Carbon polyhedrons formed by squares and hexagons obeying isolated square rule

To gain insight into the structures and stability of F4F6 polyhedrons formed by squares and hexagons,a density functional theory study was performed on all isomers of F4F6 polyhedrons with sizes from 8 to 60.The calculated results demonstrate that the six squares tend to isolate from each other,i.e.these F4F6 polyhedrons obey the isolated square rule.Those isomers with fewer B44 bonds(square-square adjacencies) are more stable than those with more B44 bonds,i.e.they obey square adjacency penalty rule.Both of the two rules in F4F6 polyhedrons are in the same status as the isolated pentagon rule and pentagon adjacency penalty rule in F5F6 fullerenes and can be used to screen the lowest energy isomers of F4F6 polyhedrons as IPR and PAPR do in classic fullerenes.Structural analysis demonstrates that the pyramidalization of carbon atoms at the square-square adjacencies determines the stability of corresponding structures.