Multi-fidelity Machine Learning Interatomic Potentials for Charged Point Defects

TL;DR

This work finds that the current generation of foundation MLIPs do not describe the defect physics of the semiconductor Sb2Se3, and introduces global defect charge embeddings that distinguish the bonding characteristics of different charge states.

Abstract

Machine learning interatomic potentials (MLIPs) can now reproduce the energy, forces and stresses of bulk materials with high accuracy compared to first-principles calculations. The description of imperfections, where coordination environments and electron counts deviate from those found in pristine reference structures, remains a challenge. We find that the current generation of foundation MLIPs do not describe the defect physics of the semiconductor Sb2Se3. We introduce global defect charge embeddings that distinguish the bonding characteristics of different charge states. We further employ a multi-fidelity approach that combines low-cost (semi-local exchange-correlation functional) reference data with high-quality (non-local hybrid functional) energies and forces that describe well the subtleties of the defect energy landscape. The resulting defect-capable force fields can find stable structural configurations and predict charge-transition levels in quantitative agreement with direct quantum mechanical calculations, at a fraction of the computational cost.

Figures (4)

• Figure 1: Failure of foundation machine learning interatomic potentials (MLIPs) to capture defect structures. (a) Root mean square deviation (RMSD) of MLIP-predicted ground-state structures relative to density functional theory (DFT) calculations using the PBE functional for $V_{\text{Sb}}$ in Sb2Se3 across five charge states. For each charge state, data points are slightly offset along the horizontal axis for clarity. The green shaded region (RMSD $\leq$ 0.1 Å) indicates successful structural identification. (b, c) Comparison of defect potential energy surfaces (PESs) and structural predictions for (b) the neutral ($q=0$) and (c) fully ionized ($q=-3$) charge states of $V_{\text{Sb}}$. The PES is mapped as a function of the bond distortion percentage, with energies referenced to the minimum of each respective landscape. In these panels, data points for the foundation models and the DFT reference are colored according to the RMSD of the relaxed atomic positions relative to the true DFT ground-state, with circles indicating RMSD $\leq$ 0.1 Å and crosses denoting RMSD $>0.1$ Å. Bottom insets compare the local atomic environment of the DFT global minimum with representative MLIP-predicted minima.
• Figure 2: Schematic diagram for the integration of global charge embeddings for point defects in machine learning interatomic potentials (MACE batatia2022mace architecture). The total charge $q_\textrm{tot}$ is added to each atomic species embedding during feature initialization. This charge conditioning propagates through the interaction layers, where node features $h_i^{(t)}$ are iteratively updated via a learned interaction function $f_\theta$ that aggregates messages from edge embeddings $\boldsymbol{e}_{ij}$ and neighboring features $h_j^{(t)}$. The interaction energy $E_\textrm{inter}$ is computed by summing the readout outputs $g_\theta^{(t)}(h_i^{(t)})$ over all atoms $i$ and message-passing iterations $t$, while a geometry-independent energy term $E_\textrm{emb}$ is extracted from the initial charge-enriched embeddings. The total energy $E_\textrm{tot}$ is defined as the sum of the atomic reference energy $E_0$, the interaction energy $E_\textrm{inter}$ and the embedding energy $E_\textrm{emb}$, with $E_0 = \sum_i E_{\textrm{ref}}(Z_i)$ denoting the sum of atomic reference energies.
• Figure 3: (a) Principal component analysis (PCA) visualization of the atomic descriptor space for $V_{\text{Se}}$ in Sb2Se3 across five charge states without (left) and with (right) global charge embeddings. The latent space is constructed using both training and test configurations. Percentages in parentheses indicate the explained variance for each component. (b) Parity plots of total energies and atomic forces predicted by the charge-embedded MACE model compared with HSE06 DFT on the test dataset. Root mean square errors (RMSEs) are shown as averages across five charge states. (c) Comparison between the charge-embedded MACE model and HSE06 DFT for ground-state defect geometries (top) and thermodynamic transition levels (bottom). For each charge state, the global minimum was identified by relaxing a set of bond-distorted structures. Key bond lengths are labeled in Å. Thermodynamic transition levels obtained from HSE06 DFT are shown as orange dashed lines, while MLIP predictions are shown as black solid lines.
• Figure 4: Schematic diagram of structure searching for neutral $V_\textrm{Se}$ using (a) a standard workflow with ShakeNBreakmosquera2022shakenbreak and (b) a multi-fidelity (MF) strategy with a MLIP. The green curves correspond to high-fidelity (HF) PESs calculated using HSE06/DFT with converged k-point sampling. The red star and grey circle denote the true global minimum and a meta-stable minimum, respectively. (a) The black curve represents the coarse PES sampling using HSE06 with $\Gamma$-point sampling, and the grey dashed arrow indicates the HF relaxation starting from the coarse sampling minimum. (b) The blue curve represents the low-fidelity PES obtained from PBE with converged k-point sampling. Blue crosses mark HF single-point calculations performed on a subset of the PBE-relaxed structures. Orange vertical arrows illustrate the $\Delta$-learning corrections learnt by the MF model.