Cross rotating frame

Cross-polarisation (CP) in the rotating frame has been introduced as a means of transferring polarisation between different nuclear species in solids [168], and has become of central importance for obtaining spectra of rare spins with low gyromagnetic ratios such as 13C, since a significant sensitivity enhancement may be achieved. Cross-polarisation can be used either for direct observation of low-sensitivity nuclei or for indirect detection of such nuclear species via high-sensitivity nuclei such as protons [169]. 

The conformation of the mixed p agonist/5 antagonist H-Tyr-c[-D-Orn-2-Nal-D-Pro-Gly-] in comparison to that of H-Tyr-c[-D-Orn-Phe-D-Pro-Gly-] was studied in DMSO-d6 by NMR spectroscopy and by molecular mechanics calculations [62,64]. Neither peptide showed nuclear Overhauser effects between C H protons or chemical exchange cross peaks in spectra obtained by total correlation and rotating frame Overhauser enhance-... 

Polymer Dynamics. 13C spin-lattice relaxation times (Ti) were determined with either an inversion-recovery sequence (16) (for carbons observed by direct polarization) or with a modified cross-polarization experiment (17). 13C rotating-frame relaxation times (Tip(C)) were derived from measurements of the carbon signal that remained after a Tjp(C) hold time of... 

The cross-relaxation rates between two spins can be experimentally measured in the laboratory (rotating frame They depend on interspin distance r and correlation time that modulates the dipole-dipole interaction [4] ... 

The cross-relaxation in the rotating frame (dashed lines in fig. 1) mono-tonically increases with correlation time. For looTc < 0.382 two crossrelaxation rates, cr" and (T have similar dependence on correlation time, and at the limit when loqTc —> 0, the extreme narrowing limit, their ratio... 

For macromolecules (or small molecules in viscous solvents at a low temperature) in a high magnetic field, wqTc 3> 1. At this spin-diffusion limit the rotating-frame cross-relaxation rate is twice as fast as in the laboratory frame, and the rates are of the opposite sign, 5 = —1/2 (fig. 1, top). 

Fig. 1. Contour plot of the dependence of the cross-relaxation rate in the laboratory frame, a" (solid line), and rotating frame, cr (dashed line), on the interproton distance, r, and correlation time, Tc. Rigid body isotropic motion is assumed (eqs. (1) and (2)). Top panel shows the dependence of the ratio of the two cross-relaxation rates on correlation time, a is always positive, whereas cr" is positive for tuoTc < v/5/2 and negative for woTi < /5/2.

Measurement of the cross-relaxation rate in either the laboratory or the rotating frame suffices. This assumes that the respective correlation time function, /(tc), is the same for all spin pairs. If the calibration of the crossrelaxation rate is not feasible (e.g., no suitable spin pair, spectral overlap, motion not isotropic, molecule has internal mobility), the value of /(tc) for each spin pair (or for a group of selected pairs), i.e., the correlation time, must be explicitly determined. 

EXSY cross peaks are also obtained in TOCSY experiments (see later) because scalar interactions in the rotating frame are not separable from exchange interactions [7]. An EXSY experiment, performed using a TOCSY sequence (see Section 8.6) is reported in Fig. 8.7 relative to the complex 5Cl-Ni-SAL-MeDPT [5]. This complex, as shown in Fig. 8.8, displays a chemical equilibrium in which the two salicylaldiminate moieties exchange their non-equivalent positions [8]. It is interesting to learn that such complex interconversion occurs with times of the order of the spin-lock time (20 ms) or shorter. 

The 2D ROE or ROESY experiment is an experiment to measure cross-relaxation in the rotating frame (Fig. 8.2B). After an initial 90° pulse and the variable evolution period t, a low power or soft spin-lock sequence (SL) is applied for a time during which magnetization transfer in the rotating frame occurs due to cross relaxation. Since scalar connectivities can also develop during spin lock, as... 

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