Strained Configurations in Three-Dimensional Analogues of Kekulé-Type Structures for Deltahedral Boranes

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Abstract
Localized structures analogous to the Kekulé structures for benzenoid hydrocarbons can be constructed for the deltahedral boranes BnHn2-. These localized structures contain exactly three two-center two-electron (2c-2e) B-B bonds and n - 2 three-center two-electron (3c-2e) B-B-B bonds. The number of equivalent such Kekulé-type structures corresponds to the index of the symmetry group of the Kekulé structure, K, in the symmetry group, D, of the deltahedron. Three-dimensional Kekulé-type structures with the following configurations exhibit excessive strain and are therefore unfavorable: (i) structures having one or more pairs of boron atoms connected simultaneously by a 2c-2e B-B bond and a 3c-2e B-B-B bond (violation of the O'Neill-Wade restrictions); (ii) structures in which the three 2c-2e B-B bonds are excessively concentrated occupying only three or four vertices (the undesirable ∆, U, and Y configurations). Computations by Lipscomb and coworkers with partial retention of diatomic differential overlap (PRDDO) 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 structure.