The nuclear Overhauser effect
المؤلف:
Peter Atkins، Julio de Paula
المصدر:
ATKINS PHYSICAL CHEMISTRY
الجزء والصفحة:
ص542-543
2025-12-14
38
The nuclear Overhauser effect
We have seen already that one advantage of protons in NMR is their high magnetogyric ratio, which results in relatively large Boltzmann population differences and hence greater resonance intensities than for most other nuclei. In the steady-state nuclear Overhauser effect (NOE), spin relaxation processes involving internuclear dipole-dipole interactions are used to transfer this population advantage to another nucleus (such as 13C or another proton), so that the latter’s resonances are modified. To understand the effect, we consider the populations of the four levels of a homo nuclear (for instance, proton) AX system; these were shown in Fig. 15.12. At thermal equilibrium, the population of the αAαX level is the greatest, and that of the βAβX level is the least; the other two levels have the same energy and an intermediate population. The thermal equilibrium absorption intensities reflect these populations as shown in Fig. 15.43. Now consider the combined effect of spin relaxation and keeping the X spins saturated. When we saturate the X transition, the populations of the X levels are equalized (NαX = NβX) and all transitions involving αX ↔ βX spin flips are no longer observed. At this stage there is no change in the populations of the A levels. If that were all there were to happen, all we would see would be the loss of the X resonance and no effect on the A resonance.
Now consider the effect of spin relaxation. Relaxation can occur in a variety of ways if there is a dipolar interaction between the A and X spins. One possibility is for the magnetic field acting between the two spins to cause them both to flop from β to α, so the αAαX and βAβX states regain their thermal equilibrium populations. However, the populations of the αAβX and βAαX levels remain unchanged at the values characteristic of saturation. As we see from Fig. 15.44, the population difference between the states joined by transitions of A is now greater than at equilibrium, so the resonance absorption is enhanced. Another possibility is for the dipolar interaction between the two spins to cause αto flip to βandβto flop to α. This transition equilibrates the populations of αAβX and βAαX but leaves the αAαX and βAβX populations unchanged. Now we see from the illustration that the population differences in the states involved in the A transitions are decreased, so the resonance absorption is diminished. Which effect wins? Does the NOE enhance the A absorption or does it diminish it? As in the discussion of relaxation times in Section 15.9, the efficiency of the intensity enhancing βAβX↔αAαX relaxation is high if the dipole field oscillates at a frequency close to the transition frequency, which in this case is about 2ν; likewise, the efficiency stationary (as there is no frequency difference between the initial and final states). A large molecule rotates so slowly that there is very little motion at 2ν, so we expect an intensity decrease (Fig. 15.45). A small molecule rotating rapidly can be expected to have substantial motion at 2ν, and a consequent enhancement of the signal. In practice, the enhancement lies somewhere between the two extremes and is reported in terms of the parameter η (eta), where
η= 
Here IA °and IA are the intensities of the NMR signals due to nucleus A before and after application of the long (> T1) radiofrequency pulse that saturates transitions due to the X nucleus. When A and X are nuclei of the same species, such as protons, η lies between −1 (diminution) and +
(enhancement). However, η also depends on the values of the magnetogyric ratios of A and X. In the case of maximal enhancement it is possible to show that
η= 
where γA and γX are the magnetogyric ratios of nuclei A and X, respectively. For 13C close to a saturated proton, the ratio evaluates to 1.99, which shows that an enhance ment of about a factor of 2 can be achieved. The NOE is also used to determine interproton distances. The Overhauser enhance ment of a proton A generated by saturating a spin X depends on the fraction of A’s spin–lattice relaxation that is caused by its dipolar interaction with X. Because the dipolar field is proportional to r−3, where r is the internuclear distance, and the relaxation effect is proportional to the square of the field, and therefore to r−6, the NOE may be used to determine the geometries of molecules in solution. The determination of the structure of a small protein in solution involves the use of several hundred NOE measurements, effectively casting a net over the protons present.
Fig. 15.43 The energy levels of an AX system and an indication of their relative populations. Each grey square above the line represents an excess population and each white square below the line represents a population deficit. The transitions of A and X are marked.
Fig. 15.44 (a) When the X transition is saturated, the populations of its two states are equalized and the population excess and deficit become as shown (using the same symbols as in Fig. 15.43). (b) Dipole–dipole relaxation relaxes the populations of the highest and lowest states, and they regain their original populations. (c) The A transitions reflect the difference in populations resulting from the preceding changes, and are enhanced compared with those shown in Fig. 15.43.
Fig. 15.45 (a) When the X transition is saturated, just as in Fig. 15.44 the populations of its two states are equalized and the population excess and deficit become as shown. (b) Dipole–dipole relaxation relaxes the populations of the two intermediate states, and they regain their original populations. (c) The A transitions reflect the difference in populations resulting from the preceding changes, and are diminished compared with those shown in Fig. 15.41.
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