Density functional studies of the ¹³C NMR chemical shifts in single - Walled carbon nanotubes

Density functional theory has been used to compute the electronic structure and ¹³C NMR chemical shifts of finite (9,0) single-walled carbon nanotubes (SWNTs) capped with fullerene hemispheres and with hydrogen atoms. The chemical shifts and HOMO-LUMO gaps were found to be dependent upon the mode of capping. The shifts of semiconducting and metallic tubes were estimated as being around 130 ppm and 141 ppm, respectively. Periodic boundary calculations on infinite zigzag (n,0) SWNTs with 7 ≤ n ≤ 17 were performed. These entities can be characterized by a family index, λ =mod(n, 3), and the chemical shifts can be fitted well by a function inversely proportional to the diameter of the tube and proportional to a constant which depends on the nanotube family. Direct comparison of the molecular and periodic approaches can be made if benzene is used as the internal reference. Such a comparison indicates that capping may have a strong effect on the computed properties. Calculations on infinite zigzag (7 ≤ n ≤ 10) amine functionalized SWNTs have been performed. The functional group may react with a C-C bond which is parallel or diagonal to the tube axis and both sites have been considered. The shifts of the carbons directly attached to the group are sensitive to the bond which has been functionalized and may therefore be used to discriminate between the two products. Functionalization induces a significant line broadening of the NMR signals but it does not dramatically change the average shift of the unfunctionalized SWNT carbons.