Atomistic Simulations of Oxide-Water Interfaces using Machine Learning Potentials

TL;DR

This work surveys how machine learning potentials (MLPs) enable ab initio–level atomistic simulations of oxide–water interfaces at scales inaccessible to traditional density functional theory. By decomposing energies into atomic contributions and leveraging descriptors that enforce invariances, MLPs achieve high accuracy with orders-of-magnitude faster evaluation, facilitating studies of water dissociation, proton transfer, defects, and dynamic surface processes across ZnO, TiO$_2$, and CeO$_2$ systems. The review highlights methods to recover electronic-structure information (oxidation states, vibrational spectra, electrostatic potentials) from ML models, enabling insights into spectroscopy and the electrical double layer at electrified interfaces. It also discusses open challenges—functional choice, nuclear quantum effects, long-range and nonlocal interactions, and transferability—while pointing to pre-trained models and future directions that will broaden applicability to complex, real-world interfacial environments.

Abstract

Oxide-water interfaces govern a wide range of physical and chemical processes fundamental to many fields like catalysis, geochemistry, corrosion, electrochemistry, and sensor technology. Near solid oxide surfaces, water behaves differently than in the bulk, exhibiting pronounced structuring and increased reactivity, typically requiring ab initio-level accuracy for reliable modeling. However, explicit ab initio calculations are often computationally prohibitive, especially if large system sizes and long simulation time scales are required. By learning the potential energy surface (PES) from data obtained from electronic structure calculations, machine learning potentials (MLPs) have emerged as transformative tools, enabling simulations with ab initio accuracy at dramatically reduced computational expense. Here, we provide an overview of recent progress in the application of MLPs to atomistic simulations of oxide-water interfaces. Specifically, we review insights that have been gained into the reactivity of interfacial systems involving the dissociation and recombination of water molecules, proton transfer processes between the solvent and the surface and the dynamic nature of aqueous oxide surfaces. Moreover, we discuss open challenges and future possible research directions in this rapidly evolving but challenging field.

Figures (9)

• Figure 1: Schematic illustration of the key principles underlying the construction and application of MLPs for water-oxide interfaces. (a) Quantum mechanical calculations (usually DFT) provide reference energies and forces for selected atomic configurations, which serve as training and testing data. (b) The local environment (i.e., atoms within a cutoff radius) of each atom $i$ is mapped to a descriptor $\mathbf{G}_i$ that encodes the required invariances of the potential energy, $E$, to translation, rotation, and permutation of chemically equivalent atoms. Such descriptors may be predefined (e.g., HDNNPs and GAP), or learned during training (e.g., DeePMD and MPNNs). In MPNNs, iterative message passing operations allow $\mathbf{G}_i$ to be influenced by atoms outside the cutoff radius. (c) The MLP is trained to reproduce the reference energies and forces using supervised learning. In most architectures, the potential energy is expressed as a sum over atomic contributions, Eq. \ref{['eq:e_decom']} (2G MLPs), though models may incorporate additional terms to capture long-range (3G MLPs) or nonlocal interactions (4G MLPs). (d) Once trained, MLPs enable MD simulations of systems much larger than those used for training, while retaining near-DFT accuracy.
• Figure 2: Side views of a polar Zn oxide slab structure (a) and (b) and the corresponding DFT Hirshfeld charge distributions (c) and (d) obtained using the PBEperdew_generalized_1996 functional. The [0001] surface of both slabs is Zn-terminated and the [$000\bar{1}$] surface is oxygen terminated. In (b) and (d), an additional hydrogen layer is attached to the [$000\bar{1}$] surface. The additional hydrogen layer alters the global charge redistribution, which leads to lower surface charges in (d) compared to (c) and thus in a reduced dipole moment of the slab. Reproduced with permission from Behler, Chem. Rev. 121, 16, 10037-10072 (2021). Copyright 2021 American Chemical Societybehler2021four.
• Figure 3: (a) Side views of atomistic models of the (a-i) ZnO($10\bar{1}0$)- and (a-ii) ZnO($11\bar{2}0$)-water interfaces. (b) Density profiles of oxygen species along the surface normal direction for the (b-i) ZnO($10\bar{1}0$)- and (b-ii) ZnO($11\bar{2}0$)-water interface models. (c) Top views of the long-range PT networks on the (c-i) ZnO($10\bar{1}0$) and (c-ii) ZnO($11\bar{2}0$) facets. Thicker lines represent PT reactions with higher rates, while color gradients from dark to light indicate larger barriers for the forward reaction. (a) and (b) Adapted with permission from Quaranta et al., J. Phys. Chem. C 123, 1293-1304 (2019). Copyright 2018 American Chemical Societyquaranta2018structure. (c) Adapted with permission from Hellström et al. Chem. Sci., 10, 1232-1243 (2019). Copyright 2019 Authors, licensed under a Creative Commons Attribution 3.0 Unported Licensehellstrom2019one.
• Figure 4: (a) Mechanistic pathways for water dissociation and PT at the anatase TiO$_2$(101)-water interface. (b) Interatomic distances used to define the collective variables $d_{ooo} = (d_1 + d_2) / 2$ and $(v_1 + v_2) / 2$ for PT reactions, where $v_i = b_i - h_i$. (c) FES for different pathways illustrated in panel (a) obtained from umbrella sampling simulations. Adapted with permission from Andrade et al., Chem. Sci., 11, 2335-2341 (2020). Copyright 2020 Authors, licensed under a Creative Commons Attribution-NonCommercial 3.0 Unported Licenseandrade2020free.
• Figure 5: Long-range PT networks at (a) the CeO$_2$(110)-water interface and (b) the CeO$_2$(111)-water interface. Different types of PT mechanisms are indicated with different colours; surface proton formation/recombination (SPF/R), adlayer PT (APT) -- where the types I and II indicate direct and solvent assisted mechanisms -- and adlayer hydroxide transfer (AHT). Adapted with permision from Kobayashi et al., Chem. Sci., 15, 6816-6832 (2024). Copyright 2024 Authors, licensed under a Creative Commons Attribution 3.0 Unported Licensekobayashi2024long.