High-resolution double-quantum NMR spectroscopy of homonuclear spin pairs and proton connectivities in solids

The NMR double-quantum response to a three-pulse sequence of dipolar coupled spin-1/2 pairs in powder samples spinning at the magic angle is investigated for arbitrary spinning frequencies. It is shown that double-quantum spinning sideband patterns result from the rotor modulation of the Hamiltonian. The existence of rotor modulated double-quantum spectra is confirmed by experiments with spin pairs of protons in barium chlorate monohydrate. The understanding of these sideband patterns now allow quantitative analysis of the double-quantum spectra to yield structural information in rigid solids. This is demonstrated by application to malonic acid. By combining single and double quantum NMR spectra proton distances within functional groups are determined, as well as connectivities between them. The 1H1H distance in the aliphatic group is 0.18 nm and the shortest distance between two carboxylic protons in the dimer structure is 0.22 nm. The closest aliphatic and carboxylic protons are separated by 0.26 nm, in agreement with neutron diffraction data.