[Paper Review] MACE-POLAR-1: A Polarisable Electrostatic Foundation Model for Molecular Chemistry

Ilyes Batatia, William J. Baldwin+11 more|arXiv (Cornell University)|Feb 23, 2026

Machine Learning in Materials Science0 citations

TL;DR

Introduces MACE-POLAR-1, a polarizable electrostatic foundation model that extends MACE with long-range induction and Fukui-function-based charge/spin equilibration to accurately model variable charge/spin states and non-local interactions.

ABSTRACT

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.

Motivation & Objective

• Develop a physics-informed foundation model that accurately captures long-range electrostatics and induction in molecular systems.
• Enable variable charge and spin states and response to external fields within a scalable MLIP framework.
• Maintain computational efficiency and training practicality while achieving high accuracy across diverse chemical domains.

Proposed method

• Extend the MACE architecture with a non-self-consistent field formalism for long-range induction.
• Introduce a learnable spin-charge density as a coarse-grained proxy for long-range interactions.
• Iteratively refine spin-charge multipoles via a global convolution and local updates, then equilibrate total charge and spin using learnable Fukui functions.
• Project the electrostatic potential from the spin-charge density onto atom-centered Gaussian bases to obtain non-local electrostatic features.
• Include a non-local energy term learned from local geometry and spin-charge/electrostatic features.
• Compute electrostatic energy from smeared multipoles using analytically tractable Gaussian basis transforms.

Experimental results

Research questions

• RQ1 How can long-range electrostatics and induction be incorporated into ML-based interatomic potentials while preserving efficiency?
• RQ2 Can a learnable, spin-resolved charge density and Fukui function-based equilibration provide accurate handling of variable charge and spin states?
• RQ3 What is the impact of explicit long-range electrostatics on challenging benchmarks like molecular crystals and protein–ligand interactions?
• RQ4 How does the model perform for charged species, transition metals, and redox chemistry in solution?

Key findings

• Explicit long-range electrostatics significantly improve descriptions of charged systems and non-covalent complexes.
• The model achieves state-of-the-art accuracy on challenging benchmarks such as molecular crystal lattice energies and protein–ligand binding.
• Inclusion of long-range interactions yields large improvements over non-electrostatic models for supramolecular complexes and protein–ligand interactions.
• The model can handle variable charge and spin states and respond to external fields with interpretable spin-resolved charge densities.
• Performance spans small molecules to protein–ligand complexes, enabling applications in drug discovery and bio-simulations.