Magic behavior of Si ₁₅ M and Si ₁₆ M (M = Cr, Mo, and W) clusters

Ab initio electronic-structure calculations based on pseudopotential plane-wave method and generalized gradient approximation for the exchange-correlation energy are performed on Si _n M (n = 14-17 and M = Cr, Mo, and W) clusters. We find an M-encapsulated silicon cage M @ Si ₁₅ derived from a cubic structure to be the optimally close packed for these elements. There are competing growth modes so that a fullerenelike capped cage of Si ₁₆ M has the lowest energy leading to their simultaneous magic behavior in agreement with experiments. The binding energy, the highest occupied-lowest unoccupied molecular orbital gap and the embedding energy of M are large, giving rise to their strong stability and complete quenching of the magnetic moment of M. Similar cubic M @ Si ₁₅ structures are predicted for M = Ti, Hf, Zr, Ru, and Os.