Family of boron fullerenes: General constructing schemes, electron counting rule, and<i>ab initio</i>calculations

Abstract

A set of general constructing schemes is unveiled to predict a large family of stable boron monoelemental, hollow fullerenes with magic numbers $32+8k$ $(k\ensuremath{\ge}0)$. The remarkable stabilities of these new boron fullerenes are then studied by intense ab initio calculations. An electron counting rule as well as an isolated hollow rule are proposed to readily show the high stability and the electronic bonding property, which are also revealed applicable to a number of newly predicted boron sheets and nanotubes.