Theoretical study of Bernal polyhedron of aluminum atomic clusters

A method based on a genetic algorithm was used to determine the lowest energy structure of an atomic cluster in an arbitrary model potential. The method operated on a population of candidate structures to produce new candidates with lower energies, and finally the lowest energy structure can be obtained. We applied the genetic algorithm to a tight-binding (TB) model potential for aluminum clusters. With this potential, the algorithm efficiently found the lowest energy structures of Al-6, Al-8, Al-9, Al-10 clusters starting from a random atomic collection of atoms. The lowest energy structures of Al-6, Al-8, Al-9, Al-10 were found to adopt four forms of Bernal polyhedron. The density function theory (DFT) calculation was also done and the result shows that the four geometries are the minimums on the potential surface.