Structures and dynamical properties of ${\mathrm{C}}_n,$ ${\mathrm{Si}}_n,$ ${\mathrm{Ge}}_n,$ and ${\mathrm{Sn}}_n$ clusters with n up to 13

Car-Parrinello molecular dynamics simulated annealings were carried out for clusters ${\mathrm{Si}}_n,$ ${\mathrm{Ge}}_n,$ and ${\mathrm{Sn}}_n$ $(n<~13).$ We investigate the temperature regions in which these clusters transform from a “liquidlike” phase to a “solidlike” phase, and then from the “solidlike” phase to the ground-state structures. Additional simulated annealing was also performed for the cluster ${\mathrm{C}}_{13}$ which is selected as a prototype of small carbon clusters. In addition to the discovery of structures for Sn and Ge clusters, our simulation results also provide insights into the dynamics of cluster formation.