(BN)n polyhedrons with octagon(s) obeying the square adjacency penalty rule

The structures and stabilities of (BN)n polyhedrons composed of squares, hexagons and octagons with the alternation of B and N atoms are studied with density functional theory method. The calculated results demonstrate that the lowest energy isomers are the structures without octagon; the second lowest energy isomers of (BN)10, (BN)12 and (BN)14 contain one, one and two octagons, respectively. The isomers with octagon(s) also satisfy the square adjacency penalty rule, and their energies markedly increase with the number of octagons. Usually, the lowest energy isomers with different number of octagons have approximate sphericity, fewest B44 bonds and large HOMO-LUMO gaps. Structural analysis demonstrates that the pyramidalization of B and N atoms determines the stability of (BN)n polyhedrons.