Magic numbers of silicon clusters

A structural model for intermediate-size silicon clusters is proposed that is able to generate unique structures without any dangling bonds. This structural model consists of a bulklike core of five atoms surrounded by a fullerenelike surface. Reconstruction of the ideal fullerene geometry results in the formation of crown atoms surrounded by π-bonded dimers. This model yields unique structures for ${\mathrm{Si}}_{33}$, ${\mathrm{Si}}_{39}$, and ${\mathrm{Si}}_{45}$ clusters without any dangling bonds and hence explains why these clusters are the least reactive towards chemisorption of ammonia. Finally, reagent-specific chemisorption reactivities observed experimentally are explained based on the electronic structures of the reagents.