Quantum-size effects in capped and uncapped carbon nanotubes

Properties of C₆₀-related finite-length nanotubes C _40+20n with armchair structures and C_42+18n with zigzag structures, in which n is, respectively, the number of cyclic cis- and trans-polyene chains inserted between the fullerene hemispheres at the two edges, are analyzed by quantum chemical calculations at the B3LYP DFT level of theory. To clarify end-cap effects on the C₆₀-related nanotubes, the corresponding nanotubes terminated by H atoms, C_20nH₂₀ and C_18nH₁₈ are also analyzed. Bond-length alternation patterns in the armchair nanotubes change in an oscillatory manner as n with a periodicity of 3, whereas those in the zigzag nanotubes are independent of the chain width. A similar tendency is seen in computed HOMO-LUMO gaps in the finite-length nanotubes. The sharp contrast in the quantum-size effects between the armchair and zigzag nanotubes is a consequence of interchain interactions in the cylinders, which depend on their edge structures. The interchain interactions in the armchair nanotubes are significant, due to the delocalization of orbital amplitudes within single cis-polyene chains, whereas those in the zigzag nanotubes are weak, due to the nodal properties of the single trans-polyene chains. The geometrical and electronic features in the C₆₀-related nanotubes are also well affected by the fullerene hemispheres at the two edges because orbital interactions between the end-caps and the cylindrical segments conserve their orbital symmetries in the frontier orbital regions. DFT calculations illuminate that the structural and electronic properties of the C₆₀-related nanotubes are dominated by tube lengths, edge structures, and end caps.