Observation of longitudinal three-spin order for measuring dipole-dipole cross correlation

Abstract

Renewed interest in cross relaxation and nuclear Overhauser effects (I) has been stimulated by the advent of two-dimensional exchange spectroscopy (NOESY) (2, 3). This technique can be used to measure the migration of longitudinal magnetization between different sites in a molecule resulting from cross relaxation. The longitudinal relaxation behavior of systems with many spins is frequently treated using generalized Solomon equations (4) in which the dynamics of the eigenstate populations are expressed solely in terms of (time-dependent) expectation values of single-spin angular momentum operators I&, i.e., (I&) = Tr{ cr(t)Zk=} . It has long been recognized, however, that relaxation phenomena cannot be treated accurately without taking into account the fact that the fluctuations of different dipolar interactions are correlated (5), and Fagerness et al. (6) have demonstrated that such dipole-dipole cross correlation may lead to partial conversion of Zeeman order (I& into longitudinal three-spin order (41&.1,,). Such cross-correlation effects are not apparent from the traditional Solomon equations, and hence it is often assumed, although seldom explicitly stated, that these effects can be neglected without severe consequences regarding the accuracy of the structural data derived from NOE studies. Recently, however, Bull (7) has shown in a theoretical paper that the time dependence of crossand diagonal-peak intensities in NOESY spectra can be significantly altered by cross-correlation effects, which give rise to additional pathways for the migration of Zeeman order, e.g., (L) --, (~uL) + (L). Cross-correlation effects can be best observed by monitoring the growth of longitudinal three-spin order (41&lmz). However, the use of 90” pulses in the normal two-dimensional NOESY experiment precludes this direct observation. Three-spin order can only be observed if two conditions are fulfilled simultaneously: the scalar couplings between at least two of the three relevant spins must be resolved, and the flip angle of the RF pulse used to monitor the state of the system must differ from 90” (8-10). If these conditions are met, longitudinal three-spin order leads to a doubly antiphase contribution to the multiplets: for a doublet of doublets in a system ofthree spin-j nuclei this contribution has the form + I:1 :1 :+ I. This antiphase component can, however, be observed separately from the intense background of Zeeman order (which gives rise to in-phase multiplets) by triple-quantum filtration techniques. Bull (7) and Jaccard et al. (1 I) have recently suggested this approach, which is analo-