Three-dimensional aromaticity in deltahedral boranes and carboranes

Methods derived from topology and graph theory indicate that the deltahedral boranes B_nH_n^2– and the corresponding carboranes C₂B_n–2H_n (6 n 12) may be regarded as three-dimensional delocalized aromatic systems in which surface bonding and core bonding correspond to -bonding and -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 Hückel 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.This work was presented at the Workshop The Modern Problems of Heteroorganic Chemistry sponsored by the A. N. Nesmeyanov Institute of Organoelement Compounds of the Russian Academy of Sciences (May 8–13, 1993).Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 8, pp. 1353–1360, August, 1993.