Molecular response to a time-independent non-uniform magnetic-field

The response of a molecule to a static inhomogeneous magnetic-field is rationalized via multipole magnetic susceptibilities and induced magnetic multipole and anapole moments. The energy of the molecule interacting with the external field is expressed as a Taylor series in the powers of the field and its gradient at the origin of the coordinate system. It involves magnetic multipole tensors of increasing rank, which can be evaluated via quantum mechanical approaches. An electronic energy shift is caused by the feedback interaction between the induced magnetic dipole moment and the external magnetic field, and between the induced magnetic quadrupole moment and the gradient of the magnetic field. It is shown that, for a static magnetic field with uniform gradient, the magnetic quadrupole moment is origin-dependent, but the total interaction energy and the induced magnetic dipole are invariant to a translation of the coordinate system. The formal advantages of a Geertsen approach to third- and fourth-rank mixed-multipole susceptibilities are discussed.