Kernel charge equilibration: efficient and accurate prediction of molecular dipole moments with a machine-learning enhanced electron density model

State-of-the-art machine learning (ML) interatomic potentials use local representations of atomic environments to ensure linear scaling and size-extensivity. This implies a neglect of long-range interactions, most prominently related to electrostatics. To overcome this limitation, we herein present a ML framework for predicting charge distributions and their interactions termed kernel charge equilibration (kQEq). This model is based on classical charge equilibration (QEq) models expanded with an environment-dependent electronegativity. In contrast to previously reported neural network models with a similar concept, kQEq takes advantage of the linearity of both QEq and Kernel Ridge Regression to obtain a closed-form linear algebra expression for training the models. Furthermore, we avoid the ambiguity of charge partitioning schemes by using dipole moments as reference data. As a first application, we show that kQEq can be used to generate accurate and highly data-efficient models for molecular dipole moments.