Atomic axial tensor magnetic dipole moment

In practice, the electric and magnetic dipole transition moments are usually expressed as summations of atomic properties, namely the atomic polar tensor (APT), Pgp, and atomic axial tensor (AAT), respectively. In the... 

The fine structure interaction involves the interaction between the magnetic dipole moments of electrons on an atom containing more than one unpaired electron. The magnitude of this interae-tion is described by the second rank D tensor. Second-order terms, D and EID correspond to the axial zero field splitting (Z)) and the asymmetry parameter EID, which varies from 0 (axial symmetry) to 1/3 (rhombic symmetry) (S.D.S). Fourth- and sixth-order corrections to the fine structure interaction tensor D may also be necessary to adequately interpret the spectrum,... 

Before proceeding with some more details regarding the evaluation of the magnetic dipole moment gradient (the atomic axial tensor, Mj in the context of a nonadiabatic wavefunction, let us first note that it is from a computational point of view advantageous to derive equations with respect to Cartesian displacements of a nucleus A rather than with respect to the normal modes. These two different representations of the nuclear motion are related by a linear transformation... 

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