We reduce the number of free fitting variables in two ways. First, fragments are constrained to carry integer charges, which reduces the number of free parameters by one for the charge fits. For example, the total charge of the central amino acid is constrained to the appropriate charge of the given amino acid, while the capping groups are constrained to have a total charge of zero (see Figure ). The constraint on the sum of charges can be realized by freely fitting only N -1 charges and assigning the final N th charge to be q N = q total -N -1 i=1 q i . A similar constraint could, in principle, be introduced for the polarizabilities, but the molecular polarizability varies between conformations, unlike the molecular charge, so such a constraint is less appropriate in that case. Second, chemically equivalent atoms are constrained to have identical charge and polarizability. Both types of constraints were enforced by only using non-redundant optimization parameters (rather than Lagrange multipliers). With this, we significantly reduce the number of free parameters in the fit. For example, for the capped valine amino-acid model, which contains 28 atoms, the number of free parameters for the polarizabilities is reduced to 18, while the number of free parameters for the charges is reduced to 15.