A particle on a hollow cylinder: the triple ring tubular cluster B27(+).

We determined the geometries and chemical bonding phenomena of the B27 system in its dicationic, cationic, neutral, anionic and dianionic states using DFT computations. In both cationic and neutral states, the triple ring tubular forms correspond to the lowest-energy isomers, especially in B27(+). The cation B27(+) represents the first stable hollow cylinder having a triple ring among the pure boron clusters. In the anionic and dianionic states, the quasi-planar structures are favoured due to a charge effect. In the triple ring tube B27(+), strong diatropic responses to external magnetic field occur in both radial and tangential types of electrons, and thus confer it a characteristic tubular aromaticity. The presence of a consistent aromatic character contributes to its high thermodynamic stability. The shapes of calculated MOs of B27(+) TR can be predicted by the eigenstates of a simple model of a particle on a hollow cylinder. The number of electrons in a hollow cylinder should attain a number of (4N + 2M) with M = 0 and 1 for both radial and tangential electrons, depending on the number of non-degenerate MOs occupied, in order to properly fulfill the closed electron shells. In the case of B27(+), M = 0 for radial electrons and M = 1 for tangential electrons.