Polyhedral boranes and elemental boron: direct structural relations and diverse electronic requirements.

Details of the electronic and structural connections between macropolyhedral boranes and elemental boron are reported. The nature of electron deficiency in the beta-rhombohedral polymorph of boron is analyzed by using a molecular fragments approach with boranes as model systems. The B57H36 molecule constructed from such an approach has three more electrons than mandated by the electron-counting rules (Balakrishnarajan, M. M.; Jemmis, E. D. J. Am. Chem. Soc. 2000, 122, 456. Jemmis, E. D.; Balakrishnarajan, M. M.; Pancharatna, P. D. J. Am Chem. Soc. 2001, 123, 4313-4323.) devised for macropolyhedral boranes. This is also confirmed by electronic structure calculations at the extended Hückel and B3LYP/6-31G levels. The aromaticity of this B57H36(3+) molecule is on par with the most stable B12H12(2-) itself, as revealed by nuclear independent chemical shift calculations. The B57 skeleton can be made electron precise by adopting a nido arrangement by eliminating an atom from the closo skeleton, so that three valence electrons will be removed. The exact site of elimination, governed by thermodynamic factors, necessitates the removal of a boron atom from any of the six symmetrically equivalent B[13] sites in the unit cell. This leads to partial occupancies, which causes disorder in packing, as revealed by X-ray structure studies. The rest of the boron atoms are distributed in icosahedral B12 fragments, whose two-electron deficiency is satisfied by the capping of extra atoms, distributed statistically in the interstitial sites. These results show that the three-dimensional network of the idealized beta-rhombohedral unit cell is not stable, unlike the electron-precise carbon polymorphs such as diamond and graphite. Thus, disorder in the form of partial occupancies, interstitial atoms, alien atoms, etc., is necessary for electron sufficiency and hence for the stability of this polymorphic form. Through these ingenious steps, all components of the unit cell attain electron sufficiency, which explains the high thermodynamic stability of the polymorph. The connection established between boranes and elemental boron in terms of their structure and distribution of electrons has important implications in understanding the structure of boron-rich solids and new strategies to utilize their diverse and technologically important properties.