Carbon polyhedrons formed by squares and hexagons obeying isolated square rule

Abstract

To gain insight into the structures and stability of F 4 F 6 polyhedrons formed by squares and hexagons, a density functional theory study was performed on all isomers of F 4 F 6 polyhedrons with sizes from 8 to 60. The calculated results demonstrate that the six squares tend to isolate from each other, i.e. these F 4 F 6 polyhedrons obey the isolated square rule. Those isomers with fewer B 44 bonds (square-square adjacencies) are more stable than those with more B 44 bonds, i.e. they obey square adjacency penalty rule. Both of the two rules in F 4 F 6 polyhedrons are in the same status as the isolated pentagon rule and pentagon adjacency penalty rule in F 5 F 6 fullerenes and can be used to screen the lowest energy isomers of F 4 F 6 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.