In accordance with the scaling scheme for short-range intramolecular interactions used in Applequist-like models , we apply a scaling factor f jk to exclude 1-2 and 1-3 chargepolarizability interactions (f jk = 0.0) and we scale 1-4 interactions by f jk = 0.5. These scalings are applied during fitting and also during simulations. Note that 1-2 and 1-3 interatomic distances vary little across molecular dynamics snapshots, due to the high spring constants of typical bond-stretch and angle-bend terms, so omitting 1-2 and 1-3 charge-polarizability interactions omits a nearly constant term, which may be at least partly adjusted for by suitably chosen partial charges. It is also worth noting that a scaling factor is not needed to avoid polarization catastrophe, because the direct approximation does not have this numerical instability, so f jk could be safely treated as an adjustable parameter to further optimize short-range electrostatics. To train the polarizabilities, we computed baseline QM ESPs, V QM, ik , for each conformer k in the training set, where i indexes the m k ESP sampling points around the conformer.