Evolving better nanoparticles: Genetic algorithms for optimising cluster geometries

Abstract

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.

Analysis of Crossover Operators for Cluster Geometry Optimization

“…It selects sub-clusters of the parents and combines them in such a way that it increases the likelihood of preserving relevant features of promising solutions. Since its proposal, C&S has been adopted by many researchers that applied EAs to cluster optimization problems (Hartke, 2001;Johnston, 2003). Results confirm that it contributes to enhance the efficacy of the optimization algorithm.…”

“…It is well-known from previous studies that hybrid approaches are particularly effective in discovering high quality solutions for cluster geometry optimization problems (Deaven & Ho, 1995;Doye et al, 2004;Hartke, 2001;Johnston, 2003). On the one hand, the EA is able to efficiently sample large areas of the search space.…”

“…Johnston proposed the first hybrid EA for this problem. It was applied to short and medium range Morse clusters and discovered all putative global optima until 50 atoms (Johnston, 2003). In 2002, Locatelli and Schoen proposed population-basin hopping with a two-phase local optimization (Locatelli & Schoen, 2002).…”

“…For an instance with N atoms, it encodes 3×N real values specifying the Cartesian coordinates of each particle. The domain for all variables is [0, N 1/3 ] (Johnston, 2003). Only interatomic distances larger than 0.5 are allowed, since the potential becomes too repulsive is two atoms approach too much.…”

“…Since the early 1990's Evolutionary Algorithms (EAs) have been increasingly applied to this task (Deaven & Ho, 1995;Doye et al, 2004;Grosso et al, 2007;Hartke, 2001;Johnston, 2003;Pereira & Marques, 2009;Zeiri, 1995). State-of-the-art methods usually combine a global evolutionary component with a gradient-driven local search procedure.…”