the same coherence antiphase with respect to different num-Proton relaxation measurements are potentially a valuable bers of spins. Dipolar cross relaxation can interconvert comsource of information on molecular dynamics. Here we describe and demonstrate methods for suppressing cross-relax-ponents of a coherence {C } that differ by two in the spins with respect to which they are antiphase. This can occur ation effects in proton relaxation measurements.
through either an exchange of spins such as occurs in the Relaxation studies undertaken to obtain motional informaprocesses {C }2I kz } {C }2I lz or a change in the total numtion about a molecule are currently largely restricted to meaber of spins with respect to which a coherence is antiphase surements of 15 N and 13 C, usually of isotopically labeled in processes such as {C } } {C }4I kz I lz . If chemical-shift samples (1-6). This is because relatively few interactions anisotropy contributes to relaxation, cross relaxation can also must be considered in analysis and the internuclear distances occur between components of coherence that differ from which are required are known with precision. In each case, each other by one in the total number of spins with respect the heteroatom can be considered to relax solely due to its to which they are antiphase, for example, {C }2I kz } own chemical-shift anisotropy and through dipolar interac-{C }4I kz I lz . tions with its bonded proton(s). Proton relaxation is usually considerably more complex: both inter-and intramolecular
The routes by which cross relaxation can affect a relaxation measurement can be classified as either direct or indi-interactions may contribute and many of the internuclear distances required for analysis may not be known with suffi-rect. Cross relaxation can be classified as direct when it occurs as a direct consequence of another species being pre-cient accuracy. We have recently demonstrated that by taking the appropriate linear combinations of relaxation rates, pared with a nonequilibrium amplitude. Indirect cross relaxation occurs when only the species of interest is prepared it is possible to isolate the mutual dipolar relaxation of a restricted set of nuclear spins, regardless of any other dipolar with a nonequilibrium amplitude and cross relaxation from it perturbs the populations of other species which in turn, interactions that they might have . This procedure has the potential to greatly simplify analysis since small sets of through cross relaxation, perturb the amplitude of the species originally selected. For example, if the relaxation of I kz is spins for which accurate internuclear distances are available can be selected. Since this method relies on taking linear being measured using a nonselective inversion-recovery experiment, all components of longitudinal magnetization will combinations of relaxation rates, it is particularly susceptible to errors in the individual rates, which can rapidly proliferate. be prepared with nonequilibrium amplitudes and cross relaxation can occur directly from any other components I lz : With existing pulse sequences designed for measuring decay rates in homonuclear spin systems, cross relaxation is usually I lz r I kz . In the corresponding selective inversion-recovery experiment, only I kz is initially prepared with a nonequilib-the most serious source of error (9-13).
rium amplitude, and for cross relaxation to affect I kz , cross Cross relaxation interconverts longitudinal modes or comrelaxation from I kz must first perturb the amplitudes of other ponents of coherence. In the case of longitudinal modes, components of longitudinal magnetization, e.g., I kz r dipolar cross relaxation can interconvert modes which differ I lz r I kz . by two spins from each other. This can occur through either an exchange of spins such as occur in the processes I kz } I lz Both direct and indirect cross-relaxation processes can have a significant effect on the measured relaxation rate, or 2I kz I lz } 2I kz I mz or a change in the total number of spins in a mode in processes such as I kz } 4I kz I lz I mz . If chemical-although those resulting from direct processes are usually most severe. Direct cross relaxation can often be eliminated shift anisotropy contributes to relaxation, cross relaxation can also occur between modes that differ from each other from one-dimensional experiments by ensuring that only the species to be measured is prepared with a nonequilibrium by a single spin, for example, I kz } 2I kz I lz . In the case of coherence, cross relaxation can interconvert components of amplitude. In two-dimension experiments, the amplitude of 278