Importance of Electronic Entropy for Machine Learning Interatomic Potentials

TL;DR

This paper highlights the importance of electronic entropy in machine learning interatomic potentials, demonstrating that embedding charge-state information improves modeling of mixed-valence materials like FePO4.

Contribution

The authors introduce a charge-state embedding approach into MLIPs, enabling accurate modeling of charge ordering and thermodynamic stability in mixed-valence systems.

Findings

Conventional MLIPs fail to reproduce correct charge ordering in FePO4.

Embedding charge-state information improves MLIP accuracy in structural optimization.

The approach enhances MLIP predictions aligning with density functional theory results.

Abstract

Machine learning interatomic potentials (MLIPs) enable large-scale atomistic simulations but remain challenged in describing mixed-valence materials where charge ordering strongly influences thermodynamic stability. Here we investigate the role of electronic entropy in MLIP structural optimization of the battery cathode material \ce{NaFePO4}. We show that conventional MLIPs fail to reproduce the correct stability of intermediate \ce{Na} concentrations because structural optimization leads to incorrect \ce{Fe^{2+}}/\ce{Fe^{3+}} charge assignments, resulting in erroneous energy ordering and convex-hull predictions. Analysis of magnetic moments during structural optimization reveals that MLIPs are unable to capture electronic entropy associated with charge ordering. To address this limitation, we introduce an approach that embeds charge-state information directly into the MLIP representation by distinguishing between \ce{Fe^{2+}} and \ce{Fe^{3+}} environments during training. Retraining CHGNet, cPaiNN, and MACE with this representation enables accurate structural optimization, correct identification of charge ordering, and improved agreement with density functional theory convex hulls. Our results demonstrate that incorporating electronic entropy into MLIP representations is essential for modeling charge-disordered materials and provide a practical framework for extending MLIP simulations to mixed-valence transition-metal systems.