Pentagonal rings and nitrogen excess in fullerene-based BN cages and nanotube caps

Classical fullerene polyhedra are considered as candidates for boron-nitrogen cages. Simple arguments show that nitrogen-rich, fullerene-like cages with the general formula B_xN_x+4 can be constructed to have just six N-N bonds, with full B,N alternation in all hexagonal rings. Systematic density-functional tight-binding calculations indicate special stability for such cages when they contain six isolated pentagon pairs. Closure of BN nanotubes with three isolated pentagon pairs gives an alternative to the usual explanation of their observed flat tips in terms of square rings. Inclusion in polyhedra of various combinations of squares, pentagon-pentagon and pentagon-heptagon pairs would lead to BN cages and shells where nitrogen excess correlates with sphericity.