Three-Spin Effects

Explain what is meant by three-spin effects, or indirect nOe effects. When do such indirect effects matter ... 

Three-spin effects arise when the nonequilibrium population of an enhanced spin itself acts to disturb the equilibrium of other spins nearby. For example, in a three-spin system, saturation of spin A alters the population of spin B from its equilibrium value by cross-relaxation with A. This change in turn disturbs the whole balance of relaxation at B, including its cross-relaxation with C, so that its population disturbance is ultimately transmitted also to C. This is the basic mechanism of indirect nOe, or the three-spin effect. 

Another interesting application motivated by medicine is the use of the three-spin effect to determine lithium concentration solely through 1H DNP measurements. In a proof of principle study by Zeghib et al., an increased concentration of 7LiOH in aqueous solution with trityl radicals resulted in a decreased H DNP enhancement at 6.8 mT due to a competing three-spin effect.96 This was proposed to allow lithium monitoring... 

The negative NOEs result from an indirect three-spin effect involving fluorine as the central spin ( 6.2.3). 

Despite the considerable advantages of the NOE experiment, its limitations must be appreciated. First, three-spin effects, or spin diffusion, may cause misleading intensity perturbations when the third spin is not close to the irradiated nucleus (H2a in Figure 5-12). Second, the size of the molecule can cause NOE effects that are positive, negative, or null. 

When direct (A-B) NOEs are positive, indirect effects at C are weak and negative, are favoured when the three spins have an approximately linear relationship (so may provide useful geometrical information), develop only slowly with a characteristic lag time and are thus also favoured by long presaturation periods. These are referred to as three-spin effects. Although further relays are theoretically possible, they are generally too weak to be observed. 

Originally the three-spin effect was postulated to explain the positive enhancements observed for certain fluorine nuclei in solvents also containing protons.The possibility arose that the fluorine nuclei were being influenced by the proton polarization as well as by the direct coupling to the electron spins. The basic idea behind the three-spin effect can be seen by considering the transitions among the Zeeman energy levels shown in Fig. 20. Since the electron—proton interaction is of the dipolar kind, the predominant coupled transition will be an... 

The presence of a three-spin effect can also be revealed by triple irradiation experiments, where both the electron and the proton spin transitions are strongly irradiated. This has the effect of removing the indirect pathway for the transfer of spin polarization from the electron to the fluorine via the proton, leaving only the direct electron—fluorine mechanism. Any additional proton—fluorine Overhauser effect due to the saturation of the proton signal is negligible in solution containing free radicals. Figure 23 shows the results of such a triple-irradiation... 

In conclusion, although it has been demonstrated that a three-spin effect exists, it is usually unimportant unless the radical concentration is low. This is readily understandable, since the magnetic moment of the electron is much larger than that of any nucleus so that nuclear-electron interactions are the dominant relaxation terms, except at low concentrations where nuclear—nuclear interactions become important. The presence of a three-spin effect can be revealed most easily either by observation of the transient relaxation behaviour of the nuclear resonance or by triple irradiation experiments. In the latter case, account must be taken of the collapse of any multiplet structure in the interpretation of the results. 

In ROESY experiments, direct and three-spin effects can be distinguished because they give rise to cross-peaks of opposite signs. This is also true for NOESY experiments with small molecules. However, in the case of NOESY experiments with slowly tumbling molecules, direct and indirect effects give rise to cross-peaks of the same sign. 

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