Filled Pentagons and Electron Counting Rule for Boron Fullerenes.

We have revisited the general constructing schemes for a large family of stable hollow boron fullerenes with 80 + 8n (n = 0, 2, 3, ...) atoms. In contrast to the hollow pentagon boron fullerenes with 12 hollow pentagons, the stable boron fullerenes constitute 12 filled pentagons and 12 additional hollow hexagons, which are more stable than the empty pentagon boron fullerenes including the "magic" B80 buckyball. On the basis of results from first-principles density-functional calculations, an empirical rule for filled pentagons is proposed along with a revised electron counting scheme to account for the improved stability and the associated electronic bonding feature.