Reassignment of 'magic numbers' for Au clusters of decahedral and FCC structural motifs

Exploring the formation of gold/silver nanoalloys with gas-phase synthesis and machine-learning assisted simulations

While nanoalloys are of paramount scientific and practical interest, the main processes leading to their formation are still poorly understood. Key structural features in the alloy systems, including the crystal phase, chemical ordering, and morphology, are challenging to control at the nanoscale, making it difficult to extend their use to industrial applications. In this contribution, we focus on the gold/silver system that has two of the most prevalent noble metals and combine experiments with simulations to uncover the formation mechanisms at the atomic level. Nanoparticles were produced using a state-of-the-art inert-gas aggregation source and analyzed using transmission electron microscopy and energy-dispersive X-ray spectroscopy. Machine-learning-assisted molecular dynamics simulations were employed to model the crystallization process from liquid droplets to nanocrystals. Our study finds a preponderance of nanoparticles with five-fold symmetric morphology, including icosahedra and decahedra which is consistent with previous results on mono-metallic nanoparticles. However, we observed that gold atoms, rather than silver atoms, segregate at the surface of the obtained nanoparticles for all the considered alloy compositions. These segregation tendencies are in contrast to previous studies and have consequences on the crystallization dynamics and the subsequent crystal ordering. We finally showed that the underpinning of this surprising segregation dynamics is due to charge transfer and electrostatic interactions rather than surface energy considerations.

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.

Reassignment of magic numbers for icosahedral Au clusters: 310, 564, 928 and 1426

Icosahedral Au clusters with three and four shells of atoms are found to deviate significantly from the commonly assumed Mackay structures. By introducing additional atoms in the surface shell and creating a vacancy in the center of the cluster, the calculated energy per atom can be lowered significantly, according to several different descriptions of the interatomic interaction. Analogous icosahedral structures with five and six shells of atoms are generated using the same structural motifs and are similarly found to be more stable than Mackay icosahedra. The lowest energy per atom obtained here is for clusters containing 310, 564, 928 and 1426 atoms, as compared with the commonly assumed magic numbers of 309, 561, 923 and 1415. Some of the vertices in the optimized clusters have a hexagonal ring of atoms, rather than a pentagon, with the vertex atom missing. An inner shell atom in some cases moves outwards by more than an Ångström into the surface shell at such a vertex site. This feature, as well as the wide distribution of nearest-neighbor distances in the surface layer, can strongly influence the properties of icosahedral clusters, for example catalytic activity. The structural optimization is initially carried out using the GOUST method with atomic forces estimated with the EMT empirical potential function, but the atomic coordinates are then refined by minimization using electron density functional theory (DFT) or Gaussian approximation potential (GAP). A single energy barrier is found to separate the Mackay icosahedron from a lower energy structure where a string of atoms moves outwards in a concerted manner from the center so as to create a central vacancy while placing an additional atom in the surface shell.

Shells in CO2 clusters

Abundance spectra of (CO₂)_N clusters up to N ≈ 500 acquired under a wide range of adiabatic expansion conditions are analyzed within the evaporative ensemble framework. The analysis reveals that the cluster stability functions display a strikingly universal pattern for all expansion conditions. These patterns reflect the inherent properties of individual clusters. From this analysis the size-dependent cluster binding energies are determined, shell and subshell closing sizes are identified, and cuboctahedral packing ordering for sizes above N ≈ 130 is confirmed. It is demonstrated that a few percent variation in the dissociation energies translates into significant abundance variations, especially for the larger clusters.

An ab initio study of size-selected Pd nanocluster catalysts for the hydrogenation of 1-pentyne

The hydrogenation of alkynes is an important reaction in the synthesis of both fine and bulk chemicals. Palladium-based catalysts are widely used and therefore size-selected Pd nanoclusters may provide enhanced performance. An investigation of the adsorption and desorption of the molecules involved in the reaction can shed light on the activity and selectivity of the catalysts. We employ ab initio calculations to investigate the binding energies of all the molecules related to the hydrogenation of 1-pentyne (1-pentyne, 1-pentene, cis-2-pentene, trans-2-pentene and pentane) on a comprehensive set of possible binding sites of two Pd₁₄₇ and Pd₅₆₁ cuboctahedral nanoclusters. We extract the site and size dependence of these binding energies. We find that the adsorption of 1-pentyne occurs preferably on the (100) facets of the nanoclusters, followed by their (111) facets, their edges and their vertices. The molecule binds more strongly on the larger nanoclusters, which are therefore expected to display higher activity. The binding energies of the pentenes are found to be lower on the smaller nanoclusters. Therefore, these molecules are expected to desorb more easily and the small clusters should display better selectivity, i.e., partial hydrogenation to 1-pentene, compared with large clusters. Our results provide guidelines for the optimal design of Pd nanocatalysts.

A Perspective on Modelling Metallic Magnetic Nanoparticles in Biomedicine: From Monometals to Nanoalloys and Ligand-Protected Particles

The focus of this review is on the physical and magnetic properties that are related to the efficiency of monometallic magnetic nanoparticles used in biomedical applications, such as magnetic resonance imaging (MRI) or magnetic nanoparticle hyperthermia, and how to model these by theoretical methods, where the discussion is based on the example of cobalt nanoparticles. Different simulation systems (cluster, extended slab, and nanoparticle models) are critically appraised for their efficacy in the determination of reactivity, magnetic behaviour, and ligand-induced modifications of relevant properties. Simulations of the effects of nanoscale alloying with other metallic phases are also briefly reviewed.

The mechanism underlying the functionalisation of cobalt nanoparticles by carboxylic acids: a first-principles computational study

The promise of biocompatible magnetic nanoparticles with high magnetic saturation in the implementation as drug carriers and hyperthermia agents has generated significant interest in functionalised cobalt nanoparticles. Carboxylic acid coatings on metallic nanoparticles have been shown as an attractive option owing to their respectable stability and biocompatibility. However, only limited information is available on the molecular mechanism leading to the formation of such protective coatings. In this study, ab initio molecular dynamics simulations have been used to unravel the functionalisation mechanism starting from a neutral cobalt cluster and valeric acid molecules. Three stages were detected in the coating process: (i) rapid initial adsorption of acid molecules, (ii) simultaneous adsorption of new molecules and dissociation of those already interacting with the cluster, and, finally, (iii) grouping of dissociated hydrogen atoms and subsequent desorption of acid molecules. The fate of the hydrogen atoms was probed through a combination of static and dynamic ab initio modelling approaches, which predicted H2 generation with favourable energetics. A better understanding of the functionalisation and interaction mechanisms will aid the rational design of biocompatible cobalt nanoparticles for various applications.

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.

Born to be different: the formation process of Cu nanoparticles tunes the size trend of the activity for CO2 to CH4 conversion

We investigate the impact of the formation process of Cu nanoparticles on the distribution of adsorption sites and hence on their activity. Using molecular dynamics, we model formation pathways characteristic of physical synthesis routes as the annealing of a liquid droplet, the growth proceeding via the addition of single atoms, and the coalescence of individual nanoparticles. Each formation process leads to different and characteristic size-dependent distributions of their adsorption sites, catalogued and monitored on-the-fly by means of a suitable geometrical descriptor. Annealed or coalesced nanoparticles present a rather homogeneous distribution in the kind and relative abundance of non-equivalent adsorption sites. Atom-by-atom grown nanoparticles, instead, exhibit a more marked occurrence of adsorption sites corresponding to adatoms and small islands on (111) and (100) facets. Regardless of the formation process, highly coordinated sites are more likely in larger nanoparticles, while the abundance of low-coordination sites depends on the formation process and on the nanoparticle size. Furthermore, we show how each characteristic distribution of adsorption sites reflects in different size trends for the Cu-nanoparticle activity, taking as an example the electro-reduction of CO₂ into CH₄. To this end, we employ a multi-scale method and observe that the faceted but highly defected structures obtained during the atom-by-atom growth become more and more active with increasing size, with a mild dependence on the original seed. In contrast, the activity of Cu-nanoparticles obtained by annealing decreases with their size, while coalesced nanoparticles' activity shows a non-monotonic behaviour.

A theoretical investigation of 38-atom CuPd clusters: the effect of potential parameterisation on structure and segregation

Understanding the structure of bimetallic clusters is increasingly important due to their emerging practical applications. Herein we investigate the structure of 38-atom CuPd clusters using a genetic algorithm with cluster energies described by the semi-empirical Gupta potential. Selected clusters are then refined with density functional theory. Three different parameterisations of the Gupta potential are used and their performance assessed to understand what features of bulk and surfaces are necessary to capture for accurate description of small clusters. Three general regions of motif stability exist; for the Pd majority clusters (Pd38 to Cu4Pd34) the truncated octahedron is most stable, while for clusters of intermediate compositions (Cu5Pd33 to Cu25Pd13) a "pancake" icosahedron is most stable, and for the Cu majority clusters (Cu26Pd12 to Cu38) again the truncated octahedron is most stable. CuPd clusters tend to segregate to a Cu-core, Pd-shell structure if possible, and at higher Cu compositions, the Pd segregates to the faces of the cluster. Using multiple parameterisations of the Gupta potential ensures the full variety of possible structures is found, and improves the search for the most stable CuPd clusters.

The transformation of cuboctahedral to icosahedral nanoparticles: atomic structure and dynamics

The rearrangement of transition metal nanoparticles from cuboctahedral to icosahedral structures is studied for up to 923 atoms. The atomic structure and temperature dependence of the transition are investigated with a well-defined collective variable. This collective variable describes the folding of the square fcc(100) facets into two triangular facets through a linear combination of the diagonals of all fcc(100) facets of all shells of the particle. Activation barriers are determined through harmonic transition state theory and constrained molecular dynamics simulations based on force field potentials. These calculations predict an activation entropy larger than 1 meV K^-1, leading to strongly temperature dependent activation barriers. Density functional theory calculations were additionally performed both as single point calculations and as full optimizations. Cu, Ag, Au and Ni clusters show low barriers for concerted, symmetric transition up to the 309-atomic clusters. In contrast, for Pd, Pt, Rh and Ir higher barriers are required, already for the 147-atomic clusters. With increasing barriers, an asymmetric but still concerted rearrangement becomes energetically more favorable than the fully symmetric transformation. The material-dependence of the transition can be correlated with the melting point of the bulk metals.

Towards a morphology of cobalt nanoparticles: size and strain effects

Cobalt nanoparticles with diameters of 8 nm have recently shown promising performance for biomedical applications. However, it is still unclear how the shape of cobalt clusters changes with size when reaching the nanoparticle range. In the present work, density functional theory calculations have been employed to compare the stabilities of two non-crystalline (icosahedron and decahedron) shapes, and three crystalline motifs (hcp, fcc, and bcc) for magic numbered cobalt clusters with up to 1500 atoms, based on the changes in the cohesive energies, coordination numbers, and nearest-neighbour distances arising from varying geometries. Obtained trends were extrapolated to a 10⁴ size range, and an icosahedral shape was predicted for clusters up to 5500 atoms. Larger sized clusters adopt hcp stacking, in correspondence with the bulk phase. To explain the crystalline/non-crystalline crossovers, the contributions of the elastic strain density and twin boundary from the specimen surfaces to the cohesive energy of different motifs were evaluated. These results are expected to aid the design and synthesis of cobalt nanoparticles for applications ranging from catalysis to biomedical treatments.

Contrasting motif preferences of platinum and gold nanoclusters between 55 and 309 atoms

The atomic structure of size-selected Pt clusters in the range 10-600 atoms is investigated with aberration-corrected scanning transmission electron microscopy and reveals significantly different behaviour from the existing data for Au clusters. The Pt clusters show a dominance of the FCC motif from relatively small sizes, whereas traditionally for Au multiple motifs - the icosahedron, decahedron and FCC motifs (and related structures) compete. The new data motivates a comprehensive computational investigation to better understand similarities and differences in the structures and energetics of the two different metallic clusters. Low energy structures of Pt and Au clusters with 55, 101, 147, 228 and 309 atoms (±2%) are identified using a global optimisation algorithm, and the relative energies found by local minimisation using density functional theory. Our computational results support the experimental observations; for Au clusters all motifs are comparably stable over the whole size range, whereas for Pt, the motifs only compete at the smallest sizes, after which the FCC motif is the most stable. Structural analysis suggests the greater tendency of Au towards amorphisation enables the icosahedron and decahedron to remain competitive at larger sizes.

Structural properties of sub-nanometer metallic clusters

At the nanoscale, the investigation of structural features becomes fundamental as we can establish relationships between cluster geometries and their physicochemical properties. The peculiarity lies in the variety of shapes often unusual and far from any geometrical and crystallographic intuition clusters can assume. In this respect, we should treat and consider nanoparticles as a new form of matter. Nanoparticle structures depend on their size, chemical composition, ordering, as well as external conditions e.g. synthesis method, pressure, temperature, support. On top of that, at finite temperatures nanoparticles can fluctuate among different structures, opening new and exciting horizons for the design of optimal nanoparticles for advanced applications. This article aims to overview geometrical features of transition metal clusters and of their various rearrangements.