Measurement of cross-correlation of fluctuations of dipolar couplings and anisotropic chemical shifts by selective spin locking

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Abstract
New experimental methods are presented that allow one to measure cross-correlation between the fluctuations of dipolar interactions and chemical shift anisotropy (CSA) in scalar coupled systems with two and three spins I = ½ in isotropic solution. The methods involve selective excitation of the transverse magnetization I A x of a chosen spin A, followed by selective spin locking of this magnetization. If the spin locking radiofrequency (RF) field is exactly on-resonance for spin A while leaving the other spins M and X unaffected, there is no cross-relaxation (Overhauser effect) in the rotating frame, i.e., no transfer from I A x to I M x or I X x . By contrast, cross-correlation between different relaxation mechanisms may give rise to single-quantum coherences of higher rank. In particular, CSA-dipolar cross-correlation may lead to a partial conversion of I A x into 2I A x I M z or 2I A x I X z , while interference between two dipole-dipole interactions leads to the appearance of terms such as 4I A x I M z I X z . After spin locking, selective pulses allow one to convert 2I A x I M z first into longitudinal two-spin order 2I A z I M z and, subsequently, into observable coherence 2I A z I M x . Similarly, 4I A x I M z I X z can be converted into 4I A z I M x I X z or 4I A z I M z I X x via 4I A z I M z I X z . The resulting signals, which can be recorded in one- or two-dimensional fashion, are directly proportional to the amount of 2- and 3-spin order created during the spin locking period. The cross-correlation rates may be measured from the build-up behaviour as a function of the duration of spin locking. Expressions are given for all relevant relaxation rates in 2- and 3-spin systems under arbitrary spin locking angles, including the effects of chemical shift anisotropy, thus generalizing the work of T. E. Bull (1988, J. magn. Reson., 80, 470). In the rotating frame, the effects of cross-correlation do not vanish in the slow-motion limit, in contrast to the situation in the laboratory frame, where the transformation of I A z into 2I A z I M z , 2I A z I X z or 4I A z I M z I X z only occurs if the spectral densities of cross-correlation have nonvanishing amplitudes at the Larmor frequency. Selective spin-locking experiments therefore allow one to measure cross-correlation regardless of motional correlation times.