General geometrical rule for stability of carbon polyhedra

Density functional theory calculations are performed on several classes of carbon polyhedra with square, pentagonal, hexagonal and heptagonal faces. The calculated results demonstrate that the polyhedra obey the isolated square rule, square–pentagon adjacency penalty rule, isolated pentagon rule and pentagon adjacency penalty rule in turn. Thus the carbon polyhedra obey the isolated strain rule in general, and the well-known isolated pentagon rule and pentagon adjacency penalty rule are subordinated to it. The binding energy is fitted to the numbers of edges shared by different types of faces and a model is proposed for predicting the relative stability of these polyhedral molecules.