Search for Global Minimum Structures of (n = 1-15) Using xTB-Based Basin-Hopping Algorithm

A new program for searching global minimum structures of atomic clusters using basin-hopping algorithm based on the xTB method was developed here. The program can be performed with a much higher speed than its replacement directly based on DFT methods. Considering the structural varieties and complexities in finding their global minimum structures, phosphorus cluster cations were studied by the program. The global minimum structures of cationic $$ (n = 1-15) clusters are determined through the unbiased structure searching method. In the last step, further DFT optimization was performed for the selected isomers. For $$ (n = 1-4, 7), the found global minimum structures are in consistent with the ones previously reported; while for $$ (n = 5, 6, 8-12), newly found isomers are more energy-favorable than those previously reported. And those for $$ (n = 13-15) are reported here for the first time. Among them, the most stable isomers of $$ (n = 4-6, 9) are characterized by their C_3v, C_s, C_2v and C_s symmetry, in turn. But those of $$ (n = 7, 8, 10-12), no symmetry has been identified. The most stable isomers of $$ and $$ are characterized by single P-P bonds bridging units inside the clusters. Further analysis shows that the pnicogen bonds play an important role in the stabilization of these clusters. These results show that the new developed program is effective and robust in searching global minimum structures for atom clusters, and it also provides new insights into the role of pnicogen bonds in phosphorus clusters.