Electric and magnetic nuclear shielding tensors: A study of the water molecule

We introduce a series of new linear-response tensors which enable one to estimate the actual electric and magnetic fields at the nuclei of a molecule immersed in an external, spatially uniform, periodical electromagnetic field. The analysis is extended to the case of an electric field gradient. These tensors may be called electromagnetic nuclear shieldings. They possess interesting properties and fulfill a series of general sum rules and equations, showing the deep relations among the electromagnetic properties of molecules. An accurate numerical test has been performed on the water molecule, with use of the random-phase approximation to decouple the polarization propagator equations.