Wannier Functions Study of Chemical Bonds in B12 and B28

We report a study of the chemical bond network in two boron polymorphs (B12 and the recently discovered high-pressure phase B28 [1]) by Maximally Localized Wannier Functions (MLWFs) [2]. Starting with the B12 phase, whose bonding network is well understood, we have found three two-center (2c) MLWFs and two three-center (3c) MLWFs connecting neighboring boron icosahedra, in addition to 13 skeletal MLWFs, in agreement with Bader's topological analysis.The situation is different in B28, which can be seen as composed by a network of B12 icosahedra linked by B2 dumbbells. There, Bader's analysis found a 3c bond between B1 and B2 atoms (see figure, left panel) and no evidence of bonding between B1 and B3 atoms. The 94 MLWFs revealed instead a pair of 3c bonds (between B1, B2 and B3 atoms), whose center, however, is shifted towards the B2-B3 bond (see Fig. 1, right panel). By carefully analyzing the MLWFs of the icosahedra, we have found that the B2-B2 centered Wannier Function has a substantial multi-center character, extending not only on the two edge-sharing faces of the icosahedron, but also towards the B2-B1-B2 triangle. Finally, we analyzed the electronic structure of the two polymorphs, by constructing and diagonalizing the minimal tight-binding Hamiltonian in the Wannier basis. References [1] A. R. Oganov, et al., Nature 457 (2009) 863. [2] N. Marzari, D. Vanderbilt, Phys. Rev. B 56 (1997) 12847.