Electron transition energies of single-walled carbon nanotubes: Hartree - Fock's CNDOL approaches for describing excitations and related properties

Optical properties of two kinds of zig-zag (13,0) and (9,0) single walled carbon nanotubes (SWCNT) are modeled by an approximate Hartree-Fock's (HF) Hamiltonian under the restrictions of the Complete Neglect of Differential Overlap considering the L azimuthal quantum numbers of basis orbitals (CNDOL). Here is shown that the procedure can bring models of electron energy transitions and exciton features through a configuration interaction of singly excited determinants (CIS). It allows the direct understanding of properties related with the total electronic wave function of the system. We show that the evolution of excited states for each SWCNT is different when the nanotube grows in length. It is discussed by taking into account electron - electron interactions. (13,0) SWCNT does not appear to decrease the lowest energy excited states when the length increases, in contrast with (9,0) SWCNT, which shows more favored conditions for photo-excitations when grows to infinite.