Structure and relative stability of Si n,Si n −,and doped Si n M clusters ( M = Sc −,Ti,V + ) in the range n = 14 – 18

Abstract

We report on first-principles quantum mechanical optimizations of the minimum energy equilibrium structure of neutral, ${\mathrm{Si}}_{\mathit{n}}$ , and anionic, ${\mathrm{Si}}_{\mathit{n}}^{-}$ , pure silicon clusters, as well as the isoelectronic ${\mathrm{Si}}_{\mathit{n}}\mathrm{M}$ doped clusters ( $\mathrm{M}={\mathrm{Sc}}^{-}\mathrm{,}\mathrm{Ti}\mathrm{,}{\mathrm{V}}^{+}$ ) for $\mathit{n}=14\text{–}18$ . We have published previously some of these results, but additional analysis is contributed here for the first time, particularly for the pure anionic silicon clusters and doped ${\mathrm{Si}}_{\mathit{n}}\mathrm{Ti}$ compounds. The lowest energy isomer of the anionic ${\mathrm{Si}}_{\mathit{n}}^{-}$ cluster shows different geometry than the neutral cluster, except for $\mathit{n}=15\mathrm{,}17$ . The geometries of a few low-lying energy isomers of doped ${\mathrm{Si}}_{\mathit{n}}\mathrm{M}$ does not relate to those of pure silicon clusters in the range of sizes considered in this work. For both pure and doped Si clusters, we analyze the trend of several electronic properties with the cluster size, like the binding energy, the addition energy of the impurity M to pure Si clusters, the second difference of total energy, the Homo-Lumo gap, the average Si-Si and Si-M distance, and the electron affinity. For ${\mathrm{Si}}_{16}\mathrm{M}$ doped clusters we found the largest binding energy, the highest second difference of energy, and the highest Homo-Lumo gap. These facts are manifestations of the special stability of ${\mathrm{Si}}_{16}\mathrm{M}$ clusters found in recent experimental mass spectra, which was rationalized in previous works as a combination of geometrical (near spherical cage-like structure) and electronic effects (l-selection rule of the spherical potential model). Here we present additional arguments, by comparing the partial orbital density of states of the near-spherical Frank-Kasper isomer of ${\mathrm{Si}}_{16}\mathrm{Ti}$ , with that of a non-spherical isomer of ${\mathrm{Si}}_{16}{\mathrm{Sc}}^{-}$ anion. We have also computed the adiabatic electron affinity of pure and doped Si clusters. For doped clusters, the computed electron affinities are in very good agreement with available estimations from experimental photoelectrons spectra, but for pure neutral clusters the calculations underestimate by more than 18% the experimental values.