  Machine learning potentials have become an important tool for atomistic
simulations in many fields, from chemistry via molecular biology to materials
science. Most of the established methods, however, rely on local properties and
are thus unable to take global changes in the electronic structure into
account, which result from long-range charge transfer or different charge
states. In this work we overcome this limitation by introducing a
fourth-generation high-dimensional neural network potential that combines a
charge equilibration scheme employing environment-dependent atomic
electronegativities with accurate atomic energies. The method, which is able to
correctly describe global charge distributions in arbitrary systems, yields
much improved energies and substantially extends the applicability of modern
machine learning potentials. This is demonstrated for a series of systems
representing typical scenarios in chemistry and materials science that are
incorrectly described by current methods, while the fourth-generation neural
network potential is in excellent agreement with electronic structure
calculations.
