Cross relaxation rates

The accuracy of obtained cross-relaxation rates and therefore the derived distance restraints is influenced by many practical aspects. A critical point is the... 

Locahzed motion can also lead to local variations in correlation times. Folded peptides with unfolded C- or N-terminal residues, for example, will have varying correlation times for the rigid and flexible parts of the molecule, resulting in different cross-relaxation rates. Such effects can usually be distinguished by the Unewidths and intensities of the corresponding diagonal signals, since the autorelaxation rates also depend on the correlation time. 

Considering all potential experimental and systematic errors of NOE/ROE crosspeak intensities, it is remarkable how robust the derived distance restraints still are. The reason Ues in the dependence of the cross-relaxation rate even if a cross-peak intensity is determined wrongly by a factor 2, the resulting distance restraint is only affected by the factor 1.12, which usually lies within the error range of distance restraints used in structure calculations. It should be further noted that the quaUty of a resulting structure is not so much determined by the... 

Exchange-transferred spectroscopy was introduced with the finding of the etNOE [97] and its theoretical explanation in terms of fast exchange several years later [98] laid the basis for the large variety of applications being present today. The core element of etNOE is the dependence of the cross-relaxation rate 0 ° on the correlation time T,-. The overall cross-relaxation rate is defined by ... 

Fig. 9.12 (A) Cross-relaxation rates with respect to the correlation time and the spectrometer frequency cOq. (B) While only positive NOE (resulting in cross-peaks with inverted sign compared to the diagonal peaks, left) are present in a mixture of free ligands, the addition of the receptor leads to the...

The number of NMR parameters available for measurement is rather small, consisting of the chemical shift, relaxation rates (/1 and lo), scalar (J) couplings, dipolar (D) couplings, cross-relaxation rates (the NOE), and hydrogen exchange rates. All of these have been quantified for many of the amide protons of A131 A, and most of the data suggest the presence of little persistent structure. 

The coupling term, traditionally denoted by cr B (which has however nothing to do with the screening coefficient of Section 2.2), is the so-called cross-relaxation rate and is a relaxation parameters which depends exclusively on the dipolar interaction between nuclei A and B, contrary to auto-relaxation rates which are compounds of several contributions. For instance, if A is a carbon-13, the auto-relaxation rate can always be written as... 

In Equation (15), R others encompasses all secondary interactions which are not included in the first two terms (for instance the interaction with an unpaired electron, the spin-rotation interaction,...). By contrast, the expression of the cross-relaxation rate is simply... 

This is the beauty of this quantity which provides specifically a direct geometrical information (1 /r% ) provided that the dynamical part of Equation (16) can be inferred from appropriate experimental determinations. This cross-relaxation rate, first discovered by Overhau-ser in 1953 about proton-electron dipolar interactions,8 led to the so-called NOE in the case of nucleus-nucleus dipolar interactions, and has found tremendous applications in NMR.2 As a matter of fact, this review is purposely limited to the determination of proton-carbon-13 cross-relaxation rates in small or medium-size molecules and to their interpretation. 

It can be noticed that the maximum NOE factor (2 when A is a carbon-13 and B a proton) is reached under extreme narrowing (see Section 6) conditions and if RA arises exclusively from the A-B dipolar interaction. On the other hand, the cross-relaxation rate gab is easily deduced from the NOE factor and from the A specific relaxation rate... 

Equation (44) is that the cross-relaxation rate can be deduced from the initial slope of the plot of as a function of tm. This initial slope is... 

Taking into account spin diffusion among the proton spin system (multiple proton-proton cross-relaxation rates), one obtain order... 

Figure 12 The C responses (bottom) obtained by selectively inverting H5 (bound to a car on 12), they lead to the cross-relaxation rates erH C6 and cl1. A reference carbon-13 spectrum is shown at the top.

When r s, one has interconversion between operators Br and Bs, and Rrs is a cross-relaxation rate. Note that the cross-relaxation may or may not contain interference effects depending on the indices l and /, which keep track of interactions Cyj and C,. Cross-correlation rates and cross-relaxation rates have not been fully utilized in LC. However, there is a recent report41 on this subject using both the 13C chemical shielding anisotropy and C-H dipolar coupling relaxation mechanisms to study a nematic, and this may be a fruitful arena in gaining dynamic information for LC. We summarize below some well known (auto-)relaxation rates for various spin interactions commonly encountered in LC studies. 

---