DFT calculation of structures and NMR chemical shifts of simple models of small diameter zigzag single wall carbon nanotubes (SWCNTs)

Abstract

Linearly conjugated benzene rings (acenes), belt-shape molecules (cyclic acenes) and model single wall carbon nanotubes (SWCNTs) were fully optimized at the unrestricted level of density functional theory (UB3LYP/6-31G*). The models of SWCNTs were selected to get some insight into the potential changes of NMR chemical shift upon systematic increase of the molecular size. The theoretical NMR chemical shifts were calculated at the B3LYP/pcS-2 level of theory using benzene as reference. In addition, the change of radial breathing mode (RBM), empirically correlated with SWCNT diameter, was directly related with the radius of cyclic acenes. Both geometrical and NMR parameters were extrapolated to infinity upon increase in the studied systems size using a simple two-parameter mathematical formula. Very good agreement between calculated and available experimental CC bond lengths of acenes was observed (RMS of 0.0173 Å). The saturation of changes in CC bond lengths and (1)H and (13)C NMR parameters for linear and cyclic acenes, starting from 7-8 conjugated benzene rings, was observed. The (13)C NMR parameters of individual carbon atoms from the middle of ultra-thin (4,0) SWCNT formed from 10 conjugated cyclic acenes differ by about 130 ppm from the corresponding open end carbon nuclei.

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

“…In this study, as an extension of our previous work, we intend to obtain a deeper insight into the changes of NMR and Raman parameters of pristine SWCNT upon carboxylation. Thus, the previously used models of linear acenes, cyclic acenes, and zigzag (4,0) SWCNTs with a single carboxyl group added are optimized at the B3LYP/6‐31 G* level of theory, their vibrational frequencies calculated, and the GIAO NMR shieldings calculated using the B3LYP/pcS‐2 method.…”

“…A regular convergence of structural, Raman, and NMR parameters with the size of the studied linear and cyclic acene models, as well as short zigzag (4,0) SWCNTs, was recently observed . However, the impact of carboxylation on NMR chemical shifts of these model systems was not analyzed.…”

“…Theoretical proton and carbon chemical shifts were calculated relative to benzene for three sets of regularly increasing molecular systems, consisting of linear acenes, cyclic acenes, and zigzag (4,0) SWCNT (schemes 1 and 2 and Fig. 1 of Kupka et al ). Numerous theoretical and experimental studies on linear and cyclic acenes are available .…”

“…The three model systems considered in this study, including atom, bond, and molecule arbitrary numbering, are shown in Schemes . Full structure optimization of benzene and linearly conjugated benzene rings (called planar structures, scheme of Kupka et al ), molecular belt conjugated benzene rings (scheme 2 of Kupka et al ), and pristine zigzag (4,0) CNT of ultra‐small diameter of about 3.38 Å (Fig. 1 of Kupka et al ), followed by harmonic frequency calculations, were performed in our previous work .…”

“…In our earlier work, nuclear isotropic shieldings were calculated with Jensen's pcS‐ n , and additionally aug‐cc‐pVTZ‐J basis sets . Because of the size of our models, the NMR calculations in this study were performed using a smaller, although of relatively high quality, pcS‐2 basis set, and the nuclear shieldings were converted to chemical shifts using benzene as a secondary reference …”