Polyhedral boranes and elemental boron: Direct structural relations and diverse electronic requirements

Details of the electronic and structural connections between macropolyhedra l boranes and elemental boron are reported. The nature of electron deficien cy in the beta -rhombohedral polymorph of boron is analyzed by using a mole cular fragments approach with boranes as model systems. The B57H36 molecule constructed from such an approach has three more electrons than mandated b y the electron-counting rules (Balakrishnarajan, M. M.; Jemmis, E:. D. J. A m. Chem. Sec. 2000, 122, 456. Jemmis, E. D.; Balakrishnarjan, M. M.; Pancha ratna, P. D. J. Aln Chem. Sec. 2001, 123, 1313-4323.) devised for macropoly hedral boranes. This is also confirmed by electronic structure calculations at the extended Huckel and B3LYP/6-31G* levels. The aromaticity of this B5 7H363+ molecule is on par with the most stable B12H122- itself, as revealed by nuclear independent chemical shift calculations. The B-57 Skeleton can be made electron precise by adopting a nido arrangement by eliminating an a tom from the close skeleton, so that three valence electrons will be remove d. The exact site of elimination? governed by thermodynamic factors, necess itates the removal of a boron atom from any of the sis symmetrically equiva lent 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 re st Of the boron atoms are distributed in icosahedral B-12 fragments, whose two-electron deficiency is satisfied by the capping of extra atoms, distrib uted statistically in tile 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 a nd graphite. Thus, disorder in the form of partial occupancies, interstitia l 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 explain s the high thermodynamic stability of the polymorph. The connection establi shed between boranes and elemental boron in terms of their structure and di stribution of electrons has important implications in understanding the str ucture of boron-rich solids and new strategies to utilize their diverse and technologically important properties.