THREE-DIMENSIONAL AROMATICITY: A TOPOLOGICAL ANALYSIS OF COMPUTATIONAL METHODS

deltahedral boranes BnHn2-(6 <= n <= 12) may be regarded as three-dimensional delocalized aromatic systems in which surface bonding and core bonding correspond to sigma-bonding and pi-bonding, respectively, in planar polygonal two-dimensional hydrocarbons CnHn(n-6)+ (n = 5, 6, 7). The two extreme types of topologies which may be used to model core bonding in deltahedral boranes are the deltahedral (D-n) topology based on the 1-skeleton of the underlying deltahedron and the complete (K-n) topology based on the corresponding complete graph. Symmetry factoring of generalized graphs representing the core-bonding interactions in the highly symmetrical octahedral borane B6H62- and icosahedral borane B12H122- leads to methods for separating the effects of core and surface bonding in molecular orbital energy parameters. Such analyses of the Hoffmann-Lipscomb LCAO-MO extended Huckel computations, the Armstrong-Perkins-Stewart self-consistent molecular orbital computations, and SCF MO ab initio Guassian 82 computations on B6H62- and B12H122- indicate that the approximation of atomic orbitals by a sum of Gaussians, as is typical in modem ab initio computations, leads to significantly weaker apparent core bonding approximated more closely by deltahedral (D-n) rather than complete (K-n) topology. Furthermore, the T-1u core orbitals which, if pure, would be nonbonding in octahedral (D-6) core topology for B6H62- and bonding in icosahedral (D-12) core topology for B12H122-, become antibonding through strong core-surface mixing. Because of this, the simpler graph-theory derived model for deltahedral boranes using complete (K-n) core bonding topology gives the correct numbers of bonding orbitals even in cases where the complete graph K-n is a poor approximation for the actual core bonding topology.