chapter  3
30 Pages

Two-Dimensional Boron Sheets

Figure 3.2 Top and side views of the flat 2D hexagonal lattice. Gray balls are atoms with rods connecting nearest neighbors. The top view shows the sp2hybrids on each atom oriented to point to the nearest neighbors. The side view shows two pz orbitals on neighboring atoms. The overlapping of these in-plane hybrids along each interatomic axis leads to s bonding and s* antibonding (i.e., symmetric and antisymmetric) combinations that are split by a large energy. If the bonding states are filled by one electron coming from each neighboring atom, then we have two-center bonding, that is, a textbook case of a pair of electrons shared by a pair of atoms. When intra-atomic overlap of hybrids is added, these bonding and antibonding states broaden into bands, but a gap still remains between these states. For the out-of-plane states, one has a single pz orbital on each atom (see Fig. 3.2), which overlaps with those of its neighbors to form p and p* bands. We will see that the sp2+pz basis will also help explain the electronic structure of other 2D boron sheets, but one will have to rotate the sp2 basis to adapt it to the particular structure under consideration.