Electronic structure of fullerenelike cages and finite nanotubes of aluminum nitride

We report a density functional study of alternate fullerenelike cage structures and finite closed, capped single-wall nanotubes of aluminum nitride. The cages and nanotubes studied are modeled as Al₂₄N₂₄, Al₂₈N₂₈, Al₃₂N₃₂, Al₃₆N₃₆, Al₄₈N₄₈, and Al₉₆N₉₆. The structure optimization and calculation of the electronic structure, vertical ionization potential, and the electron affinity are performed at the all-electron level by the analytic Slater-Roothaan method, using a polarized Gaussian basis set of double zeta quality. All structures are energetically stable with binding energy of about 10--110.3em0exeV per AlN pair. For the larger Al₉₆N₉₆, the fullerenelike cage is energetically less favorable than the two-shell cluster that has Al₂₄N₂₄ as an inner shell. The vertical ionization potential and the electronic affinity are in the range 6.7--6.90.3em0exeV and 1.5--2.00.3em0exeV, respectively. The binding energy shows systematic increase with increase in the length of the (4,4) nanotube. The energy band gap, determined using the ΔSCF method, shows that these structures are characterized by a fairly large band gap of about 4--50.3em0exeV, which is, however, smaller than the gap for the corresponding boron nitride structures.