Deriving effective electrode-ion interactions from free-energy profiles at electrochemical interfaces

TL;DR

The paper tackles ion-specific adsorption at electrified metal–electrolyte interfaces by mapping free-energy profiles for Na+, Cl−, and F− at the Au(111)-water interface using enhanced-sampling MD with both classical force fields and UMA-S(OMat) MLIPs. It reveals that standard Lennard-Jones mixing rules can qualitatively alter adsorption behavior and demonstrates a systematic scheme to reparametrize cross-terms to align classical results with MLIP benchmarks. By embedding atomistic adsorption energetics into a one-dimensional continuum model of the electric double layer, the authors show that specific adsorption significantly reshapes interfacial ion populations, PZC, and differential capacitance, highlighting the importance of accurate interfacial potentials. The work provides a practical framework for bridging molecular insights with continuum electrochemical models and suggests that MLIPs can serve as transferable surrogates to guide force-field parameterization for interfacial phenomena. Overall, the study establishes a path toward more predictive, multiscale modeling of ion-specific effects at electrochemical interfaces.

Abstract

Understanding ion adsorption at electrified metal-electrolyte interfaces is essential for accurate modeling of electrochemical systems. Here, we systematically investigate the free energy profiles of Na$^+$, Cl$^-$, and F$^-$ ions at the Au(111)-water interface using enhanced sampling molecular dynamics with both classical force fields and machine-learned interatomic potentials (MLIPs). Our classical metadynamics results reveal a strong dependence of predicted ion adsorption on the Lennard-Jones parameters, highlighting that -- without due care -- standard mixing rules can lead to qualitatively incorrect descriptions of ion-metal interactions. We present a systematic methodology for tuning the cross-term LJ parameters to control adsorption energetics in agreement with more accurate models. As a surrogate for an ab initio model, we employed the recently released Universal Models for Atoms (UMA) MLIP, which validates classical trends and displays strong specific adsorption for chloride, weak adsorption for fluoride, and no specific adsorption for sodium, in agreement with experimental and theoretical expectations. By integrating molecular-level adsorption free energies into continuum models of the electric double layer, we show that specific ion adsorption substantially alters the interfacial ion population, the potential of zero charge, and the differential capacitance of the system. Our results underscore the critical importance of force field parameterization and advanced interatomic potentials for the predictive modeling of ion-specific effects at electrified interfaces and provide a robust framework for bridging molecular simulations and continuum electrochemical models.

Figures (22)

• Figure 1: Comparison of the free energy profile of Na+ (a), F- (b), Cl- (c) in TIP3P water as a function of their distance from a Au(111) surface. (d) Schematic of a classical MD system with a single Na+ ion, water, and the gold slab.
• Figure 2: Snapshot from the classical MD trajectory for Na+ (purple, top, Cheatham), F- (blue, center, Jorgensen), and Cl- (green, bottom, Merz). The other elements are Au (yellow), O (red), and H (white). The distance from the Au(111) surface for each snapshot is given in the top-right corner. Water molecules above a cutoff radius of 5 Å from the ion were removed for visualization purposes. The numbering corresponds to the minima labeled in Fig. \ref{['fig:free_energies']}.
• Figure 3: Effective force field parameters between the ions and the gold ($\varepsilon_{\text{Au-ion}}$ and $\sigma_{\text{Au-ion}}$) calculated with the mixing rules of Eq. \ref{['eq:Au-ion_mix']}. The “optimized” parameters are the effective gold-ion interaction calculated after reparametrization as discussed in Sec. \ref{['subsec:cont_mod']} and summarized in Tab. \ref{['tab:FF_params_opt']}.
• Figure 4: (a) Free energy profile of a Na+ cation calculated with metadynamics while varying the ratio of the LJ $\varepsilon$ parameter with respect to that computed by the geometric mean (Cheatham's parameters). (b) Free energy difference between the curves shown in (a).
• Figure 5: Lennard-Jones correction of the adsorption free energy for two sets of parameters. The dotted lines represent the estimated free energy when correcting from F$_{\text{Dang}}$$\rightarrow$ F$_{\text{Jorgensen}}$ and from Cl$_{\text{Merz}}$$\rightarrow$ Cl$_{\text{Cheatham}}$.