The distribution pattern of squares on the stability of F4F6-(BN)n (n = 10-22) polyhedrons

To gain an insight into the structures and stability of F4F6-(BN)n polyhedrons with alternation of B and N atoms, a density functional theory study was performed on all isomers of F4F6-(BN)n polyhedrons with n between 10 and 22. The calculation results demonstrate that the lowest energy isomers do not contain B44 bonds (the bonds shared by two squares) and the energies of those isomers containing B44 bonds increase with the number of B44 bonds linearly, indicating that the energetically favored structures of F4F6-(BN)n polyhedrons satisfy the isolated square rule and square adjacency penalty rule. The structural analysis reveals that the stability is determined by the pyramidalization of B and N atoms at the square-square fusion. The binding energy is fitted to the numbers of edges and a model is proposed for predicting the relative stability of these B-N polyhedral molecules.