B cluster stability, reactivity, and its planar structural precursor.

We report a comprehensive first-principles study of the structural and chemical properties of the recently discovered B cage. It is found to be highly reactive and can exothermically dimerize, regardless of the orientation, by overcoming a small energy barrier ≃0.06 eV. The energy gap of the system varies widely with the aggregation of the increasing number of B cages, from 3.14 eV in a single B, to 1.54 eV in the dimer, to 1.25 eV in the trimer. We also explore a recipe for protecting the B cage by sheathing it within a carbon shell and identify carbon nanotubes with a radius of ∼6 Å as optimal hosts for an isolated cage. It is demonstrated that B can be unfolded into a planar 'molecule' that tessellates the plane. The corresponding 2D boron sheet constitutes a structural precursor foldable into this unique boron cage structure of current interest.