Pushing charge equilibration-based machine learning potentials to their limits

Aug 5, 2026

Machine learning interatomic potentials aim to match first-principles accuracy while scaling to large atomistic systems by learning energy contributions from local environments. Yet locality assumptions miss long-range electrostatics and non-local charge-transfer effects, which become critical in polar interfaces and ionic interactions. This work analyzes limits of charge-equilibration-based ML, using Kernel Charge Equilibration with local short-ranged potentials, across systems with different total charge states and static electric fields, revealing spurious charge transfer and overpolarization and motivating new methodology.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages9

Reading Time23 min

AccessFree to download

Introduction

Local MLIP limitations for long-range electrostatics

Charge equilibration-based approaches (QEq/kQEq)

Scope and Findings

Benchmarking across charge states and electric fields

Observed pathologies and implications

npj | computational materials Article Published in partnership with the Shanghai Institute of Ceramics of the Chinese Academy of Sciences [https://doi.org/10.1038/s41524-025-01791-3](https://doi.org/10.1038/s41524-025-01791-3) Pushing charge equilibration-based machine learning potentials to their limits Check for updates passing longer distances, alleviating some of the constraints imposed by the locality However, message passing is not effective for describing - based 19 range (DPLR) models cant work on developing MLIPs capable of capturing the | Martin Vondrák1,2, Karsten Reuter2 & Johannes T. Margraf1,2 | | | --- | --- | | Machine learning (ML) has demonstrated its potential in atomistic simulations to bridge the gap between accurate ﬁrst-principles methods and computationally efﬁcient empirical potentials. This is achieved by learning mappings between a system’s structure and its physical properties. State-ofthe-art models for potential energy surfaces typically represent chemical structures through (semi-) local atomic environments. However, this approach neglects long-range interactions (most notably electrostatics) and non-local phenomena such as charge transfer, leading to signiﬁcant errors in the description of molecules or materials in polar anisotropic environments. To address these challenges, ML frameworks that predict self-consistent charge distributionsin atomistic systems using the Charge Equilibration (QEq)method are currently popular. In this approach, atomic charges are derived from an electrostatic energy expression that incorporates environment-dependent atomic electronegativities. Herein, we explore the limits of this concept at the example of the previously reported Kernel Charge Equilibration (kQEq) approach, combined with local short-ranged potentials. To this end we consider prototypical systems with varying total charge states and applied electric ﬁelds. We ﬁnd that charge equilibration-based models perform well in most situations. However, we also ﬁnd that some pathologies of conventional QEq carry over to the ML variants in the form of spurious charge transfer and overpolarization in the presence of static electric ﬁelds. This indicates a need for new methodological developments. | | | One of the most signiﬁcant advances in molecular and materials simulation over the past decade has been the introduction of atomistic machine learning interatomic potentials (MLIPs)1–4. These methods can approach the accuracy of ab initio techniques while scaling to systems containing hundreds of thousands of atoms, opening the door to discoveries previously thought impossible5–7. This breakthrough relies generally on the assumption that the total energy of a system can be decomposed into atomic contributions. These contributions are modeled as a function of each atom’s local chemical environment within a deﬁned cutoff radius, using ML techniques such as Neural Networks (NN)8,9 or Gaussian Process Regression (GPR)10, 11.
However, due to their inherent locality approximation, these models are fundamentally limited by their inability to account for long-range interactions and non-local effects such as charge transfer. This is often unproblematic since long-range effects are effectively screened in isotropic condensed phase systems. It can become signiﬁcant in systems involving polar interfaces or complex ionic interactions, however12. In such cases, local models reach the boundaries of their applicability. | To address these limitations, considerable effort is being devoted to developing methods that incorporate interactions beyond the cutoff oflocal descriptors. One promising approach involves the use of messageneural networks (MPNNs), which extend the effective receptive ﬁeld of the models by propagating information through a graph representation of the
atomistic structure. This enables such models to capture interactions over assumption9, 13–16.
truly long-range interactions

FAQs

Why are locality-based machine learning potentials limited?

They rely on local atomic environments within a cutoff, so they cannot properly capture long-range interactions and non-local phenomena like charge transfer, which can cause large errors in polar or ionic settings.

What approach does the document evaluate to include electrostatics?

It focuses on charge equilibration-based models, specifically Kernel Charge Equilibration (kQEq) combined with local short-ranged potentials, and analyzes how well they handle self-consistent charge distributions.

What problems are found when electric fields are applied?

Some conventional charge equilibration pathologies persist in the ML variants, showing spurious charge transfer and overpolarization under static electric fields, indicating the need for new methodological developments.

Aug 5, 2026

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