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Machine Learning (ML) approximations to Density Functional Theory (DFT)potential energy surfaces (PESs) are showing great promise for reducing thecomputational cost of accurate molecular simulations, but at present they arenot applicable to varying electronic states, and in particular, they are notwell suited for molecular systems in which the local electronic structure issensitive to the medium to long-range electronic environment. With this issueas the focal point, we present a new Machine Learning approach called bpopNNfor obtaining efficient approximations to DFT PESs. The methodology is based onapproaching the true DFT energy as a function of electron populations on atoms,which may be realized in practice with constrained DFT (CDFT). The new approachcreates approximations to this function with deep neural networks. Theseapproximations thereby incorporate electronic information naturally into a MLapproach, and optimizing the model energy with respect to populations allowsthe electronic terms to self-consistently adapt to the environment, as in DFT.We confirm the effectiveness of this approach with a variety of calculations onLi$_n$H$_n$ clusters.

Incorporating electronic information into Machine Learning potential  energy surfaces via approaching the ground-state electronic energy as a  function of atom-based electronic populations