Cross-relaxation extreme narrowing

Given the specific, internuclear dipole-dipole contribution terms, p,y, or the cross-relaxation terms, determined by the methods just described, internuclear distances, r , can be calculated according to Eq. 30, assuming isotropic motion in the extreme narrowing region. The values for T<.(y) can be readily estimated from carbon-13 or deuterium spin-lattice relaxation-times. For most organic molecules in solution, carbon-13 / , values conveniently provide the motional information necessary, and, hence, the type of relaxation model to be used, for a pertinent description of molecular reorientations. A prerequisite to this treatment is the assumption that interproton vectors and C- H vectors are characterized by the same rotational correlation-time. For rotational isotropic motion, internuclear distances can be compared according to... 

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... 

At ambient temperature, H, and 0 relaxation is in the extreme narrow range and dispersion curves are perfectly flat (see Fig. 9 bottom) precluding any correlation time determination. Furthermore as inter- and intramolecular contributions to proton relaxation cannot be easily separated and as the deuterium and 0 quadrupole coupling constants are not known with sufficient accuracy, there is a real problem for determining a meaningful correlation time. This problem was solved only in the early 1980s by resorting to the cross-relaxation rate which is purely intramolecular... 

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... 

Therefore, for a complete characterization of the cross-relaxation network, it is best to do all three experiments and to extract from each of them information that can be interpreted unambiguously. If the number of possible experiments is limited, then in the extreme-narrowing and the spin-diffusion regime it is best to record NOESY and in the intermediate motional regime ROESY or T-ROESY spectra. 

Fairly recently it has been pointed out that, even when the extreme narrowing condition is satisfied, equation (16) may not be correct if cross-correlation of the H and relaxation processes is at all important. Consequently equation (19) should be used instead (cf. refs. 257 and 258) ... 

Although it is not obvious from Eq. (7), the second term arises because of cross-relaxation, and Noggle and Schirmer (1971) have shown in detail how this term contributes to successful conformational analyses. When I = P and all other interacting atoms are H (when the extreme narrowing condition is met) and when p = 0, then J H) = yH/2yp = 1.24, and this maximum enhancement will be found in a multispin system when all hydrogens that can contribute to phosphorus relaxation via dipolar coupling are... 

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