Self-Organization of Alloy Catalysts into Selectively Active Ensembles

Abstract

The active sites of alloy catalysts may emerge only under reaction conditions, yet how reactive atmospheres select these sites remains unresolved. Here, we reveal how reactive atmospheres reorganize complex alloy surfaces into functional active-state distributions by using a machine-learning-potential-accelerated multiscale framework. Using selective acetylene hydrogenation on Pd–Ag alloys as a model reaction, we show that adsorbates reverse the intrinsic Ag-segregation tendency, enrich Pd in the outermost layer, and generate a distribution of Pd₃ hollow ensembles with distinct second-shell coordination environments. These dynamically formed ensembles, rather than the as-prepared isolated Pd sites, govern the calculated activity and selectivity trends. Ensemble-resolved energetics and kinetics identify the adsorption free-energy gap between ethylene and acetylene as a predictive descriptor that captures the activity-selectivity trade-off and defines an optimal window balancing acetylene hydrogenation and ethylene desorption. Extending the analysis across multiple alloy families further reveals a general scaling relationship in which adsorbate-driven self-organization is governed by adsorption asymmetry and alloy stability. These results establish dynamic ensemble selection as a transferable framework for understanding and designing adaptive alloy catalysts, shifting catalyst optimization from static structural descriptors toward reaction-condition-directed control of active-state distributions.

Introduction

Alloy catalysts are prized for their tunable geometric and electronic properties, which have made them indispensable in many catalytic processes. − However, this very tunability implies that their surface composition and structure can, and often do, respond dynamically to temperature, pressure, and adsorbate chemical potential. − Catalytic performance, however, is still routinely interpreted from the static as-prepared structurean assumption that is fundamentally insufficient for systems operating under reactive atmospheres. A central challenge in heterogeneous catalysis is therefore to determine whether the catalytically relevant state is encoded in the initial alloy or instead emerges operando through environment-driven restructuring.

This issue is especially acute in selective hydrogenation, where the catalytic performance depends sensitively on the balance between substrate activation and product release. − Even modest changes in the surface composition, ensemble size, or local coordination can induce disproportionate changes in activity, selectivity, and stability. However, the active state is still often inferred from nominal alloy composition, average dispersion, or simplified static site models rather than being resolved under working conditions. A predictive description of alloy catalysis thus requires treating adsorption, segregation, and reaction kinetics as coupled processes so that dynamic surface evolution can be linked directly to the catalytic function.

Selective hydrogenation of trace acetylene in ethylene-rich streams provides a stringent test of this issue. This reaction is a key purification step in the production of polymer-grade ethylene, and under industrial tail-end conditions, the catalyst must remove acetylene in the presence of excess ethylene and hydrogen within a narrow operating window. − Insufficient acetylene conversion compromises product purity, whereas excessive hydrogenation consumes valuable amounts of ethylene, results in the formation of ethane, and accelerates the deposition of oligomeric green oil, thereby decreasing the catalyst stability. Pd-based catalysts remain highly effective because they efficiently activate H₂ and rapidly hydrogenate alkynes; however, these same properties can also promote product retention, overhydrogenation, and deactivation when reactive intermediates and products compete for common surface sites. − The challenge is therefore not simply to increase reactivity but also to impose a surface state that activates acetylene efficiently while suppressing ethylene retention and further hydrogenation.

Pd–Ag alloys are among the most successful materials for overcoming this trade-off and are commonly interpreted in terms of geometric dilution and ligand effects. In this context, Ag disrupts extended Pd ensembles and weakens ethylene adsorption, thereby facilitating desorption and suppressing overhydrogenation. − Although these ideas capture useful trends, they rely on a largely static view of the alloy structure. They do not explain why performance depends so sensitively on the alloy composition, feed ratio, temperature, or pretreatment history, nor do they identify the active surface that actually exists under reaction conditions. More fundamentally, they overlook the possibility that the reacting atmosphere itself may reorganize the alloy into a different steady-state ensemble landscape. This raises a central unresolved question: what alloy surface is actually present under reaction conditions during selective acetylene hydrogenation, and how does the operando surface determine the activity–selectivity trade-off?

Here, we use Pd–Ag acetylene hydrogenation not only as a specific catalytic system but also as a model platform for resolving active-state formation in adaptive alloy catalysts. By integrating machine-learning-potential-accelerated hybrid grand-canonical Monte Carlo–molecular dynamics simulations with ensemble-resolved free-energy analysis and microkinetic modeling, we directly capture the coupled evolution of adsorbates, surface segregation, local ordering, and catalytic turnover under reaction chemical potentials. This framework predicts that the working Pd–Ag surface is not simply a static Ag-diluted alloy but a reaction-selected ensemble landscape in which adsorbates reverse the vacuum segregation tendency, enrich Pd in the outermost layer, and generate Pd₃ hollow motifs with tunable second-shell coordination. These dynamically formed Pd₃ ensembles control the MKM-derived activity-selectivity balance through a simple adsorption-energy gap descriptor, thereby rationalizing experimentally reported composition-dependent performance trends and the optimal Ag content observed in Pd–Ag catalysts. More broadly, extension to multiple alloy families demonstrates that adsorbate-driven self-organization follows a general scaling relationship governed by adsorption asymmetry and alloy stability. In this way, the present work moves beyond a static description of Pd–Ag acetylene hydrogenation and establishes a transferable framework for predicting and designing reaction-condition-selected active ensembles in alloy catalysis (Scheme ).

1. Self-Organization of Catalytic Alloys into Selectively Active Ensembles .

^a Panel 1 shows the as-prepared Pd₁Ag₃(111) surface with isolated Pd sites in an Ag matrix. Panel 2 illustrates the adsorbate-driven surface reorganization that reverses the vacuum segregation tendency. Panel 3 highlights an optimal ΔG window (where ΔG = ΔG _ads(C₂H₄) – ΔG _ads(C₂H₂)) that balances C₂H₂ activation and C₂H₄ release. Panel 4 summarizes the design principle, where the segregation ratio R is determined by adsorption asymmetry and alloy stability.

Thermodynamic Properties of Pd–Ag Alloys: Bulk and Surface Perspectives

Establishing the thermodynamic baseline of Pd–Ag alloys is essential for understanding surface evolution under reaction conditions. Density functional theory (DFT) calculations revealed that Pd and Ag form exothermic solid solutions across the full composition range while retaining the face-centered cubic lattice (Figures a, S1, and Table S1). The formation energies are shallow, reaching a minimum of −0.06 eV atom^–1 near Pd₁Ag₃, indicating weak Pd–Ag interactions and a near-surface composition that is readily perturbed by adsorbates. Notably, this composition matches the Pd:Ag ratios commonly used in industrial acetylene hydrogenation catalysts (≈1:3–1:4).

1.

Thermodynamic drivers of bulk mixing and adsorbate-induced surface restructuring in Pd–Ag alloys. (a) DFT-calculated formation energies of fcc Pd–Ag alloys as a function of composition. (b) Adsorption energies of C₂H₂, C₂H₄, and H on the Pd(111), Ag(111), and Pd₁Ag₃(111) surfaces. Insets depict side views of the corresponding C₂H₂ adsorption configurations. Color scheme: Pd (cyan), Ag (purple), C (gray), H (white), maintained throughout. (c) Relative surface energies as a function of the top-layer Pd composition at 373 K under vacuum (red, reference state), acetylene adsorption (blue), and hydrogen atom adsorption (green). Relative energies are defined with respect to pure Pd, pure Ag, and the corresponding gas-phase molecule (C₂H₂ or H₂). Reaction conditions: P(C₂H₂) = 0.33 atm, P(H₂) = 0.67 atm. (d) Top views of the optimized adsorption geometries on surfaces with increasing Pd content in the top layer (Pd₀ to Pd₄). (e) Energy changes associated with key subsurface processes: carbon/hydrogen incorporation and Pd/Ag atomic exchange. (f) Standard deviation of the vertical positions of top-layer Pd atoms (σ _z (Pd_top)) obtained from a 10 ps AIMD simulation at 373 K under saturating C₂H₂ coverage.

To evaluate how reactive adsorbates influence surface composition, we compared the adsorption energetics of C₂H₂, C₂H₄, and H on Ag(111), Pd(111), and Pd₁Ag₃(111), where the alloy surface features isolated Pd atoms embedded in Ag (Figures b and S2). Ag(111) interacts only weakly with C₂ species (ΔE _ads ≈ 0 eV) and binds H endothermically (+0.19 eV), whereas Pd(111) strongly chemisorbs all three adsorbates (C₂H₂ – 2.06 eV; C₂H₄ – 0.92 eV; H – 0.62 eV). In contrast, Pd₁Ag₃(111) shows intermediate behavior but with nearly identical adsorption energies for C₂H₂ and C₂H₄ (−0.63 and −0.62 eV, respectively) and substantially weakened H adsorption (−0.17 eV). This strong contrast between Pd- and Ag-rich environments indicates that adsorption thermodynamics can provide a substantial driving force for Pd enrichment in the outermost layer under reactive conditions.

We quantified this restructuring tendency by varying the top-layer Pd fraction in a p(2 × 2) slab under representative tail-end conditions (373 K; P(C₂H₂) = 0.33 atm; P(H₂) = 0.67 atm). , Under vacuum, the minimum surface free energy corresponds to Ag termination, which is consistent with the lower surface energy of Ag (Figures c,d, S3, and Table S2). In a C₂H₂ atmosphere, however, the most stable surface state shifts sharply to ∼0.75 ML Pd in the top layer, reflecting strong Pd–C interactions and stabilization of Pd₃ hollow motifs. Under H₂ alone, the preferred Pd fraction is lower (∼0.50 ML), and the thermodynamic stabilization is weaker, which is consistent with weaker H adsorption. These results show that realistic reaction chemical potentials of C₂H₂ and H₂ an partially or fully reverse the intrinsic segregation tendency, thereby biasing the surface toward contiguous Pd ensembles despite the Ag-rich bulk.

Finally, we examined whether this restructuring extends into the subsurface. Subsurface processes, including C/H incorporation and Pd/Ag exchange into deeper layers, are strongly endothermic (Figures e and S4), indicating that restructuring is largely confined to the outermost layer, while the subsurface remains close to the Pd₁Ag₃ bulk composition. Ab initio molecular dynamics (AIMD) simulations of a Pd-enriched top layer under saturating C₂H₂ coverage further show limited vertical mobility, with the standard deviation of the vertical positions of top-layer Pd atoms (σ _z (Pd_top)) between 0.05 and 0.23 Å and a peak-to-peak height variation below 1 Å (Figures f and S5). Therefore, the dominant structural response observed in AIMD is lateral rearrangement within the surface plane rather than substantial rumpling, likely assisted by tensile strain from the larger Ag lattice, which stabilizes Pd in the plane.

Atomic-Scale Evolution of the Pd₁Ag₃(111) Surface under Reaction Conditions

To capture restructuring beyond small-cell constraints, we modeled Pd₁Ag₃(111) using an extended p(10 × 10) slab, which enables lateral heterogeneity and mesoscale ordering to emerge without artificial periodic coupling. Under representative tail-end conditions (373 K; P(C₂H₂) = 0.33 atm, P(H₂) = 0.67 atm, P(C₂H₄) = 9 atm, and P(C₂H₆) = 0.1 atm), we employed a hybrid grand-canonical Monte Carlo–molecular dynamics (GCMC–MD) workflow accelerated by the recursively embedded atom neural network (REANN) potential (Figures a and S6). ,, This approach enables direct determination of the steady-state surface composition and dynamic structure of Pd₁Ag₃(111) under realistic reaction conditions. During each cycle, GCMC movesincluding adsorption, reaction, desorption, and metal-exchange eventsevolve both the surface composition and adsorbate population, followed by 1 ns of NVT MD to relax the interface, promote adsorbate diffusion, and allow further surface ordering (see the Supplementary Methodology).

2.

Atomic-scale restructuring of the Pd₁Ag₃(111) surface under reaction conditions. (a) Schematic of the hybrid GCMC–MD simulation protocol used to model the coevolution of adsorbates and surface metal atoms on a p(10 × 10) slab under representative tail-end feed conditions (373 K; P(C₂H₂) = 0.33 atm, P(H₂) = 0.67 atm, P(C₂H₄) = 9 atm, P(C₂H₆) = 0.1 atm). (b) Definition of the coordination environment for an adsorbed C₂H _x species, showing the first (R ₁ = 3.0 Å) and second (R ₂ = 5.5 Å) coordination shells. (c) Atomic structures of the initial Pd₁Ag₃(111) and the five identified coordination environments, denoted as Pd₃@Pd₅Ag₄, Pd₃@Pd₆Ag₃, Pd₃@Pd₇Ag₂, Pd₃@Pd₈Ag₁, and Pd₃@Pd₉Ag₀. (d) Probability distribution of the five distinct active-site motifs shown in panel (c). (e) Potential energy surface for exchanging a surface Pd atom with a neighboring Ag atom under vacuum and in the presence of adsorbed C₂H₂.

The simulations converge to a mixed C₂H _x (C₂H₂/C₂H₃) coverage of ∼ 0.38 ML and reveal a pronounced, adsorbate-driven compositional response: the top-layer Pd fraction increases from the nominal 0.25 to 0.84 (Figure S7). To classify the resulting reactive environments in a chemically meaningful way, we defined local coordination shells around each adsorbed C₂H _x species (R ₁ = 3.0 Å for the first shell; R ₂ = 5.5 Å for the second shell; Figure b). All first-shell neighbors are Pd, indicating that Pd₃ hollow sites constitute the dominant binding motifs. The key variability therefore shifts to the second shell (nine metal atoms), which tunes the local electronic and strain environment without changing the immediate Pd₃ geometry. Statistical analysis revealed five prevalent second-shell components, denoted as Pd₃@Pd₅Ag₄, Pd₃@Pd₆Ag₃, Pd₃@Pd₇Ag₂, Pd₃@Pd₈Ag₁, and Pd₃@Pd₉Ag₀, where the notation Pd₃@Pd _x Ag _y indicates a Pd₃ hollow ensemble with x = number of second-shell Pd atoms and y = number of second-shell Ag atoms (x + y = 9).

The distribution is centered at Pd₃@Pd₇Ag₂ (47%), with substantial populations of Pd₃@Pd₆Ag₃ and Pd₃@Pd₈Ag₁ (21% each) and minor fractions of Pd₃@Pd₅Ag₄ and Pd₃@Pd₉Ag₀ (3% and 8%) (Figure c,d). This ensemble distribution is consistent with strong surface Pd enrichment but does not indicate macroscopic phase separation. Instead, it describes a Pd-rich surface containing incorporated Ag atoms that modulate the local second-shell coordination environment. The Pd–Ag(111) interface can therefore be viewed as a laterally dispersed population of Pd₃ hollow ensembles embedded in a Pd-rich surface, with tunable second-shell Pd/Ag coordination that generates a spectrum of distinct catalytic microenvironments.

The term Pd₃ hollow ensemble denotes the three first-shell Pd atoms directly coordinating the adsorbate and does not necessarily describe the full size of the connected Pd-rich region. Pd₃ hollow sites can therefore be embedded in a more Pd-rich second-shell environment, such as Pd₃@Pd₉Ag₀. The GCMC-derived ensemble distribution reflects thermodynamic probabilities under the imposed chemical potentials and adsorbate environment, indicating that larger Pd-rich ensembles are thermodynamically less favored under the present conditions rather than being directly kinetically excluded.

The second-shell composition around Pd₃ hollow sites is not a purely stochastic decoration. Instead, it is determined by the interplay of the Pd–Ag chemical-potential constraint, adsorbate-induced Pd enrichment, Pd–Ag alloy stability, and local structural relaxation. While C₂H _x adsorption promotes Pd enrichment near the adsorption site, excessive Pd enrichment is opposed by alloy thermodynamics, adsorbate–adsorbate repulsion, and lattice-mismatch strain, resulting in a thermodynamically selected distribution of second-shell ensembles under reaction conditions.

To assess how the parent Pd/Ag composition influences the reconstructed surface ensembles, we performed additional GCMC–MD simulations using Pd–Ag chemical potentials derived from Pd₁Ag₃ and Pd₂Ag₂ bulk-alloy reservoirs under otherwise identical reaction conditions (Figures S8–S9). The Pd-rich Pd₂Ag₂-derived reservoir leads to stronger surface Pd enrichment, increasing the top-layer Pd fraction from the nominal 50% to ∼88%, whereas the Ag-rich Pd₁Ag₃-derived reservoir yields a lower but still substantial enrichment from the nominal 25% to ∼67% and favors more Ag-containing second shells. In both cases, adsorbate-driven Pd₃ hollow ensemble formation is retained, indicating that the restructuring mechanism is robust over the tested range of parent alloy compositions.

We validated these motifs using explicit DFT calculations on p(4 × 4) slabs by systematically increasing the surface Pd content while placing 1–6 C₂H₂ molecules to stabilize Pd hollow sites (Figure S10). Stable configurations were obtained at C₂H₂ coverages of 0.25 ML (75% surface Pd), 0.31 ML (87.5% surface Pd), and 0.38 ML (100% surface Pd), with comparable total energies across these states, which is consistent with the near-degeneracy implied by the REANN-accelerated sampling. The slightly higher C₂H _x coverage obtained from GCMC–MD relative to the pure C₂H₂ DFT survey can be rationalized by coadsorbed C₂H₃, whose more extended binding footprint reduces the number of blocked metal atoms per adsorbate and thus permits a marginally larger steady-state hydrocarbon population (Figure S7).

We further tested the sensitivity of Pd₁Ag₃(111) segregation energetics under C₂H₂ adsorption to the exchange–correlation functional using PBE+vdW and RPBE (Figure S11). Both benchmark functionals support the conclusion that C₂H₂ adsorption can promote Pd enrichment and Pd₃ ensemble formation. Specifically, PBE+vdW predicts stronger stabilization of Pd-rich surface configurations, whereas RPBE predicts weaker stabilization, providing strong- and weak-binding limits for adsorbate–surface interactions. The PBE results fall within the range spanned by these two functionals, indicating that the main conclusions are not based on an outlying functional description.

To assess the microscopic feasibility of this restructuring pathway, we computed the activation barrier for direct Pd/Ag exchange at the surface using explicit DFT calculations (Figures e and S12). Under vacuum, exchanging a surface Pd atom with a neighboring Ag atom to form a Pd–Pd contact requires a high activation barrier of 2.38 eV, which is consistent with kinetically frozen segregation at 373 K and explains why vacuum thermodynamics alone does not result in rapid surface reordering. , In the presence of adsorbed acetylene, however, the activation barrier decreases markedly to 1.30 eV. These results show that C₂H₂ does not simply probe the surface composition but actively reshapes it by stabilizing exchange intermediates and reducing the penalty associated with transiently undercoordinated metal atoms during the swap. Moreover, when a surface Ag vacancy is present, a subsurface Pd atom can segregate to the surface with an activation barrier of only 0.77 eV, providing an additional pathway for Pd enrichment (Figure S13). Notably, these results indicate that pre-existing defects can facilitate Pd enrichment but are not required for adsorbate-induced Pd₃ ensemble formation.

Reaction Energetics of the Pd₁Ag₃(111) Surface

With the surface distribution established, we quantified acetylene and ethylene hydrogenation in five dominant Pd₃ hollow environmentsPd₃@Pd₅Ag₄, Pd₃@Pd₆Ag₃, Pd₃@Pd₇Ag₂, Pd₃@Pd₈Ag₁, and Pd₃@Pd₉Ag₀and benchmarked them against the isolated single-Pd motif of pristine Pd₁Ag₃(111). All DFT-derived free energies were evaluated under representative tail-end conditions (373 K; P(C₂H₂) = 0.33 atm, P(H₂) = 0.67 atm, P(C₂H₄) = 9 atm, and P(C₂H₆) = 0.1 atm). Under this atmosphere, Ag-rich regions remain catalytically inactive because C₂ adsorption is weak and H₂ activation is kinetically hindered, confining turnover to Pd-exposed sites. With respect to these motifs, acetylene semihydrogenation follows the canonical Horiuti–Polanyi sequence (C₂H₂* → C₂H₃* → C₂H₄* → C₂H₅* → C₂H₆*), with hydrogen supplied from nearby hollow reservoirs within the Pd-enriched top layer (Figures a–c and S14–S19).

3.

Ensemble-resolved reaction energetics on the Pd₁Ag₃(111) surface. (a) Horiuti–Polanyi pathway for acetylene hydrogenation on Pd₃ hollow sites embedded in an Ag matrix, with hydrogen supplied from adjacent hollow reservoirs. (b) Top-view optimized transition-state structures for the first and second hydrogenation steps; relevant bonds are highlighted. (c) Gibbs free-energy profiles for the single-Pd motif (gray) and the five prevalent Pd₃@Pd _x Ag _y coordination environments. Transition states (TS1–TS4) are labeled with the corresponding activation barriers in eV. (d) Competition between ethylene desorption, ΔG _des(C₂H₄* → C₂H₄(g) + *), and ethylene overhydrogenation, E _a(C₂H₄* + H* → C₂H₅* + *). (e) C₂H₄ selectivity descriptor, ΔG _s(C₂H₄) = E _a - ΔG _des, comparing the preference for ethylene desorption versus further hydrogenation.

Although the Pd₃ hollow ensembles share an identical first-shell geometry, their second-shell composition substantially alters adsorption thermodynamics and hydrogenation barriers. The acetylene adsorption free energy varies from −0.70 eV on Pd₃@Pd₇Ag₂ to −0.24 eV on Pd₃@Pd₆Ag₃, showing that the effective binding strength is not determined solely by the three first-shell Pd atoms but is also tuned by the nine-atom second shell (Figure c). This second-shell sensitivity also appears in the hydrogenation barriers: the first-step barriers span 0.30–0.76 eV, and the second-step barriers span 0.22–0.73 eV across the ensemble series. Pd₃@Pd₆Ag₃ gives the lowest early step barriers (0.30 and 0.22 eV), whereas the Pd-deficient Pd₃@Pd₅Ag₄ and Pd-rich Pd₃@Pd₉Ag₀ limits are less favorable. These barrier differences are further rationalized below by transition-state H coordination and Pd–H stabilization (Figure b).

Selectivity is governed by the competition between ethylene desorption and overhydrogenation. For all Pd₃ ensembles, ethylene desorption is thermodynamically favorable (ΔG _des = −0.09 to −0.64 eV), whereas the barrier to C₂H₅ formation remains high (E _a ≥ 0.67 eV), indicating a preference for ethylene release over further hydrogenation (Figure d). The isolated single-Pd motif behaves differently, with weak acetylene binding (ΔG _ads(C₂H₂) = +0.08 eV), low early step hydrogenation barriers (E _a = 0.54 and 0.13 eV), and a comparatively accessible ethylene hydrogenation barrier of 0.35 eV. The selectivity metric ΔG _s(C₂H₄) = E _a – ΔG _des provides a semiquantitative measure of the preference for ethylene desorption over overhydrogenation; it exceeds 0.85 eV for all Pd₃ ensembles but is only 0.40 eV for pristine Pd₁Ag₃(111). This contrast supports the hypothesis that, under ethylene-rich feeds, the selective catalytic behavior is primarily associated with operando-formed Pd₃ hollow ensembles rather than isolated Pd atoms. Additional PBE+vdW and RPBE benchmarks for representative ensembles show that the first and second hydrogenation barriers and the C₂H₄ selectivity descriptor preserve the same qualitative ensemble-dependent activity–selectivity trend (Table S3), indicating that this relationship is qualitatively robust with respect to the choice of functional.

Microkinetic Analysis of Selective Hydrogenation

To translate the ensemble-resolved energetics into catalytic performance, we constructed a microkinetic model parametrized with the DFT-derived free energies at 373 K under representative tail-end conditions (P(C₂H₂) = 0.33 atm, P(H₂) = 0.67 atm, P(C₂H₄) = 9 atm, and P(C₂H₆) = 0.1 atm). The kinetics were evaluated independently for each Pd₃ environmentPd₃@Pd₅Ag₄, Pd₃@Pd₆Ag₃, Pd₃@Pd₇Ag₂, Pd₃@Pd₈Ag₁, and Pd₃@Pd₉Ag₀and compared to the isolated single-Pd motif on the pristine Pd₁Ag₃(111) surface (Figure a,b and Tables S4–S5). The resulting rates highlight a pronounced structural sensitivity governed by the second-shell composition. Among the Pd₃ motifs, the Pd₃@Pd₆Ag₃ ensemble is predicted to be the most productive, with an ethylene formation rate of r _C2H4 = 1.3 × 10⁵ s^–1 and the lowest apparent activation energy (E _app = 0.25 eV). The more prevalent Pd₃@Pd₇Ag₂ and Pd₃@Pd₈Ag₁ environments exhibit intermediate activity (r _C2H4 ≈ 10² s^–1; E _app = 0.37–0.39 eV), whereas the Pd-deficient Pd₃@Pd₅Ag₄ and Pd-rich Pd₃@Pd₉Ag₀ limits are relatively sluggish (r _C2H4 = 2.8 and 0.7 s^–1; E _app = 0.61 and 0.58 eV, respectively).

4.

Microkinetic origin of the activity–selectivity trade-off in Pd ₃ ensembles. (a, b) Predicted ethylene formation rates (r _C2H4) and apparent activation energies (E _app) for acetylene hydrogenation at 373 K under industrially relevant feed conditions, evaluated for the five distinct Pd₃ coordination environments and the single-Pd motif. A negative r _C2H4 value indicates net C₂H₄ consumption and is displayed as -log₁₀(-r _C2H4). (c) Catalytic activity is inversely correlated with the adsorption free-energy gap (ΔG), which is plotted as log₁₀(r _C2H4) versus ΔG. The overall reaction energy span from C₂H₂ to C₂H₄ simultaneously increases with ΔG. Owing to its distinct transition-state geometry, the Pd₃@Pd₅Ag₄ ensemble appears as an outlier. (d) Schematic phase diagram illustrating how the descriptor ΔG, tuned by the second-shell Pd coordination, governs catalytic performance. An optimal window for concurrent high activity and selectivity emerges at intermediate ΔG values, where dynamic alloy ordering stabilizes under reaction conditions. The colors denote three regimes of the adsorption free-energy gap: red indicates a large-gap regime with reduced activity due to overstabilization of C₂H₂-derived species, green indicates a small-gap regime with reduced selectivity due to insufficient C₂H₂/C₂H₄ discrimination and ethylene overhydrogenation, and blue indicates the intermediate regime that provides the optimal activity–selectivity balance.

In stark contrast, the unreconstructed single-Pd motif yields net ethylene consumption (negative r _C2H4), which is consistent with its weak acetylene affinity, limited discrimination between C₂H₂ and C₂H₄ adsorption, and a low barrier for undesired ethylene hydrogenation. The negative r _C2H4 does not indicate reversal of a single elementary step but represents the network-level balance between C₂H₄ formation and consumption. The transition from net C₂H₄ production on Pd₃ ensembles to net C₂H₄ consumption on isolated single-Pd motifs reflects competition among multiple pathways in the MKM network, where thermodynamics determine reaction equilibria and site-dependent kinetics control the relative fluxes.

The MKM-derived rates are intrinsic, site-normalized upper-bound estimates for the most active local ensembles. Because C₄ formation, oligomerization, site blocking, particle-size effects, and mass-transport limitations are not included, these rates are not intended to reproduce absolute macroscopic rates. Population weighting by the GCMC-derived ensemble distribution further reduces the contribution of the most active local ensemble to the overall surface activity; therefore, the MKM results are used mainly to compare relative ensemble-dependent activity–selectivity trends.

A central outcome of the microkinetic analysis is that activity trends across the ensembles are captured quantitatively by the adsorption free-energy gap ΔG = ΔG _ads(C₂H₄) – ΔG _ads(C₂H₂). Plotting log₁₀(r _C2H4) versus ΔG reveals a systematic, nonmonotonic dependence (Figure c): turnover is maximized within an intermediate ΔG window, while both small and large ΔG values suppress activity. Physically, a ΔG that is too small decreases the discrimination between acetylene and ethylene, increasing ethylene retention and enabling overhydrogenation, whereas a ΔG that is too large overstabilizes acetylene-derived intermediates and inflates the effective energy span from C₂H₂ to C₂H₄. The Pd₃@Pd₅Ag₄ environment appears to be an outlier (ΔG = 0.77 eV), which is consistent with its distinct transition-state geometry in which H and C₂H₂ compete for the same Pd atom, and H sampling is partially diverted toward inert Ag sites, reducing the benefit expected from ΔG-based scaling.

Collectively, the microkinetic results establish that dynamic alloy ordering is not a secondary perturbation but a prerequisite for selectivity: reaction conditions preferentially generate Pd₃ hollows embedded in Ag with second-shell environments that place ΔG in the optimal regime, maximizing ethylene productivity while suppressing overhydrogenation (Figure d). In this sense, ΔG is both a mechanistic diagnostic and an actionable descriptor that directly links ensemble-dependent adsorption energetics to the MKM-derived activity–selectivity trends. Operational variables (H₂/C₂H₂ ratio, temperature, and coadsorbates) and material variables (Ag content and alternative promoters that tune strain/electronic effects) can steer the steady-state ensemble distributionand thus the effective surface ΔGtoward the high-activity/high-selectivity window defined by the operational catalyst surface.

Structure–Electronic Coupling Underlying Ensemble-Dependent Activity

To elucidate the origin of the ensemble-dependent kinetics, we contrasted the most active Pd₃ environment, Pd₃@Pd₆Ag₃, with the least active extremes, Pd₃@Pd₅Ag₄ and Pd₃@Pd₉Ag₀, which bracket the range of second-shell Ag coordination. Degree-of-rate-control analysis revealed that the first hydrogenation step (C₂H₂* + H* → C₂H₃* + *; TS1) governs turnover on Pd₃@Pd₅Ag₄ and Pd₃@Pd₆Ag₃, which is consistent with the low steady-state coverage of C₂H₃ (Figures S20–S21). As the second-shell Pd concentration increases (and Ag decreases), the control shifts progressively toward the second hydrogenation step (C₂H₃* + H* → C₂H₄* + *; TS2) for Pd₃@Pd₇Ag₂ and Pd₃@Pd₈Ag₁, culminating in fully rate-determining TS2 on Pd₃@Pd₉Ag₀. Across all ensembles, the relevant initial states for TS1 and TS2 involve coadsorption of C₂H₂ and H on neighboring hollow sites, emphasizing that differences in kinetics arise primarily from how the local environment stabilizes hydrogen in the transition state rather than from changes in the overall mechanistic sequence.

For TS1, the decisive distinction between Pd₃@Pd₆Ag₃ and Pd₃@Pd₅Ag₄ is the coordination preference of the transferred hydrogen. On Pd₃@Pd₅Ag₄, H resides on a top site, whereas on Pd₃@Pd₆Ag₃, it occupies a more stable hollow position. This coordination shift provides intrinsic stabilization of TS1 on Pd₃@Pd₆Ag₃ and is accompanied by stronger electronic coupling between Pd and H. Differential charge–density maps show enhanced electron accumulation around H on Pd₃@Pd₆Ag₃, indicating greater Pd → H donation (Figure a). Consistent with this picture, the density of states (DOS) reveals stronger Pd–H hybridization for Pd₃@Pd₆Ag₃, whereas Pd₃@Pd₅Ag₄ exhibits weaker orbital overlap between Pd d states and H s character (Figure b). Bonding analysis via projected crystal orbital Hamilton population (pCOHP) further corroborates this stabilization: the Pd–H interaction is stronger for Pd₃@Pd₆Ag₃, reflected by a larger – IpCOHP (2.16) relative to Pd₃@Pd₅Ag₄ (1.72) (Figure c). Notably, the H adsorption energy in TS1 is markedly lower on Pd₃@Pd₆Ag₃ (0.46 eV) than on Pd₃@Pd₅Ag₄ (0.70 eV), further confirming the superior stabilization of the hydrogen atom in the more favorable coordination environment (Figure a). Therefore, the enhanced activity of Pd₃@Pd₆Ag₃ originates from its ability to place H in a higher-coordination site and electronically reinforce Pd–H bonding in the rate-determining transition state.

5.

Electronic structure origin of ensemble-dependent activity. (a) Differential charge-density isosurfaces for TS1 on Pd₃@Pd₆Ag₃ and Pd₃@Pd₅Ag₄, with insets showing the effective H-binding energy in TS1. Yellow and cyan denote electron accumulation and depletion, respectively; isovalues = 0.0014 e Å^–3. (b) DOS analysis of the H adsorption state in TS1. Pd d-orbital contributions are averaged per atom and scaled by 1/2 for clarity. (c) pCOHP analysis of the Pd–H bond in TS1. (d) Differential charge-density isosurfaces for TS2 on Pd₃@Pd₆Ag₃ and Pd₃@Pd₉Ag₀, with insets showing the effective H-binding energy in TS2. (e) DOS analysis of the H adsorption state in TS2. Pd d-orbital contributions are averaged per atom and scaled by 1/2. (f) pCOHP analysis of the Pd–H bond in TS2.

An analogous structure–electronic origin governs the second hydrogenation step when Pd₃@Pd₆Ag₃ and Pd₃@Pd₉Ag₀ are compared. In TS2, H binds at a top site in the Pd-rich Pd₃@Pd₉Ag₀ environment but adopts a more favorable bridge configuration on Pd₃@Pd₆Ag₃, again strengthening Pd–H bonding and stabilizing the transition state. Charge density differences reveal greater electron accumulation on H for Pd₃@Pd₆Ag₃ (Figure d), and the DOS features show correspondingly stronger Pd–H hybridization relative to that of Pd₃@Pd₉Ag₀ (Figure e). pCOHP analysis corroborates this stabilization, with a substantially larger – IpCOHP for Pd–H in TS2 on Pd₃@Pd₆Ag₃ (2.28) than on Pd₃@Pd₉Ag₀ (1.59) (Figure f). Similarly, the H adsorption energy in TS2 is lower on Pd₃@Pd₆Ag₃ (0.37 eV) than on Pd₃@Pd₉Ag₀ (0.81 eV), underscoring the energetic advantage conferred by the bridge-bound configuration (Figure d).

Collectively, these comparisons identify a consistent mechanistic principle: the highest activity arises when the local second-shell environmenttogether with the associated Ag-induced strain and electronic modulationenables H to occupy bridge- or hollow-like configurations in the rate-relevant transition states, thereby maximizing Pd → H charge transfer and Pd–H bond strength. This coupling between the ensemble geometry and transition-state electronic structure explains why Pd₃@Pd₆Ag₃ uniquely stabilizes both TS1 and TS2, delivering the lowest barriers and the highest predicted C₂H₄ formation rates.

Extending the Framework: Self-Organization in Other Catalytic Alloys

To determine whether the reaction-driven ordering identified for Pd–Ag is system-specific or instead reflects a more general principle of bimetallic catalysis, we extended the analysis to seven chemically distinct alloy families relevant to acetylene hydrogenation: Pd–Cu, Pd–Au, Pd–Pt, Pd–Rh, Cu–Pt, Pd–Ni, and Cu–Ni (Figure ). For each system, we followed the same workflow established for Pd–Ag: the most stable bulk alloy phase was first identified, and the corresponding (111) surface was then constructed for DFT analysis. The resulting surface models were p(4 × 4) Pd₁Cu₃(111), Pd₂Au₂(111), Pd₂Pt₂(111), Pd₃Rh₁(111), Cu₃Pt₁(111), Pd₁Ni₃(111), and Cu₃Ni₁(111) (Figure S22 and Table S6).

6.

General scaling of reaction-driven ordering across bimetallic alloys. (Left) Scatter plot showing the linear correlation between the predicted and true surface segregation ratios (R) for eight chemically distinct alloy families (Pd–Ag, Pd–Cu, Pd–Au, Pd–Pt, Pd–Rh, Cu–Pt, Pd–Ni, and Cu–Ni). (Right) Atomic structures of the studied alloys under C₂H₂ coverage, illustrating the systematic variation in surface enrichment across alloy chemistries.

For each alloy, we determined the most stable surface configuration under reactive conditions by evaluating the equilibrium C₂H₂ coverage and the resulting surface composition. In every case, acetylene adsorption drives segregation of the more strongly interacting metal to the outermost layer, demonstrating that adsorbate-induced self-organization is not unique to Pd–Ag but is general across chemically distinct alloy families. The degree of enrichment varies systematically with alloy chemistry. Alloys with a greater adsorption contrast and a lower thermodynamic penalty for segregation show stronger surface enrichment, whereas more stable alloys or those with lower adsorption asymmetry exhibit only partial enrichment. Consistent with this trend, the surface fraction of the enriched metal increases from 25% to 62.5% for Pd₁Cu₃(111) and Cu₃Pt₁(111), from 50% to 87.5% for Pd₂Au₂(111) and Pd₂Pt₂(111), and to 100% for Pd₃Rh₁(111), Pd₁Ni₃(111), and Cu₃Ni₁(111) under their respective equilibrium C₂H₂ coverages (Figures S23–S29).

To quantify the extent of restructuring, we defined the segregation ratio (R) as the net increase in one metal species on the surface normalized by the initial surface population of the other metal species (Figure ). Across the alloy set, this ratio R shows a linear dependence on two key thermodynamic descriptors: the difference in the adsorption energy between the constituent pure-metal (111) surfaces, ΔΔG _ads, and the alloy formation energy, ΔH (Tables S7–S8). The resulting relation

$$R=0.79-0.13\times {\mathrm{\Delta }\mathrm{\Delta }G}_{\mathrm{ads}}+0.78\times \mathrm{\Delta }H$$

captures the balance between the adsorbate-driven driving force for segregation and the bulk thermodynamic penalty for alloy decomposition. More negative ΔΔG _ads values favor enrichment of the more reactive metal at the surface, whereas more negative ΔH values reflect greater alloy stability and thus suppressed segregation. These findings demonstrate that the adsorbate-induced self-organization of alloy surfaces is a general phenomenon rather than a peculiarity of Pd–Ag. The established scaling relation offers a simple predictive framework for estimating segregation tendencies from adsorption energetics and alloy stability, providing a transferable basis for understanding and tuning the dynamic surface composition of bimetallic catalysts.

Discussion

Our findings advance the understanding of Pd–Ag-catalyzed acetylene hydrogenation by moving beyond a static, site-centric description toward a dynamic framework of reaction-selected surface architecture, wherein adsorption, surface segregation, and reaction kinetics are inherently coupled. Within this framework, the reactive atmosphere drives the surface away from its as-prepared alloy state toward a steady-state ensemble population dominated by Pd₃ hollow sites. The second-shell chemical environment of these sites fine-tunes both acetylene activation and ethylene retention. This perspective provides a possible explanation for why Ag promotion cannot be reduced to a single static effectsuch as simply “weakening ethylene adsorption”but instead establishes geometric and electronic boundary conditions, while the reacting feed dynamically selects the distribution of active ensembles.

A central and testable prediction of this dynamic model is the adsorbate-driven reversal of the vacuum segregation tendency, which increases Pd in the outermost layer while the subsurface remains near-bulk stoichiometry. This provides a possible mechanistic interpretation for several long-standing but previously fragmented observations: (i) Industrial experience, noted for example by Chevron Phillips at the 1993 Ethylene Producers’ Conference, holds that effective catalysts require a Pd-rich surface for hydrogen activation and alkyne hydrogenation coupled with an Ag-rich core to maintain selectivity and inhibit hydride formation; (ii) An optimal Ag composition of ∼40 at % is widely reported for peak performance, which is consistent with our finding that moderate Ag content enables sufficient dynamic Pd enrichment without compromising structural stability; and (iii) Operando surface-sensitive spectroscopies (e.g., XPS, AES depth profiling) have reported reaction-dependent Pd/Ag ratios that are difficult to reconcile with static, Ag-terminated surface models under hydrogen or strongly bound adsorbates. −

These computational results should be viewed as testable mechanistic predictions rather than direct experimental proof. The proposed dynamic-ensemble mechanism could be examined by operando AP-XPS, XAS/EXAFS, or environmental microscopy, which would be expected to detect reversible Pd surface enrichment and enhanced Pd–Pd coordination under C₂H _x -rich feeds. Experimental validation of these predictions will provide a critical test of the proposed mechanism.

Ensemble-resolved analysis further clarified why identifying “Pd₃ sites” alone is insufficient. Although Ag is often regarded as a geometric diluent that disrupts Pd(111)-like ensembles, catalysts with similar apparent Pd dispersions can exhibit markedly different selectivities under tail-end conditions. Once Pd₃ hollows form under reaction conditions, the first-shell geometry remains largely conserved; the decisive variable becomes the second shell, which modulates the adsorption thermodynamics and transition-state stabilization. This insight offers a concrete explanation for “same motif, different performance” trends across catalysts with similar bulk compositions but different preparation histories, supports, or operating historiesall of which bias the steady-state second-shell statistics.

A key outcome is that the activity–selectivity trade-off collapses onto a simple descriptor, ΔG = ΔG _ads(C₂H₄) – ΔG _ads(C₂H₂). Intermediate ΔG values maximize acetylene hydrogenation while minimizing ethylene retention and overhydrogenation, whereas values that are too small or too large either reduce adsorption discrimination or overstabilize reaction intermediates. This descriptor-based view aligns with prior experimental and theoretical work linking Pd–Ag selectivity to weakened ethylene adsorption but further demonstrates that the relevant adsorption balance is not fixed by alloy composition alone; rather, it emerges from the operational ensemble distribution. Within this landscape, Pd₃@Pd₆Ag₃ is predicted to be a dominant selective center because its second-shell environment positions the surface closest to the optimal ΔG window.

The present results also clarify that Ag contributes beyond geometric dilution. In the most active ensembles, Ag-induced tensile strain stabilizes bridge- or hollow-bound H in key hydrogenation transition states, strengthens Pd–H interactions, and decreases relevant barriers. Ag therefore plays a dual role: it limits excessive Pd contiguity associated with overhydrogenation while creating a local environment that promotes efficient hydrogen transfer. Thus, the conventional statement that “Ag weakens ethylene adsorption” remains phenomenologically useful, but the underlying mechanism is more dynamic and ensemble-specific: apparent ethylene weakening arises not only from static Pd dilution but also from the self-organization of Pd₃ ensembles whose second-shell Ag coordination fine-tunes adsorption energetics.

More broadly, the extension to Pd-, Cu-, and Ni-based alloys suggests that adsorbate-driven self-organization is not unique to Pd–Ag but reflects a more general principle of bimetallic catalysis. The linear scaling relationship between segregation, adsorption asymmetry, and alloy stability indicates that dynamic surface enrichment can be anticipated from simple thermodynamic quantities. This framework also yields clear experimental expectations: near-surface Pd enrichment should increase with increasing C₂H _x coverage; selectivity should correlate more strongly with second-shell coordination statistics than with the abundance of Pd₃ motifs alone; and catalysts with similar bulk compositions but different strain states or pretreatment histories should display distinguishable selectivity at fixed conversion. In this sense, the active phase of alloy catalysts is best understood not as a fixed site but as an adaptive surface architecture selected by the working chemical environment.

Conclusions

Alloy catalysts can self-organize under reaction conditions into active ensemble distributions that are not encoded in the as-prepared structure. Using Pd–Ag acetylene hydrogenation as a model system, we demonstrate that reaction-driven alloy ordering governs catalytic function through tunable local coordination and an adsorption-energy gap descriptor that captures the activity–selectivity trade-off. Beyond conventional geometric dilution, alloy-induced strain contributes directly to catalytic performance by stabilizing key transition states. More importantly, extension across multiple alloy families indicates that adsorbate-driven self-organization is a general principle of adaptive alloy catalysis. These results move beyond a static view of alloy surfaces and provide a broader basis for understanding and designing catalysts whose active states are selected by the working chemical environment.

DFT Calculations

All periodic DFT calculations were performed using the Vienna Ab initio Simulation Package (VASP). The exchange–correlation energy was described with the Perdew–Burke–Ernzerhof (PBE) functional, and core–valence interactions were treated with the projector augmented wave (PAW) method. , The Pd–Ag(111) surface was modeled as a four-layer slab. To construct the primary training data set for the neural network energy calculator, a p(4 × 4) supercell with varying Pd/Ag compositions was used. For improved model generalizability, a limited number of p(2 × 2) and p(6 × 6) supercells were also included. The bottom layer was fixed in its bulk positions, while the upper three layers and adsorbates were fully relaxed. A plane-wave kinetic energy cutoff of 400 eV was employed, with electronic self-consistency and ionic force convergence thresholds set to 10^–4 and 0.1 eV/Å, respectively. The Brillouin zone was sampled with a (2 × 2 × 1) Monkhorst–Pack k-point mesh for the p(4 × 4) supercell. A vacuum spacing of at least 15 Å was applied along the z direction to eliminate interactions between periodic images.

The REANN potential was trained on approximately 60,000 DFT-labeled configurations, achieving energy and force errors of 2.82 meV atom^–1 and 0.05 eV Å^–1, respectively, on an independent test set (Figure S6). Although this large training set represents a practical limitation, a tested off-the-shelf MACE model showed a much higher energy RMSE of 40.61 meV atom^–1 without system-specific fine-tuning (Figure S30), which is insufficient for resolving subtle Pd/Ag segregation and ensemble effects. Therefore, we used a dedicated REANN potential for the present large-scale GCMC–MD simulations, while foundation models remain promising for future broad screening across diverse alloy systems and for identifying general catalytic trends.

For subsequent explicit DFT energy evaluationsincluding adsorbate adsorption, metal segregation energetics, and the C₂H₂ selective hydrogenation reaction mechanismall calculations were conducted with a stricter force convergence criterion of 0.02 eV/Å while maintaining the 400 eV energy cutoff and 10^–4 eV energy tolerance.

The adsorption free energy was calculated as follows

$$\mathrm{\Delta }{G}_{\mathrm{a}\mathrm{d}\mathrm{s}}=E_{\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}}-E_{\mathrm{s}\mathrm{l}\mathrm{a}\mathrm{b}}-G_{\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{ecu}\mathrm{l}\mathrm{e}(\mathrm{g})}$$ 1

where E _total, E _slab, and G _molecule(g) represent the total energy of the adsorbed system, the clean slab, and the gas-phase molecule, respectively. Specifically, H adsorption was referenced to 1/2H₂(g), whereas C₂H₂ and C₂H₄ adsorption were referenced to C₂H₂(g) and C₂H₄(g), respectively.

Gas-phase chemical potentials were evaluated using VASPKIT task 502 under the specified temperature and pressure conditions. No zero-point energy (ZPE) or vibrational entropy corrections were applied to adsorbed intermediates or transition states in the main analysis; for consistency, the ZPE correction for gaseous molecules was also omitted. This approximation was assessed by using ZPE- and vibrationally corrected free-energy profiles for representative Pd₁Ag₃(111) and Pd₃@Pd₆Ag₃ systems. These benchmark calculations yielded only small quantitative shifts in energy barriers, within 0.10 eV, and left the mechanistic conclusions unchanged, with similar deviations observed for the two representative systems (Figure S31).

The surface metal replacement energy was computed as follows

$$E_{\mathrm{seg}}=E_{\mathrm{total}}-N_{\mathrm{Ag}}{E}_{\mathrm{Ag}-\mathrm{bulk}}-N_{\mathrm{Pd}}{E}_{\mathrm{Pd}-\mathrm{bulk}}$$ 2

where E _total, E _Ag‑bulk, and E _Pd‑bulk denote the total energy of the system and the energy per atom of bulk Ag and Pd, respectively.

Transition states were located using a combination of the climbing image nudged elastic band (CI-NEB) method, the improved dimer method, , and the force reversal method. Surface configurations were extracted from stable GCMC-MD trajectories using a p(10 × 10) supercell and represented via p(6 × 6) unit cells, with a (2 × 2 × 1) Monkhorst–Pack k-point mesh. All of the transition states were verified by the presence of a single imaginary frequency along the reaction coordinate.

AIMD simulations were performed in the NVT ensemble at 373 K using a Nose–Hoover thermostat for temperature coupling. A plane-wave basis set with an energy cutoff of 350 eV was employed, and the Brillouin zone was sampled at the Γ point. A time step of 1 fs was used, and each simulation was carried out for 10 ps. The electronic structure was analyzed via the LOBSTER program using the projected crystal orbital Hamilton population (pCOHP) method.

The REANN potential was used exclusively to accelerate the large-scale p(10 × 10) GCMC–MD simulations, from which the adsorbate coverage, surface composition, structural evolution, and ensemble distributions were obtained. All reported energetic and electronic-structure properties were calculated explicitly using DFT. The catalytic rates, apparent activation energies, steady-state coverages, and degree-of-rate-control values were obtained from microkinetic simulations parametrized with DFT-derived energetics.

Further methodological details concerning REANN training, hybrid GCMC–MD simulations, and microkinetic modeling are provided in the Supporting Information.

Key optimized structures, representative GCMC–MD configurations, GCMC–MD workflow scripts, representative DFT input files, and the REANN model file supporting the main analyses of this study have been deposited in Zenodo at DOI: 10.5281/zenodo.21220369.

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/jacsau.6c00819.

• REANN potential, GCMC, MD, and microkinetic simulation methods; complementary energy values and optimized atomic structures; analysis of catalyst restructuring during the GCMC–MD simulations; full potential energy surface for acetylene hydrogenation; influence of Pd–Ag alloy ordering on catalytic performance metrics (PDF)

The authors declare no competing financial interest.