Direct determination of a molecular torsional angle by solid-state NMR

A solid-state NMR method for the determination of the torsional angle of a C-13-labelled H-C-C-H moiety is demonstrated. The method exploits the evolution of C-13 double-quantum coherence under the influence of magnetic fields from the neighbouring proton spins. The experiment operates under magic-angle-spinning conditions, does not require molecular orientational order, is insensitive to shielding tensor orientations, and has high sensitivity and resolution. Experimental demonstrations and numerical simulations are shown. We obtain a torsional angle resolution of approximate to +/-20 degrees in the neighbourhood of the cis geometry and approximate to +/-10 degrees in the neighbourhood of the trans geometry.