Cross-relaxation chemical exchange

In this chapter, we will introduce a new level of theoretical tools—the density matrix— and show by a bit of matrix algebra what the product operators actually represent. The qualitative picture of population changes in the NOE will be made more exact, the precise basis of cross-relaxation will be revealed, and a new phenomenon of cross-relaxation— chemical exchange—will be introduced. With these expanded tools, it will be possible to understand the 2D NOESY (nuclear Overhauser and exchange spectroscopy) and DQF-COSY experiments in detail. 

CHEMICAL SHIFT CORRELATIONS THROUGH CROSS-RELAXATION AND EXCHANGE... 

Chemical Shift Correlations Through Cross>Relaxation and Exchange 285... 

Chemical Shift Correlations Through Cross-Relaxation and Exchange 287... 

Multidimensional and heteronuclear NMR techniques have revolutionised the use of NMR spectroscopy for the structure determination of organic molecules from small to complex. Multidimensional NMR also allows observation of forbidden multiple-quantum transitions and probing of slow dynamic processes, such as chemical exchange, cross-relaxation, transient Over-hauser effects, and spin-diffusion in solids. 

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 water nucleus chosen also has an impact on relaxation data. Proton relaxation is affected by chemical exchange and cross-relaxation, 2H by chemical exchange, and lyO by proton-exchange broadening (scalar spin-spin coupling between lH and lyO nuclei affects T2, but not 7)) (Glasel,... 

In the laboratory frame of reference, the net effects of the chemical exchange and the cross-relaxation are indistinguishable in the spin-diffusion regime. The individual contributions of each cannot be determined from a single exchange experiment. 

Quantitative analysis of exchange spectra directly provides data about the chemical exchange and the cross-relaxation rates. Whereas the chemical exchange rate constants are used directly, the cross-relaxation rates are usually processed further for determination of interproton distances and correlation times. 

Cross relaxation can occur in principle also between nuclei coupled by a time-dependent scalar interaction. In this case only wo can contribute to it (see Section 3.5). The correlation time for the reorientation is either chemical exchange or the relaxation rate of nucleus J if nucleus / is observed. The correlation time is generally too long to make the experiment successful. 

A Real Example Chemical Exchange and Cross Relaxation... 

FIGURE 10.4 Pulse sequence for measuring chemical exchange and cross relaxation (NOESY). 

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