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Machine learning potentials have become an important tool for atomisticsimulations in many fields, from chemistry via molecular biology to materialsscience. Most of the established methods, however, rely on local properties andare thus unable to take global changes in the electronic structure intoaccount, which result from long-range charge transfer or different chargestates. In this work we overcome this limitation by introducing afourth-generation high-dimensional neural network potential that combines acharge equilibration scheme employing environment-dependent atomicelectronegativities with accurate atomic energies. The method, which is able tocorrectly describe global charge distributions in arbitrary systems, yieldsmuch improved energies and substantially extends the applicability of modernmachine learning potentials. This is demonstrated for a series of systemsrepresenting typical scenarios in chemistry and materials science that areincorrectly described by current methods, while the fourth-generation neuralnetwork potential is in excellent agreement with electronic structurecalculations.

A Fourth-Generation High-Dimensional Neural Network Potential with Accurate Electrostatics Including Non-local Charge Transfer