Chapter 14 - Three-dimensional Analogues of Kekulé Structures for Deltahedral Boranes

Abstract

Localized structures analogous to the Kekulé structures of benzenoid hydrocarbons can be constructed for the deltahedral boranes BnHn2- (6 ≤ n ≤ 12) containing three two center-two electron (2c-2e) B-B bonds and n - 2 3c-2e B-B-B bonds so that the 3c-2e bonds cover exactly half of the 2n - 4 deltahedral faces. Such Kekulé-type structures are more readily visualized in the duals of the borane deltahedra where the 3c-2e B-B-B bonds become special vertices and the 2c-2e B-B bonds become special edges so that the sums of the numbers of special vertices and edges for every face are exactly three and neither vertex of any special edge is also a special vertex. Comparison of the Kekulé-type structures for borane deltahedra obtained by maximizing their symmetries with those obtained from PRDDO computations by Lipscomb and coworkers suggest that wide distribution of the three 2c-2e B-B bonds throughout the deltahedron and a minimum number of empty faces are more important than maximum symmetry in leading to the most favorable Kekulé-type structures. The sum of the electron densities of the set of equivalent Kekulé-type structures for a given BnHn2- deltahedron has the geometry of a symmetric skyrmion arising from the non-linear field theory of a system of interacting mesons and B = &frac1s2;(n + 2) baryon (nucleon) sources within a nucleus.