http:/www.paper.edu.cn Possible Paths towards Magic Clusters Formation Hong H. Liu, En Y. Jiang*, Hai L. Bai, Ping Wu and Zhi Q. Li Tianjin Key Laboratory of Low Dimensional Materials Physics and Preparing Technology, Institute of Advanced Materials Physics, Faculty of Science, Tianjin University, Tianjin 300072, Peoples Republic of China enyong_jiangyahoo.com.cn Chang Q. Sun School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore 639798 Abstract Using a virtual probe method in molecular dynamics approach, we have explored the growing process of atomic clusters by adding atoms in a one-by-one manner to a tetrahedron up to 50 atoms and found that the growing path repeats a process of split-then-merge chaining. The sequential chains merge in the vicinity of the ones with atoms of magic number and then diverge, meaning that, in the cluster growing sequences, the merging of growing paths near magic clusters may increase the appearing probability of the most stable magic clusters. Findings not only demonstrate the possible ways of magic cluster growth but also further clarify the stability of such magic clusters. Key Words: sequence of cluster growth; virtual probe; magic cluster 11. Introduction Growth of isolated or supported nanoclusters has attracted tremendous interests 1,2,3,4. However, it is rather difficult to observe directly how the clusters are formed in experiments due to the small size and the low thermal stability of such small clusters 5,6. Theoreticians often employ the clusters in ground-state structures (GSS) using global optimization arithmetics 7,http:/www.paper.edu.cn 2could form through different sequential paths but merge in the vicinity of the magic sizes. We present a framework focusing on the growing process of Lennard-Jones clusters, using which we simulate the growth of clusters up to 50 atoms with an approach of virtual probe (VP), as described in the next section. We found the clusters grow in a sequential splitting-and-merging manner. The merging of different growing paths on the cluster size of = 12 and 20 shows the process of icosahedrons forming and clarifies why these icosahedrons bind stronger, as observed in the mass spectroscopic studies N5. 2. Principle and approach The method described in Ref. 4 is effective in searching for the GSS of clusters. Adding atoms to the geometric centers or the mass centers of the facets is a favorable way to get compact structures. However, it seems questionable to presume that an atom be trapped exactly at the geometric or the mass center of the facet, instead, the adatom tends to find a position attracting it most. Therefore, a modification of the optimizing method is herein essentially established. It is easy to understand that an atom could be adhered to different positions on the surface of the cluster due to the total cohesive energy of the specific atom. However, it is rather a time-consuming process to try all possible positions in calculation. Therefore, in the calculation, we pick the position attracting the adatom most in one growing path and then others in another path, the merging of different growing paths is found. The key ideas in this method are as follows: (i) the adatom is assumed to be adsorbed at the site where attracts it most; (ii) http:/www.paper.edu.cn 3the growing process of clusters falls into two stages: adatom adsorption and structure relaxation. The only factor determining where an adatom should be added to is the potential energy at the specific site. No one knows what kind of structure will form until the atom has properly settled itself down alone. Thus we can consider that the adatom does not mind what kind of structure it is facing, whether a cluster, a flat surface, or others. Therefore, this method is general to the growth of different structures with different kinds of interatomic interactions. In the MD simulation, Verlet algorithm 18 is adoped. The atoms are binded by Lennard-Jones pair potential: ( )()()612/4ijijijrrrP=, (1) where is the distance between atom andjirij . Unity values for and are assumed for convenience. In calculation, the cluster is put into a closed spherical space of radius R with a perfect reflection boundary. The spherical space is divided into grids. In order to find the growing position (grid) of the adatom, we introduce an imaginary atom as VP to detect the potential energy on each site of the grids. The VP is assumed to interact with other atoms through Eq. 1. With the assistance of the VP, we can obtain the potential energy at each grid contributed from the N atoms of the cluster, http:/www.paper.edu.cn 4( ) =NiivvrPwP1)(, where w is the coordinate of the VP and the VP is denoted with v. is the cluster size prior to the addition of the new atom. NIn the present calculation, the new atom is added to the position where the VP possesses the minimal potential energy, ()(minwP