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:

${\mathbf {H}}=-{\frac {\mu _{0}}{4\pi r_{jk}^{3}}}\left(3({\mathbf {m}}_{j}\cdot {\mathbf {e}}_{jk})({\mathbf {m}}_{k}\cdot {\mathbf {e}}_{jk})-{\mathbf {m}}_{j}\cdot {\mathbf {m}}_{k}\right)$

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:

${\mathbf {H}}=-{\frac {\mu _{0}}{4\pi }}{\frac {\gamma _{j}\gamma _{k}}{r_{jk}^{3}}}\left(3({\mathbf {I}}_{j}\cdot {\mathbf {e}}_{jk})({\mathbf {I}}_{k}\cdot {\mathbf {e}}_{jk})-{\mathbf {I}}_{j}\cdot {\mathbf {I}}_{k}\right)$

$\gamma _{j}$, $\gamma _{k}$ 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