Boron fullerenes B(32+8k) with four-membered rings and B32 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 < or = k < or = 7) with four-membered rings and B(32) 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 B(32) 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 B(32) 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 B(32) solids are metallic, but the bct phase is a semimetal.