In a DFT setting, the theoretical framework which considers the electronic current density as a basic variable was introduced in the '80s and is now known as current-density-functional theory . In general, an external vector potential A ext induces a current density and allows to define the mechanical momentum operator π r = -i∇ r +A ext (r). The induced current density, j ψ (r), carried by an eigenstate ψ of the Hamiltonian under study is