d2qi01222g

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