In practice, the quantities in eqs ( ) and ( ) are computed in the local molecular basis of the individual fragments (and not the supermolecular basis). The evaluation of these operators therefore scales linearly with the number of fragments in the environment. In the present implementation, the evaluation of the induction operator in eq (2) scales quadratically with the number of polarizable sites. However, this can be reduced to linear scaling by introducing, e.g., a fast multipole method for the evaluation of the electric fields from the induced dipoles.