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

A set of general constructing schemes is unveiled to predict a large family of stable boron monoelemental, hollow fullerenes with magic numbers $32+8k$ $\left(k\ge 0\right)$. 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.

Figure 1

(Color online) The snowdroplike structures in ${\text{B}}_{80}$ and new boron sheet (NBS). (a) A snowdroplike motif, in which a filled hexagon (FH) is surrounded by three FHs and three hollows (pentagons or hexagons, denoted by circles); (b) ${\text{B}}_{80}$; (c) NBS, the yellow parallelogram indicates a unit cell of the NBS. The blue atoms form the snowdroplike units in ${\text{B}}_{80}$ and NBS.

Figure 2

(Color online) Illustration of leapfrog and modified leapfrog transformations. (a) A three-connected vertex becomes a new hexagon (in leapfrog) or a hexagon with an additional atom in center (in modified leapfrog); (b) a ${\text{C}}_{20}$ converts to ${\text{C}}_{60}$ and ${\text{B}}_{80}$ by the leapfrog and modified leapfrog transformations, respectively; (c) a ${\text{C}}_{24}$ transforms to ${\text{C}}_{72}$ and ${\text{B}}_{96}$.

Figure 3

(Color online) Schematic structures and Mulliken atomic charge populations of several boron S-fullerenes. The unit of color bar is electrons/${\text{bohr}}^3$.

Figure 4

(Color online) (a) Energy levels near HOMO-LUMO gaps of ${\text{C}}_{60}$, ${\text{B}}_{80}$, ${\text{C}}_{72}$, ${\text{B}}_{96}$, ${\text{C}}_{78}$, and ${\text{B}}_{104}$; the profiles of HOMO and LUMO orbitals of (b) ${\text{B}}_{80}$, (c) ${\text{B}}_{96}$, and (d) ${\text{B}}_{104}$.