Role of Intermediate Dynamics in Controlling Hydrogenation Selectivity by Heterogeneous Catalysis

Abstract

Selectivity in heterogeneous catalysis is essential while being the most difficult parameters to obtain from theoretical simulations. Although theory holds the key for catalytic design, in the search of complex reaction networks, intermediates are considered static and different configurations for addition reactions are not considered. Here, we present the crucial role of intermediate dynamics to understand reaction selectivity of heterogeneous catalysts by studying the dynamic properties. The hydrogenation of two different intermediates hydroperoxide (OOH) and vinyl (HCCH₂) is crucial to in the direct synthesis of water peroxide and alkyne semi-hydrogenation are taken as examples on the bare and alloyed surfaces. For them, the reaction network is studied by density functional theory coupled to molecular dynamics to present the role of rotations and how they affect paths for the addition of atomic hydrogen to lead to the products. In summary, the thermodynamic selectivity can be mapped to the dynamic control in the kinetics of the process.

1. Introduction

Hydrogenation typically constitutes the addition of pairs of hydrogen atoms to a molecule, often an alkene, and plays a key role in chemical synthesis. It requires a catalyst to make the reaction proceed at a reasonable rate. Heterogeneously catalyzed hydrogenations are one of the most important processes of the chemical industry which involves both thermodynamics and kinetics. From thermodynamic point of view, the stability of the products control product distribution in a chemical reaction. Kinetics describes the relative rates of corresponding product formation and how fast equilibrium is reached, thus in turn to the relative activation energies.

Noble metal species with different size (single atoms, nanoclusters, and nanoparticles) show different catalytic behaviors for various hydrogenation reactions. Many factors including the particle size, shape, chemical composition, metal–support interaction, and metal–reactant/solvent interaction can have significant influences on the catalytic properties of noble metal catalysts.¹ In general, the enhanced performance of noble metal catalysts may be rationalized by a combination of ligand, geometric, and/or ensemble effects. Ligand and geometric effects which describe influences of charge transfer between nearest neighbor atoms, orbital rehybridization and lattice strain generally affect the strength of interactions of reactants, intermediates, and products. In our previous work we have shown the outstanding activity, selectivity, and stability of ligand-modified Pd nanoparticles in the direct synthesis of H₂O₂.² On the other hand, the ensemble effects result when more than one reactive site, composed of different metal atoms, catalyzes distinct steps in a particular reaction mechanism. Our recent study showed that the supported palladium sulfides possess unique ensembles with face- and phase-dependent geometric and electronic characteristics and high stability, demonstrating exciting potential as catalysts for the selective hydrogenation of alkynes.³

Heterogeneous bimetallic catalysts, formed by adding a second metal to a host metal, garnered much research attention recently because they exhibit distinctly different and often superior activities for many chemical transformations as compared to pure monometallic systems as determined in experimental and theoretical investigations (e.g., selectivity, activity, and stability).⁴⁻¹⁰

The palladium–gold (Pd–Au) bimetallic catalyst has shown promising catalytic properties in aerobic oxidation of primary alcohols, direct synthesis of H₂O₂, hydrocarbon hydrogenation, CO oxidation, and oxidation of alcohols to aldehydes.¹¹⁻¹⁴ For example, it was found that isolated single Pd atoms constitute the minimum ensemble needed for CO adsorption while a larger set is required for proton adsorption. For hydrogen peroxide formation, Au shows a promotional effect because it drives the formation of the preferred selective catalytic ensemble.¹⁵ Other Au-containing alloys like AuNi have been reported active in oxidized CO at very low temperatures (77 K) because of the participation of Au in the active sites adsorbing the reactants.¹⁶ Furthermore, the combination of silver and palladium (Ag–Pd) has been widely applied in ethylene hydrogenation,¹⁷ hydrogenation of CO₂ to produce formic acid,¹⁸ hydrogenation of acetylene to ethylene, and oxygen reduction.^6,19,20 It was shown that for alloys of AgPd, the surface contained single Pd atoms surrounded by Ag atoms, which maximized the ability of a hetero atomic site to amplify the activity of each Pd atom.⁶

Moreover, acetylene hydrogenation reactions have been studied theoretically on both pure Pd and bimetallic PdAg surfaces.^17,21−24 It is found that on alloying with Ag and Au, the selectivity of Pd(111) surfaces for the hydrogenation of acetylene to ethylene is enhanced.²¹

Much is understood about heterogeneous bimetallic catalysts for hydrogenations but some issues remain unresolved and a deeper understanding of this mechanism on the bimetallic catalysts is necessary for a rational design of selective hydrogenation catalysts. We herein first report and compare the reaction network for two different hydrogenation reactions on the bare and alloyed surfaces by density functional theory (DFT). For the first reaction we study the O₂ hydrogenation in the direct synthesis of water peroxide mechanism on Pd and PdAu surfaces and for the second one the alkyne hydrogenation over Pd and AgPd surfaces is taken as another example. Particularly, the reaction barriers of hydroperoxide (OOH) and vinyl (HCCH₂) hydrogenation over both bare and alloyed surfaces are compared to each other. Second, the dynamic aspects of two different intermediates (OOH and HCCH₂) on the bare and alloyed surfaces are investigated by Born-Oppenheimer molecular dynamics (MD) calculations to understand reaction selectivity of heterogeneous catalysts. The paper is organized as follows: in the next section, the details of the computational methods employed to compute the reaction profiles and molecular dynamic calculations are presented. In Sections 2.1 and 2.2, the energy profiles for oxygen hydrogenation on Pd and PdAu surfaces and acetylene hydrogenation on Pd and AgPd surfaces are described. Section 2.3 covers the molecular dynamic calculations of OOH and HCCH₂ intermediates on different surfaces. In the last section we summarize our studies and present the conclusions.

2. Results and Discussion

2.1. Oxygen Hydrogenation on Pd and PdAu Surfaces

All possible reactions in the direct synthesis of hydrogen peroxide (DSHP) mechanism are summarized in Figure 1a. The scheme shows not only the hydrogenation steps conducting to H₂O₂ formation but also lateral decomposition paths readily including dissociation of reactants and intermediates, 2O, O + OH, 2OH, or over hydrogenation to O + H₂O and OH + H₂O. Combining several of these steps they provide all possible decomposition routes.

Figure 1.

Competitive paths involved in the direct hydrogen peroxide synthesis (a) and acetylene hydrogenation reactions (b). Reactions that drive to the formation of the desired products H₂O₂ and C₂H₄ formation are written in green color.

The DSHP mechanism essentially requires that oxygen is adsorbed molecularly on the catalyst surface, and the dissociated hydrogen atoms are added to it sequentially at both oxygen ends. However, several of the intermediates, O₂, O₂H, and H₂O₂ are likely to undergo spurious reactions like O–O bond scission and over hydrogenation to an already formed OH fragment. Table 1 summarizes all possible reactions in this mechanism including reactant adsorption, hydrogenation, and product desorption with the respective reaction energies and activation barriers and Table 2 reports the adsorption energies for the all intermediate states. The full energy profiles for the DSHP mechanism on Pd and PdAu surfaces are illustrated in Figure 2a.

Table 1. Reaction Energy (ΔE) and Corresponding Activation Barrier (E_a) for the Elementary Steps Involved in the H₂O₂ Formation on Pd and PdAu Surfaces^a.

	Pd		PdAu
elementary step	ΔE/eV	Ea/eV	ΔE/eV	Ea/eV
O2* + 2H* → O2H* + H*	–0.11	0.68	–0.22	0.68
O2H* + H* → OH* + H* + O*	–1.47	0.44	–0.77	0.53
O2H* + H* → H2O* – O* syn	–2.34	0.35	–2.33	0.56
O2H* + H* → H2O2* trans	–0.21	0.89	–0.45	0.39
H2O2* → H2O2	0.26		0.17
H2O2* → OH* – OH*	–1.63	0.21	–1.48	0.51
H2O2* → H2O2* + H*	–0.34		–0.21
H2O2* + H* → H2O* – OH*	–2.43	0.11	–2.3	0.49
O2* + 2H* → 2O* + 2H*	–1.16	0.76	–0.81	0.99
2O* + 2H* → OH* + H* + O*	–0.42	1.08	–0.19	0.58
OH* + H* + O* → OH* + OH	–0.37	1.14	–1.16	0.37
OH* + OH → H2O* + O*	–0.50	0.42	–0.40	0.42

^aThe asterisks denote adsorbed atoms.

Table 2. Adsorption Energy (E_ads) of the Intermediate States on Pd and PdAu Surfaces with Respect to a Free O₂ Molecule and a Reference Surface^a.

	Pd	PdAu
intermediate	Eads/eV	Eads/eV
O2* + 2H*	–1.22	–0.78
O2H* + H*	–1.33	–0.88
H2O2*	–1.54	–1.46
H2O2* – H*	–1.89	–1.66
H2O* – OH*	–4.30	–3.96
2O* + 2H*	–2.38	–1.58
OH* + H* + O*	–2.80	–1.77
OH* + OH*	–3.17	–2.93
H2O* + O*	–3.67	–3.33

^aThe asterisks denote adsorbed atoms.

Figure 2.

(a) Reaction pathway for the hydrogen peroxide formation from its elements, and for the competitive formation of water or hydroxyl groups on Pd and PdAu surfaces. (b) Energy profile of the full acetylene hydrogenation mechanism on Pd and AgPd surfaces.

The first reaction step of the H₂O₂ direct synthesis mechanism on Pd and PdAu surfaces is the adsorption of molecular O₂. This process is exothermic (−1.22 eV for Pd and −0.78 eV for PdAu, 1 eV = 96 kJ mol^–1) on both the surfaces where the O₂ molecule adsorbed on a tfcc configuration on the Pd while it adsorbed on a tbt configuration on the PdAu surface. The O–O bond stretches from 1.23 Å in the gas phase to 1.36 Å on the Pd and 1.31 Å on the PdAu surfaces. On the Pd surface, the charge transfer to the oxygen atom on the fcc site (−0.29 e) is slightly larger than to the atom on the top site (−0.23 e), thus causing the magnetic moment of the atom at the top site to be slightly smaller. On the PdAu surface, the charge transfer to both the oxygen atoms (−0.20 e) is similar and the partial magnetic moment for each atom is 0.27 μ_B. Table 3 compiles the charges and magnetic moments that characterize O₂, OOH, and H₂O₂ species. This behavior of O₂ molecule on both Pd and PdAu surfaces is compatible with a superoxo (O₂^–) character. These results indicate that O₂^* cleavage to 2O* is more feasible on the Pd surface than that on the PdAu one.

Table 3. Atomic (Δq_O) and Molecular (Δq_tot) Bader Charges, Partial (μ_O) and Total (μ_tot) Magnetic Moment, and the O–O Bond Length (d_O–O) for O₂, OOH, and H₂O₂ in the Gas Phase, on Pd(111) and on PdAu(111) Surfaces^a.

species		ΔqO e	Δqtot e	μO, μB	μtot, μB	dO–O, Å
O2	gas phase			0.85	1.70	1.23
	Pd(111)	–0.23b (−0.29)c	–0.52	0.10b (0.09)c	0.19	1.36
	PdAu(111)	–0.20	–0.40	0.27	0.54	1.31
OOH	gas phase			0.60 (0.25)d	0.85	1.35
	Pd(111)	–0.19 (−0.20)d	–1.01	0.08 (0.03)d	0.11	1.50
	PdAu(111)	–0.13 (−0.15)d	–0.90	0.00 (0.00)d	0.00	1.44
H2O2	gas phase			0.0	0.0	1.47
	Pd(111)	–0.04	–0.08	0.02	0.04	1.52
	PdAu(111)	–0.02		0.00	0.0	1.48

^aThe values in parenthesis refer to the oxygen atom:

^bon top site,

^con fcc site,

^dbound to hydrogen.

Hydrogenation of O₂ leads to the formation of the key peroxyl (OOH) intermediate. On both the surfaces, this process is exothermic and energetically more favorable than the dissociation to 2O*. The reaction energy and activation barrier for this reaction on the clean surface are −0.11 and 0.68 eV. The corresponding values on the top PdAu surface are −0.22 and 0.68 eV. The O–O bond length of the OOH intermediate on Pd and PdAu surfaces is 1.50 and 1.44 Å, respectively, which is compatible with a peroxo (O₂^2–) bond length. The smaller bond length of O–O indicates that on the PdAu surface OOH dissociation on PdAu is more impeded than on the clean surface.

The addition of the second hydrogen atom to the OOH intermediate leads to the formation of H₂O₂^*; at the same time, this process also may yield water. In addition, the dissociation of OOH* to O* + OH* may happen as well. On the clean surface, the barrier energy of both side reactions is lower than the formation of H₂O₂ limiting the selectivity of the clean Pd surface as a catalyst. Dissociation of the OOH* intermediate to OH* + O* is hindered by 0.44 eV on the bare surface.

However, as shown in Figure 2a, different positions for OOH hydrogenation are possible: the attack on the already hydrogenated O, or as syn or trans on the nonhydrogenated one. The first reaction on the bare surface is hindered by a barrier of 0.35 eV and leads to the formation of coadsorbed water and oxygen (H₂O* + O*). As for the two attacks on the resting O both lead to the formation of H₂O₂, the barrier being 0.89 eV with a reaction energy of −0.21 eV, which indicates that this is an exothermic process. Hydrogenation of OOH on the PdAu surface is more exothermic than that on the clean surface with an activation barrier and reaction energy of 0.39 and −0.45 eV, respectively, thereby the PdAu surface should be more selective than the clean Pd surface for H₂O₂ formation. This process on the PdAu surface has lower energetic requirements than side reactions (0.53 eV for OH* + O* and 0.56 eV for H₂O* + O*). This means that the two channels for selectivity reduction (OOH breaking and over hydrogenation to H₂O* + O*) are no longer open. The bond length of O–O in H₂O₂ on the PdAu surface is 1.48 Å which is smaller than that on top of the clean surface (1.52 Å) (Table 3).

Still two routes are possible for dissociation of this moiety on the surface, namely, direct decomposition to 2OH or over hydrogenation to coadsorbed water and a hydroxyl group. The activation barriers for decomposition and over hydrogenation on the bare Pd surface are smaller than H₂O₂ desorption. By comparing the H₂O₂ steps, it can be judged that on the clean Pd surface no H₂O₂ will be obtained. In contrast, the barrier for H₂O₂ desorption on the PdAu surface is lower than the barriers for H₂O₂ decomposition and over hydrogenation. As a result, other intermediates cannot compete with H₂O₂ desorption and H₂O₂ will be desorbed from the PdAu surface.

On the other hand, oxygen can dissociate to 2O* on the surface and the process is detrimental to selectivity. However, the activation energy for this reaction on both surfaces is smaller than that of the desired hydrogenation to OOH* this barrier energy is increased by 0.23 eV on the PdAu surface with respect to the Pd one. This process on both Pd and PdAu surfaces is exothermic with a reaction energy of −1.16 and −0.81 eV. The next side reaction is hydrogenation of oxygen atoms: the first hydrogenation on both surfaces has a higher barrier than the second one. The last side reaction (OH* + OH* → H₂O* + O*) has the same barrier energy (0.42 eV) on both surfaces with a reaction energy of −0.5 and −0.4 eV for Pd and PdAu surfaces, respectively.

PdAu alloys have been found to be active and selective in different reactions showing complex mechanisms. In the present case the first main difference with the clean Pd(111) surface is the increase in the barrier for O₂ dissociation for the PdAu case with respect to the Pd one (from 0.76 to 0.99 eV). This is due to two main aspects, first due to the presence of Au blocks, active sites enforce a different path for O₂ dissociation, see Figure 3. In addition, hydrogen transfer is eased because of the presence of Au on the surface; the result being a better branching reaction than in the previous case. In addition, the resting hydrogenation reactions are also more competitive than in the previous case, thus reducing side reactions.

Figure 3.

Initial, final, and transition state for the decomposition of molecular oxygen on the Pd surface, and on a gold-containing alloy, PdAu.

2.2. Acetylene Hydrogenation on Pd and AgPd Surfaces

The reaction scheme for acetylene hydrogenation is also described in Figure 1b. The complete reaction pathways of acetylene hydrogenation with all respective reaction energies and activation barriers are reported in Table 4. In addition, the adsorption energies for all intermediate states are reported in Table 5. The full energy profiles for the acetylene hydrogenation mechanism on Pd and AgPd surfaces are illustrated in Figure 2b. The reaction network starts by the adsorption of the alkyne on the surface, which is considerably exothermic on Pd(111) by −2.51 while it is slightly exothermic on AgPd by—0.05 eV (with respect to gas-phase acetylene and H₂). Afterward, the sequential addition of the H atom follows a Horiuti–Polanyi mechanism.²⁵ The first hydrogenation of the adsorbed acetylene moiety is exothermic and leads to a single product vinyl (HCCH₂) on both surfaces. The reaction energies for this step are −0.17 and −1.26 eV with activation barriers of 0.67 and 0.77 eV on Pd and AgPd, respectively. The second hydrogen addition can result in two competitive products, ethene (H₂CCH₂) or ethylidene (HCCH₃). The formation of the former features E_a of 0.66 and 1.36 eV for Pd and AgPd, respectively, and show an exothermic behavior by −0.31 and −1.52 eV. Because of kinetic reason, ethane formation on the clean Pd surface is more favored than the formation of ethylidene, where E_a is 0.72 eV and ΔE is +0.05 eV. While ethylene formation on AgPd is impeded because the barrier of vinyl hydrogenation to ethylidene (HCCH₃) is lower (E_a = 0.92 and ΔE = −0.41). At this stage, the H₂CCH₂ desorption could eventually undergo over hydrogenation to ethyl (H₂CCH₃). The desorption of H₂CCH₂ is impeded on Pd(111) surface since its energy (0.85 eV) is higher than the third hydrogenation barrier (0.45 eV) whereas on AgPd surface (E_a = 0.68 eV) it is energetically advantageous over its further hydrogenation (1.21 eV). The ethyl formation on both surfaces is exothermic by a reaction energy of −0.20 and −0.24 eV for clean Pd and AgPd surfaces, respectively. On the other hand, HCCH₃ hydrogenation can also lead to H₂CCH₃ formation which is exothermic on both surfaces by −0.54 and −1.35 eV and a barrier of 1.07 and 0.52 eV for Pd and AgPd. The fourth hydrogenation leads to ethane which is exothermic on both surfaces with a reaction energy (activation barrier) of −0.67 (0.44) eV on Pd and −1.10 (1.46) eV on AgPd. The last step is ethane desorption which is easy on the Pd (0.05 eV) surface while it has a reaction energy of 0.38 eV on the AgPd surface.

Table 4. Reaction Energy, ΔE, and Corresponding Activation Barrier, E_a, for the Elementary Steps in Acetylene Hydrogenation on Pd(111) and AgPd(111) Surfaces^a.

	Pd		AgPd
elementary step	ΔE/eV	Ea/eV	ΔE/eV	Ea/eV
HCCH* + H* → HCCH2*	–0.17	0.67	–1.26	0.77
HCCH2* + H* → H2CCH2	–0.31	0.66	–1.52	1.36
HCCH2 + H* → HCCH3*	0.05	0.72	–0.41	0.92
H2CCH2* → H2CCH2	0.85		0.68
H2CCH2* + H* → H2CCH3	–0.20	0.45	–0.24	1.21
HCCH3* + H* →H2CCH3	–0.54	1.07	–1.35	0.52
H2CCH3* + H* → H3CCH3	–0.67	0.44	–1.1	1.46
H3CCH3* → H3CCH3	0.05		0.38

^aThe asterisks denote the adsorbed species.

Table 5. Adsorption Energy, ΔE_ads, of the Intermediate Species on the Pd(111) and AgPd(111) Surfaces with Respect to a Free HCCH Molecule and a Reference Surface.

	Pd	AgPd
intermediate	Eads/eV	Eads/eV
HCCH*	–2.51	–0.05
HCCH2*	–2.68	–1.31
HCCH3*	–2.64	–1.72
H2CCH2*	–2.99	–2.83
H2CCH3*	–3.18	–3.07
H3CCH3*	–3.85	–4.17

2.3. Dynamic Properties of Intermediates

An important aspect concerns the dynamic properties of hydroperoxide on the surface. Figure S1 depicts the top views of the DFT-optimized adsorption configuration of the OOH and HCCH₂ intermediates on different surfaces that we used for MD calculations. The OOH intermediate fluctuates between the 6 Pd atoms neighboring the Pd–O bond; rotation of this moiety requires an energy of 0.10 eV on the Pd surface. The fluctuation of this system on the PdAu surface occurs between the two pairs of Pd atoms separated by Au atoms (Figure 4a). The barrier for OOH rotation on the PdAu surface is 0.16 eV which is greater than that on the Pd surface. The Born-Oppenheimer MD (BOMD) results unveiled that the OOH fluctuation is limited in a small area on both the Pd and PdAu surface at 300 K (Figure S2). By increasing the temperature to 400 K our results show that OOH has a complete rotation on the bare Pd surface while no rotation has been seen for this moiety on the PdAu surface. Figure 4c,d and Movies 1 and 2 illustrate the BOMD results for OOH on clean Pd and PdAu surfaces. In addition, the OH group rotates also almost freely along the O–O atom. The potential energy surface for the dynamics OH group at 300 and 400 K is shown in Figure S3. Both movements effectively lead to the unselective hydrogenation of OOH or its dissociation over the bare Pd surface because the contact time with the active Pd site is smaller than any other process, and thus only the already hydrogenated O in the hydroxyl group can be attacked by H. In contrast, the nonhydrogenated oxygen of the hydroxyl group can be attacked by hydrogen atoms over the PdAu surface resulting in the H₂O₂ product.

Figure 4.

Dynamics properties of hydroperoxide (O₂H) and vinyl (HCCH₂) on the surface: (a) barrier for rotation of the O₂H intermediate on Pd and PdAu surfaces, (b) barrier for rotation of the HCCH₂ on Pd and AgPd surfaces, trajectory of two oxygen atoms in the O₂H intermediate on Pd(c) and PdAu(d) at 400 K from the BOMD simulation, and trajectory of two carbon atoms in the HCCH₂ intermediate on Pd (e) and AgPd (f) at 473 K from the BOMD simulation. Color code: oxygen (red cycle), carbon (black cycle), hydrogen (light grey cycle), Pd (blue cycle), Au (orange cycle), and Ag (dark yellow cycle).

On the other hand, rotation of the HCCH₂ intermediate requires an energy of 0.26 eV on the Pd surface which is much greater than the barrier on the AgPd surface (0.025 eV) which means rotation on the AgPd surface is easier. The energy barrier for HCCH₂ fluctuation on Pd and AgPd surfaces is depicted in Figure 4b. The BOMD results revealed that the HCCH₂ fluctuation is limited in a small area between 3 Pd atoms on the clean Pd surface at 473 K while a complete rotation occurred for this moiety on the AgPd surface (Figure 4e,f and Movies 3 and 4). This movement over the PdAg surface effectively blocks the selective semihydrogenation to H₂CCH₂ formation. While on the bare Pd surface, limited HCCH₂ fluctuation leads to the HC head of the HCCH₂ molecule to be attacked by H which forms H₂CCH₂.

3. Conclusions

We have analyzed the O₂ hydrogenation in the direct synthesis of the water peroxide mechanism on Pd and PdAu surfaces and the alkyne hydrogenation to alkene over Pd and AgPd surfaces by means of DFT. Particularly, the energy profiles of hydroperoxide (OOH) and vinyl (HCCH₂) hydrogenation over both bare and alloyed surfaces were compared to each other. Moreover, BOMD were performed to study the dynamic aspects of OOH and HCCH₂ intermediates in the selectivity of hydrogenation by heterogeneous catalysts. Our results show that OOH hydrogenation on the PdAu surface is more exothermic than that on the clean Pd surface, thereby the PdAu surface should be more selective than the clean Pd surface for H₂O₂ formation. On the clean Pd surface, the barrier energy of side reactions (OOH* dissociation and water formation) is lower than the formation of H₂O₂ limiting the selectivity of the clean Pd surface as a catalyst. The BOMD results confirm that the OOH intermediate has a complete rotation on the bare Pd surface while no rotation has been seen for this moiety on the PdAu surface. Therefore, only the already hydrogenated O in the hydroxyl group can be attacked by H over the bare Pd surface resulting in water formation. In contrast, on the PdAu surface the nonhydrogenated oxygen of OOH can be attacked by hydrogen atoms which lead to the H₂O₂ product. Likewise, the complete rotation of the HCCH₂ intermediate on the AgPd surface effectively blocks the selective semi-hydrogenation to H₂CCH₂ formation. This moiety has limited fluctuation on the bare Pd surface resulting in higher selectivity toward formation of H₂CCH₂ in comparison with the AgPd surface. Our results show that intermediate dynamics control selectivity in hydrogenation by heterogeneous catalysis.

4. Computational Methods

DFT calculations in this study were performed using the Vienna Ab initio Simulation Package,²⁶ with the generalized gradient approximation, and the revised Perdew–Burke–Ernzerhof²⁷ functional as exchange–correlation functional to obtain the energy. Spin-polarized effects were taken into account for intermediates including oxygen atoms. Monoelectronic valence states were expanded in plane waves with kinetic cutoff energy of 450 eV, while core electrons were described with the projected augmented wave method.²⁸ In all calculations, van der Waals contributions were described using the semiempirical DFT-D2 approach^29,30 and the parameters were reoptimized for this metal.³¹ All calculations were performed on the (111) surfaces as it is the most stable for fcc metals. The clean Pd and Ag slabs were modeled by a slab consisting of a 3 × 3 surface unit cell whereas a 4 × 2 surface unit cell was used to study the hydrogenation reactions on the alloyed slabs (PdAu and AgPd). In all calculations, each slab contained five atomic layers (the three at the bottom were fixed and the two on the top were fully relaxed) and an empty space of 15 Å was introduced in the direction perpendicular to the surfaces (z-direction), which ensured that the interaction between the adsorbed molecules and the periodic images of the slabs is negligible. Sampling of the Brillouin zones was performed by using the Monkhorst–Pack methodology with gamma-centered k-point 4 × 4 × 1 and 3 × 6 × 1 grids for the clean and alloyed surfaces, respectively. The Climbing Image-modified Nudged Elastic Band method^32,33 was used to assess the activation energies of the different reaction paths. The nature of all reaction minima and transition states was confirmed by means of numerical frequency analyses obtained from the numerical Hessian calculated with displacements of 0.015 Å. The PdAu slabs were represented by a substitutional model where only a 0.25 ML of Pd atoms on the surface was replaced by Au atoms. Under these conditions Au atoms tend to stay on the surface because of the lower surface energy of Au that provokes segregation of the surface.³⁴ In the AgPd slabs only a 0.125 ML of Ag atoms on the surface was replaced by Pd atoms.

Standard BOMD were performed on the same slabs under the NVT ensemble. BOMD calculations for the OOH intermediate were performed at 300 and 400 K while the temperature for the CHCH₂ intermediate was set to 473 K controlled.^35,36 All BOMD runs were performed over 11 ps for OOH and over 20 ps for CHCH₂ using a time step of 1 fs.

Supporting Information Available

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsomega.9b03845.

• Movie of the fluctuation of the hydroperoxide (O₂H) intermediate on the Pd surface by BOMD calculations (MP4)

• Movie of the fluctuation of the hydroperoxide (O₂H) intermediate on the PdAu surface by BOMD calculations (MP4)

• Movie of the fluctuation of the HCCH₂ intermediate on the Pd surface (MP4)

• Movie of the fluctuation of the HCCH₂ intermediate on the AgPd surface (MP4)

• The DFT-optimized adsorption configuration of the OOH and HCCH₂ intermediates on different surfaces; trajectory of two oxygen atoms in the O₂H intermediate on Pd and PdAu at 300 K from the BOMD simulation; and dynamics properties of hydroperoxide (O₂H) on the Pd and PdAu surfaces at 300 and 400 K from the BOMD simulation (PDF)

The author declares no competing financial interest.