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

Abstract

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.