Quadrupolar coupling

From NMR Wiki

Quadrupolar coupling is an interaction that occurs in nucleus that has more than 2 different spin states. Only nuclei with spin 0 or 1/2 do not have this interaction. On one hand this interaction is source of additional information, but on the other hand it could make the signal decrease too fast to be observed (as it is for ¹⁴N). This interaction exists even without any applied magnetic field, where the energy of corresponding splitting (even in the absence of external field) between the different states could be quite strong (kHz, to hundreds of MHz). This splitting is what is detected by nuclear quadrupolar resonance (NQR).

Source of this interaction

A nucleus with a spin I>1/2 has a quadrupole moment (Q) which will interact with an electric field gradient (efg) causing the degeneracy of the nuclear energy levels to be lifted (there will be 2I+1 energy levels). The electric field gradient is provided by an asymmetric distribution of electron density around the nucleus. So highly symmetric molecules will not have this electric field gradient, and so there will not be this energy splitting. The size of the splittings depend on the magnitude of the quadrupole moment (traditionally measured in milliBarns - a unit of area) and the size of the electric field gradient (a second order tensor). The efg tensor (unlike the chemical shift tensor) is traceless so in solution the quadrupole interaction is averaged to zero.

Consequence of the interaction

The rapid change caused by the fluctuation of the electric field gradient usually leads to fast relaxation. If the quadrupole moment is small, as it is for deuterium, or the efg is small the relaxation effects are not too severe.

In NMR this fast relaxation has the effect of decoupling the quadrupole nucleus so scalar (spin-spin) coupling is rarely seen. The NMR lines for quadrupolar nuclei are also often very broad also due to the fast relaxation.

Strength of this interaction

Usage of this interaction

• determination the orientation of methyl groups using deuterium NMR in solid state.
• determination of dynamics using the fast relaxation of deuterium in solution for macromolecules
• determining the binding of water (²³Na or ²H)

References

[1]