Quantum Chemical Calculations of Proposed Multicage Boron Fullerenes

The Descartes−Euler formula, P + F = C + 2, which is known to apply to single cage carbon and boron fullerenes, is shown here to apply to multicage fullerenes as well. Every carbon multicage fullerene has a corresponding boron multicage geometrical dual, of identical symmetry, as for example in the case of C47 and B30H302-, shown here. The proposed boron multicage fullerenes are studied with molecular orbital calculations to establish their energetic stability, bond lengths, and ionic charge state.