The boron conundrum: which principles underlie the formation of large hollow boron cages?

Extensive optimisation calculations are performed for the B(80) isomers in order to find out which principles underlie the formation of large hollow boron cages. Our analysis shows that the most stable isomers contain triangular B(10) or rhombohedral B(16) building blocks. The lowest-energy isomer has C(3v) symmetry and is characterised by a belt of three interconnected B(16) units and two separate B(10) units. At the B3LYP/6-31G(d) level of theory, this newly discovered isomer is 2.29, 1.48, and 0.54 eV below the leapfrog B(80) of Szwacki et al., the T(h) -B(80) of Wang, and the D(3d) -B(80) of Pochet et al., respectively. Our C(3v) isomer is therefore identified as the most stable hollow cage isomer of B(80) presently known. Its HOMO-LUMO gap of 1.6 eV approaches that of the leapfrog B(80). The leapfrog principle still remains a reliable scheme for producing boron cages with larger HOMO-LUMO gaps, whereas the thermodynamically most stable B(80) cages are formed when all pentagonal faces are capped. We show that large hollow cages of boron retain a preference for fullerene frames. The additional capping is in accordance with the following rules: preference for capping of pentagonal faces, formation of B(10) and/or B(16) units, homogeneous distribution of the hexagonal caps, and hole density approaching 1/9. Although our most stable B(80) isomer still remains higher in energy than the B(80) core-shell structure, we show that by applying the bonding principles to larger structures it is possible to construct boron cages with higher stabilisation energy per boron atom than the core-shell structure; a prototypical example is B(160). This clearly shows the continuous competition between the two suggested construction schemes, namely, the formation of multiple-shell structures and hollow cages.