  We combine density-functional tight-binding (DFTB) with deep tensor neural
networks (DTNN) to maximize the strengths of both approaches in predicting
structural, energetic, and vibrational molecular properties. The DTNN is used
to learn a non-linear model for the localized many-body interatomic repulsive
energy, which so far has been treated in an atom-pairwise manner in DFTB.
Substantially improving upon standard DFTB and DTNN, the resulting
DFTB-NN$_{\sf{rep}}$ model yields accurate predictions of atomization and
isomerization energies, equilibrium geometries, vibrational frequencies and
dihedral rotation profiles for a large variety of organic molecules compared to
the hybrid DFT-PBE0 functional. Our results highlight the high potential of
combining semi-empirical electronic-structure methods with physically-motivated
machine learning approaches for predicting localized many-body interactions. We
conclude by discussing future advancements of the DFTB-NN$_{\sf{rep}}$ approach
that could enable chemically accurate electronic-structure calculations for
systems with tens of thousands of atoms.
