  In recent years, machine learning (ML) methods have become increasingly
popular in computational chemistry. After being trained on appropriate ab
initio reference data, these methods allow to accurately predict the properties
of chemical systems, circumventing the need for explicitly solving the
electronic Schr\"odinger equation. Because of their computational efficiency
and scalability to large datasets, deep neural networks (DNNs) are a
particularly promising ML algorithm for chemical applications. This work
introduces PhysNet, a DNN architecture designed for predicting energies, forces
and dipole moments of chemical systems. PhysNet achieves state-of-the-art
performance on the QM9, MD17 and ISO17 benchmarks. Further, two new datasets
are generated in order to probe the performance of ML models for describing
chemical reactions, long-range interactions, and condensed phase systems. It is
shown that explicitly including electrostatics in energy predictions is crucial
for a qualitatively correct description of the asymptotic regions of a
potential energy surface (PES). PhysNet models trained on a systematically
constructed set of small peptide fragments (at most eight heavy atoms) are able
to generalize to considerably larger proteins like deca-alanine (Ala$_{10}$):
The optimized geometry of helical Ala$_{10}$ predicted by PhysNet is virtually
identical to ab initio results (RMSD = 0.21 \r{A}). By running unbiased
molecular dynamics (MD) simulations of Ala$_{10}$ on the PhysNet-PES in gas
phase, it is found that instead of a helical structure, Ala$_{10}$ folds into a
wreath-shaped configuration, which is more stable than the helical form by 0.46
kcal mol$^{-1}$ according to the reference ab initio calculations.
