where χ A m , χ B m ∈ R serve as labels for unknown scalar variables that allow the net atomic contributions to the eigendensity of the molecules to match the ideal ab initio calculated Mulliken partial charges, whereas the constants labeled by c A m,n , c B m,n , λ A m,n and λ B m,n are taken from our previously tabulated atomspecific values. A new set of atom-specific coefficients, for the full electron variant of our model, is calculated, and tabulated in Table of the supplementary material, for all elements in the first three rows of the periodic table. This new set of coefficients are optimized so that the last three Gaussian contributions are the same as their ECP counterparts, thus allowing us to separate between core and valence electrons. We obtain the polarization variables from the following minimization problem: