Three-dimensional Huckel theory for closo-carboranes

We have;recently developed a 3-dimensional Huckel method for cluster compounds. The method uses a set of approximations for Coulomb, resonance, and overlap integrals very similar to those employed in the familiar 2-dimensional Huckel theory for the pi electrons of planar conjugated hydrocarbons. The method can be adapted to heteroatomic clusters by introducing heteroatomic Coulomb integrals, alpha(Y) = alpha(X) + h beta, where it is a parameter for heteroatom Y. In this paper, we use the 3-dimensional Huckel method to study the properties of the closo-carboranes, C2Bn-2Hn. We calibrate the method by choosing a value of the heteroatomic parameter it that distinguishes positional isomers by energy and gives them relative energies in rough agreement with those established by observation and ab initio calculations. We obtain modest improvement in matching ab initio relative energies of isomers by means of a three-parameter, first-order perturbation treatment. We use the calibrated method to evaluate various mechanisms proposed for the isomerizations of C2B4H6, C2B5H7, and C2B6H8, all of which have been observed to undergo intramolecular isomerizations. Rearrangements of C2B6H8 have been satisfactorily explained by a single-DSD (diamond-square-diamond) process. Those for C2B5H7 require at least two DSD processes, concerted, consecutive, or overlapping. Several different mechanisms have been proposed for the rearrangement of C2B4H6. In evaluating intermediate and transition State structures, the 3-dimensional Huckel method gives higher energies to those structures with a larger number of nontriangular faces, a plausible conclusion except that occasionally it is wrong. In comparison with ab initio results, the 3-dimensional Huckel method fails to give low energies for classical structures.