Investigating the Electrochemical Double Layer with Quantum-Chemical Simulations and Implicit Solvation Models

Abstract

We assess the dielectrically consistent reference interaction site model (DRISM) as an implicit electrolyte framework for modeling the electrochemical double layer, and compare it with the Poisson-Boltzmann model and explicit molecular dynamics results from the literature. We use the gold-electrolyte interface as the main test case and analyze solvent and ionic density profiles, the differential capacitance, and the solvation contribution to CO adsorption. The results show a strong sensitivity to the Lennard-Jones parametrization of metal-ion and metal-water interactions. In particular, we find that the default Lorentz-Berthelot mixing rules to be inadequate and lead to excessive Na+ accumulation at the interface, which results in an increase of the differential capacitance at negative electrode potentials. We demonstrate that introducing pair-specific metal-ion parameters yields more symmetric charging behavior and provides greater flexibility. Our findings suggest that using pair-specific parameters, rather than relying on Lorentz-Berthelot mixing rules, improves the accuracy of the model and opens the way for future studies with this improved yet equally performant model.

Figures (10)

• Figure 1: Panel (a) displays hydrogen (light gray) and oxygen (red) particle density profiles computed with DRISM (continuous line) and explicit MD simulations (segmented line) [taken from Hughes et al.hughesStructureElectricalDouble2014] for the $\ce{Au}(111)$ facet in water. The mTIP3P water model is used in both cases. For the DRISM calculation, we adjusted the LJ parameter for $\ce{Au}$ to match the $\ce{Au}$-$\ce{O}$ GolP parametrization. Panel (b) shows the respective charge density profiles.
• Figure 2: Comparison between solvent modeling in PB and DRISM. In (a), the particle density profiles of water computed by DRISM are shown, whereas in the PB model, the solvent is replaced with a continuum dielectric. In (c) and (d) are shown the charge density profile from DRISM and the bound charge from the PB for a negative electrode surface charge $\sigma=-8.3\,\upmu\text{C/cm}^{-2}$ potential with respect to the PZC. In (e) and (f), the same applies for a positive electrode potential.
• Figure 3: Ionic density profiles for the $\ce{Au}(111)$ facet in contact with $1\,\text{M}$$\ce{NaCl}$. (a), (b) and (c) negative surface charge $\sigma = - 8.3\,\upmu\text{C/cm}^{2}$; (d), (e) and (f) neutral electrode $\sigma = 0\, \upmu\text{C/cm}^{2}$; (g), (h) and (i) $\sigma = + 8.3\,\upmu\text{C/cm}^{2}$. The continuous lines refer to the UFF parametrization for the $\ce{Au}$ electrode, while the segmented line refers to the parametrization from heinzAccurateSimulationSurfaces2008.
• Figure 4: Density profiles for the $\ce{Au}(111)$ facet in contact with $1\,\text{M}$$\ce{NaCl}$ in water. The profiles represented as dotted lines are taken from a classical MD simulation of ntimMolecularDynamicsSimulations2023 using a polarizable force field for $\ce{Au}$. The continuous profiles are obtained from DRISM using the mSPCE water model, the Heinz parametrization for the $\ce{Au}$ slab, and the joungDeterminationAlkaliHalide2008 parametrization for the ions. In both cases, the electrode is at the PZC. Although the parametrization of the pair potentials is not identical, there is qualitative agreement in the positions of the first peaks for sodium and chloride.
• Figure 5: Density profiles for $\ce{Au}(111)$ facet in contact with $0.01\,\text{M}$ electrolyte. The calculations are performed at a surface charge of $\sigma = -0.27\,\upmu \text{C}/\text{cm}^{2}$, PZC, $\sigma = +0.27\,\upmu \text{C}/\text{cm}^{2}$, and $\sigma = -8.33\,\upmu \text{C}/\text{cm}^{2}$ in (a), (b), (c), and (d) respectively. The segmented lines are computed with the $\ce{Au}$ Heinz / mSPCE / $\ce{NaCl}$ Joung parameterization and the default LB mixing rules. For the continuous lines, pair-specific parameters are given for the $\ce{Au}$-$\ce{Na}$LJ interaction. In (d) results from the non-linear and linear PB model are also shown for comparison.