Accelerating and enhancing thermodynamic simulations of electrochemical interfaces

TL;DR

This work tackles the prediction of stable electrochemical surface structures by explicitly coupling surface reconstructions with bulk-electrolyte equilibria under varying $pH$ and $U_{SHE}$. It introduces three core innovations: adapting the Virtual Surface Site Relaxation-Monte Carlo method to aqueous electrochemical conditions, fine-tuning force fields (CHGNet/MACE) to reproduce DFT energetics at surfaces, and constructing equilibrium surface Pourbaix diagrams that include dissolved-ion concentrations, $c_{H_xAO_y^{z-}}$. Across Pt(111) and LaMnO3(001), the approach recovers known Pt phases and uncovers new LaMnO3 reconstructions, while revealing that electrolyte-bulk coupling can dramatically reshape surface stability domains. Together, the framework provides a scalable path to design electrochemical interfaces by mapping stable surfaces as functions of $pH$, $U_{SHE}$, and $c_{H_xAO_y^{z-}}$, with practical implications for catalysis and energy materials.

Abstract

Electrochemical interfaces are crucial in catalysis, energy storage, and corrosion, where their stability and reactivity depend on complex interactions between the electrode, adsorbates, and electrolyte. Predicting stable surface structures remains challenging, as traditional surface Pourbaix diagrams tend to either rely on expert knowledge or costly $\textit{ab initio}$ sampling, and neglect thermodynamic equilibration with the environment. Machine learning (ML) potentials can accelerate static modeling but often overlook dynamic surface transformations. Here, we extend the Virtual Surface Site Relaxation-Monte Carlo (VSSR-MC) method to autonomously sample surface reconstructions modeled under aqueous electrochemical conditions. Through fine-tuning foundational ML force fields, we accurately and efficiently predict surface energetics, recovering known Pt(111) phases and revealing new LaMnO$_\mathrm{3}$(001) surface reconstructions. By explicitly accounting for bulk-electrolyte equilibria, our framework enhances electrochemical stability predictions, offering a scalable approach to understanding and designing materials for electrochemical applications.

Figures (5)

• Figure 1: Thermodynamic analysis for electrochemical interfaces. (a) Two-step process for comparing surface Pourbaix grand potential differences ($\Delta \Omega_{\text{surf}}(U_{\text{SHE}}, \text{pH})$) between two slabs. The figure shows the case of a single-atom dissolution, but more complicated changes can be constructed as a sequence of dissolution/adsorption steps. (b-c) Two regimes for constructing surface Pourbaix diagrams. (b) Conventional surface Pourbaix diagram at fixed dissolved species concentrations. (c) Equilibrium surface Pourbaix diagram derived from bulk-electrolyte equilibrium conditions. (d) To construct the equilibrium surface Pourbaix diagram, the 3D species Pourbaix diagram is generated to define the equilibrium conditions for bulk stability in pH-$U_{\text{SHE}}$-$c_\mathrm{H_x A O_y^{z-}}$ space. Afterwards, a 3D surface Pourbaix diagram is constructed from the surface Pourbaix diagram in (b) and the equilibrium Pourbaix region traced out to produce the final equilibrium surface Pourbaix diagram.
• Figure 2: Pt(111) energy analysis and surface Pourbaix diagrams with various energy models. (a-c) $\Delta \Omega_{\text{surf}}(U_{\text{SHE}}, \text{pH})$ comparison of handpicked Pt(111) surfaces with respect to the pristine surface in eV/surface unit cell across $U_{\text{SHE}}$ at fixed pH = 0 with (a) DFT, (b) pre-trained NFF (CHGNet), and (c) fine-tuned NFF (MACE) energies. The bulk species domains are differentiated through the background color and labeled in gray. Dotted lines are a guide for the eye. (d-f) Pt(111) surface Pourbaix diagrams for (d) DFT, (e) pre-trained NFF, and (f) fine-tuned NFF.
• Figure 3: LaMnO3(001) surface Pourbaix diagrams and energy analysis with various energy models. (a-c) LaMnO3(001) surface Pourbaix diagrams from energies computed with (a) DFT, (b) pre-trained NFF, and (c) fine-tuned NFF. The LaMnO3 bulk stability regions at $10^{-6}$ M dissolved species concentrations are enclosed by the dashed lines. (d-e) $\Delta \Omega_{\text{surf}}(U_{\text{SHE}}, \text{pH})$ comparison of handpicked LaMnO3(001) surfaces with respect to the pristine surface in eV/surface unit cell across $U_{\text{SHE}}$ at fixed pH = 12 with (d) DFT, (e) pre-trained NFF, and (f) fine-tuned NFF energies. The color sequence approximately follows increasing oxidation level. The stable species domains are differentiated through the background color, with La+3 as the dominant La species and the dominant Mn species labeled in gray. Dotted lines are a guide for the eye.
• Figure 4: LaMnO3(001) energy analysis and surface Pourbaix diagrams. (a) $\Delta \Omega_{\text{surf}}(U_{\text{SHE}}, \text{pH})$ with respect to the pristine surface in eV/surface unit cell of handpicked and VSSR-MC sampled structures evaluated with fine-tuned CHGNet energies across $U_{\text{SHE}}$ at fixed pH = 12. Handpicked structures are labeled while sampled structures are grayed. (b) Revised LaMnO3(001) surface Pourbaix diagram at the DFT level with additional stable phases sampled using VSSR-MC. (c) Top-down view of stable sampled phases colored approximately in increasing oxidation level.
• Figure 5: LaMnO3 species and LaMnO3(001) surface Pourbaix diagrams at thermodynamic equilibrium in the pH-$U_{\text{SHE}}$-$\log_{10} c_\mathrm{H_x A O_y^{z-}}$ axes. Phases are colored approximately in increasing oxidation level from pale to dark. The black dashed contour lines correspond to different $c_\mathrm{H_x A O_y^{z-}}$. (a-b) Equilibrium species Pourbaix diagrams labeled by species domains adjacent to the bulk stability region. (a) 3D perspective. (b) 2D perspective in the pH-$U_{\text{SHE}}$ axes viewed from high $c_\mathrm{H_x A O_y^{z-}}$. (c-d) 2D perspectives of equilibrium surface Pourbaix diagrams with (c) only literature surfaces and (d) including additional sampled surfaces.