  Machine Learning (ML) approximations to Density Functional Theory (DFT)
potential energy surfaces (PESs) are showing great promise for reducing the
computational cost of accurate molecular simulations, but at present they are
not applicable to varying electronic states, and in particular, they are not
well suited for molecular systems in which the local electronic structure is
sensitive to the medium to long-range electronic environment. With this issue
as the focal point, we present a new Machine Learning approach called bpopNN
for obtaining efficient approximations to DFT PESs. The methodology is based on
approaching the true DFT energy as a function of electron populations on atoms,
which may be realized in practice with constrained DFT (CDFT). The new approach
creates approximations to this function with deep neural networks. These
approximations thereby incorporate electronic information naturally into a ML
approach, and optimizing the model energy with respect to populations allows
the electronic terms to self-consistently adapt to the environment, as in DFT.
We confirm the effectiveness of this approach with a variety of calculations on
Li$_n$H$_n$ clusters.
