When moving to the polarization energy, it is important to note that the AMOEBA polarization energy is not a variational function of the induced dipoles because it involves two sets of induced dipoles, µ d and µ p , polarized by the electric fields, E d and E p , that differ by their scaling factor between closest bonded atoms. Still, as described in, one can devise a function of these two sets of induced dipoles that have the correct expression at its minimum. Such a formulation allows seamless coupling with additional degrees of freedom, as is the case for polarizable or more complex embeddings. The variational formulation of the polarization energy is: