Learning charges and long-range interactions from energies and forces

TL;DR

The paper tackles the challenge of accurately modeling long-range electrostatics in MLIPs by extending Latent Ewald Summation (LES) to learn latent charges from energies and forces. LES decomposes energy into short-range and long-range parts, predicting latent charges $q_i$ from local descriptors and computing long-range contributions via Ewald summation, with optional charge-state encoding and neutrality considerations. Across diverse systems—random charges, electrolytes, charged dimers, polar dipeptides, and interfacial/solid-solid interfaces—LES demonstrates the ability to infer physically meaningful charges and predict dipole and quadrupole moments with high accuracy, often outperforming explicit-charge MLIPs. The work highlights LES as a flexible, interpretable, and scalable framework for capturing long-range interactions in complex materials, while also noting limitations in edge cases involving long-range charge transfer and the potential for improved uncertainty quantification.

Abstract

Accurate modeling of long-range forces is critical in atomistic simulations, as they play a central role in determining the properties of materials and chemical systems. However, standard machine learning interatomic potentials (MLIPs) often rely on short-range approximations, limiting their applicability to systems with significant electrostatics and dispersion forces. We recently introduced the Latent Ewald Summation (LES) method, which captures long-range electrostatics without explicitly learning atomic charges or charge equilibration. Extending LES, we incorporate the ability to learn physical partial charges, encode charge states, and the option to impose charge neutrality constraints. We benchmark LES on diverse and challenging systems, including charged molecules, ionic liquid, electrolyte solution, polar dipeptides, surface adsorption, electrolyte/solid interfaces, and solid-solid interfaces. Our results show that LES can effectively infer physical partial charges, dipole and quadrupole moments, as well as achieve better accuracy compared to methods that explicitly learn charges. LES thus provides an efficient, interpretable, and generalizable MLIP framework for simulating complex systems with intricate charge transfer and long-range

Figures (10)

• Figure 1: a A configuration of gas made of point charges. b Comparison of the true and the predicted charges for the CACE-LR models with a cutoff radius of $4$ Å and trained on $N$ configurations. c The mean absolute errors (MAEs) on energy, forces, and charges for short-range (SR) and long-range (LR) models trained using different $N$ numbers of samples.
• Figure 2: a A bulk electrolyte configuration (upper panel) and an electrolyte-vapor configuration (lower panel). b Comparison of the true and the predicted charges for the CACE-LR models with a cutoff radius of $4.5$ Å and trained on $N$ configurations. c The mean absolute errors (MAEs) on forces, and charges for short-range (SR) and long-range (LR) models trained using different $N$ numbers of samples. The MP1 indicates models using one message-passing layer.
• Figure 3: a A snapshot of the molecular dimer configuration of C$_3$N$_3$H$_{10}^+$/C$_2$O$_2$H$_3^-$. b The comparison between the true and predicted force components (left panel), and the binding energy curves (the energy difference between the dimer and two isolated monomers) from SR and LR models. c The predicted charge distribution from the CACE-LR model.
• Figure 4: a Top: A snapshot of a dipeptide conformer composed of arginine and aspartic acid from the SPICE dataset eastman2023spice. Bottom: The predicted LES charge distribution. b The predicted charges from LES compared to minimal basis iterative stockholder (MBI) charges in SPICE. c The predicted dipole components computed from the LES charges ($\mathbf{\mu} = \sum_{i=1}^N q_i \mathbf{r}_i$) compared to the DFT dipole components in SPICE. d The predicted traceless quadrupole components computed from the LES charges ($Q = \sum_{i=1}^N q_i \mathbf{r}_i \otimes \mathbf{r}_i)$) compared to the DFT quadrupole components in SPICE.
• Figure 5: Illustrations of the four systems with different charge states and charge transfer, taken from Ref. ko2021fourth. a The C$_{10}$H$_{2}$/C$_{10}$H$_{3}^{+}$ set. b The Ag$^{+/-}_{3}$ set has Ag trimers in positive or negative charge states. c The Na$_{8/9}$Cl$_{8}^{+}$ set. d The Au$_{2}$-MgO(001) set has a wetting (left) or unwetting (right) Au$_{2}$ on the doped (left) or undoped (right) MgO(001) surface.