PGA: A new particle swarm optimization algorithm based on genetic operators for the global optimization of clusters.

ABSTRACT

We have developed a global optimization program named PGA based on particle swarm optimization algorithm coupled with genetic operators for the structures of atomic clusters. The effectiveness and efficiency of the PGA program can be demonstrated by efficiently obtaining the tetrahedral Au20 and double-ring tubular B20, and identifying the ground state ZrSi 17 - 20 - $$ {\mathrm{ZrSi}}_{17\hbox{--} 20}^{-} $$ clusters through the comparison between the simulated and the experimental photoelectron spectra (PESs). Then, the PGA was applied to search for the global minimum structures of Mg n - $$ {\mathrm{Mg}}_n^{-} $$ (n = 3-30) clusters, new structures have been found for sizes n = 6, 7, 12, 14, and medium-sized 21-30 were first determined. The high consistency between the simulated spectra and the experimental ones once again demonstrates the efficiency of the PGA program. Based on the ground-state structures of these Mg n - $$ {\mathrm{Mg}}_n^{-} $$ (n = 3-30) clusters, their structural evolution and electronic properties were subsequently explored. The performance on Au20, B20, ZrSi 17 - 20 - $$ {\mathrm{ZrSi}}_{17\hbox{--} 20}^{-} $$ , and Mg n - $$ {\mathrm{Mg}}_n^{-} $$ (n = 3-30) clusters indicates the promising potential of the PGA program for exploring the global minima of other clusters. The code is available for free upon request.