Density functional calculations of the ¹³C NMR chemical shifts in (9,0) single-walled carbon nanotubes

The electronic structure and ¹³C NMR chemical shift of (9,0) single-walled carbon nanotubes (SWNTs) are investigated theoretically. Shielding tensor components are also reported. Density functional calculations were carried out for C₃₀-capped and H-capped fragments which serve as model systems for the infinite (9,0) SWNT. Based on the vanishing HOMO-LUMO gap, H-capped nanotube fragments are predicted to exhibit "metallic" behavior. The ¹³C chemical shift approaches a value of ≈133 ppm for the longest fragment studied here. The C₃₀-capped SWNT fragments of D_3d/D_3h symmetry, on the other hand, are predicted to be small-gap semiconductors just like the infinite (9,0) SWNT. The differences in successive HOMO-LUMO gaps and HOMO and LUMO energies, as well as the ¹³C NMR chemical shifts, converge slightly faster with the fragment's length than for the H-capped tubes. The difference between the H-capped and C₃₀-capped fragments is analyzed in some detail. The results indicate that (at least at lengths currently accessible to quantum chemical computations) the H-capped systems represent less suitable models for the (9,0) SWNT because of pronounced artifacts due to their finite length. From our calculations for the C₃₀-capped fragments, the chemical shift of a carbon atom in the (9,0) SWNT is predicted to be about 130 ppm. This value is in reasonably good agreement with experimental estimates for the ¹³C chemical shift in SWNTs.