Response Properties of Periodic Materials Subjected to External Electric and Magnetic Fields

The ab initio treatment of external field response in crystalline solids poses particular challenges, since the operator representing the external field must be reformulated so to be consistent with periodic boundary conditions. In this chapter, we review our recent work to formulate implementable working equations for polarizability and hyperpolarizabilities in solids, in the framework of a local (gaussian) basis set. This includes the combination of electric field response with geometrical distorsion, i.e. infrared and Raman intensities, as well as piezoelectricity. In addition, we outline a pathway for including magnetic fields in a consistent way, and speculate on future possible developments.