# 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.