Calculation of the nuclear overhauser effect and the determination of proton-proton distances in the presence of internal motions

Methods for calculation of NOE intensities of proton pairs on molecules where internal motion occurs are discussed in the framework of the full-relaxation-matrix approach. Model systems mimicking 180° flips of aromatic rings and methyl group rotation are considered. The simultaneous effect of these dynamic processes and that of spin diffusion can be described in two ways: the first is to add a kinetic matrix to the relaxation matrix and the second involves a weighted average of the relaxation-matrix elements. For motions that are fast compared to the correlation time for molecular tumbling such as methyl group rotation the individual proton-proton vectors are averaged as 〈 r −3 〉 and the appropriate spectral density functions need to be used. The effect of motion on the back transformation from NOE intensities to proton-proton distances has also been examined for these model systems. Since inclusion of motion results in averaging of intensities, pseudoatom corrections on the determined distances are usually needed. It is shown that in the case of the rotating methyl group 〈 r −3 ) averaging leads to a pseudoatom correction of only 0.3 A rather than the often used 1.0 A.