Cross relaxation rate for

In expression 3, (Tab is the average cross relaxation rate between protons a and b Xl is the mole fraction of one of the conformers, and aiab and a2ab are the cross relaxation rates for the individual conformers. In expression 4, Ei and E2 are the molecular mechanics energies for the conformers, k is the Boltzmann constant and T is the temperature at which the data were obtained. The pseudoenergy term may be... 

Theoretically, the cross-relaxation rate for a dipole-dipole transfer can be obtained from the formula (Reisfeld, 1976a)... 

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. 

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 ... 

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... 

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. 

The DD-CSA cross-correlated relaxation, namely that between 13C-1H dipole and 31P-CSA, can also be used to determine backbone a and C angles in RNA [65]. The experiment requires oligonucleotides that are 13C-labeled in the sugar moiety. First, 1H-coupled, / - DQ//Q-II CP spectra are measured. DQ and ZQ spectra are obtained by linear combinations of four subspectra recorded for each q-increment. Then, the cross-relaxation rates are calculated from the peak intensity ratios of the doublets in the DQ and ZQ spectra. The observed cross-correlation rates depend on the relative orientations of CH dipoles with respect to the components of the 31P chemical shift tensor. As the components of the 31P chemical shift tensor in RNA are not known, the barium salt of diethyl phosphate was used as a model compound with the principal components values of -76 ppm, -16 ppm and 103 ppm, respectively [106]. Since the measured cross-correlation rates are a function of the angles / and e as well, these angles need to be determined independently using 3/(H, P) and 3/(C, P) coupling constants. 

Cross-correlation effects between 15N CSA and 1H-15N dipolar interactions [10] will result in different relaxation rates for the two components of the 15N spin doublet, which could significantly complicate the analysis of the resulting bi-exponential decay of the decoupled signal in T, or T2 experiments. To avoid this problem, 180° 1H pulses are applied during the 15N relaxation period [3, 4], which effectively averages the relaxation rates for the two components of the 15N spin doublet... 

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