Dipole polarizability of isovalent carbon and boron cages and fullerenes

Recent works have shown that the nonmetallic alpha-boron cages and fullerenes have valence electronic structures that are identical to those of the corresponding carbon cages and fullerenes to which they are structurally related. By studying the first-order response of these systems (C-60, B-80, C-240, and B-320 fullerenes and C-24 and B-32 cages) to an applied static electric field, we show that this similarity in valence electron structures results in an interesting relation between their dipole polarizabilities. The dipole polarizabilities of the alpha-boron cages and fullerenes obtained by density functional calculations are simply proportional to the dipole polarizabilities of the related carbon cages and fullerenes.