The structure of atomic and molecular clusters, optimised using classical potentials

Abstract

The problem of the determination of the minimum energy configuration of an arrangement of point particles under the interaction of their interatomic forces is discussed. The interatomic forces are described by classical many body potentials. Different optimisation methods are considered, multi level single link, topographical differential evolution and a genetic algorithm but it is shown that genetic algorithms combined with an efficient local optimisation method is especially quick and reliable for this task. In addition to comparing some different optimisation methods, the structures of clusters of atoms described by interatomic potential functions containing up to a few hundred atoms are calculated including some with some special symmetries. A number of applications are given including covalent carbon and silicon clusters, close-packed structures such as argon and silver and the two-component carbon-hydrogen system.

Epitaxial growth of polymorphic systems: The case of sulfathiazole

“…Thus DE has reduced number of user-defined control parameters than other evolutionary algorithms (K, F, G max and population size (N p )). Despite the simplicity of the algorithm, DE has been shown to be a robust and efficient optimisation algorithm in many areas including crystal structure determination from powder X-ray diffraction data, 20 refinement of disordered crystal structures, 21 bankruptcy prediction in banks, 22 optimisation of atomic and molecular clusters 23 and digital filter design. 24 This work investigates the expitaxial interactions between STZ forms II and IV using a computational approach to understand the factors behind the creation of the hybrid materials.…”

Structural studies of Au–Pd bimetallic nanoparticles by a genetic algorithm method

“…Theoretically, the global optimization for searching the stable structures of nanoparticles is a nonpolynomial-complete problem [34]. In this paper, we employed a genetic algorithm (GA) to solve this combinatorial optimization problem, and this algorithm has been proved effectiveness [35,36]. In general, a classical GA procedure mainly includes initialization of population, calculation of fitness, selection, crossover and mutation.…”

Creation of a ternary complex between a crown ether, 4-aminobenzoic acid and 3,5-dinitrobenzoic acid

“…This process is repeated until the population converges onto one solution or a user-defined number of generations (G max ) have passed. DE is a general purpose optimization method and has been successfully applied to many problems in science and engineering including crystalstructure determination from powder diffraction data Tremayne et al, 2002;, the optimization of atomic clusters and hydrocarbon isomers (Ali et al, 2006), modelling E-coli metabolism (Ceric & Kurtanjek, 2006) and the analysis of Xray absorption fine structure (Dimakis & Bunker, 2006). The DE methodology was selected for this problem since a large number of potential minima would be expected and an efficient optimization algorithm is required to interrogate such a complicated hypersurface.…”