  Current neural networks for predictions of molecular properties use quantum
chemistry only as a source of training data. This paper explores models that
use quantum chemistry as an integral part of the prediction process. This is
done by implementing self-consistent-charge Density-Functional-Tight-Binding
(DFTB) theory as a layer for use in deep learning models. The DFTB layer takes,
as input, Hamiltonian matrix elements generated from earlier layers and
produces, as output, electronic properties from self-consistent field solutions
of the corresponding DFTB Hamiltonian. Backpropagation enables efficient
training of the model to target electronic properties. Two types of input to
the DFTB layer are explored, splines and feed-forward neural networks. Because
overfitting can cause models trained on smaller molecules to perform poorly on
larger molecules, regularizations are applied that penalize non-monotonic
behavior and deviation of the Hamiltonian matrix elements from those of the
published DFTB model used to initialize the model. The approach is evaluated on
15,700 hydrocarbons by comparing the root mean square error in energy and
dipole moment, on test molecules with 8 heavy atoms, to the error from the
initial DFTB model. When trained on molecules with up to 7 heavy atoms, the
spline model reduces the test error in energy by 60% and in dipole moments by
42%. The neural network model performs somewhat better, with error reductions
of 67% and 59% respectively. Training on molecules with up to 4 heavy atoms
reduces performance, with both the spline and neural net models reducing the
test error in energy by about 53% and in dipole by about 25%.
