DFT calculations of structures, (13)C NMR chemical shifts, and Raman RBM mode of simple models of small-diameter zigzag (4,0) carboxylated single-walled carbon nanotubes.

Linearly conjugated benzene rings (acenes), belt-shaped molecules (cyclic acenes), and models of single-walled carbon nanotubes (SWCNTs) with one carboxylic group at the open end were fully optimized at the B3LYP/6-31G* level of theory. These models were selected to obtain some insight into the nuclear isotropic changes resulting from systematically increasing the basic building units of open-tip-monocarboxylated SWCNTs. In addition, the position of radial breathing mode (RBM), empirically correlated with the SWCNT diameter, was directly related with the radius of model cyclic acene rings. A regular convergence of selected structural, NMR, and Raman parameters with the molecular system size increase was observed, and a simple two-parameter mathematical formula enabled their estimation in infinity. The predicted (13) C NMR chemical shifts of carbon atoms close to the substituted rim of carboxylated models of zigzag (4,0) SWCNTs differed significantly from the pristine nanotubes.