Design Space of Self--Consistent Electrostatic Machine Learning Interatomic Potentials

Machine learning interatomic potentials (MLIPs) have become widely used tools in atomistic simulations. For much of the history of this field, the most commonly employed architectures were based on short-ranged atomic energy contributions, and the assumption of locality still persists in many modern foundation models. While this approach has enabled efficient and accurate modelling for many use cases, it poses intrinsic limitations for systems where long-range electrostatics, charge transfer, or induced polarization play a central role. A growing body of work has proposed extensions that incorporate electrostatic effects, ranging from locally predicted atomic charges to self-consistent models. While these models have demonstrated success for specific examples, their underlying assumptions, and fundamental limitations are not yet well understood. In this work, we present a framework for treating electrostatics in MLIPs by viewing existing models as coarse-grained approximations to density functional theory (DFT). This perspective makes explicit the approximations involved, clarifies the physical meaning of the learned quantities, and reveals connections and equivalences between several previously proposed models. Using this formalism, we identify key design choices that define a broader design space of self-consistent electrostatic MLIPs. We implement salient points in this space using the MACE architecture and a shared representation of the charge density, enabling controlled comparisons between different approaches. Finally, we evaluate these models on two instructive test cases: metal-water interfaces, which probe the contrasting electrostatic response of conducting and insulating systems, and charged vacancies in silicon dioxide. Our results highlight the limitations of existing approaches and demonstrate how more expressive self-consistent models are needed to resolve failures.

MACE-POLAR-1: A Polarisable Electrostatic Foundation Model for Molecular Chemistry

Accurate modelling of electrostatic interactions and charge transfer is fundamental to computational chemistry, yet most machine learning interatomic potentials (MLIPs) rely on local atomic descriptors that cannot capture long-range electrostatic effects. We present a new electrostatic foundation model for molecular chemistry that extends the MACE architecture with explicit treatment of long-range interactions and electrostatic induction. Our approach combines local many-body geometric features with a non-self-consistent field formalism that updates learnable charge and spin densities through polarisable iterations to model induction, followed by global charge equilibration via learnable Fukui functions to control total charge and total spin. This design enables an accurate and physical description of systems with varying charge and spin states while maintaining computational efficiency. Trained on the OMol25 dataset of 100 million hybrid DFT calculations, our models achieve chemical accuracy across diverse benchmarks, with accuracy competitive with hybrid DFT on thermochemistry, reaction barriers, conformational energies, and transition metal complexes. Notably, we demonstrate that the inclusion of long-range electrostatics leads to a large improvement in the description of non-covalent interactions and supramolecular complexes over non-electrostatic models, including sub-kcal/mol prediction of molecular crystal formation energy in the X23-DMC dataset and a fourfold improvement over short-ranged models on protein-ligand interactions. The model's ability to handle variable charge and spin states, respond to external fields, provide interpretable spin-resolved charge densities, and maintain accuracy from small molecules to protein-ligand complexes positions it as a versatile tool for computational molecular chemistry and drug discovery.

Accurate Crystal Structure Prediction of New 2D Hybrid Organic Inorganic Perovskites

Low dimensional hybrid organic-inorganic perovskites (HOIPs) represent a promising class of electronically active materials for both light absorption and emission. The design space of HOIPs is extremely large, since a diverse space of organic cations can be combined with different inorganic frameworks. This immense design space allows for tunable electronic and mechanical properties, but also necessitates the development of new tools for in silico high throughput analysis of candidate structures. In this work, we present an accurate, efficient, transferable and widely applicable machine learning interatomic potential (MLIP) for predicting the structure of new 2D HOIPs. Using the MACE architecture, an MLIP is trained on 86 diverse experimentally reported HOIP structures. The model is tested on 73 unseen perovskite compositions, and achieves chemical accuracy with respect to the reference electronic structure method. Our model is then combined with a simple random structure search algorithm to predict the structure of hypothetical HOIPs given only the proposed composition. Success is demonstrated by correctly and reliably recovering the crystal structure of a set of experimentally known 2D perovskites. Such a random structure search is impossible with ab initio methods due to the associated computational cost, but is relatively inexpensive with the MACE potential. Finally, the procedure is used to predict the structure formed by a new organic cation with no previously known corresponding perovskite. Laboratory synthesis of the new hybrid perovskite confirms the accuracy of our prediction. This capability, applied at scale, enables efficient screening of thousands of combinations of organic cations and inorganic layers.