Chemical Sciences: A Manual for CSIR-UGC National Eligibility Test for Lectureship and JRF/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 ejk is a unit vector parallel to the line joining the centers of the two dipoles. rjk is the distance between two dipoles, mk and mj.

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 rjk 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.