Boron fullerenes B_32+8k with four-membered rings and B ₃₂ solid phases: Geometrical structures and electronic properties

Based on ab initio calculations, we have studied the geometrical, electronic properties and chemical bonding of boron fullerenes B_32+8k (0 ≤k≤ 7) with four-membered rings and B₃₂ solid phases. The relative energies and the energy gaps between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) have been calculated, showing that the stabilities grow with the increase of fullerene size, where the smallest cage B₃₂ bears the largest HOMO-LUMO gap. The frontier orbitals of B_32+8k show some similarities with those of the corresponding carbon fullerenes C_24+6k, implying that they may have similar chemical properties. It is found that B₃₂ cages can condense to form solid phases of simple cubic (sc), face-centered cubic (fcc), body-centered cubic (bcc), and body-centered tetragonal (bct) structures, where the bct phase is observed to be the most stable. Electronic structure calculations reveal that the sc, fcc and bcc phases of B₃₂ solids are metallic, but the bct phase is a semimetal.