Kekule-Type Structures in Polyhedral Boranes

This concept of Kekule structures can be extended to the 3D deltahedral borane anionsB H (6 n 12). Such Kekule structures make use of three-center B-B-B bonds instead of the carbon-carbon double bonds in benzenoid Kekule structures. Lipscomb s semitopological method for studying the electron and orbital balance in boron networks containing mixtures of B-B two-center and B-B-B three-center bonds is essential for extending the concept of Kekule structures from 2D benzenoid hydrocarbons to 3D deltahedral boranes. 

Lipscomb s semitopological methods make the following assumptions  

Each B-H-B three-center bridge bond corresponds to a filled three-center localized bonding orbital requiring the hydrogen orbital and one hybrid orbital from each boron atom. 

The orbitals and electrons of any particular boron atom are allocated to satisfy first the requirements of the external B-H single bonds and the bridge B-H-B bonds. The remaining orbitals and electrons are allocated to framework molecular orbitals. 

Solving the simultaneous equation (19) leads toy = 3 and t = n - 2 implying the presence of three two-center B-B bonds and - 2 three-center B-B-B bonds. Since a deltahedron with n vertices has 2n - 4 faces, the n - 2 three-center B-B-B bonds will cover exactly half of the faces. In that sense a Kekule-type structure for the deltahedral boranes B H has exactly half of the faces covered by three-center B-B-B bonds just like a Kekule structure for a benzenoid hydrocarbon has half of the edges covered by C=C double bonds. 

---