Ionization of medium-sized silicon clusters and the geometries of the cations

We have performed a systematic ground state geometry search for the singly charged ${\mathrm{Si}}_n$ cations in the medium-size range $\text{(n⩽20)}$ using density functional theory in the local density approximation (LDA) and generalized gradient approximation (GGA). The structures resulting for $\text{n⩽18}$ generally follow the prolate “stacked ${\mathrm{Si}}_{\mathrm{9}}$ tricapped trigonal prism” pattern recently established for the lowest energy geometries of neutral silicon clusters in this size range. However, the global minima of ${\mathrm{Si}}_n$ and ${\mathrm{Si}}_n^{+}$ for $\text{n=6,}$ 8, 11, 12, and 13 differ significantly in their details. For ${\mathrm{Si}}_{\mathrm{19}}$ and ${\mathrm{Si}}_{\mathrm{20}}$ neutrals and cations, GGA renders the prolate stacks practically isoenergetic with the near-spherical structures that are global minima in LDA. The mobilities in He gas evaluated for all lowest energy ${\mathrm{Si}}_n^{+}$ geometries using the trajectory method agree with the experiment, except for $\text{n=18}$ where the second lowest isomer fits the measurements. The effect of gradient corrections for either the neutral or cationic clusters is subtle, but their inclusion proves to be critical for obtaining agreement with the mobility measurements in the $\text{n=15–20}$ range. We have also determined ionization potentials for our ${\mathrm{Si}}_n$ neutral geometries and found that all experimental size-dependent trends are reproduced for $\text{n⩽19.}$ This particularly supports our structural assignments for ${\mathrm{Si}}_{\mathrm{9}},$ ${\mathrm{Si}}_{\mathrm{11}},$ ${\mathrm{Si}}_{\mathrm{12}},$ and ${\mathrm{Si}}_{\mathrm{17}}$ neutrals. The good overall agreement between the measured and calculated properties supports the elucidation of the “prolate” family of silicon clusters as stacks of trigonal prisms.