5.1. Nanoalloys of Group 11 (Cu, Ag, Au) 865 5.1.1. Cu−Ag 866 5.1.2. Cu−Au 867 5.1.3. Ag−Au 870 5.1.4. Cu−Ag−Au 872 5.2. Nanoalloys of Group 10 (Ni, Pd, Pt) 872 5.2.1. Ni−Pd 872 * To whom correspondence should be addressed. Phone: +39010 3536214. Fax:+39010 311066. E-mail: ferrando@fisica.unige.it. † Universita di Genova. ‡ Argonne National Laboratory. § University of Birmingham. | As of October 1, 2007, Chemical Sciences and Engineering Division. Volume 108, Number 3

Nanoalloys: From Theory to Applications of Alloy Clusters and Nanoparticles

The structural properties of free nanoclusters are reviewed. Special attention is paid to the interplay of energetic, thermodynamic, and kinetic factors in the explanation of cluster structures that are actually observed in experiments. The review starts with a brief summary of the experimental methods for the production of free nanoclusters and then considers theoretical and simulation issues, always discussed in close connection with the experimental results. The energetic properties are treated first, along with methods for modeling elementary constituent interactions and for global optimization on the cluster potential-energy surface. After that, a section on cluster thermodynamics follows. The discussion includes the analysis of solid-solid structural transitions and of melting, with its size dependence. The last section is devoted to the growth kinetics of free nanoclusters and treats the growth of isolated clusters and their coalescence. Several specific systems are analyzed.

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Structural properties of nanoclusters: Energetic, thermodynamic, and kinetic effects

The prediction of structure at the atomic level is one of the most fundamental challenges in condensed matter science. Here we survey the current status of the field and consider recent developments in methodology, paying particular attention to approaches for surveying energy landscapes. We illustrate the current state of the art in this field with topical applications to inorganic, especially microporous solids, and to molecular crystals; we also look at applications to nanoparticulate structures. Finally, we consider future directions and challenges in the field.

Crystal structure prediction from first principles

A review is presented of the design and application of genetic algorithms for the geometry optimisation of clusters and nanoparticles, where the interactions between atoms, ions or molecules are described by a variety of potential energy functions. A general introduction to genetic algorithms is followed by a detailed description of the genetic algorithm program that we have developed to identify the lowest energy isomers for a variety of atomic and molecular clusters. Examples are presented of its application to model Morse clusters, ionic MgO clusters and bimetallic “nanoalloy” clusters. Finally, a number of recent innovations and possible future developments are discussed.

Evolving better nanoparticles: Genetic algorithms for optimising cluster geometries

Global optimization of cluster geometries is of fundamental importance in chemistry and an interesting problem in applied mathematics. In this work, we introduce a relatively new swarm intelligence algorithm, i.e. the artificial bee colony (ABC) algorithm proposed in 2005, to this field. It is inspired by the foraging behavior of a bee colony, and only three parameters are needed to control it. We applied it to several potential functions of quite different nature, i.e., the Coulomb–Born–Mayer, Lennard-Jones, Morse, Z and Gupta potentials. The benchmarks reveal that for long-ranged potentials the ABC algorithm is very efficient in locating the global minimum, while for short-ranged ones it is sometimes trapped into a local minimum funnel on a potential energy surface of large clusters. We have released an efficient, user-friendly, and free program “ABCluster” to realize the ABC algorithm. It is a black-box program for non-experts as well as experts and might become a useful tool for chemists to study clusters.

ABCluster: the artificial bee colony algorithm for cluster global optimization.

A study has been made of the structures and stabilities of copper and gold clusters and copper–gold nanoalloy clusters, with up to 56 atoms, modeled by the many-body Gupta potential. For pure copper clusters, the lowest energy structures are found to be based on icosahedral packing, while pure gold clusters tend to form less symmetrical (often amorphous) structures. In a number of cases, the replacement of a single gold atom by copper is found to be sufficient to convert the structure to that of the more symmetrical copper cluster. The lowest energy clusters are generally more difficult to find for the bimetallic clusters than for the pure metallic clusters, due to the presence of homotops (related by permuting Cu and Au atoms), as well as geometrical isomers. The structures of the lowest energy bimetallic clusters exhibit primarily icosahedral packing, with (CuAu)M and (CuAu3)M clusters tending to form layered structures and (Cu3Au)M clusters showing greater Cu–Au mixing.

Theoretical study of Cu–Au nanoalloy clusters using a genetic algorithm

This article describes the application of a genetic algorithm for the structural optimization of 19–50-atom clusters bound by medium-range and short-range Morse pair potentials. The GA is found to be efficient and reliable for finding the geometries corresponding to the previously published global minima [Doye JPK, Wales DJ (1997) J Chem Soc Faraday Trans 93: 4233]. Using the genetic algorithm, only a relatively small number of energy evaluations and minimizations are required to find the global minima. By contrast, a simple random search algorithm often cannot find the global minima of the larger clusters, even after many thousands of searches.

A genetic algorithm for the structural optimization of Morse clusters

The application of a genetic algorithm, for optimizing the geometries of stoichiometric and non-stoichiometric MgO clusters, bound by a simple Coulomb-plus-Born–Mayer potential, is investigated. The genetic algorithm is shown to be efficient and reliable for finding, reproducibly the global minima for these clusters. The variation of the structures of MgO clusters are investigated as a function of the formal charges (±q) on the ions—ranging from q = 1 to q = 2. In agreement with previous studies, lower charges are found to favour compact, rocksalt-like cuboidal clusters, while the higher formal charges favour hollow pseudo-spherical structures. Hexagonal stacks are also found to be stable for small (MgO)N clusters with N = 3n. Comparisons are made with experimental mass spectral
abundances and the results of previous empirical calculations, as well as with more sophisticated model potential and ab initio calculations. Finally, possible ways in which the genetic algorithm search method could be coupled with more accurate calculation methods are discussed.

Investigation of the structures of MgO clusters using a genetic algorithm

A detailed study is made of the structures and relative stabilities of nickel and aluminium clusters and nickel-aluminium "nanoalloy" clusters, with up to 55 atoms, modelled by the many-body Gupta potential. Random search and genetic algorithms are used to find the lowest energy isomers (both geometrical and permutational). For the pure Al and Ni clusters, the lowest energy structures are identical for most nuclearities but different structures are found for clusters with 15-18 atoms -- the Al clusters having non-icosahedral structures. For these nuclearities, we investigate the effect of doping Al atoms into pure Ni clusters and vice versa, finding that the replacement of a single atom by a dopant atom is often sufficient to change the cluster geometry. The lowest energy isomers of nanoalloy clusters with the approximate composition "Ni3Al" generally have structures based on icosahedral packing, though truncated octahedral (fcc packing) motifs are also observed. In agreement with previous studies, the atom ordering in the mixed Ni-Al clusters is found to depend on the maximization of the number of Ni-Al interactions, the minimization of the cluster surface energy, and atom size effects.

Structures, stabilities and ordering in Ni-Al nanoalloy clusters

The application of a Genetic Algorithm, for optimising the geometry of aluminium clusters with 21-55 atoms bound by the many-body Murrell-Mottram potential, is described. In this size regime, a number of different structural motifs are identified-face centred cubic, hexagonal close packed, decahedral and icosahedral structures. The larger clusters consist of hollow icosahedral geometric shells, with Al 55 having a centred icosahedral structure. Evolutionary Progress Plots for Al 19 and Al 38 reveal how the best structure evolves from generation to generation upon operation of the Genetic Algorithm.

Christopher Roberts

Papers

Theoretical study of Cu–Au nanoalloy clusters using a genetic algorithm

A genetic algorithm for the structural optimization of Morse clusters

Investigation of the structures of MgO clusters using a genetic algorithm

Structures, stabilities and ordering in Ni-Al nanoalloy clusters

Geometry Optimisation of Aluminium Clusters Using a Genetic Algorithm