An Efficient Method Based on Lattice Construction and the Genetic Algorithm for Optimization of Large Lennard-Jones Clusters

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Abstract
Geometric methods for the construction of three structural motifs, the icosahedron, Ino's decahedron, and the complete octahedron, are proposed. On the basis of the constructed lattices and the genetic algorithm, a method for optimization of large size Lennard-Jones (LJ) clusters is presented. Initially, the proposed method is validated by optimization of LJ13-309 clusters with the above structural motifs. Results show that the proposed method successfully located all the lowest known minima with an excellent performance; for example, based on Ino's decahedron with 147 lattice sites, the mean time consumed for successful optimization of LJ75 is only 0.61 s (Pentium III, 1 GHz), and the percentage success is 100%. Then, putative global minima of LJ310-561 clusters are predicted with the method. By theoretical analysis, these global minima are reasonable, although further verification or proof is still needed.