Structure and vibrational spectra of low-energy silicon clusters

Abstract

We have identified low-energy structures of silicon clusters with 9 to 14 atoms using a nonorthogonal tight-binding method (TB) based on density-functional theory (DF). We have further investigated the resulting structures with an accurate all-electron first-principles technique. The results for cohesive energies, cluster geometries, and highest occupied to lowest unoccupied molecular orbital (HOMO-LUMO) gaps show an overall good agreement between DF-TB and self-consistent-field (SCF) DF theory. For Si${}_9$ and Si${}_{14},$ we have found equilibrium structures, whereas for Si${}_{11},$ Si${}_{12},$ and Si${}_{13},$ we present clusters with energies close to that of the corresponding ground-state structure recently proposed in the literature. The bonding scheme of clusters in this size range is different from the bulk tetrahedral symmetry. The most stable structures, characterized by low energies and large HOMO-LUMO gaps, have similar common subunits. To aid in their experimental identification, we have computed the full vibrational spectra of the structures, along with the Raman activities, IR intensities, and static polarizabilities, using SCF-DF theory within the local-density approximation (LDA). This method has already been successfully applied to the determination of Raman and IR spectra of silicon clusters with 3–8, 10, 13, 20, and 21 atoms.