where µ and ν, here and in the following equations, are indices of AOs belonging to the core region and γ and δ belong to AOs of fragments in the environment. The first term of eq 1 accounts for the repulsion between electrons in the core region and electrons in the environment, while the second term accounts for the attraction between electrons in the core region and nuclei in the environment. The density matrices are optimized for each fragment in isolation and then kept frozen during the optimization of the core-region electronic density, consistent with the fact that the polarization is described classically (as described below).