When coupling KS-DFT with the AMOEBA model, we use the total QM/AMOEBA Lagrangian, as formulated by Nottoli and Lipparini and implemented in the Tinker-HP software, where the induced dipoles µ p are the Lagrange multipliers as discussed in more detail in a review by. The Lagrangian can be rewritten in general terms as a sum of three contributions, the QM energy, the MM energy and a mixed QM/MM term (Eq. 11), which is further decomposed into permanent and induced parts in Eq. 12