Rotating-frame NOEs

Unlike the corresponding equation for transient NOEs (Eq. (8.12)), this expression remains positive for all values of Tc, and the undeniable benefit of ROEs is, quite simply, that they remain positive for all realistic molecular tumbling rates. For small molecules, the magnitude of the ROE matches that of the transient NOE, whilst for larger molecules it reaches a maximum for homonuclear spins of 68%, but under no circumstances does it become zero (Fig. 8.23). Similarly, the NOE and ROE growth rates are identical for small molecules but differ for very large ones. For a small molecule that has wqTc 1, both Eqs 8.12 and 8.15 simplify to  

In contrast, for very large molecules which have uioTc 1, the left hand expression within the brackets of both Eqs 8.12 and 8.15 becomes negligible, giving  

For very large molecules, the ROE therefore grows twice as fast as the NOE, and has opposite sign [8]. 

Set against these obvious benefits are a number of experimental problems, principally TOCSY transfers also occurring during the spin-lock and signal attenuation from off-resonance effects. These issues are further addressed in the practical sections that follow, so it is sufficient to note here that even more care is required when acquiring and using ROEs than is needed for NOEs, so much so that some would regard this only as a specialist s technique. 

The situation during the spin-lock may be viewed as the transverse equivalent of events during the transient NOE mixing time (Fig. 8.25). The action of the spin-lock is to maintain the opposing disposition of magnetisation vectors which would otherwise be lost through differentia] chemical shift evolution, 

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PSTE Pulsed field gradient stimulated echo ROE Rotating-frame NOE RTIL Room-temperature ionic liquid Tf2N Bis(trifluoromethylsulfonyl)amide TSIL Task-specific ionic liquid... 

Which of these two approaches is adopted in the laboratory may be dictated by the motional properties of the molecule(s) under study, and more specifically the rates at which the molecules tumble in solution. Pre-empting what is to follow, it will be shown that the steady-state experiments are only appropriate for molecules that tumble rapidly in solution (we shall also see what defines rapidly in this context). Such measurements have traditionally been the home territory of small organic molecules in relatively non-viscous solutions. In contrast, very much larger molecules that tumble slowly in solution (or smaller molecules in very viscous solutions) can only be meaningfully studied with the transient NOE techniques, which may also suitable for small molecule studies. Between these two extremes of molecular tumbling rates the conventional NOE can become weak and even vanishingly small, a condition most likely to occur for those molecules with masses of around l(XX)-20()0 daltons. It is here that rotating-frame NOE measurements play a vital role, and these shall also be presented below. 

The maximum possible negative NOE in a homonuclear system is —100%. Between the extreme narrowing and spin diffusion limits, lies the difficult region in which NOEs can become zero (when cooTc 1) or at least rather weak, often demanding a change in experimental conditions or the use of rotating-frame NOE measurements. 

Figure 8.24. A general scheme for observing rotating-frame NOEs. The ROE develops during the long spin-lock pulse which constitutes the mixing [jeriod, Xm-...

Figure 8.25. The rotating-frame NOE experiment can be viewed as the transverse equivalent of the transient NOE experiment.

ROESY (rotating frame noe spectroscopy) Same as NOESY, through-space interactions Same as NOESY plus can distinguish between exchange and ROE peaks Same as NOESY and also insensitive Same as NOESY... 

Method of measuring rotating-frame nOes (or rOes). Of importance for mid-sized molecules, for which nOes can be zero whereas the rOes will still be measurable. Gives approximately the same information (though more care is required in interpretation). 

Figure 6 Rotating frame NOE pulse sequences. The 1D experiment requires two sequences, represented by (A) and (B). (A) is the reference experiment in which a 90 non-selective pulse is applied on all the spins, followed by a spin-lock along the y-direction for a time and the state of the spin system is detected. (B) The control experiment in which a selective 180 pulse, inverts the magnetization of the spin from which the NOE is to be observed before the 90j pulse and the experiment is continued as (A). The 1D NOE spectrum is the difference between the spectra obtained with the sequence (A) and (B). (C) The 2D ROESY sequence. The times and fs are the evolution and detection periods and is the mixing time. SL refers to the low power spin-locking RF field.

Figure 7 Plot of maximum rotating frame NOE (from Equation (18)) for a homonuclear two spin4 system as a function of coTc. The rotating frame NOE is positive for all values of correlation time.

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