Direct measurement of angles between bond vectors in high-resolution NMR

Angles between two interatomic vectors are measured for structure elucidation in solution nuclear magnetic resonance (NMR). The angles can be determined directly by using the effects of dipole-dipole cross-correlated relaxation of double-quantum and zero-quantum coherences. The measured rates can be directly related to the angular geometry without need for calibration of a Karplus-type curve, as is the case for scalar coupling measurements, and depend only on the rotational correlation time of the molecule as an empirical parameter. This makes the determination of torsional angles independent from the measurement of coupling constants. The two interatomic vectors can in principle be arbitrarily far apart. The method was demonstrated on the measurement of the peptide backbone angle ψ in the protein rhodniin, which is difficult to determine in solution by NMR spectroscopy.