First-principles study of the possibility of condensed phases of endohedral silicon cage clusters

Recently, a new set of clusters in which twelve Si atoms encapsulate one transition metal atom were found to be especially stable. Making use of $M{\mathrm{Si}}_{12}$ clusters $(M=\mathrm{N}\mathrm{b},\mathrm{W})$ we carry out a first-principles study of the possibility of synthesizing a crystalline phase using such clusters as elementary building blocks. To this end we carry out an ab initio study of the interaction energy between two $M{\mathrm{Si}}_{12}$ clusters as a function of their separation. We also perform an ab initio Langevin quantum molecular dynamics simulation of solid $M{\mathrm{Si}}_{12}$ at constant temperature and pressure. We find that the interaction energy between Si atoms in neighboring clusters is comparable to that found in bulk Si. In the solid phase, the cage structure of $M{\mathrm{Si}}_{12}$ disappears during the simulation. These results indicate that the clusters should not conserve their integrity in condensed phases.