Structures and properties of new carbon allotropes: Fullerenes and single-walled carbon nanotubes

The geometries and NMR chemical shifts of fullerenes C60-C 90 have been calculated using density functional theory. The predicted NMR spectra for fullerenes C70, C76, C78 are accurate enough to confirm earlier experimental isomer assignments. The NMR peaks above 140 ppm compare with measured values better than those below 140 ppm. The predicted chemical shifts for isomer C80:2 agree with measured values, whereas large discrepancy exists for those of C80:1, for which the Hartree-Fock approximation produces reasonable results. The calculated NMR chemical shifts for C82, C84, C 86, C88 and C90 are used to identify the observed isomers by comparing the predicted spectra with the experimental data. For the nine observed isomers of C84, the pi-orbital axis vector (POAV) angle is mainly determined by the connectivity. The chemical shifts generally increase as the POAV angles increase, but no simple relationship is found.;Based on theoretical frequencies and intensities, the strong peaks in the Raman spectrum of C70 are assigned and an assignment of the weak peaks is proposed. When C70 is reduced to C70 6-, significant intensity enhancement is seen for some IR and Raman peaks.;The charge induced strain (change of the C-C bond in percentage) in doped trans-polyacetylene and graphite intercalation compounds has been calculated. The optimized geometrical parameters of doped compounds agree with experimental data. The strain of charged trans-polyacetylene and graphene agrees with the calculations including counterions, showing that the carbon network is the predominant factor.;The optimized geometries and band structures of single-walled carbon nanotubes are calculated. For armchair (n, n) nanotubes, the bonds perpendicular and parallel to the tube axis have similar bond lengths, whereas for zigzag (n, 0) nanotubes, the perpendicular bonds are longer than the parallel bonds. In small zigzag nanotubes, the band gaps are reduced due to the lowering of a sigma band. The strain curves for charged armchair nanotubes follow that of graphene, whereas three different strain behaviors are predicted for zigzag nanotubes with n = 3i, 3i + 1 and 3i + 2, which is explained by the different positions of the allowed k-points corresponding to the orbitals involved in the charge transfer process.