Constraints on \({\rm I}\beta\) cellulose twist from DFT calculations of \(^{13}\hbox {C}\) NMR chemical shifts

We investigate theoretically the NMR response of twisted configurations of \({\rm I}\beta\) cellulose in the tg conformation. These finite helical angle structures were constructed by a mathematical deformation of zero-angle configurations obtained via the periodic density functional energy minimizations with dispersion corrections (DFT-D2). Subsequent calculations of the \({^{13}\hbox {C}}\) nuclear magnetic resonance chemical shifts \(({\delta}^{13} \hbox {C})\) were compared with experimental findings by Erata et al. (Cellul Commun 4:128–131, 1997) and Kono et al. (Macromolecules 36:5131–5138, 2003). We determine the sensitivity of the NMR chemical shifts to helical deformation of the microfibril and find that a substantial range of helical angle, ±2 degrees/nm, is consistent with current experimental observations, with a most probable angle of ∼0.2 degree/nm. Through exhaustive combinatorial provisional assignments, we also demonstrate that there are different choices of the chemical shift \(({\delta}^{13} \hbox {C})\) assignments which are consistent with the experiments, including ones with lower deviations than existing identifications.