  A ubiquitous approach to obtain transferable machine learning-based models of
potential energy surfaces for atomistic systems is to decompose the total
energy into a sum of local atom-centred contributions. However, in many systems
non-negligible long-range electrostatic effects must be taken into account as
well. We introduce a general mathematical framework to study how such
long-range effects can be included in a way that (i) allows charge
equilibration and (ii) retains the locality of the learnable atom-centred
contributions to ensure transferability. Our results give partial explanations
for the success of existing machine learned potentials that include
equilibriation and provide perspectives how to design such schemes in a
systematic way. To complement the rigorous theoretical results, we describe a
practical scheme for fitting the energy and electron density of water clusters.
