# Magnetic dipole-dipole interaction

- Magnetic dipole-dipole interaction
**Magnetic dipole-dipole interaction**, also called **dipolar coupling**, refers to the direct interaction between two magnetic dipoles. The energy of the interaction is as follows:

:$old\{H\}\; =\; -\; frac\{\; mu\_0\; \}\; \{4\; pi\; r\_\{jk\}^3\; \}\; left(\; 3\; (old\{m\}\_j\; cdot\; old\{e\}\_\{jk\})\; (old\{m\}\_k\; cdot\; old\{e\}\_\{jk\})\; -\; old\{m\}\_j\; cdot\; old\{m\}\_k\; ight)$

where **e**_{jk} is a unit vector parallel to the line joining the centers of the two dipoles. r_{jk} is the distance between two dipoles, **m**_{k} and **m**_{j}.

For two interacting nuclear spins:

:$old\{H\}\; =\; -\; frac\{\; mu\_0\; \}\{\; 4\; pi\; \}\; frac\{\; gamma\_j\; gamma\_k\; \}\{\; r\_\{jk\}^3\; \}\; left(\; 3\; (old\{I\}\_j\; cdot\; old\{e\}\_\{jk\})\; (old\{I\}\_k\; cdot\; old\{e\}\_\{jk\})\; -\; old\{I\}\_j\; cdot\; old\{I\}\_k\; ight)$

γ_{j}, γ_{k} and r_{jk} are gyromagnetic ratios of two spins and spin-spin distance respectively.

** Dipolar coupling and NMR spectroscopy **

The direct dipole-dipole coupling is very useful for molecular structural studies, since it depends only on known physical constants and the inverse cube of internuclear distance. Estimation of this coupling provides a direct spectroscopic route to the distance between nuclei and hence the geometrical form of the molecule. Although internuclear magnetic dipole couplings contain a great deal of structural information, in isotropic solution, they average to zero as a result of rotational diffusion. However, their effect on nuclear spin relaxation results in measurable nuclear Overhauser effects (NOEs).

The residual dipolar coupling (RDC) occur if the molecules in solution exhibit a partial alignment leading to an incomplete averaging of spatially anisotropic magnetic interactions i.e. dipolar couplings. RDC measurement provides information on the global folding of the protein-long distance structural information. It also provides information about "slow" dynamics in molecules.

**References**

*Malcolm H. Levitt , "Spin Dynamics: Basics of Nuclear Magnetic Resonance". ISBN 0-471-48922-0.

** See also **

*J-coupling

*Magic angle

*Residual dipolar coupling

*Nuclear Overhauser effect

*Wikimedia Foundation.
2010.*

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