Comparison of μ₂-scaled Hückel theory and Hartree-Fock theory of boranes and carboranes

The μ₂-scaled Hückel method is used to calculate the electronic energy surfaces of the four boranes B_nH_n ^2- (n=8-11) and the carborane C₂B₈H ₁₀^2-. These electronic energy surfaces and their minimum energy geometries are directly compared to both the single crystal x-ray determined structures and to Hartree-Fock optimized geometries. Bond distances differ on the average by 0.04 Å between alternate methods. It is shown that μ₂-scaled Hückel results may be directly interpreted by analysis of the highest occupied and lowest unoccupied molecular orbitals. Also studied by the μ₂-scaled Hückel and Hartree-Fock methods are the isomerization pathways of B₈H₈^2-, B ₁₁H₁₁^2-, and C₂B₈H ₁₀^2-. Reaction barriers and transition state geometries found by the two different calculational methods are in fair agreement with each other and known literature values. Using the μ₂-scaled Hückel method one can readily deduce that the B₈H ₈^2- and B₁₁H₁₁^2- isomerizations are Woodward-Hoffmann allowed reactions. In the case of B ₈H₈^2- this allowed mechanism is contrasted to an alternate Woodward-Hoffmann forbidden pathway. Hartree-Fock calculations on the C₂B₈H₁₀^2- confirm earlier μ₂-scaled Hückel based findings, that a second less stable isomer of C₂B₈H₁₀^2- exists which, in contradiction to Wade's rules of electron deficient clusters, has a pair of open square faces in the cluster.