Linking chemical reactivity, magic numbers, and local electronic properties of clusters

The interplay of local energetics, local electron occupancies, and local density of states is the key to the understanding of chemical reactivity. We define local measures, within a nonorthogonal tight-binding scheme, which clearly and unambiguously determine these local properties for an aggregate of atoms, such as a solid or a cluster. Using these measures, we identify the electronic level mechanisms responsible for the chemical reactivity of clusters of different sizes. A clear and concise picture of why Si₃₃ is chemically inert while Si49A is reactive emerges from this analysis. A scheme for quantifying the dangling bonds is also presented in this work.