Predicting the charge density response in metal electrodes

The computational study of energy storage and conversion processes calls for simulation techniques that can reproduce the electronic response of metal electrodes under electric fields. Despite recent advancements in machine-learning methods applied to electronic-structure properties, predicting the nonlocal behavior of the charge density in electronic conductors remains a major open challenge. We combine long-range and equivariant kernel methods to predict the Kohn-Sham electron density of metal electrodes in response to various kinds of electric field perturbations. By taking slabs of gold as an example, we first show how the nonlocal electronic polarization generated by the interaction with an ionic species can be accurately reproduced in electrodes of arbitrary thickness. A finite-field extension of the method is then derived, which allows us to predict the charge transfer and the electrostatic potential drop induced by the application of a homogeneous and constant electric field. Finally, we demonstrate the capability of the method to reproduce the charge density response in a gold/electrolyte capacitor under an applied voltage, predicting the system polarization with a greater accuracy than state-of-the-art classical atomic-charge models.