Bonding and structural characteristics of Zn-, Cu-, and Ni-encapsulated Si clusters: Density-functional theory calculations

Abstract

The bonding and structural characteristics of metal $(M)$ embedded silicon clusters $\mathrm{M}@{\mathrm{Si}}_{12}$ and $\mathrm{M}@{\mathrm{Si}}_{10}$, $M=\mathrm{Zn},\mathrm{Cu},\mathrm{Ni}$ have been studied in parallel within the framework of the density functional theory with the hybrid nonlocal exchange and correlation functional of Becke and Lee, Yang and Parr (B3LYP). It is illustrated that for Zn and Cu, which are characterized by filled $d$ shells the bonding and structure are largely characterized by the valence metal electrons, contrary to Ni and other transition metals where the bonding is dominated by the filling of the empty $d$ shells by cage electrons. In $\mathrm{M}@{\mathrm{Si}}_{12}$ clusters there is a strong competition between cubic, icosahedral, and hexagonal prismatic structures. However, with the possible exception of $\mathrm{Zn}@{\mathrm{Si}}_{12}$, the corresponding fully symmetric ${O}_{\mathrm{h}}$, ${I}_{\mathrm{h}}$, and ${D}_{6\mathrm{h}}$ structures for all three metals are statically and/or dynamically unstable due to Jahn-Teller distortions. In addition to $\mathrm{M}@{\mathrm{Si}}_{12}$, hydrogenated $\mathrm{M}@{\mathrm{Si}}_{12}{\mathrm{H}}_{12}$, $M=\mathrm{Ni},\mathrm{Zn}$ clusters have been studied in order to examine the changes in the bonding and structural properties induced by saturating the dangling bonds with surface-hydrogen. In these clusters the effect of hydrogen consists in weakening considerable (up to zero) the metal-cage interactions, enhancing the $s{p}^{3}$ cage interactions. This leads in many cases to empty hydrogenated silicon cages, after the removal of the metal atom, which are very stable and symmetrical with large highest occupied-lowest unoccupied molecular orbital (HOMO-LUMO) energy and optical gaps.