Editing Nuclear Overhauser effect (section)

==Structure elucidation==
[[File:Noe examples.png|thumb|First NOE's reported by Anet and Bourne<ref name="Anet"/>]]

While the relationship of the steady-state NOE to internuclear distance is complex, depending on relaxation rates and molecular motion, in many instances for small rapidly tumbling molecules in the extreme-narrowing limit, the semiquantitative nature of positive NOE's is useful for many structural applications often in combination with the measurement of J-coupling constants. For example, NOE enhancements can be used to confirm NMR resonance assignments, distinguish between structural isomers, identify aromatic ring substitution patterns and aliphatic substituent configurations, and determine conformational preferences.<ref name="Claridge" />

Nevertheless, the inter-atomic distances derived from the observed NOE can often help to confirm the three-dimensional structure of a molecule.<ref name="Claridge" /><ref name="Derome" /> In this application, the NOE differs from the application of [[J-coupling]] in that the NOE occurs through space, not through chemical bonds. Thus, atoms that are in close proximity to each other can give a NOE, whereas spin coupling is observed only when the atoms are connected by 2–3 chemical bonds. However, the relation ''&eta;''<sub>I</sub><sup>S</sup>(max)={{frac|1|2}} obscures how the NOE is related to internuclear distances because it applies only for the idealized case where the relaxation is 100% dominated by dipole-dipole interactions between two nuclei I and S. In practice, the value of &rho;<sub>I</sub> contains contributions from other competing mechanisms, which serve only to reduce the influence of ''W''<sub>0</sub> and ''W''<sub>2</sub> by increasing ''W''<sub>1</sub>. Sometimes, for example, relaxation due to electron-nuclear interactions with dissolved oxygen or paramagnetic metal ion impurities in the solvent can prohibit the observation of weak NOE enhancements. The observed NOE in the presence of other relaxation mechanisms is given by

:::<math>\eta_{I} = \frac {\sigma_{IS}} {\rho_{I}+\rho^{*}}</math>
where &rho;<sup>⋇</sup> is the additional contribution to the total relaxation rate from relaxation mechanisms not involving cross relaxation. Using the same idealized two-spin model for dipolar relaxation in the extreme narrowing limit:
:::<math>\rho_{I} \propto \frac {\tau_{c}} {r^{6}}</math>

It is easy to show<ref name="Derome"/> that
:::<math>\eta_{I}^{S} \propto \left( \frac {\tau_{c}} {\rho^{*}}  \right)\frac {1}{r^{6}}</math>

Thus, the two-spin steady-state NOE depends on internuclear distance only when there is a contribution from external relaxation. Bell and Saunders showed that following strict assumptions &rho;<sup>⋇</sup>/&tau;<sub>c</sub> is nearly constant for similar molecules in the extreme narrowing limit.<ref name="Bell"/>  Therefore, taking ratio's of steady-state NOE values can give relative values for the internuclear distance ''r''. While the steady-state experiment is useful in many cases, it can only provide information on relative internuclear distances. On the other hand, the initial ''rate'' at which the NOE grows is proportional to ''r''<sub>IS</sub><sup>−6</sup>, which provides other more sophisticated alternatives for obtaining structural information via transient experiments such as 2D-NOESY.