Ionized Gold Shifts to Flat Shapes, Simulations Reveal

Researchers have demonstrated that the structural preferences of gold clusters undergo a surprising shift upon ionization. Mohammad Ismaeil Safa, Ehsan Rahmatizad Khajehpasha, and Stefan Goedecker, all from the Department of Physics at the University of Basel, report that planar structures become energetically favoured ground states in gold clusters ranging from 22 to 100 atoms when positively ionized. This finding challenges the established understanding that larger clusters predominantly adopt compact configurations and reveals a previously unrecognised role for charge in dictating cluster geometry. By employing the Minima Hopping algorithm with a machine-learned potential, enhanced with a novel charge-correction term, the team have mapped the potential energy surface and shown that thermodynamic effects at finite temperatures further stabilise these planar arrangements.

Scientists have long sought to control matter at the atomic scale, envisioning advances in catalysis and materials science. Understanding the behaviour of gold clusters, tiny groupings of atoms, is a key step towards this goal. New work suggests these clusters dramatically change shape when electrically charged, favouring flat arrangements that could unlock unexpected properties.

Researchers have uncovered a surprising trend in the behaviour of gold clusters as they become positively ionized. While neutral gold clusters of a certain size typically favour compact, three-dimensional structures, this work demonstrates that adding a positive charge can fundamentally alter their preferred shape. Specifically, planar configurations, essentially two-dimensional sheets of gold atoms, become energetically favoured as the level of ionization increases.

This structural transition, observed in clusters ranging from 22 to 100 atoms, challenges conventional understanding of gold cluster stability. Until now, studies indicated a shift from planar to compact structures around the Au14 mark for neutral clusters, a finding refined by machine-learning approaches. Yet, this research reveals that ionization introduces a new variable, prompting a preference for planar arrangements even in larger clusters.

The team’s findings suggest that the positive charge distributed across the cluster’s surface creates repulsive forces between the gold ions, making extended, planar structures more stable than tightly packed, compact ones. Beyond simply identifying this shift, the study also examines how temperature influences these structures, finding that higher temperatures further enhance the stability of planar configurations relative to their three-dimensional counterparts.

To map the complex energy landscape of these clusters, researchers employed a sophisticated computational technique called Minima Hopping, combined with a machine-learned potential. Recognising that standard machine-learning models struggle with ionized systems, they incorporated a charge-correction term to accurately account for the effects of Coulomb interactions and charge screening.

This methodological advancement allowed for a detailed exploration of the potential energy surface, revealing the surprising preference for planar structures under specific conditions. These findings open new avenues for designing and controlling the properties of gold nanostructures, with potential applications in catalysis, electronics, and materials science.

Recent investigations have shown that atomically thin gold monolayers can be created through various methods, including ligand-assisted self-assembly and dealloying. These monolayers exhibit remarkable stability and conductivity, suggesting that planar gold structures are not limited to small clusters but represent a broader class of two-dimensional materials.

This work provides evidence that positive ionization can actively promote the formation and stabilisation of planar gold configurations, offering a new pathway for creating and manipulating these materials. The research team systematically investigated the potential energy surface of ionized gold clusters, ranging in size from 22 to 100 atoms, using a combination of advanced computational methods.

The Minima Hopping algorithm was coupled with a machine-learned potential to efficiently explore the vast configuration space. Since machine-learned potentials typically do not account for ionized clusters, a crucial charge-correction term was introduced to accurately model the Coulomb interactions and charge screening effects. This allowed for a precise determination of the relative stability of compact, cage-like, and planar structures under varying degrees of ionization.

Results indicate that as the positive charge increases, planar structures become increasingly favoured, even in larger clusters where compact structures are typically dominant. This suggests a fundamental interplay between charge state and structural preference, with significant implications for the design of novel gold-based nanomaterials. Furthermore, the study considered the impact of temperature on structural stability.

Finite-temperature calculations revealed that thermodynamic effects further reinforce the preference for planar configurations at elevated temperatures. This finding is particularly relevant for potential applications where gold nanostructures are exposed to realistic operating conditions. The ability to control the shape and charge state of gold clusters opens up possibilities for tailoring their electronic and optical properties.

This could lead to the development of more efficient catalysts, advanced sensors, and novel electronic devices. At larger sizes, clusters typically oscillate between icosahedral, decahedral, or octahedral motifs, but ionization provides a means to direct the system towards a planar arrangement. The work not only confirms earlier trends in gold cluster behaviour but also provides a comprehensive, size-resolved structural map, including several previously unreported low-energy isomers. This detailed understanding of the potential energy surface will be invaluable for future research aimed at designing and synthesizing gold nanostructures with tailored properties.

Ionization drives structural transitions to planar configurations in gold clusters

Calculations reveal a surprising trend in ionized gold clusters, with planar structures becoming energetically favoured for larger sizes. Specifically, work with clusters ranging from 22 to 100 gold atoms demonstrates a shift away from the typically observed compact structures when positively ionized. This transition to planar configurations occurs as the charge increases, altering the inherent stability of the clusters.

The research employed the Minima Hopping algorithm, coupled with a machine-learned potential and a charge-correction term to accurately model these ionized systems. Beyond structural preference, finite-temperature stability analyses further reinforce the prevalence of planar arrangements. Thermodynamic effects consistently stabilise planar configurations relative to their compact counterparts, even at elevated temperatures.

This suggests that these planar structures are not merely theoretical possibilities but potentially observable states. The machine-learned potential, enhanced by the charge-correction term, allowed exploration of the potential energy surface with improved accuracy. For instance, the study found that introducing a charge significantly alters the energy landscape, favouring planar motifs where neutral clusters would typically be compact.

The precise charge required to induce this transition varies with cluster size, demanding careful consideration of electrostatic interactions. At larger sizes, the energy difference between planar and compact structures diminishes, but the thermodynamic stabilisation consistently tips the balance towards planar configurations. By combining computational efficiency with accuracy, the research provides a detailed map of structural stability across a range of cluster sizes and ionization states.

Machine learning and global optimisation for modelling charged gold cluster stability

A machine-learned potential, coupled with the Minima Hopping algorithm, underpinned the exploration of potential energy surfaces for gold clusters. Minima Hopping, a global optimisation technique, was selected for its ability to efficiently navigate complex landscapes and locate multiple low-energy structures, unlike methods that might become trapped in local minima.

To address the limitations of the machine-learned potential when applied to ionized clusters, a charge-correction term was introduced. This term accounts for the significant influence of Coulomb interactions and charge screening effects on the cluster’s stability, ensuring greater accuracy in calculations involving positively ionized gold. Consequently, the research team implemented a bespoke correction, tailored to incorporate the effects of excess charge on the gold clusters.

Once established, this charge-corrected potential was then used to calculate the energies of various cluster configurations, ranging in size from 22 to 100 gold atoms. Still, understanding the behaviour of these clusters at realistic temperatures required further investigation. Finite-temperature effects were therefore studied to determine how thermal energy influences structural preferences.

By examining the stability of structures at elevated temperatures, researchers could assess whether planar configurations, favoured by the calculations, would persist under conditions more closely resembling experimental settings. This approach provides a more complete picture of structural stability than static, zero-temperature calculations alone. For a detailed analysis, the work focused on comparing compact, cage, and planar structures, identifying transitions between these motifs as cluster size and charge state change.

By systematically varying these parameters, the study aimed to map the structural landscape of ionized gold clusters and reveal the factors governing their stability. This detailed mapping is essential for interpreting experimental observations and predicting the behaviour of these clusters in various applications.

Ionised gold clusters reveal structural transitions via machine learning modelling

Scientists have long sought to understand how matter behaves at the smallest scales, yet predicting the structure of even relatively small clusters of atoms proves surprisingly difficult. This research offers a new understanding of how gold clusters, when electrically charged, change shape, specifically, how they transition from tightly packed forms to flatter, more extended arrangements.

For years, simulations struggled to accurately model these ionized clusters, hampered by the complexity of balancing quantum mechanical effects with computational cost. Now, a combination of advanced algorithms and machine learning offers a pathway around these limitations. Yet, the implications extend beyond fundamental physics. Controlling the shape and properties of nanoscale materials is central to advances in catalysis, sensing, and even medicine.

Gold nanoparticles, for example, are already used in diagnostic tests and drug delivery systems, and their effectiveness depends heavily on their precise structure. Understanding how external factors, like charge, influence this structure allows for greater control over their function. However, accurately modelling these systems has remained a significant challenge, requiring substantial computational resources.

While the machine-learning approach demonstrates impressive accuracy when compared to more traditional calculations, it relies on initial data generated from those same methods. This creates a degree of dependence, and the potential for unforeseen errors in entirely new systems cannot be dismissed. Furthermore, the study focuses on gold, and it is unclear how readily these findings translate to other metals or more complex cluster compositions.

Once these hurdles are addressed, the next step will be to explore how these structural changes affect the clusters’ reactivity and optical properties. Beyond that, researchers might investigate how to actively induce these transitions using external fields, creating materials that can dynamically change their shape and function on demand. This work represents a step towards designing materials with tailored properties at the atomic level, a prospect that promises to reshape numerous technologies.