Magic behavior of (formula presented) and (formula presented) (formula presented) 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 (formula presented) (formula presented) and (formula presented) Mo, and W) clusters. We find an M-encapsulated silicon cage (formula presented) 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 (formula presented) 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 (formula presented) structures are predicted for (formula presented) Hf, Zr, Ru, and Os.