Magnetizabilities of diatomic and linear triatomic molecules in a time-independent nonuniform magnetic field

The theory of response of a molecule in the presence of a static nonuniform magnetic field with uniform gradient is reviewed and extended. Induced magnetic dipole, quadrupole, and anapole moments are expressed via multipole magnetic susceptibilities. Dependence of response properties on the origin of the coordinate system with respect to which they are defined is investigated. Relationships describing the change of multipole and anapole susceptibilities in a translation of the reference system are reported. For a single molecule, two quantities are invariant and, in principle, experimentally measurable, that is, the induced magnetic dipole and the interaction energy. The trace of a second-rank anapole susceptibility, related to a pseudoscalar obtained by spatial averaging of the dipole-quadrupole susceptibility, of different sign for D and L enantiomeric systems, is origin independent. Therefore, in an isotropic chiral medium a homogeneous magnetic field induces an electronic anapole, having the same magnitude but opposite sign for two enantiomorphs. Calculations have been carried out for a set of diatomic and linear triatomic systems characterized by the presence of magnetic-field induced toroidal electron currents.