Teaching oxidation states to neural networks

While the accurate description of redox reactions remains a challenge for first-principles calculations, it has been shown that extended Hubbard functionals (DFT+U+V) can provide a reliable approach, mitigating self-interaction errors, in materials with strongly localized d or f electrons. Here, we first show that DFT+U+V molecular dynamics is capable to follow the adiabatic evolution of oxidation states over time, using representative Li-ion cathode materials. In turn, this allows to develop redox-aware machine-learned potentials. We show that considering atoms with different oxidation states (as accurately predicted by DFT+U+V) as distinct species in the training leads to potentials that are able to identify the correct ground state and pattern of oxidation states for redox elements present. This can be achieved, e.g., through a systematic combinatorial search for the lowest energy configuration or with stochastic methods. This brings the advantages of machine-learned potentials to key technological applications (e.g., rechargeable batteries), which require an accurate description of the evolution of redox states.

💡 Research Summary

The paper demonstrates that extended Hubbard‑functional DFT+U+V, when combined with first‑principles molecular dynamics (FPMD), can faithfully track the adiabatic evolution of oxidation states (OS) in lithium‑ion cathode materials, using LiₓMnPO₄ as a prototypical system. Standard DFT suffers from self‑interaction errors, leading to a delocalized charge distribution and continuous, unphysical OS values (e.g., Mn²·⁵⁺). In contrast, DFT+U+V introduces on‑site U for Mn 3d orbitals and inter‑site V between Mn 3d and O 2p, which sharply localizes added electrons on individual Mn ions. This produces a “digital” change: each Li insertion reduces a specific Mn³⁺ to Mn²⁺, clearly visible in Löwdin occupations and reflected in accurate voltage predictions. The authors show that even when Hubbard parameters are fixed to their average values across compositions, the digital OS switching persists, greatly reducing the computational burden of recalculating U and V at every MD step.

Building on this reliable OS information, the authors develop an equivariant graph neural network (GNN) interatomic potential (e.g., NequIP/MACE) that treats atoms of the same element but different OS as distinct species. No auxiliary charge or spin networks are required. The trained potential reproduces DFT+U+V energies and forces while automatically assigning the correct OS pattern. Two strategies for finding the ground‑state OS configuration are explored: exhaustive combinatorial enumeration of all possible OS assignments, and stochastic optimization (Monte‑Carlo or genetic algorithms). Both recover the adiabatic OS rearrangements observed in the FPMD trajectories and yield voltage‑capacity curves in good agreement with experiment.

The work thus bridges the gap between accurate, but costly, first‑principles redox modeling and fast, scalable machine‑learned potentials. By embedding oxidation‑state awareness directly into the GNN architecture, the authors enable large‑scale, long‑time simulations of redox‑active materials, opening pathways for accelerated design of batteries, catalysts, and other transition‑metal‑based technologies where electron localization plays a pivotal role.