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

TL;DR

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.

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.

Figures (19)

• Figure 1: Overview of the MACE-POLAR-1 architecture and benchmarked applications. (A) Model architecture. Atomic positions and species are passed to a MACE model, which predicts local node features, a local energy contribution, and an initial set of spin-charge multipoles. The local features richly encode semi-local geometry and chemistry. Then, the spin-charge multipoles are iteratively refined through a long-range operation. First, a physically inspired global convolution maps the spin-charge multipoles into atom-centred electrostatic features $v_{i,nlm}$. Then, a local operation followed by a global normalisation predicts a new set of spin-charge multipoles. The process is iterated twice, before the final set of multipoles is used to compute a Coulomb energy and an additional learned non-local energy contribution. (B) Construction of long-range electrostatic features. Information is propagated between distant atoms by constructing a smooth charge density $\rho(\mathbf{r})$ from the spin-charge multipoles and convolving with the Coulomb kernel to give an electric potential $v(\mathbf{r})$. Then, one can project the potential onto atom-centred functions to give equivariant electrostatic features. (C) Physical extrapolation capabilities: charge localisation when fragmenting a cluster, response of the model charge density to an electric field, and correct prediction of the oxidation state of transition metal ions in water. (D) Application domains benchmarked: protein-ligand binding, molecular crystals, transition-metal redox potentials, and supramolecular complexes.
• Figure 2: Thermochemistry and reaction barrier benchmarks on GSCDB138 subsets. Bar heights show the weighted total mean absolute deviation (WTMAD-2) in kcal/mol for each model, where lower values indicate better accuracy. WTMAD-2 rescales errors by the characteristic energy scale of each subset to enable fair comparison across datasets of different magnitudes (definition in SI \ref{['sec:wtmad2']}). For these summary bars, extreme outliers are filtered by excluding points with $|\Delta E|>100$ kcal/mol (details in SI \ref{['sec:exclusions']}). (a) Thermochemistry subsets grouped by property class: ionisation potentials, electron affinities, proton affinities, and bond dissociation energies. (b) Reaction-barrier subsets: barrier heights, proton-transfer reactions, and general reaction energies. Models compared: $\omega$B97M-V (reference hybrid DFT), g-xTB (semi-empirical), UMA-S-1P1 /UMA-M-1P1 , MACE-OMOL , ORBMOL (local MLIPs), and the electrostatic MACE-POLAR-1-M /MACE-POLAR-1-L .
• Figure 3: Comprehensive evaluation of non-covalent interaction accuracy. (a) Bar heights show mean absolute errors in kcal/mol for small-molecule non-covalent interaction datasets with CCSD(T)/CBS references: S22 and S66 (hydrogen bonding and dispersion), XB20 (halogen bonding), X40 (mixed interactions), WATER27 (water clusters), HB49 (diverse hydrogen bonds), NC11 (charge-transfer complexes), and O24x4 (potential energy curves). (b) Mean absolute errors for protein-ligand fragment benchmarks: QUID (quantum-chemistry dimers from pocket-ligand motifs) and PLF547 (protein-ligand fragments with MP2-F12 + DLPNO-CCSD(T) references). (c) Mean absolute errors on the IHB100x10 ionic hydrogen bond dataset from NCI Atlas, where electrostatic polarisation is critical. (d) Potential energy curves for gas-phase alkali halide dissociation (LiCl, NaCl, KBr), plotting energy versus interatomic distance to test long-range $1/r$ Coulombic behaviour. (e) Mean absolute errors for PLA15 complete protein-ligand active sites (259--584 atoms). (f) Mean absolute errors for S30L supramolecular host-guest complexes (up to 200 atoms, charge states $-1$ to $+4$). (g) Mean absolute errors for X23-DMC molecular crystal lattice energies with diffusion Monte Carlo references. In all bar charts, lower values indicate better accuracy.
• Figure 4: Absolute lattice energy errors for CPOSS209 molecular crystals. Bar heights show mean absolute errors in kcal/mol for predicted lattice formation energies, grouped by molecular family. The dataset comprises 209 experimental and predicted polymorphs from 20 small drug molecules. Reference calculations are performed at the $\omega$B97M-D3(BJ) level with 1-body CCSD(T) corrections. Lower values indicate better accuracy.
• Figure 5: Accuracy on transition metal complexes and molecular conformers. Bar heights show mean absolute errors in kcal/mol for each model; lower values indicate better accuracy. (a) Transition metal datasets on logarithmic scale due to large error ranges: CUAGAU83 (coinage metal Cu, Ag, Au complexes), DAPD (palladium diatomics), MOBH28 (organometallic barrier heights), and TMD10 (transition metal diatomics). (b) Transition metal datasets on linear scale: 3dTMV (vertical ionisation energies, ph-AFQMC references), MME52 (metalloenzyme models, DLPNO-CCSD(T) references), ROST61 (open-shell reactions), MOR13 (closed-shell reactions), and TMB11 (barrier heights). (c) Conformational energy benchmarks: 37CONF8 (small organics), ACONFL (n-alkane conformers), DipConfS (amino acids and dipeptides), Maltose222 (carbohydrates), MPCONF196 (medicinal fragments), OpenFF-Tors (torsional profiles), and UPU46 (RNA backbone fragments). All reference values are CCSD(T) or equivalent. The GSCDB138 transition metal sets use updated references with spin-contaminated structures removed.