Three-dimensional aromaticity: A topological analysis of computational methods

Abstract

The deltahedral boranes Bn Hn2− (6 ≤n ≤ 12) may be regarded as three-dimensional delocalized aromatic systems in which surface bonding and core bonding correspond to σ-bonding andπ-bonding, respectively, in planar polygonal two-dimensional hydrocarbons Cn Hn(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 (Dn) topology based on the 1-skeleton of the underlying deltahedron and the complete (Kn) topology based on the corresponding complete graph. Symmetry factoring of generalized graphs representing the core-bonding interactions in the highly symmetrical octahedral borane B6 H6 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 Mickel 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 (Dn) rather than complete (Kn) topology. Furthermore, theT1u core orbitals which, if pure, would be nonbonding in octahedral (D6) core topology for B6 H62− and bonding in icosahedral (D12) 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 (Kn) core bonding topology gives the correct numbers of bonding orbitals even in cases where the complete graphKn is a poor approximation for the actual core bonding topology.