The polarizable density embedding (PDE) model 22 is a fragment-based mixed quantumclassical embedding model where the permanent charge distributions of environment fragments are described quantum mechanically by their electronic densities and nuclear charges, while the induced charge distributions are described classically through an induced-dipole model based on localized dipole-dipole polarizabilities. It was introduced as an extension of the PE model in order to improve electrostatic interactions and to avoid electron spill-out.