Forces at the nuclei of a molecule in the presence of non-uniform electric field

The interaction Hamiltonian within the Bloch gauge for the potentials of the electric field has been used to define electric multipole moment operators. Perturbation theory has been applied to evaluate the induced electronic moments and electric field at the nuclei in the presence of spatially non-uniform electric fields of high intensity. Multipole nuclear electric shielding tensors have been defined to describe the contributions arising from a non-homogeneous electric field. These quantities are useful to rationalize linear and non-linear responses of a molecule in the presence of intense external electric perturbations.