text: The secular dipolar coupling Hamiltonian of two spins,  and  is given by:
  where
  * is the reduced Planck constant.
  * and  are the gyromagnetic ratios of spin  and spin  respectively.
  * is the inter-spin distance.
  * is the angle between the inter-spin vector and the external magnetic field.
  * and  are vectors of spin operators.
  The above equation can be rewritten in the following form:
  where
  In isotropic solution molecular tumbling reduces the average value of  to zero. We thus observe no dipolar coupling. If the solution is not isotropic then the average value of  may be different from zero, and one may observe residual couplings.
  RDC can be positive or negative, depending on the range of angles that are sampled.
  In addition to static distance and angular information, RDCs may contain information about a molecule's internal motion. To each atom in a molecule one can associate a motion tensor B, that may be computed from RDCs according to the following relation:
  where A is the molecular alignment tensor.
  The rows of B contain the motion tensors for each atom. The motion tensors also have five degrees of freedom. From each motion tensor, 5 parameters of interest can be computed. The variables S, η, α, β and γ are used to denote these 5 parameters for atom i. S is the magnitude of atom i’s motion; η is a measure of the anisotropy of atom i’s motion; α and β are related to the polar coordinates of the bond vector expressed in the initial arbitrary reference frame (i.e., the PDB frame). If the motion of the atom is anisotropic (i.e., η = 0), the final parameter,  γ measures the principal orientation of the motion.
  Note that the RDC-derived motion parameters are local measurements.