Summary Of The Nuclear Overhauser Effect

1. Perturbation of the equilibrium population difference for one nucleus (increased spin temperature) spreads over time to perturb the population difference (increase or decrease the spin temperature) of other nuclei that are nearby in space. For small molecules, increasing the spin temperature of one nucleus will decrease the spin temperature of nearby nuclei ("negative NOE"). This leads to an enhancement of peak intensities corresponding to the nearby nuclei. For large molecules, increasing the spin temperature of one nucleus will increase the spin temperature of nearby nuclei ("positive NOE"), leading to a reduction in peak intensity.

2. The NOE effect (perturbation of population difference in nearby nuclei) takes time to develop—this process is called the NOE buildup. The time allowed for the NOE to build up is called the mixing time and is on the order of magnitude of T1, or typically hundreds of milliseconds (ms) for small molecules.

3. The heteronuclear NOE, for example, from *H to 13C, is used to enhance the signal-to-noise ratio of 13C peaks in the spectrum. All protons are irradiated equally and simultaneously during the relaxation delay to "pump up" the z magnetization of13 C above the equilibrium value of Mo. Theoretically this can triple the Mz of 13C.

4. The homonuclear NOE, almost always between two protons, is used to measure distances and determine stereochemical relationships. The NOE intensity (the percent increase or decrease of z magnetization observed at a nearby proton) is proportional to the inverse sixth power of distance between the two protons (1/r6), and is generally too weak to be observed for distances over 5 A.

5. There are two experimental methods for observing the NOE: steady-state NOE and transient NOE. The steady-state NOE involves a long, continuous-wave irradiation at the resonant frequency of the proton of interest, which equalizes the populations ("saturation"). During this time, the NOE builds up and reaches a steady state with the processes of NOE buildup and relaxation back to equilibrium in balance. The transient NOE (Chapter 8) involves a sudden perturbation (usually by a selective 180° pulse) followed by a mixing time with no pulses. During the mixing period, the perturbation propagates to nearby protons, changing their z magnetization. In both cases, at the end of the mixing time a 90° pulse samples the z magnetization of all nuclei, and enhancement or reduction of peak heights is observed in the spectrum.

6. The NOE is caused by dipole-dipole interaction (through-space) of two nuclear magnets, modulated by the tumbling of the molecule in solution. The NOE is an effect of mutual relaxation (or cross relaxation) of two nuclei. Mutual relaxation can occur in two ways: zero-quantum (ZQ) relaxation involves a transition from the aft state (one spin up and one down) to the fta state (one spin down and one up); double-quantum (DQ) relaxation involves a transition from the ftft state (both spins down) to the aa state (both spins up). These transitions are driven by a population difference out of equilibrium (Boltzmann) for the two states, and are stimulated by molecular tumbling at the frequency of the transition (va - vb for ZQ and va + vb for DQ) that leads to an oscillating magnetic field at both nuclei whose amplitude is strongly dependent on the distance between the two nuclei (overall inverse sixth power).

7. Longitudinal (population) relaxation of large molecules is dominated by ZQ relaxation, leading to a positive NOE (reduction of peak intensity). Small-molecule relaxation is dominated by DQ relaxation, leading to a negative NOE (enhancement of peak intensity). This effect can be understood by a thought experiment in which the mixing period of the NOE experiment consists exclusively of ZQ or DQ relaxation, which goes to completion (equilibrium population difference between the two states) before the 90° "read" pulse.

8. Molecules in the transition area of molecular weight (2000-4000 Da depending on molecular shape, rigidity, and solvent viscosity) show little or no NOE. For these molecules an alternative experiment called ROESY (rotating-frame Overhauser effect spectroscopy, Chapters 8 and 10) is effective.

9. Conformational flexibility can lead to loss of NOE interactions because the observed NOE is the weighted average over all conformations. A strong NOE resulting from a close approach of two protons in one conformation may be "diluted" by larger distances in other conformations to the extent that it is not observed at all. Rigid small molecules (e.g., fused ring systems) and tightly folded large molecules (proteins and nucleic acids) give the best NOE information. Flexible molecules, such as lipids, peptides, and oligosaccarides, give few useful NOEs.

10. Long NOE mixing times can lead to spin diffusion, in which perturbation of one proton leads to perturbation of a second proton, whose nonequilibrium population now perturbs a third proton. The appearance of an NOE between the first and third proton may be misinterpreted as a close (<5 A) approach.

11. Organic chemists often misinterpret the NOE experiment by: (a) making distance predictions based on two-dimensional drawings rather than energy-minimized three-dimensional models, (b) testing only one isomer in a pair of stereo- or regioisomers, (c) calculating distances from NOE intensities rather than from initial rates of NOE buildup, or, (d) reading subtraction artifacts as NOE peaks. NOEs are always weak and must be interpreted with great care.

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