Determining the geometry of hydrogen bonds in solids with picometer accuracy by quantum-chemical calculations and NMR spectroscopy.

The structure of multiply hydrogen-bonded systems is determined with picometer accuracy by a combined solid-state NMR and quantum-chemical approach. On the experimental side, advanced 1H-15N dipolar recoupling NMR techniques are capable of providing proton-nitrogen distances of up to about 250 pm with an accuracy level of +/-1 pm for short distances (i.e., around 100 pm) and +/-5 pm for longer ones (i.e., 180 to 250 pm). The experiments were performed under fast magic-angle spinning, which ensures sufficient dipolar decoupling and spectral resolution of the 1H resonance lines. On the quantum-chemical side, the structures of the hydrogen-bonded systems were computationally optimised, yielding complete sets of nitrogen-proton and proton-proton distances, which are essential for correctly interpreting the experimental NMR data. In this way, nitrogen-proton distances were determined with picometer accuracy, so that vibrational averaging effects on dipole-dipole couplings need to be considered. The obtained structures were finally confirmed by the complete agreement of computed and experimental 'H and '5N chemical shifts. This demonstrates that solid-state NMR and quantum-chemical methods ideally complement each other and, in a combined manner, represent a powerful approach for reliable, high-precision structure determination whenever scattering techniques are inapplicable.