Magic Electron Counts and Bonding in Tubular Boranes

Ring stacking in some closo-borane dianions and the hypothetical capped borane nanotubes, predicted to be stable earlier, is analyzed in a perturbation theoretic way. A "staggered" building up of rings to form nanotubes is explored for four- and five-membered B(n)H(n) rings. Arguments are given for the stacking of B(5)H(5) rings being energetically more favorable than the stacking of B(4)H(4) rings. Elongated B[bond]B distances in the central rings are predicted for some nanotubes, and the necessity to optimize ring-cap bonding is found to be responsible for this elongation. This effect reaches a maximum in B(17)H(17)(2-); the insertion of additional rings will reduce this elongation. These closo-borane nanotubes obey Wade's n + 1 rule, but the traditional explanation based on a partitioning into radial/tangential molecular orbitals is wanting.