Topology of 1-pentagon carbon nanocones - Topological efficiency and magic sizes

In this article topological modeling techniques have been applied to the study of one pentagon carbon nanocones (apical angle 19°) to derive important results about preferred sizes and chemical reactivity. This theoretical model looks to the nanocone just like a 3-connected graph and considers the topological efficiency (or topological roundness) of such a system as the longrange topological potential whose local minima correspond to magic sizes of the nanocone with high probability of formation. This study moreover shows that topology alone can determine a migration of the stable regions of the nanocone along the nanocone itself, leaving in such a way the apical pentagon in a topologically reactive status. This study expands and systematizes previous works on the same subject.