Genetic algorithms for determining the topological structure of metallic clusters
Genetic algorithms (GA) are applied for the optimization of the structure of metallic clusters by the calculation of the ground-state energies from a tight-binding (Hückel) Hamiltonian. The optimum topology or graph is searche by the use of the adjacency matrix A ij as a natural coding. The initial population for N-atom clusters are generated from a representative group of fit cluster structures having N — 1 atoms by the addition Of random connections or hoppings between the Nth atom and the rest of the cluster atoms (A iN = 0 or 1). The diversity of geometries is enlarged by 20% with fully random structures. Several crossover strategies are proposed for the genetic evolution that combine the “parent” clusters while trying to preserve or transmit the physical characteristics of the parents’ topologies. The performance of the different procedures is tested. For N≤ 13, the present GA yield topological structures that are in agreement with previous geometry optimizations performed using an enumerative search (N ≤ 9) or simulated annealing Monte Carlo (10 ≤ N ≤ 13) methods. Limitations and extensions for N ≥ 14 are discussed.
PACS61.46.+w Clusters, nanoparticles and nanocrystalline materials 36.40.Cg Electronic and magnetic properties of clusters 02.60.Pn Numerical optimization
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