In systems with dipolar relaxation in isotropic phase, it is possirates'' ) provides the key to the determination of molecuble to measure the extent of cross correlation of the fluctuations lar structure in solution ( 1 -3 ) . Overhauser effects can of two selected dipole-dipole interactions A-M and A-X by selecbe rationalized in terms of a migration of Zeeman magnetively exciting and spin-locking the transverse magnetization of tization from one spin to another, e.g., from I A z to I X z and spin A. If the system comprises only three spins A, M, and X, the vice versa. The rates of such processes are usually deterconversion of in-phase magnetization I A x into doubly antiphase mined by analysis of two-dimensional nuclear Overmagnetization 4I A x I M z I X z during the spin-locking period occurs hauser ( NOESY ) spectra ( 4, 5 ) . It is normally assumed spontaneously through relaxation. The rate of this conversion is that the magnetic dipoles of the nuclei interact solely in proportional to the spectral density of the cross correlation of the a pairwise manner. At this level of description, crossrandom fluctuations of the dipolar A-M and A-X interactions. relaxation effects involving N spins can be described by In this paper, larger systems, comprising at least a fourth spin K, are investigated. The complexity of the situation is increased, since an N 1 N relaxation matrix ( generalized Solomon maother forms of three-spin order such as 4 I A x I K z I X z or 4I A x I M z I K z betrix ) , which describes the coupling of the N Zeeman come accessible. Furthermore, this paper addresses the role of order terms I A z , I M z , I X z , etc. ( 6, 7
) . This ''total relaxation scalar couplings, which are a prerequisite for making three-spin matrix'' description is based on the assumption that order observable, but which are also a source of perturbations, three-spin effects can be neglected. In actual fact, there since scalar couplings can contribute significantly to the creation may be a spontaneous conversion of Zeeman magnetizaof various three-spin-order terms. If the spin-locking field is too tion I A z into longitudinal three-spin order 4 I A z I M z I X z ( 8weak compared to the width of the multiplet under investigation, 11 ) , which is sometimes called ''octupolar'' order. This residual scalar interactions lead to the generation of three-spin conversion is due to cross correlation of the fluctuations order. If the spin-locking field is too strong compared to the relaof the A -M and A -X dipolar interactions. The effect is tive offsets of other ''passive'' spins, further complications occur.
These can be avoided most effectively by using very high static most pronounced if the three spins A, M, and X are in a magnetic fields. If coherent contributions to three-spin order can rigid linear arrangement, so that cross-and auto-correlabe suppressed or accounted for through simulations, the remaining tion functions have equal magnitudes ( 11 ) . In nonlinear buildup of three-spin-order terms arising from dipolar cross-correconfigurations, provided the overall motion is isotropic, lation effects can be interpreted in terms of structural and motional the importance of cross-correlation effects is proporparameters.