🔬 materials science

Temperature-Induced Reorganization of Supported Zn $_3$ Clusters on Cu(111): From Minimum-Energy Structures to Finite-Temperature Ensembles

This study demonstrates that finite-temperature entropic effects fundamentally alter the preferred structures of supported Zn $_3$ clusters on Cu(111) from compact triangular shapes to extended linear configurations, challenging the reliability of identifying catalytic active sites based solely on static 0 K minimum-energy models.

Original authors: Jiayan Xu, Zheng Yu, Abhirup Patra, Amar Deep Pathak, Sharan Shetty, Detlef Hohl, Roberto Car

Published 2026-08-19

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CC BY 4.0

Original authors: Jiayan Xu, Zheng Yu, Abhirup Patra, Amar Deep Pathak, Sharan Shetty, Detlef Hohl, Roberto Car

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

In the world of industrial chemistry, catalysts are the unsung heroes that make reactions happen faster and more efficiently without being used up themselves. Think of a catalyst as a specialized workbench where raw materials meet, break apart, and reassemble into something new. For decades, scientists have tried to understand exactly what these workbenches look like at the atomic level, hoping that if they can see the precise arrangement of atoms, they can design better catalysts. A common belief has been that the most stable arrangement of atoms—the one that requires the least amount of energy to hold together—is the one that does the work. This idea works well when things are cold and still, but real-world chemical reactions happen at high temperatures where atoms are constantly jiggling and moving. The question that has long puzzled researchers is whether the static, cold picture of a catalyst's structure is enough to explain how it behaves when the heat is turned on.

A team of researchers has tackled this problem by studying a specific type of catalyst used to make methanol, a vital fuel and chemical building block. This catalyst is a mixture of copper, zinc oxide, and alumina. While the copper surface is well understood, the role of tiny zinc clusters sitting on top of it has been a mystery. For a long time, scientists assumed these zinc clusters settled into a tight, triangular shape because that was the most energy-efficient form when the system was cold. However, the researchers suspected that this cold, static view might be misleading. To test this, they used advanced computer simulations powered by machine learning to watch how these tiny zinc clusters behave as the temperature rises from freezing to the hot conditions found in an industrial reactor.

The study focused on small groups of three zinc atoms, often surrounded by oxygen and hydrogen, sitting on a copper surface. The researchers first confirmed what everyone expected: at zero degrees, these clusters prefer to huddle together in a compact triangle. But when they simulated the environment at higher temperatures, the story changed completely. As the temperature increased, the clusters began to stretch out. Instead of staying in their tight triangle, they unfolded into long, straight lines. This shift was not driven by the atoms finding a lower energy state; in fact, the stretched-out shape actually required slightly more energy to hold together. The reason for the change was something else entirely: entropy. In simple terms, the stretched-out shape offered the atoms more ways to wiggle and move around. At high temperatures, this freedom of movement became more valuable than the energy savings of staying in a tight triangle, causing the clusters to reorganize into these linear forms.

The researchers also looked at how the surface underneath the clusters affected this behavior. They tested surfaces that were pure copper, surfaces with just a single zinc atom mixed in, and surfaces where a quarter of the top layer was zinc. On the pure copper and the single-zinc surfaces, the clusters remained free to move around, sliding across the surface like marbles on a table. This mobility is a problem because if the clusters move too much, they can crash into each other and merge into larger, inactive blobs, a process known as sintering. However, on the surface with a high concentration of zinc, the clusters stopped moving. The zinc atoms in the surface acted like anchors, locking the clusters in place. This finding suggests that while the clusters might change their shape due to heat, the composition of the surface determines whether they stay put or wander off.

Perhaps the most surprising discovery was that the presence of a specific chemical intermediate, a formate molecule, did not change the fundamental rules of the game. Even with this extra molecule attached, the clusters still shifted from triangles to lines as the temperature rose, and the zinc-rich surface still kept them from moving. The study showed that the traditional method of looking only at the lowest-energy, cold structure misses the true nature of the active site. Under real operating conditions, the catalyst is not a single, rigid shape but a dynamic ensemble of different forms, constantly shifting between compact and stretched configurations.

These results challenge the standard way scientists model catalysts. For years, the assumption was that the most stable structure at zero temperature is the one that matters most. This paper demonstrates that assumption is flawed. The active sites are not static statues but fluid populations that change with temperature. The researchers found that the competition between the energy needed to hold a shape and the entropy gained by moving around dictates the structure. By using machine learning to speed up their simulations, they were able to see these temperature-driven changes that would have been impossible to capture with older, slower methods.

The implications for designing better catalysts are significant. If engineers want to create a catalyst that lasts longer and works better, they cannot just look for the most stable atomic arrangement in a cold lab. They must consider how the atoms will behave when the reactor is hot and full of moving molecules. The study suggests that adding more zinc to the copper surface is a key strategy, not just for changing the shape of the clusters, but for pinning them down so they don't wander off and lose their activity. This work provides a clearer, more realistic picture of what happens inside a catalyst, moving the field from a static snapshot to a dynamic movie of atomic life.

Technical Summary: Temperature-Induced Reorganization of Supported Zn3 Clusters on Cu(111)

Problem Statement
In heterogeneous catalysis, particularly for the industrial copper/zinc oxide/alumina (CZA) catalyst used in methanol synthesis, the atomic-scale structure and stability of active sites remain controversial. While small Zn-based species at the Cu interface are proposed as active sites, their identification relies heavily on zero-temperature ($0$ K) density functional theory (DFT) optimizations. This approach assumes that the minimum-energy configuration at $0$ K represents the active site under reaction conditions. However, catalysts often exhibit significant structural flexibility, atom migration, and dynamic interactions with adsorbates at finite temperatures. Consequently, the thermodynamically relevant active site may be an ensemble of configurations populated at operating temperatures rather than a single static structure. Explicitly sampling the finite-temperature free-energy landscape using first-principles methods is computationally prohibitive due to the required time and length scales.

Methodology
To address these challenges, the authors employed a multi-scale computational framework combining machine learning interatomic potentials (MLIPs), global optimization, molecular dynamics (MD), and enhanced-sampling free-energy calculations.

MLIP Development: A Deep Potential (DP) model was trained on a dataset of 44,269 structures spanning pure metals (Cu, Zn), alloys, oxides, and supported clusters. The training data was generated using DFT at the PBE+D3 level. The resulting model achieves root-mean-squared errors of 0.005 eV/atom for energies and 0.056 eV/Å for forces, enabling near-DFT accuracy with significantly accelerated simulation speeds.
System Models: The study investigated two cluster models relevant to methanol synthesis: hydroxylated $Zn_3(OH)_3$ $Z n_{3} (O H)_{3}$ and formate-containing $Zn_3(OH)_2CHOO$ $Z n_{3} (O H)_{2} C H O O$ . These were supported on three distinct Cu(111)-based surfaces to simulate varying degrees of Zn alloying:
- Pristine Cu(111) (0% Zn).
- Single-Zn-site surface (dilute alloying, ~1.56% Zn).
- Alloyed $Cu_3Zn$ surface (25% Zn).
Global Optimization: Genetic algorithms were used with the DP model to identify low-energy triangular and linear configurations of the clusters on each surface, followed by DFT validation.
Finite-Temperature Sampling:
- Unbiased MD: 20 ns simulations were performed at 300 K and 450 K to observe spontaneous structural transitions and cluster mobility.
- Enhanced Sampling: The On-the-fly Probability Enhanced Sampling (OPES) method was used to reconstruct free-energy landscapes at 150, 300, and 450 K. Two collective variables (CVs) were employed: the maximum Zn-Zn-Zn angle ( $\theta_{max}$ ) to distinguish triangular ( $\approx 60^\circ$ ) from linear ( $\approx 170^\circ$ ) geometries, and a distance-based descriptor ( $\tilde{d}_{max}$ ) to accelerate transitions.
Mobility Analysis: Mean squared displacement (MSD) of the cluster center of mass and site correlation functions were calculated to assess spatial stability and resistance to sintering.

Key Results

Temperature-Induced Configurational Reorganization:
- At $0$ K, compact triangular configurations are generally the minimum-energy structures for $Zn_3(OH)_3$ on pristine Cu(111).
- Finite-temperature free-energy calculations reveal a pronounced shift toward extended linear configurations as temperature increases. At 450 K, the linear configuration becomes thermodynamically competitive with the triangular one.
- This transition is driven primarily by entropic stabilization. While the potential energy difference between configurations remains relatively constant across temperatures, the linear configuration possesses higher entropy, which increasingly offsets its enthalpic disadvantage as temperature rises.
Impact of Surface Alloying:
- Pristine and Dilute Surfaces: On pristine Cu(111) and the single-Zn-site surface, increasing temperature progressively stabilizes the linear ensemble, leading to comparable populations of triangular and linear structures at 450 K.
- Alloyed Surfaces: On the $Cu_3Zn$ surface, the energetic ordering is reversed even at $0$ K, with the linear configuration being more stable by 0.19 eV. Extensive Zn alloying stabilizes and rigidifies the linear configuration across the entire temperature range.
- Role of Adsorbates: The presence of formate ( $Zn_3(OH)_2CHOO$ ) shifts the energetic balance further toward the linear configuration but preserves the same qualitative trends regarding temperature and alloying.
Spatial Stability and Mobility:
- On pristine Cu(111), supported $Zn_3$ clusters exhibit substantial lateral mobility, indicating a high propensity for migration and coalescence (sintering).
- Zn alloying strongly suppresses diffusion. On the single-Zn-site surface, while the configurational equilibrium is similar to the pristine surface, the presence of isolated surface Zn atoms creates stable $Zn_c$ -adsorbate- $Zn_s$ bridging motifs. These motifs act as anchoring centers, significantly prolonging the residence time of the cluster and suppressing migration compared to the labile $Zn_c$ -Cu interactions.
- On the highly alloyed $Cu_3Zn$ surface, diffusion is negligible, effectively stabilizing isolated interfacial Zn species against sintering.

Significance and Claims
The paper demonstrates that the thermodynamically relevant structures of supported Zn-based clusters differ fundamentally from those predicted by static $0$ K optimization. The active-site ensemble is governed by a competition between enthalpic and entropic effects, where entropy can drive a shift from compact to extended geometries under reaction conditions.

The authors claim that identifying catalytic active sites solely based on minimum-energy structures is insufficient. Instead, active sites should be viewed as dynamic ensembles whose populations and surface mobility evolve with temperature, adsorbate coverage, and local composition. The study highlights that while static optimization may predict triangular clusters as dominant, finite-temperature sampling reveals a significant population of linear structures, particularly at operating temperatures. Furthermore, the work underscores that surface composition controls not only the configurational equilibrium but also the spatial stability of the clusters, with Zn alloying playing a critical role in preventing sintering by creating stable anchoring motifs.

The findings provide a framework for interpreting experimental observations (such as cryogenic STM data showing triangular structures) and suggest that operando characterization should target the emergence of extended, dynamic ensembles near operating temperatures. The study validates the use of MLIP-accelerated free-energy sampling as a practical route to bridging the gap between idealized static models and the complex, dynamic structures present in working catalysts.

Technical Summary: Temperature-Induced Reorganization of Supported Zn3 Clusters on Cu(111)

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