We again use a "double SOAP" kQEq model trained on 2000 randomly drawn QM9 molecules for comparison. This model has a mixed performance for this test. For polyenonic and n-amino carboxylic acids, the performance is very good. This is both in terms of the qualitative features (linear increase in dipole moments, vs. quick saturation) and the quantitative agreement. Furthermore, kQEq is a strong improvement over conventional QEq here. In contrast, the performance for the polypeptides is less satisfactory. While the linear trend is correctly captured, the magnitude of the dipoles is significantly underestimated, in particular for the β-strand. This behaviour is analogous to the underestimation of dipoles typically observed with local functionals, due to the delocalization error. While this shows that kQEq does not automatically cure all pathologies of QEq, a clear advantage of a ML approach is that it can be improved with more data. Indeed, by including the longest chains of each type explicitly in the training set, a retrained kQEq model can be generated that captures these trends more accurately, see Fig. . Potentially, an improved extrapolation behaviour could be obtained by using a more flexible expression for the site-energy in Eq. 3, effectively tackling the problem at its root. Figure also shows the best MuML model from Ref. [20] for comparison. This model performs quite well overall, in particular for the polypeptide systems, with slightly worse performance for the carboxylic acids. In this context, it is worth discussing the fundamental differences between MuML and kQEq. The former uses a fully local decomposition of the overall dipole moment. This works very well for situations where the charge distribution of a large system is essentially just a sum of smaller fragments (as for the polypeptides). In contrast, long-range charge transfer and polarization effects cannot be described by such a model, which is reflected in the underestimated dipole moments of longer polyenoic amino acid chains. QEq and kQEq are in principle able to describe such non-local effects. The QEq curve for n-amino carboxylic acid reveals that this is not necessarily an advantage however, as large unphysical charge transfer is predicted in this case. In other words, a purely local model will generally lead to more systematic and less dramatic failures than a poor non-local one. Fortunately, kQEq and related methods now provide a framework for sophisticated non-local charge equilibration models.