Experimental evidence of orbital order inα-B12andγ-B28polymorphs of elemental boron

Abstract

The electron density of the $\ensuremath{\alpha}$ form of boron has been obtained by multipole refinement against high-resolution, single-crystal x-ray diffraction data measured on a high-quality single crystal at a temperature of 100 K. Topological properties of this density have been used to show that all chemical bonds between B${}_{12}$ clusters in $\ensuremath{\alpha}$-B${}_{12}$ are formed due to one orbital on each boron atom that is oriented perpendicular to the surface of the cluster. It is shown that the same orbital order on B${}_{12}$ clusters persists in both $\ensuremath{\alpha}$-B${}_{12}$ and $\ensuremath{\gamma}$-B${}_{28}$ polymorphs and in several dodecaboranes, despite the fact that in every case the B${}_{12}$ clusters participate in entirely different kinds of exocluster bonds. It is likely that the same orbital order of B${}_{12}$ clusters can explain bonding in other boron polymorphs and boron-rich solids.