13C NMR Chemical Shifts of Single-Walled Carbon Nanotubes (SWNTs)

The properties, separation and potential applications of SWNTs are currently under intense study. The wide range of proposed applications stems from the fact that carbon nanotubes have a diverse range of weights, electronic structures, helicities and so forth. Considerable effort has been placed into determining the experimental parameters that affect the molecular architecture of the tubes. However, such efforts have been hampered by the fact that even a combination of many experimental techniques does not fully characterize a given sample.

One of the most versatile experimental tools to study the geometry and electronic structure of molecules and solids is nuclear magnetic resonance (NMR). Calculated 13C NMR chemical shifts of different SWNTs might be useful in helping experimentalists characterize the contents of a given sample. Eventually, it might even be possible to predict the widths and shapes of NMR signals from nanotube samples with different compositions using the data obtained from ab initio calculations. To this end, we have performed Density Functional Theory (DFT) calculations on finite and infinite SWNTs.

We have calculated the electronic structure and NMR chemical shifts of progressively larger (9,0) tubes capped either by half of a fullerene hemisphere or by hydrogen [1]. The results indicate that the former is a small gap semi-conductor, in agreement with other theoretical and experimental work. The latter, on the other hand, was found to be metallic. The chemical shift of the (9,0) tube was predicted to be about 130 ppm. This value was estimated to be an upper bound with an error of about 5 ppm. Taking into account previous theoretical studies [2], the chemical shifts of metallic tubes were estimated to be around 141 ppm.

Recently, we have computed the chemical shifts of a number of infinite (n,0) SWNTs with 7 ≤ n ≤ 17 [3]. Such tubes may be subdivided into three families characterized by Λ=mod(n,3). For the Λ=1, 2 families it was previously found [4] that the chemical shifts δ can be fitted well by the function


where D is the tube's diameter, B is the chemical shift limit for infinite diameter and A(Λ) is a constant depending upon the nanotube family. The calculated shifts are given below in Fig. 1. We have also studied the small band gap (9,0), (12,0) and (15,0) species which were calculated to have a significantly lower shift than the other two families. However, it remains to be determined how to identify these tubes from large diameter members with Λ=1, 2. Moreover, we have found that it is possible to compare the results of infinite and finite calculations if benzene is used as the internal "computational" reference. For the (9,0) tube capping was found to have a large effect on the calculated shifts.

Fig. 1. Calculated chemical shifts of various SWNTs as a function of the optimized tube diameter.

Currently we are studying the effects of functionalization, defects, helicity and finite-size on the NMR chemical shifts of SWNTs. Eventually, a study of metallic tubes is also planned.

[1] Zurek, E.; Autschbach, J. J. Am. Chem. Soc, 2004, 126, 13079.
[2] Latil, S.; Henrard, L.; Goze-Bac, C.; Bernier, P.; Rubio, A. Phys. Rev. Lett, 2001, 86, 3160.
[3] Zurek, E.; Pickard, C.J.; Walczak, B.; Autschbach, J. J. Phys. Chem. A,, ASAP.
[4] Marques, M. A. L,; d'Avezac, M.; Mauri, F. Phys. Rev. B, 2006, 73, 125433.