Simultaneous Learning of Static and Dynamic Charges

TL;DR

This paper compares methods for learning static and dynamic charges in condensed systems, finding that independent modeling is often more practical despite their physical connection.

Contribution

It introduces and evaluates coupled learning approaches for static and dynamic charges, highlighting the importance of environment-dependent screening.

Findings

Environment-dependent screening improves dynamic charge accuracy.

Coupled learning offers minimal accuracy gains over independent models.

Independent modeling is more practical due to lower computational cost.

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 participate in 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, 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 dynamical charges. However, the accuracy gain over independent dynamic predictions is negligible, while the computational cost increases compared to using separate models for static and dynamical 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.