Chemical Applications of Topology and Group Theory. 23. A Comparison of Graph-Theoretical and Extended Huckel Methods for Study of Bonding in Octahedral and Icosahedral Boranes.

The graph theory derived model for the bonding topology in the globally delocalized polyhedral boranes B6H62- is evaluated by comparison of the energies of the core molecular orbitals with those obtained by the 1962 LCAO-MO extended Huckel calculations of Hoffmann and Lipscomb. Of particular interest is how well the complete graphs K sub 6 and K sub 12 used in the graph theory derived model approximate the bonding topologies of the unique internal orbital radial orbitals of the octahedron and icosahedron, respectively. In the case of the B6H62- octahedron the single positive eigenvalue of the K sub 6 graph corresponds to the results from the extended Huckel calculations. In the case of the B12H122- icosahedron the graph theory derived model is far less satisfactory since the singl positive eigenvalue of the K sub 12 graph disagrees with the four bonding core molecular orbitals an A1g and three triply degenerate T sub 1u molecular orbitals found by the extended Huckel calculations after removing the effect of the mixing of core and surface bonding orbitals corresponding to the same irreducible representations. However, this core-surface orbital mixing raises the energy of the triply degenerate T sub 1u core molecular orbitals to antibonding levels so that the graph theory derived model fortuitiously gives correct skeletal electron counts for the regular icosahedron despite this fundamental error.