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 LJ 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 LJ is only 0.61 s (Pentium III, 1 GHz), and the percentage success is 100%. Then, putative global minima of LJ clusters are predicted with the method. By theoretical analysis, these global minima are reasonable, although further verification or proof is still needed.
On the basis of the icosahedral and decahedral lattices, the lowest energies of the Lennard-Jones (LJ) clusters containing 562-1000 atoms with the two motifs are obtained by using a greedy search method (GSM). Energy comparison between the decahedra and icosahedra shows that icosahedral structures are predominant. However, most of the icosahedral structures with the central vacancy are more stable than that without the central vacancy. On the other hand, in the range of 562-1000 atoms, there are 41 LJ clusters with the decahedral motif. The number of decahedra increases remarkably compared with the smaller LJ clusters. Consequently, the magic numbers and growth characters of decahedral clusters are also studied, and the results show that the magic numbers of intermediate decahedral clusters occur at 654, 755, 807, 843, 879, 915, and 935.
The lowest icosahedral and decahedral energies of LJ1001-1610 clusters are obtained using a greedy search method (GSM) based on lattice construction. By comparing the lowest energies of icosahedral and decahedral clusters with the same atoms, the structural transition of LJ clusters is studied. Results show that the critical size from icosahedra to decahedra is located at N = 1034. When the cluster size is larger than 1034, the optimal structures are decahedra except the LJ1367-1422 clusters near the magic number, 1402, of icosahedra. However, the energies of icosahedra near the next magic number, 2044, are higher than that of decahedra, which implies that decahedra will be the optimal structure when the cluster size is larger than 1422, even for those clusters near the magic numbers of icosahedra.
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