Electronic Structure of Tubular Aromatic Molecules Derived from the Metallic (5,5) Armchair Single Wall Carbon Nanotube

All-electron static and time-dependent DFT electronic calculations, with complete geometrical optimization, are performed on tubular molecules up to C₂₁₀H₂₀ that are finite sections of the (5,5) metallic single wall carbon nanotube with hydrogen termination at the open ends. We find pronounced C−C bond reconstruction at the tube ends; this initiates bond alternation that propagates into the tube centers. For the especially low band gap molecules C₁₂₀H₂₀, C₁₅₀H₂₀, and C₁₈₀H₂₀, alternation increases, and a second nearly isoenergic structural isomer of different alternation is found. A small residual C−C bond alternation and band gap may be present in the infinite tube. The van Hove band gap forms quickly with length, while the metallic Fermi point (at the crossing of linear bands) forms very slowly with length. There are no end-localized states at energies near the Fermi energy. The HOMO−LUMO gap and the lowest singlet excited state, whose energies show a periodicity with length as previously calculated, are optically forbidden. However, each molecule shows an intense visible “charge transfer” transition, not present in the infinite tube, whose energy varies smoothly with length; this transition should be an identifying signature for these molecules. The static axial polarizability per unit length increases rapidly with N as the “charge transfer” transition moves into the infrared; this indicates increasing metallic character. However, the ionization potential, electron affinity, chemical hardness, and relative energetic stability all show the length periodicity seen in the HOMO−LUMO gap, in contrast to the optical “charge transfer” transition and the static axial polarizability. These periodicities, due to a one-dimensional quantum size effect as originally modeled by Coulson in 1938, nevertheless cancel in the calculated Fermi energy, which varies smoothly toward a predicted bulk work function near 3.9 eV. A detailed study of C₁₉₀H₂₀ with up to eight extra electrons or holes shows the total energy is closely fit by a simple classical charging model, as is commonly applied to metallic clusters.