A Fast, Accurate, and Reactive Equivariant Foundation Potential

TL;DR

QET addresses the electrostatics bottleneck in machine-learning interatomic potentials by combining a charge-aware, equivariant architecture with an analytically solvable charge-equilibration scheme, enabling linear-time simulations in large systems. It matches state-of-the-art foundation potentials on near-equilibrium benchmarks while delivering qualitatively different, more accurate predictions in systems with significant charge transfer, such as ionic liquids and battery interfaces. The authors train on MatQ, a large charge-informed dataset spanning 86 elements, and demonstrate reactive, voltage-aware simulations at scale, e.g., at Li/Li$_6$PS$_5$Cl interfaces, after targeted fine-tuning. This work paves the way for broadly applicable, physically grounded, scalable FPs with transformative potential for energy storage, catalysis, and beyond.

Abstract

Electrostatics govern charge transfer and reactivity in materials. Yet, most foundation potentials (FPs) either do not explicitly model such interactions or pay a prohibitive scaling penalty to do so. Here, we introduce charge-equilibrated TensorNet (QET), an equivariant, charge-aware architecture that attains linear scaling with system size via an analytically solvable charge-equilibration scheme. We demonstrate that a trained QET FP matches state-of-the-art FPs on standard materials property benchmarks but delivers qualitatively different predictions in systems dominated by charge transfer. The QET FP reproduces the correct structure and density of the NaCl-CaCl2 ionic liquid, which charge-agnostic FPs miss. We further show that a fine-tuned QET captures reactive processes at the Li/Li6PS5Cl solid-electrolyte interface and supports simulations under applied electrochemical potentials. These results remove a fundamental constraint in the atomistic simulation of accurate electrostatics at scale and establish a general, data-driven framework for charge-aware FPs with transformative applications in energy storage, catalysis, and beyond.

Figures (6)

• Figure 1: QET architecture. QET takes the atomic number $Z_i$ and atomic positions $R_i$ as inputs to an embedding block, which generates a set of rank-2 tensors representing atomic features. These features are subsequently refined through a series of interaction blocks to capture the latent representation of atomic environments. In this work, the cutoff used to define bonds between atoms was set at 5.0 . The number of interaction blocks and the hidden channel for the embedding, interaction and readout blocks were set to 3 and 64. The graph-convoluted atomic features $h_i$ and total charge $Q_{\mathrm{tot}}$ are passed to the LQeq block to compute atomic charges. The LQeq block employs a two-step process to compute atomic charges. First, atomic features are fed into two distinct MLPs to predict environment-dependent electronegativities and hardnesses. To avoid undefined solutions in Eqn. \ref{['eq:qeq_solution']}, the softplus activation is used to ensure that the predicted hardness values are positive. These quantities are then used to calculate globally distributed charges, constrained by the total charge, using an analytical charge equilibration scheme. The charges are then used to calculate the Coulomb potential $V_{i}$ acting on the central atom arising from neighboring atoms. Finally, the atomic features, charges, and Coulomb potential are concatenated and fed into a gated multi-layer perceptron (MLP) to predict atomic energies $E_i = \phi(h_i\oplus q_{i}\oplus V_{i})$, which are in turn summed to obtain the total energy.
• Figure 2: Relaxed geometry of Ag trimer. Structures of Ag$_3^{+}$ and Ag$_3^{-}$ optimized using (left) TensorNet and (right) QET. The numbers near each structure indicate the root mean squared structural deviation with respect to the DFT-relaxed structures in units of $10^{-3}$. The atoms in the QET-relaxed structures are colored based on the QET-predicted partial charges. The structures and charges were visualized using Ovito.stukowski2009visualization
• Figure 3: Charge transfer in an Au dimer on the MgO(001) surface.a The DFT-optimized geometry of the Au dimer on the undoped surface and the Al-doped surface. b Relative (left) energies and (right) forces acting on the Au dimer along the direction perpendicular to the surface for the undoped and Al-doped systems. Predicted energies are referenced to the minimum DFT energy for each case. The Au–O bond length corresponds to the distance between the Au atom nearest to the surface and its neighboring oxygen atom.
• Figure 4: Simulated structure of NaCl-CaCl2 ionic liquid.a, Calculated structure factor and b, averaged densities of NaCl-CaCl2 obtained from 100 ps NPT MD simulations at 1200 K using the QET-MatQ, TensorNet-MatQ and GRACE-2L-OMat24 FPs. The experimental density was obtained from Ref.janz1988thermodynamicjanz1979physical
• Figure 5: Reactive simulations of the Li/Li6PS5Cl interface.a, Snapshots of the solid electrolyte interphase at t = 1.1 ns from NVT MD simulations performed using fine-tuned QET and TensorNet potentials. b, Radial distribution function, calculated from the last 1 ns of the trajectory. c, Potential energy and interphase thickness of the Li/Li6PSCl5 interphase obtained from the last 1 ns under applied potentials of $+4$ V and $-4$ V. d, Comparison of the charge distribution on Li atoms at $t = 1.1$ ns for applied potentials of $+4$ V and $-4$ V. All visualizations were performed using Ovito. The heatmap colors indicate the partial charges predicted by QET.