Longitudinal vector potentials for molecular magnetic properties

A gauge transformation of the transverse Coulomb vector potential is studied to define a new vector potential with anon-vanishing component in the direction of magnetic field. In this longitudinal gauge the diamagnetic contribution tomagnetic susceptibility is an isotropic tensor, whereas the diagonal and average diamagnetic contributions to nuclearmagnetic shielding are the same as in the Coulomb gauge. The paramagnetic contributions to magnetic propertiesundergo gauge transformation, in such a way that total niagnetic tensors are left invariant, provided that a series ofsum rules involving the virial tensor operator is satisfied.