Theoretical Study of Structural Symmetry in Ternary Clusters

Abstract

The geometrical symmetry presents an intriguing theoretical problem in many kinds of clusters. The diversity of geometrical structures is associated with cluster sizes, different model functions and potential parameters, and ternary clusters are investigated to study the relationship between geometrical symmetry and homotopic symmetry. Ternary Lennard-Jones model potential is studied with different parameters, and the putative global minimum structures of A13B30C12 clusters are optimized using an adaptive immune optimization algorithm. The results show that there mainly exist five geometrical symmetry structures, i.e., Mackay icosahedral, fivefold partial Mackay icosahedral, sixfold pancake, partial double Mackay icosahedral, and amorphous structures. Furthermore, the number of bonds is used to distinguish the geometrical symmetry. The importance of geometrical symmetry and homotopic symmetry determined by potential parameters is discussed. It was found that in the optimization it is more important to generate geometrical symmetry than to optimize homotopic symmetry.