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 (${\text{C}}_{60}$, ${\text{B}}_{80}$, ${\text{C}}_{240}$, and ${\text{B}}_{320}$ fullerenes and ${\text{C}}_{24}$ and ${\text{B}}_{32}$ 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.

Figure 1

(Color online) The structures of boron fullerenes from the $80n^2$ series and their parent carbon fullerenes from $60n^2$ series.

Figure 2

(Color online) The optimized structures of the ${\text{C}}_{24}$ (left) and ${\text{B}}_{32}$ (right) cages.