Better without U: Impact of Selective Hubbard U Correction on Foundational MLIPs

TL;DR

This work reveals that common MLIP datasets built on Materials Project PBE+$U$ schemes induce systematic energy misrepresentations when O or F encounters $U$-corrected metals, due to two incompatible PES surfaces. By diagnosing via adsorption and adhesion tests, the authors show severe pathologies that scale with dataset composition, particularly oxygen density. They propose a simple per-atom energy shift to align $PBE$ and $PBE$+$U$ energies, demonstrating substantial reductions in adsorption energy errors and smoother PES while noting that excluding $+U$ entirely (as in MatPES) is the most robust solution. The proposed post-hoc shift offers a low-cost remedy for existing datasets, guiding future fMLIP development toward datasets without selective Hubbard $U$ corrections or, at minimum, PES-consistent corrections; this advances reliable MD simulations across metals, oxides, and interfaces.

Abstract

The training of foundational machine learning interatomic potentials (fMLIPs) relies on diverse databases with energies and forces calculated using ab initio methods. We show that fMLIPs trained on large datasets such as MPtrj, Alexandria, and OMat24 encode inconsistencies from the Materials Project's selective use of the Hubbard U correction, which is applied to certain transition metals only if O or F atoms are present in the simulation cell. This inconsistent use of +U creates two incompatible potential-energy surfaces (PES): a lower-energy GGA surface and a higher-energy GGA+U one. When trained on both, MLIPs interpolate between them, leading to systematic underbinding, or even spurious repulsion, between U-corrected metals and oxygen- or fluorine-containing species. Models such as MACE-OMAT and -MPA exhibit repulsion between U-corrected metals and their oxides, limiting their value for studying catalysis and oxidation. We link the severity of this pathology to the oxygen number density in U-corrected training configurations. This explains why OMAT-trained models are most affected and suggests the issue might worsen as expanding future datasets increasingly include configurations with low oxygen content, such as those generated through combinatorial exploration of multi-element or defect-containing systems. Our simple per-U-corrected-atom shift aligns PBE+U and PBE energies for identical structures, yielding a smoother PES compared to existing correction schemes, which target phase diagram accuracy. As a result, models trained on datasets with our shift applied exhibit smaller mean absolute errors for the adsorption energies of oxygen on U-corrected elemental slabs. Since datasets omitting +U entirely (e.g. MatPES, MP-ALOE) avoid these pathologies, we recommend excluding +U in future fMLIP datasets. For existing datasets, our post-hoc correction provides a low-cost improvement.

Figures (7)

• Figure 1: The high energy of a Materials Project (MPRelaxSet) DFT calculation for a chromium surface with a distant O$_2$ molecule arises because the +$U$ correction is applied only in this combined system, not in the separate surface or O$_2$ calculations. The PBE energy for the combined system is -683 eV.
• Figure 2: Comparison of oxygen binding energies across fMLIPs. These heatmaps show the difference between the adsorption energy predictions of various MACE models and PBE for oxygen adsorbed on top of elemental slabs. The oxygen resides on top of the site furthest along the surface's normal direction at a distance which minimizes the energy according to MACE-MATPES-r2SCAN-0, as depicted in c). a) and b) show models with and without severe systematic underbinding on $U$-corrected metals respectively. MACE-OMAT-0 consistently predicts a total lack of binding whilst MACE-MPA-0 and -MP-0b3 predict barriers and significant underbinding. Energy differences are mapped to colours via the inverse hyperbolic sine function. Heatmaps generated with pymatviz riebesell_pymatviz_2022.
• Figure 3: Metal-oxide adhesion energies according to different models and DFT. (Left) Comparison of adhesion energies for different metal-oxide interfaces. (Right) Schematic explanation of adhesion energy $W_{adh}$. Negative adhesion energies indicate unstable interfaces. Interfaces were constructed using the (100) facets of the experimentally observed face-centered cubic (FCC) metal and rocksalt oxide polymorphs.
• Figure 4: Adsorption energies of fluorine on the Fe side of an Fe-FeO interface. Although the number of (100) layers is constant, the underbinding of $U$-afflicted models is clearly worst for the all-iron slab. This occurs because iron sites with nearby oxygen atoms already produce higher-energy predictions consistent with the +$U$ regime.
• Figure 5: Oxygen underbinding worsens with lower oxygen density in +$U$ training data. The Y axis shows the model’s degree of oxygen underbinding relative to PBE on an elemental slab, with values identical to those in Figure \ref{['fig:heatmaps']}a. Each X value corresponds to the mean oxygen number density ($N_\text{O}/V_\text{cell}$) across all configurations in the training dataset that contain both oxygen and the respective element.