Electronic structures of [n]-cyclacenes (n=6-12) and short, hydrogen-capped, carbon nanotubes

Density functional (M06-L and B3LYP) and multiconfigurational second-order perturbation (CASPT2) theories are applied to [n]-cyclacenes having n = 6-12 in order to assess their strain energies and the degree of di- or polyradical character inherent in their electronic structures. In the case of density functional theory, a broken symmetry approach must be employed and the sensitivity of the results to choice of functional and broken-symmetry protocol is explored. Viewing the [n]-cyclacenes as monomeric building blocks which may be joined to grow finite length (n, 0) single-walled carbon nanotubes, density functional calculations are further employed to explore changes in electronic structure associated with increasing nanotube length. Spin-state energy gaps are predicted to decrease both with increasing cyclacene size and with increasing nanotube length; [n]-cyclacenes with odd values of n are predicted to develop polyradical character for smaller n than is the case for even values n.