Structure and electronic states of capped carbon nanotubes by a tight-binding approach

Geometric structure and electronic states of capped carbon nanotubes are investigated using tight-binding methods. Optimized geometric structure of capped nanotubes are determined numerically by energy minimization techniques, allowing finite curvature effects to manifest in a natural way. Distributions of bond length, curvature, charge density, local density of state, and dimerization structures are investigated, revealing significant increases in electron charge, local curvature, and bond length in the vicinity of five-membered rings in the half-fullerene caps. Structural distortions are found to be limited spatially depending on the metallic or semiconducting nature of the nanotubes (NT) involved. The distortions are restricted to the cap, where rotational symmetry is broken, for semiconducting NT's. For metallic tubes, distortions are found to extend into the tube in the form of $\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}$ dimerization, in which case rotational symmetry is found to break when dimerization is unable to align with five-membered rings in the cap.