DFT study of zigzag (n, 0) single-walled carbon nanotubes: 13C NMR chemical shifts

Abstract

13C NMR chemical shifts of selected finite-size models of pristine zigzag single walled carbon nanotubes (SWCNTs) with a diameter of ∼0.4–0.8nm and length up to 2.2nm were studied theoretically. Results for finite SWCNTs models containing 1, 4 and 10 adjacent bamboo-type units were compared with data obtained for infinite tubes in order to estimate the reliability of small finite models in predicting magnetic properties of real-size nanotubes and to assess their tube-length dependence. SWCNTs were fully optimized using unrestricted density functional theory (DFT-UB3LYP/6-31G*). Cyclacenes, as the shortest models of open-ended zigzag SWCNTs, with systematically varying diameter were calculated as well. GIAO NMR calculations on the SWCNT and cyclacene models were performed using the BHandH density functional combined with relatively small STO-3Gmag basis set, developed by Leszczyński and coworkers for accurate description of magnetic properties. Regular changes of carbon 13C chemical shifts along the tube axis of real size (6, 0) and (9, 0) zigzag carbon nanotubes were shown. The 13C NMR shifts according to increasing diameter calculated for zigzag (n, 0, n=5–10) cyclacenes followed the trends observed for zigzag (n, 0) SWCNTs. The results for 4-units long SWCNTs match reasonably well with the data obtained for infinite zigzag (n, 0) SWCNTs, especially to those with bigger diameter (n=8-15). The presence of rim hydrogens obviously affects theoretical 13C chemical shieldings and shifts in cyclacenes and thus cyclacenes can provide only approximate estimation of 13C NMR parameters of real-size SWCNTs. The NMR properties predicted for the longest 10-units long models of SWCNTs reliably correspond to results obtained for infinite nanotubes. They were thus able to accurately predict also recently reported experimental chemical shift of chiral (6, 5) SWCNT.