in each Lagrangian to denote the average of the absolute difference between the model and DFT energies over all geometries used in the H-bond and stacking profiles. Dipole terms in each fitted Lagrangian will be explicitly stated. As site centered densities are spherically symmetric, the scaling of their ζ frz exponents does not affect the molecular dipole moments. Thus, the restraint function over dipole moments in equation 34 ensures that more emphasis is given towards scaling the density exponents rather than the total populations. Initial DRESP fits do result in accurate dipole moments for each of the 4 nucleobases (see section 4), however, scaling the charge populations will inevitably also scale the error in these vectors and this cost function serves to mitigate this error.