A new hole density as a stability measure for boron fullerenes.

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