Simultaneous learning of static and dynamic charges

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Phys. Chem. Chem. Phys., 2026, Advance ArticleDOI: 10.1039/D6CP00911E, Paper Open Access &nbsp This article is licensed under a Creative Commons Attribution 3.0 Unported Licence.Philipp Stärk, Henrik Stooß, Marcel F. Langer, Egor Rumiantsev, Alexander Schlaic…

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Simultaneous learning of static and dynamic charges

a Stuttgart Center for Simulation Science (SC SimTech), University of Stuttgart, 70569 Stuttgart, Germany

b Institute for Computational Physics, University of Stuttgart, 70569 Stuttgart, Germany

c Institute for Physics of Functional Materials, Hamburg University of Technology, 21073 Hamburg, Germany
E-mail: [email protected]

d Laboratory of Computational Science and Modeling, IMX, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
E-mail: [email protected]

e Department of Physics, Technical University of Munich, Garching, Germany
E-mail: [email protected]

f Atomistic Modelling Center, Munich Data Science Institute, Technical University of Munich, Germany

g Munich Center for Machine Learning (MCML), Munich, Germany

Abstract

Long-range interactions and electric response are essential for accurate modeling of condensed-phase systems, but capturing them efficiently remains a challenge for atomistic machine learning. Traditionally, these two phenomena can be represented by static charges that underlie Coulomb interactions between atoms, and dynamic charges such as atomic polar tensors—aka Born effective charges—describing the response to an external electric field. We critically compare different approaches to learn both types of charges within a single model architecture, taking bulk water and water clusters as paradigmatic examples: (1) learning them independently; (2) coupling static and dynamic charges based on their physical relationship with a single global coupling constant to account for dielectric screening; (3) coupled learning with a local, environment-dependent screening factor. In the coupled case, correcting for dielectric screening is essential, yet the common assumption of homogeneous, isotropic screening breaks down in heterogeneous systems such as water clusters. A learned, environment-dependent screening restores high accuracy for the dynamic charges. However, the accuracy gain over independent dynamic predictions is negligible, while the computational cost increases compared to using separate models for static and dynamic charges. This suggests that, despite the formal connection between the two charge types, modeling them independently is the more practical choice for both condensed-phase and isolated cluster systems.