The Homonuclear Nuclear Overhauser Effect NOE

Now let s us have some fun by perturbing this equilibrium population distribution Selective saturation of the Ha transitions (aa — Pa and ap — PP) by low-power 

Exercise Go through the same thought experiment with relaxation occurring to completion 

What is the equilibrium population difference between ap and Pal After cross-relaxation, what is the percentage change in the z magnetization of Hb, and is it increased (enhanced) or decreased  

Each of these numbers is multiplied by 1/r6, reflecting the distance dependence of the dipole-dipole interaction. Now we see that double-quantum relaxation does in fact dominate the dipole-dipole relaxation of small molecules, and our cartoon model of relaxation exclusively by the DQ pathway during the mixing time is not that far off. Likewise, the assumption that only ZQ relaxation occurs for large molecules (see exercise above) is also qualitatively correct. 

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. 

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Since the discovery of the nuclear Overhauser effect (NOE, see previous section) [4, 5] and scalar coupling constants [36, 37] decades ago, NMR-derived structure calculations of biomolecules largely depended on the measurement of these two parameters [38]. Recently it became possible to use cross-correlated relaxation (CCR) to directly measure angles between bond vectors [39] (see also Chapt 7). In addition, residual dipolar couplings of weakly aligned molecules were discovered to measure the orientation of bond vectors relative to the alignment tensor (see Sect 16.5). Measurement of cross-correlated relaxation was described experimentally earlier for homonuclear cases [40, 41] and is widely used in solid-state NMR [42 14]. 

In solution, dipole-dipole interactions constitute a relaxation mechanism, and the dipolar relaxation which is the basis for the well-known nuclear Overhauser effect (NOE), mostly used in the homonuclear H, H case. The 2D HOESY method between H and Li has been used to obtain structural information of many organolithium systems in solution and this field was reviewed in 1995. Li is commonly used as the relaxation is dominated by the dipole-dipole mechanism and the relaxation time is relatively long. Knowledge of the proximity of the lithium cation relative to protons in the substrate is used to derive information about the structure and aggregation of organolithium systems in solution. In a few cases quantitative investigations have been made °. An average error of the lithium position of ca 0.2 A was reported. 

Chemical shift correlated NMR experiments are the most valuable amongst the variety of high resolution NMR techniques designed to date. In the family of homonuclear techniques, four basic experiments are applied routinely to the structure elucidation of molecules of all sizes. The first two, COSY [1, 2] and TOCSY [3, 4], provide through bond connectivity information based on the coherent (J-couplings) transfer of polarization between spins. The other two, NOESY [5] and ROESY [6] reveal proximity of spins in space by making use of the incoherent polarization transfer (nuclear Overhauser effect, NOE). These two different polarization transfer mechanisms can be looked at as two complementary vehicles which allow us to move from one proton atom of a molecule to another proton atom this is the essence of a structure determination by the H NMR spectroscopy. 

All of the protons in each of 12 thermo- and photochromic BIPS were assigned through a combination of homonuclear decoupling experiments and correlation spectroscopy. The relative stereochemistry of the gem-dimethyl groups could be assigned on the basis of Nuclear Overhauser Effect (NOE) experiments.131... 

The nuclear Overhauser effect (NOE), caused by dipole-dipole crossrelaxation, has great potential in the elucidation of the molecular structure and conformation (Noggle and Shirmer, 1971 Hall and Sanders, 1980). A homonuclear NOE can theoretically be as large as 50%, but is usually much smaller, and depends on the inverse sixth power of the distance between the nuclei, so that the relative magnitudes of enhancements reflect the spatial relationships of the atoms involved. 

We will briefly consider in this section various aspects of homonuclear spin-de-coupling experiments and nuclear Overhauser effect (NOE) difference spectra. Obviously any detailed treatment is far beyond the size limitations of this chapter. Moving next to ID NMR techniques, we wiU briefly consider the utilization of selective spin-population transfer (SPT) and experiments which rely on these principles such as INEPT and DEPT, off-resonance proton decoupling techniques, decoupler gating experiments, and finally spin—lattice or Tj relaxation techniques. 

It is not only chemical shifts or couplings that can be used to define correlations in a 2D NMR spectrum information from through-space interactions as in the Nuclear Overhauser Effect (NOE, Section 4.11.4) can also be used. The NOES Y (Nuclear Overhauser Effect Spectroscop Y) experiment is one of the most useful in this context. It is a homonuclear technique that allows correlation of nuclei through space separated by less than 5 A. The occurrence of a cross peak therefore indicates that the corresponding two nuclei are close in... 

A handy method for solving these types of problems is nuclear Overhauser effect (NOE) difference spectroscopy. This technique is based on the same phenomenon that gives rise to the nuclear Overhauser effect (Section 4.5), except that it uses homonuclear, rather than a heteronuclear, decoupling. In the discussion of the nuclear Overhauser effect, attention was focused on the case in which a hydrogen atom was directly bonded to a atom, and the hydrogen nucleus was saturated by a broadband signal. In fact, however, for two nuclei to interact via the nuclear Overhauser effect. 

The nuclear Overhauser effect provides information on the spatial proximity of nuclei (Section 5-4). NOE determinations are usually homonuclear, in the case of protons, but also can be heteronuclear, with signals irradiated and those of heteronuclei observed. NOE s occupy both an intermediary and a final position in the overall progression of structural determination. In most cases, NOE s afford information on the three-dimensional structure of a molecule after its two-dimensional structure has been determined. NOE s, however, also can be used earlier in the structural elucidation process, to provide answers to questions concerning stereochemistry in systems containing double bonds or rings. 

Nuclei that undergo mutual relaxation via dipolar coupling are said to be dipolar coupled and give rise to the nuclear Overhauser effect. Whether the nuclei in question also may be scalar (or spin) coupled is not pertinent to the discussion (Section 5-4). NOE experiments can be either homonuclear or heteronuclear in nature, although the former, involving protons, are much more common. One-dimensional homonuclear Overhauser experiments are discussed in Section 7-3 their 2D versions, NOESY and ROESY, are treated in this section. 

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