Bonding and structures in silicon clusters: A valence-bond interpretation

Electronic-structure calculations using the ab initio generalized-valence-bond approach have been used to investigate the structure and bonding of silicon clusters ${\mathrm{Si}}_3$–${\mathrm{Si}}_{10}$. While several previous studies of the structures of these clusters have been presented, this is the first to provide an in-depth analysis of the bonding. The importance of including electronic correlation effects self-consistently in determining the cluster structures is emphasized. New geometrical structures are found for ${\mathrm{Si}}_8$ and ${\mathrm{Si}}_{10}$ that have nearly identical energies to previously proposed structures. In addition, for ${\mathrm{Si}}_6$ we find the relative stabilities of two structures to be reversed from previous work, leading to a different ground state. It is found that these clusters exhibit bonding characteristics typical of both metals (charge density in interstitial regions) and covalent semiconductors (charge density between pairs of atoms). The insight gained regarding the bonding in the small clusters is used to predict the structures for larger ‘‘magic-number’’ silicon clusters containing 21, 25, 33, 39, and 45 atoms, whose positive ions are found experimentally to have significantly lower reactivities than the ions containing other numbers of atoms. These proposed cluster structures are based on 17-atom bulklike cores whose surfaces resemble those found in reconstructed silicon surfaces. The relationship of the bonding in the small clusters to the bonding at surfaces is also considered. The analogies are quite striking and strongly suggest that local-bonding considerations may be a critical component in understanding the structures and properties in both situations.