General Definitions

We premise that our study of the interaction of a molecule with external electric and magnetic fields is a semi-classical one, i.e., the molecular system is treated at the QM level, while the fields are considered at the classical level. Therefore, we start recalling the basic equations of the classical electromagnetic field theory that will be used in the following. Then the quantum mechanical Hamiltonian in the Born-Oppenheimer approximation, without and with relativistic corrections, will be outlined, together with some of the tools needed for the topological analysis of the scalar field \(\rho (\boldsymbol{r})\) , useful also for the analysis of the current density exposed later.