| Summary: | 碩士 === 臺灣大學 === 化學研究所 === 95 === In the present thesis, we performed a systematic study on the ground and excited states of carbon nanotubes with arbitrary chiral vectors based on the semi-empirical Pariser-Parr-Pople (PPP) model.
We found that the generally accepted relationship about the band gaps of single-walled carbon nanotube (CNT) and the chiral vectors, $(m,n)$, is only valid in the tight-binding approximation. When the electron interaction, as present in the PPP Hamiltonian, is included even at the level of mean field approximation, the accidental degeneracies in the energy bands of CNTs satisfying the condition, mod(m-n, 3)=0, are removed completely except armchair CNTs.
We have analyze the symmetry requirement of the existence of degeneracy in CNTs. We have also calculated the their Hartree-Fock band structures using the PPP Hamiltonian. The agreements with DFT calculations for semiconducting CNTs in the literature are satifying. For metallic CNTs, the absence of zero band-gap is also justified computationally for non-armchair systems.
Finally, we investigated the effect of electron-electron correlation on the excitonic electronic structures of intrinsically semiconducting carbon nanotubes (CNTs) by using the intermediate exciton theory with the long-ranged Pariser-Parr-Pople Hamiltonian. By taking full advantage of double helical symmetry and periodic condition, we are able to reduce the number of carbon atoms in a unit cell to two to facilitate the single configuration interaction calculation tremendously. The dependence of the excitation energies of low-lying excited states on the diameters and helicity of CNT is studied.
This thesis is organized as follows. In chapter 1, we first introduced Bloch''s theorem for ordinary system with translational symmetry and establish the double helical symmetry by making a correlation between graphene and CNT. The results of HF calculation and some general properties of band structure of CNT are presented in chapter 2. Finally some formula for performing intermediate exciton calculation are derived and the results are given in chapter 3. The quantum chemistry toolbox with matlab developed for this thesis are summarized in appendix with some comments.
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