Fig. 4.
Dependence of molecular orbitals on the geometrical parameters of nanotubes. (a) The lowest unoccupied molecular orbitals (LUMOs) of chiral (6,5) and zigzag (8,0) carbon nanotubes. The positive and the negative lobes of the wavefunction are shown in the red and blue, respectively. The orbital density distribution strongly follows the tube helicity. (b) Schematic presentation of the nanotube geometrical parameters. Vectors a1 and a2 are the unit vectors of the hexagonal graphene lattice. The chirality vector Ch = na1 + ma2 (black arrow), chiral angle Θ, and translational vector Zi directed along the tube length (blue arrow) of a (6,2) tube are shown as an example. (Inset) Natural helical coordinates of a chiral tube. All points on the surface area between the two blue lines satisfy Eq. 1.