Density Functional Study of the ¹³C NMR Chemical Shifts in Small-to-Medium-Diameter Infinite Single-Walled Carbon Nanotubes

NMR chemical shifts were calculated for semiconducting (n,0) single-walled carbon nanotubes (SWNTs) with n ranging from 7 to 17. Infinite isolated SWNTs were calculated using a gauge-including projector-augmented plane-wave (GIPAW) approach with periodic boundary conditions and density functional theory (DFT). In order to minimize intertube interactions in the GIPAW computations, an intertube distance of 8 Å was chosen. For the infinite tubes, we found a chemical shift range of over 20 ppm for the systems considered here. The SWNT family with λ = mod(n, 3) = 0 has much smaller chemical shifts compared to the other two families with λ = 1 and λ = 2. For all three families, the chemical shifts decrease roughly inversely proportional to the tube's diameter. The results were compared to calculations of finite capped SWNT fragments using a gauge-including atomic orbital (GIAO) basis. Direct comparison of the two types of calculations could be made if benzene was used as the internal (computational) reference. The NMR chemical shifts of finite SWNTs were found to converge very slowly, if at all, to the infinite limit, indicating that capping has a strong effect (at least for the (9,0) tubes) on the calculated properties. Our results suggest that ¹³C NMR has the potential for becoming a useful tool in characterizing SWNT samples.