Stabilization mechanism of Si12 cage clusters by encapsulation of a transition-metal atom:: A density-functional theory study

We systematically studied the geometrical and electronic structures of transition-metal (M)-encapsulating Si-12 cage clusters, MSi12 (M=Hf, Ta, W, Re, Os, Ir, Pt, and Au), mainly focusing on their outstanding stability, using calculations based on density-functional theory. We found that the MSi12 clusters except HfSi12 belong to either of two distinct structural classes, the D-6h-symmetric hexagonal prism (HP; for M=Ta, W, Re, and Os; total number of valence electrons per cluster, N-nu, ranging from 53 to 56) and less-symmetric four pentagonal face (FPF; M=Re, Os, Ir, Pt, and Au; N-nu ranging from 55 to 59) structures. The HP structure is particularly stabilized at N-nu=54, which is understood in terms of the electronic shell closure of the M atoms due to the 18-electron rule, and the geometrical symmetry is maintained for N-nu=53, 55, and 56 by the covalent bonding between the M atom and the Si cage accompanied by the cage-to-M charge transfer. The FPF structure is lowest in energy for N-nu=56 and is maintained by the same covalent-bond/charge-transfer mechanism for other values of N-nu. We propose that all these results originate from the electronic rigidness of the HP and FPF Si cages against the variation of N-nu, which is the leading factor governing the stability of MSi12.