Boron–nitrogen analogues of the fullerenes: the isolated-square rule

Abstract

Trivalent polyhedra with six square and (x– 4) hexagonal faces are candidates for fully alternating (BN)_x‘inorganic fullerene’ cages. Systematic density-functional tight-binding calculations for 4 ⩽x⩽ 30 show that the most stable isomer of this type will have isolated squares, whenever mathematically possible. This rule of thumb for (BN)_x cages is the counterpart of the powerful isolated-pentagon rule for the all-carbon fullerenes.