Nuclear Overhauser Effect (NOE)

 The effect which changes the intensity of one spin system (either same or different kind of nuclei like H or C) when the transition of another spin system (another nuclei like H) is perturbed from equilibrium population (via saturation or relaxation processes) by irradiating with a second tunable radiofrequency pulse applied at the precessional frequency of latter nuclei.

The NOE effect will be homonuclear when both the nuclei are same (like H and H) and will be heteronuclear when both the nuclei will be different (like C and H).

It may be positive as well as negative and its magnitude depends on the gyromagnetic ratios of the nuclei involved in dipolar coupling.

It will be positive when the gyromagnetic values of both the nuclei are positive and is given by below equation:  

NOE_max = ½ (γ_irr/γ_obs)

While the total intensity = 1 + NOE_max

The nuclei which are irradiated with the second radiofrequency is represented as S and its gyromagnetic ratio as γ_irr. While the nuclei whose intensity changes as a result of dipolar coupling with irradiating nuclei is represented as I and its gyromagnetic ratio as γ_obs.

NOE between Carbon and Proton nuclei:

When heteronuclear NOE between carbon and hydrogen nuclei is observed and hydrogen nuclei are irradiated then the intensity of ¹³C signals can be enhanced maximum up to 199%.

While in the reverse case when the carbon nuclei are irradiated then the intensity of ¹H signals can be enhanced maximum up to 50 % only.

Higher the number of hydrogens attached to a carbon, higher will be total NOE for that carbon nuclei and it decreases in the following order: CH₃ > CH₂ > CH > C

Since the polarization transfer (cross-polarization) in case of dipolar coupling occurs through space, the nuclei need not be directly connected via bonds but they have to be close enough in space orientation as depicted by the below expression.

NOE = 1/r³

Where, r = distance between the nuclei showing dipolar coupling

Mechanism of NOE

The intensity of peaks in NMR spectra is directly proportional to the excess population.

Excess population = Number of nuclei in lower spin state () - Number of nuclei in higher spin state (β)

Diagram depicting NOE and gain of excess population in Observed nuclei (I)

Before irradiating the nuclei, there are more nuclei in lower energy state of both types. When we irradiate one nuclei at its precessional frequency then it will reach the saturation state (i.e. the population of both lower and higher spin state become equal).

Now, when this second radiofrequency source is turned off, the spin of the nuclei will undergo relaxation. The relaxation will also increase the excess population of observed nuclei thereby leading to increase in its intensity.

These relaxation processes are of two types:

1. W₂ (Double Quantum transfer process)

2. W₀ (Zero Quantum transfer Process)

W₂ transfer processes are generally found in smaller molecules and lead to increase in their intensity on account of NOE

while W₀ transfer processes are found larger macromolecules or polymers and lead to decrease in intensity.