Three-dimensional aromaticity in deltahedral boranes and carboranes

Abstract

Methods derived from topology and graph theory indicate that the deltahedral boranes B n H n 2− and the corresponding carboranes C2Bn−2H n (6 ≤n ≤ 12) may be regarded as three-dimensional delocalized aromatic systems in which surface bonding and core bonding correspond to σ-bonding and π-bonding, respectively, in planar polygonal two-dimensional hydrocarbons CinnH n (n−6)+ (n=5/7). The two extreme types of topologies which may be used to model core bonding in deltahedral boranes and carboranes are the deltahedral (D n ) topology based on the skeleton of the underlying deltahedron and the complete (K n ) topology based on the corresponding complete graph. Analyses of the Hoffmann-Lipscomb LCAO extended Huckel computations, the Armstrong—Perkins—Stewart self-consistent molecular orbital computations, and SCF MOab initio GAUSSIAN-82 computations on B6H6 2− indicate that the approximation of the atomic orbitals by the sum of the molecular orbitals, as is typical in modernab initio computations, leads to significantly weaker apparent core bonding approximated more closely by deltahedral (D n ) topology than by complete (K n ) topology.