Nanotech 2010

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

A.L. Montero, M.E. Fuentes, E. Menéndez, W. Orellana, C. Bunge, L.A. Montero, J.M. García de la Vega
Universidad de La Habana, CU

Keywords: excited states, carbon nanotubes, exciton bounding

Abstract:

Electronic properties of two kinds of zig-zag (13,0) and (9,0) single walled carbon nanotubes (SWCNT) are studied using both Density Functional Theory (DFT) and an approximate Hartree-Fock (HF) named as Complete Neglect of Differential Overlap considering the L azimuthal quantum numbers of basis orbitals (CNDOL) molecular-orbital method. The CNDOL procedure models the electron energy transitions and excited state charge distributions through a configuration interaction of singly excited determinants (CIS) allowing the direct understanding of properties related with the total electronic wave function of the system. Band structures and densities of states (DOS) of both SWCNT´s are initially calculated using DFT, showing insulating character for (13,0) and almost metallic character with a very small conduction gap for (9,0) SWCNTs. Similar behaviours of either insulating or metallic SWCNT’s were interpreted in the framework of the above mentioned HF’s scheme by increasing the lengths of the tubes above 3 nm. 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 as considered in the framework of the HF - CIS procedure. The predicted insulator (13,0) SWCNT does not show a decrease in the lowest energy excited states when the length increases, in contrast to the (9,0) SWCNT, which shows more favoured conditions for photo-excitations. Analyzing the size-scaling behaviour of the excitation energies with the nanotube length, the (13,0) SWCNT presents a forbidden transition at the lowest energy followed by a strong dipole-allowed transition between 0.8 and 0.9 eV. They show no significant changes in longer systems, whereas the (9,0) SWCNT spectrum shows the lowest-allowed energy transition at less than 0.3 eV when nanotube length tend to infinite. Excitons appear more bounded in the insulating than in the conducting nanotube, as expected.
 
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