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We investigate the stability of boron fullerene sets B76, B78 and B82. Weevaluate the ground state energies, nucleus-independent chemical shift (NICS),the binding energies per atom and the band gap values by means offirst-principles methods. We construct our fullerene design by capping ofpentagons and hexagons of B60 cage in such a way that the total number of atomsis preserved. In doing so, a new hole density definition is proposed such thateach member of a fullerene group has a different hole density which depends onthe capping process. Our analysis reveal that each boron fullerene set has itslowest-energy configuration around the same normalized hole density and themost stable cages are found in the fullerene groups which have relatively largedifference between the maximum and the minimum hole densities. The result is anew stability measure relating the cage geometry characterized by the holedensity to the relative energy.

A New Hole Density as a Stability Measure for Boron Fullerenes