Structural properties of sub-nanometer metallic clusters

Hierarchical self-assembly of Au-nanoparticles into filaments: evolution and break

We compare the assembly of individual Au nanoparticles in a vacuum and between two Au(111) surfaces via classical molecular dynamics on a timescale of 100 ns. In a vacuum, the assembly of three nanoparticles used as seeds, initially showing decahedral, truncated octahedral and icosahedral shapes with a diameter of 1.5-1.7 nm, evolves into a spherical object with about 10-12 layers and a gyration radius ∼2.5-2.8 nm. In a vacuum, 42% show just one 5-fold symmetry axis, 33% adopt a defected icosahedral arrangement, and 25% lose all 5-fold symmetry and display a face-centred-cubic shape with several parallel stacking faults. We model a constrained version of the same assembly that takes place between two Au(111) surfaces. During the dynamics, the two Au(111) surfaces are kept fixed at distances of 55 Å, 55.5 Å, 56 Å, and 56.5 Å. The latter distance accommodates 24 Au layers with no strain, while the others correspond to nominal strains of 1.5%, 2.4%, and 3.3%, respectively. In the constrained assembly, each individual seed tends to reorganize into a layered configuration, but the filament may break. The probability of breaking the assembled nanofilament depends on the individual morphology of the seeds. It is more likely to break at the decahedron/icosahedron interface, whilst it is more likely to layer with respect to the (111) orientation when a truncated octahedron sits between the decahedron and the icosahedron. We further observe that nanofilaments between surfaces at 56 Å have a >90% probability of breaking, which decreases to 8% when the surfaces are 55 Å apart. We attribute the dramatic change in probability of breaking to the peculiar decahedron/icosahedron interface and the higher average atomic strain in the nanofilaments. This in silico experiment can shed light on the understanding and control of the formation of metallic nanowires and nanoparticle-assembled networks, which find applications in next-generation electronic devices, such as resistive random access memories and neuromorphic devices.

Layer-by-layer unsupervised clustering of statistically relevant fluctuations in noisy time-series data of complex dynamical systems

Complex systems are typically characterized by intricate internal dynamics that are often hard to elucidate. Ideally, this requires methods that allow to detect and classify in an unsupervised way the microscopic dynamical events occurring in the system. However, decoupling statistically relevant fluctuations from the internal noise remains most often nontrivial. Here, we describe "Onion Clustering": a simple, iterative unsupervised clustering method that efficiently detects and classifies statistically relevant fluctuations in noisy time-series data. We demonstrate its efficiency by analyzing simulation and experimental trajectories of various systems with complex internal dynamics, ranging from the atomic- to the microscopic-scale, in- and out-of-equilibrium. The method is based on an iterative detect-classify-archive approach. In a similar way as peeling the external (evident) layer of an onion reveals the internal hidden ones, the method performs a first detection/classification of the most populated dynamical environment in the system and of its characteristic noise. The signal of such dynamical cluster is then removed from the time-series data and the remaining part, cleared-out from its noise, is analyzed again. At every iteration, the detection of hidden dynamical subdomains is facilitated by an increasing (and adaptive) relevance-to-noise ratio. The process iterates until no new dynamical domains can be uncovered, revealing, as an output, the number of clusters that can be effectively distinguished/classified in a statistically robust way as a function of the time-resolution of the analysis. Onion Clustering is general and benefits from clear-cut physical interpretability. We expect that it will help analyzing a variety of complex dynamical systems and time-series data.

Structural Determination and Hierarchical Evolution of Transition Metal Clusters Based on an Improved Self-Adaptive Differential Evolution with Neighborhood Search Algorithm

Determining the optimal structures and clarifying the corresponding hierarchical evolution of transition metal clusters are of fundamental importance for their applications. The global optimization of clusters containing a large number of atoms, however, is a vastly challenging task encountered in many fields of physics and chemistry. In this work, a high-efficiency self-adaptive differential evolution with neighborhood search (SaNSDE) algorithm, which introduced an optimized cross-operation and an improved Basin Hopping module, was employed to search the lowest-energy structures of CoN, PtN, and FeN (N = 3-200) clusters. The performance of the SaNSDE algorithm was first evaluated by comparing our results with the parallel results collected in the Cambridge Cluster Database (CCD). Subsequently, different analytical methods were introduced to investigate the structural and energetic properties of these clusters systematically, and special attention was paid to elucidating the structural evolution with cluster size by exploring their overall shape, atomic arrangement, structural similarity, and growth pattern. By comparison with those results listed in the CCD, 13 lower-energy structures of FeN clusters were discovered. Moreover, our results reveal that the clusters of three metals had different magic numbers with superior stable structures, most of which possessed high symmetry. The structural evolution of Co, Pt, and Fe clusters could be, respectively, considered as predominantly closed-shell icosahedral, Marks decahedral, and disordered icosahedral-ring growth. Further, the formation of shell structures was discovered, and the clusters with hcp-, fcc-, and bcc-like configurations were ascertained. Nevertheless, the growth of the clusters was not simply atom-to-atom piling up on a given cluster despite gradual saturation of the coordination number toward its bulk limit. Our work identifies the general growth trends for such a wide region of cluster sizes, which would be unbearably expensive in first-principles calculations, and advances the development of global optimization algorithms for the structural prediction of clusters.

Combining Deep Learning Neural Networks with Genetic Algorithms to Map Nanocluster Configuration Spaces with Quantum Accuracy at Low Computational Cost

The configuration spaces for bimetallic AuPd nanoclusters of various sizes are explored efficiently and analyzed accurately by combining genetic algorithms with neural networks trained on density functional theory. The methodology demonstrated herein provides an optimizable solution to the problem of searching vast configuration spaces with quantum accuracy in a way that is computationally practical. We implement a machine learning algorithm which learns the density functional theory potential with increasing performance while simultaneously generating and relaxing structures within the system's global configuration space unbiasedly. As a result, the algorithm naturally converges onto the system's energy minima while mapping the configuration space as a function of energy. The algorithm's simple design applies not only to nanocluster configurations, as demonstrated, but to bulk, substrate, and adsorption sites as well, and it is designed to scale. To demonstrate its computational efficiency, we work with AuPd nanoclusters of sizes 15, 20, and 25 atoms. Results focus primarily on evaluating the algorithm's performance; however, several physical insights into possible configurations for these nanoclusters naturally emerge as well, such as geometric Au surface segregation and stoichiometric Au minimization as a function of stability.

Detecting dynamic domains and local fluctuations in complex molecular systems via timelapse neighbors shuffling

It is known that the behavior of many complex systems is controlled by local dynamic rearrangements or fluctuations occurring within them. Complex molecular systems, composed of many molecules interacting with each other in a Brownian storm, make no exception. Despite the rise of machine learning and of sophisticated structural descriptors, detecting local fluctuations and collective transitions in complex dynamic ensembles remains often difficult. Here, we show a machine learning framework based on a descriptor which we name Local Environments and Neighbors Shuffling (LENS), that allows identifying dynamic domains and detecting local fluctuations in a variety of systems in an abstract and efficient way. By tracking how much the microscopic surrounding of each molecular unit changes over time in terms of neighbor individuals, LENS allows characterizing the global (macroscopic) dynamics of molecular systems in phase transition, phases-coexistence, as well as intrinsically characterized by local fluctuations (e.g., defects). Statistical analysis of the LENS time series data extracted from molecular dynamics trajectories of, for example, liquid-like, solid-like, or dynamically diverse complex molecular systems allows tracking in an efficient way the presence of different dynamic domains and of local fluctuations emerging within them. The approach is found robust, versatile, and applicable independently of the features of the system and simply provided that a trajectory containing information on the relative motion of the interacting units is available. We envisage that "such a LENS" will constitute a precious basis for exploring the dynamic complexity of a variety of systems and, given its abstract definition, not necessarily of molecular ones.

Theory of Anisotropic Metal Nanostructures

A significant challenge in the development of functional materials is understanding the growth and transformations of anisotropic colloidal metal nanocrystals. Theory and simulations can aid in the development and understanding of anisotropic nanocrystal syntheses. The focus of this review is on how results from first-principles calculations and classical techniques, such as Monte Carlo and molecular dynamics simulations, have been integrated into multiscale theoretical predictions useful in understanding shape-selective nanocrystal syntheses. Also, examples are discussed in which machine learning has been useful in this field. There are many areas at the frontier in condensed matter theory and simulation that are or could be beneficial in this area and these prospects for future progress are discussed.

Nucleation-mediated reshaping of facetted metallic nanocrystals: Breakdown of the classical free energy picture

Shape stability is key to avoiding degradation of performance for metallic nanocrystals synthesized with facetted non-equilibrium shapes to optimize properties for catalysis, plasmonics, and so on. Reshaping of facetted nanocrystals is controlled by the surface diffusion-mediated nucleation and growth of new outer layers of atoms. Kinetic Monte Carlo (KMC) simulation of a realistic stochastic atomistic-level model is applied to precisely track the reshaping of Pd octahedra and nanocubes. Unexpectedly, separate constrained equilibrium Monte Carlo analysis of the free energy profile during reshaping reveals a fundamental failure of the classical nucleation theory (CNT) prediction for the reshaping barrier and rate. Why? Nucleation barriers can be relatively low for these processes, so the system is not locally equilibrated before crossing the barrier, as assumed in CNT. This claim is supported by an analysis of a first-passage problem for reshaping within a master equation framework for the model that reasonably captures the behavior in KMC simulations.

Exploring AuRh Nanoalloys: A Computational Perspective on the Formation and Physical Properties

We studied the formation of AuRh nanoalloys (between 20-150 atoms) in the gas phase by means of Molecular Dynamics (MD) calculations, exploring three possible formation processes: one-by-one growth, coalescence, and nanodroplets annealing. As a general trend, we recover a predominance of Rh@Au core-shell ordering over other chemical configurations. We identify new structural motifs with enhanced thermal stabilities. The physical features of those selected systems were studied at the Density Functional Theory (DFT) level, revealing profound correlations between the nanoalloys morphology and properties. Surprisingly, the arrangement of the inner Rh core seems to play a dominant role on nanoclusters' physical features like the HOMO-LUMO gap and magnetic moment. Strong charge separations are recovered within the nanoalloys suggesting the existence of charge-transfer transitions.

Enhanced Methanol Electro-Oxidation Activity of Nanoclustered Gold

Size-selected 3 nm gas-phase Au clusters dispersed by cluster beam deposition (CBD) on a conducting fluorine-doped tin oxide template show strong enhancement in mass activity for the methanol electro-oxidation (MEO) reaction compared to previously reported nanostructured gold electrodes. Density functional theory-based modeling on the corresponding Au clusters guided by experiments attributes this high MEO activity to the high density of exposed under-coordinated Au atoms at their faceted surface. In the description of the activity trends, vertices and edges are the most active sites due to their favorable CO and OH adsorption energies. The faceted structures occurring in this size range, partly preserved upon deposition, may also prevent destructive restructuring during the oxidation-reduction cycle. These results highlight the benefits of using CBD in fine-tuning material properties on the nanoscale and designing high-performance fuel cell electrodes with less material usage.

Shape Changes in AuPd Alloy Nanoparticles Controlled by Anisotropic Surface Stress Relaxation

The shape of AuPd nanoparticles is engineered by surface stress relaxation, achieved by varying the Au content in nanoparticles of Pd-rich compositions. AuPd nanoparticles are grown in the gas phase for several compositions and growth conditions. Their structure is atomically resolved by HRTEM/STEM and EDX. In pure Pd distributions the dominant structures are FCC truncated octahedra (TO), while increasing the Au content there is a transition to icosahedral (Ih) structures in which Au atoms are preferentially placed at the nanoparticle surface. The transition is sharper for growth conditions closer to equilibrium. The physical origin of the transition is determined with the aid of computer simulations. Global optimization searches and free energy calculations confirm that Ih become the equilibrium structure for increasing the Au content. Atomic stress calculations demonstrate that the TO → Ih shape change is caused by a better relaxation of anisotropic surface stress in icosahedra.

Structure, Energetics, and Thermal Behavior of Bimetallic Re-Pt Clusters

Bimetallic Re-Pt is a widely used catalyst in petroleum reforming to obtain high-octane gasoline, but experimental and theoretical information of such systems at the subnanometer scale-namely, as cluster aggregates-is currently lacking. Thus, in this work, we performed a density functional theory-based global optimization study to determine the physicochemical properties of the most stable Re-Pt gas-phase clusters up to six atoms for all compositions. Our results indicate that in these putative global minima (GM) geometries, Re atoms tend to aggregate, while most Pt atoms remain separated from each other. This is even observed in Pt-rich clusters-an indication of the strength of the Re-Re and Re-Pt bonds over pure Pt-Pt ones-due to a strong, directional hybridization of the Re half-filled 5d and the nearly full Pt 5d states. We observe that doping monometallic Pt clusters even with a single Re atom increases their binding energy values and widens the bimetallic cluster highest occupied molecular orbital-lowest unoccupied molecular orbital gap. As catalysis occurs at elevated temperatures, we explore the concept of cluster fluxionality for Re-Pt minima in terms of the calculated isomer occupation probability, P(T). This allows us to quantify the abundance of GM and low-energy isomer configurations as a function of temperature. This is done at size 5 atoms due to the wide isomer observed variety. Our calculations indicate that for pure Re₅, the P(T) of the GM configuration substantially decreases after 750 K. Especially, for Re₄Pt₁, the GM is the dominant structure up to nearly 700 K when the second-energy isomer becomes the stable one. Although no ordering changes are seen for Re₃Pt₂, Re₂Pt₃, and Re₁Pt₄, we do observe a structural transition-between the GM and the second isomer-for pure Pt₅ above 1000 K. We expect this type of combined first-principles analysis to add to the overall, continuous understanding of the stability and energetics of ultrafine and highly-dispersed Re-Pt petroleum-reforming catalysts and the scarce available information on this particular bimetallic system.

Development of a Structural Comparison Method to Promote Exploration of the Potential Energy Surface in the Global Optimization of Nanoclusters

A structural comparison method (SCM) was created to quantify the structural diversity of nanoclusters and was implemented into a global optimization algorithm to evaluate structural diversity between generated clusters on the fly and promote exploration of the potential energy surface. The SCM evaluated topological differences between clusters using the common neighbor analysis and provided a numerical measure of similarity between the two clusters. The SCM was implemented into a genetic algorithm by integrating it into a new structure + energy fitness operator such that structural diversity of clusters in the population and their energies were used to assign fitness values to clusters. The efficiency of the genetic algorithm with this new fitness operator was benchmarked against several Lennard-Jones clusters (LJ₃₈, LJ₇₅, and LJ₉₈) known to be difficult cases for global optimization algorithms. For LJ₃₈ and LJ₇₅, this new structure + energy fitness operator performed equally well or better than the energy fitness operator. However, the efficiency of locating the global minimum of LJ₉₈ decreased using this new structure + energy fitness operator. Further analysis of the genetic algorithm with this fitness operator showed that the algorithm did indeed promote exploration of the PES of LJ₉₈ as desired but hindered refinement of clusters, preventing it from locating the global minimum even if the energy funnel of the global minimum had been located.

Structural Evolution of the Surface and Interface in Bimetallic High-Index Faceted Heterogeneous Nanoparticles

Bimetallic high-index faceted heterostructured nanoparticles represent a new class of high-performance nanocatalysts. In this work, we investigated the structural evolution of PtAu tetrahexahedral heterostructured nanoparticles enclosed by {210} facets using molecular dynamics simulations. The surface and interface were specifically addressed. The results show that the PtAu nanoparticle exhibits a heterogeneous melting pattern, leading to solid-liquid coexistence over a wide temperature range. In terms of particle shape evolution, the critical transformation temperature for the surface structure of the PtAu heterostructured nanoparticle is much lower than the melting point of each domain. In comparison, the interface could be basically retained even when the Au domain completely melts. These results extend our fundamental understanding of the thermally driven structural evolution of the surface and interface in bimetallic high-index faceted heterostructured nanoparticles and provide insight into the design and application of metallic nanoparticles with multifunctional performance.

Correlating Oxygen Reduction Reaction Activity and Structural Rearrangements in MgO-Supported Platinum Nanoparticles

We develop a multi‐scale approach towards the design of metallic nanoparticles with applications as catalysts in electrochemical reactions. The here discussed method exploits the relationship between nanoparticle architecture and electrochemical activity and is applied to study the catalytic properties of MgO(100)‐supported Pt nanosystems undergoing solid‐solid and solid‐liquid transitions. We observe that a major increment in the activity is associated to the reconstruction of the interface layers, supporting the need for a full geometrical characterisation of such structures also when in‐operando.

Role of electron-magnon interaction in non-Fermi liquid behavior of SrRuO3

SrRuO₃ is a popular material extensively used as a bottom electrode in various applications, however, a few problems which will certainly change the interface band structure and greatly alter the device's property are still not fully understood, such as the change of carrier types at a certain temperature and the quasiparticle scattering for non-Fermi liquid behavior below ferromagnetic transition temperature. In this study, magnetic, transport (electrical and thermal) properties and x-ray photoemission spectra have been used to understand the role of quasiparticle interactions in the SrRuO₃ bulk system. At the Fermi level, the hybridization of Ru4dt _2g   ↓  and O2p  bands form a typical two band system. In order to explain the problems as mentioned, our present work reveals that there must be an impurity band that couples with the bands around Fermi level and serves as a charge reservoir. In the present case, the impurity is attributed to the Ru vacancies. As a result, the conduction electrons scatter strongly with the Ru vacancies and couple with the Ru magnons to give rise to a dominant electron-magnon coupling that overwhelms the electron-phonon coupling in the temperature range of 90-150 K.