Christopher Roberts

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

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.

Investigation of the structures of MgO clusters using a genetic algorithm

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.

Geometry Optimisation of Aluminium Clusters Using a Genetic Algorithm

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 Al55 having a centred icosahedral structure. Evolutionary Progress Plots for Al19 and Al38 reveal how the best structure evolves from generation to generation upon operation of the Genetic Algorithm.

Global optimization analysis of water clusters (H2O)n (11⩽n⩽13) through a genetic evolutionary approach

The structures and stabilities of water clusters (H2O)n with 11⩽n⩽13 are determined by a genetic algorithm approach with two new evolutionary operators—namely annihilator and history operators. These studies show that the modified genetic algorithm provides an efficient procedure for calculating global minima with an especial attention to molecular water clusters. The actual results are in quantitative agreement with previous calculations using the basin hopping Monte Carlo method.

Genetic Algorithms for the Geometry Optimization of Clusters and Nanoparticles

A review is presented of the design and application of Genetic Algorithms for the geometry optimization (energy minimization) of clusters and nanoparticles, where the interactions between atoms, ions or molecules are described by a variety of potential energy functions (force fields). A detailed description is presented of the Birmingham Cluster Genetic Algorithm Program, developed in our group, and a number of specific applications are highlighted. Finally, a number of recent innovations and possible future developments are discussed.