Field-Aware Interfaces in Continuum Solvation

Soft-sphere continuum solvation models for nonaqueous solvents

Solvation effects profoundly influence the characteristics and behavior of chemical systems in liquid solutions. The interaction between solute and solvent molecules intricately impacts solubility, reactivity, stability, and various chemical processes. Continuum solvation models gained prominence in quantum chemistry by implicitly capturing these interactions and enabling efficient investigations of diverse chemical systems in solution. In comparison, continuum solvation models in condensed matter simulation are very recent. Among these, the self-consistent continuum solvation (SCCS) and the soft-sphere continuum solvation models (SSCS) have been among the first to be successfully parameterized and extended to model periodic systems in aqueous solutions and electrolytes. As most continuum approaches, these models depend on a number of parameters that are linked to experimental or theoretical properties of the solvent, or that can be tuned based on reference data. Here, we present a systematic parameterization of the SSCS model for over 100 nonaqueous solvents. We validate the model's efficacy across diverse solvent environments by leveraging experimental solvation-free energies and partition coefficients from comprehensive databases. The average root means square error over all the solvents was calculated as 0.85 kcal/mol which is below the chemical accuracy (1 kcal/mol). Similarly to what has been reported by Hille et al. (J. Chem. Phys. 2019, 150, 041710.) for the SCCS model, a single-parameter model accurately reproduces experimental solvation energies, showcasing the transferability and predictive power of these continuum approaches. Our findings underscore the potential for a unified approach to predict solvation properties, paving the way for enhanced computational studies across various chemical environments.

Thermodynamic and kinetic modeling of electrocatalytic reactions using a first-principles approach

The computational modeling of electrochemical interfaces and their applications in electrocatalysis has attracted great attention in recent years. While tremendous progress has been made in this area, however, the accurate atomistic descriptions at the electrode/electrolyte interfaces remain a great challenge. The Computational Hydrogen Electrode (CHE) method and continuum modeling of the solvent and electrolyte interactions form the basis for most of these methodological developments. Several posterior corrections have been added to the CHE method to improve its accuracy and widen its applications. The most recently developed grand canonical potential approaches with the embedded diffuse layer models have shown considerable improvement in defining interfacial interactions at electrode/electrolyte interfaces over the state-of-the-art computational models for electrocatalysis. In this Review, we present an overview of these different computational models developed over the years to quantitatively probe the thermodynamics and kinetics of electrochemical reactions in the presence of an electrified catalyst surface under various electrochemical environments. We begin our discussion by giving a brief picture of the different continuum solvation approaches, implemented within the ab initio method to effectively model the solvent and electrolyte interactions. Next, we present the thermodynamic and kinetic modeling approaches to determine the activity and stability of the electrocatalysts. A few applications to these approaches are also discussed. We conclude by giving an outlook on the different machine learning models that have been integrated with the thermodynamic approaches to improve their efficiency and widen their applicability.

An Electrostatically Embedded QM/MM Scheme for Electrified Interfaces

Atomistic modeling of electrified interfaces remains a major issue for detailed insights in electrocatalysis, corrosion, electrodeposition, batteries, and related devices such as pseudocapacitors. In these domains, the use of grand-canonical density functional theory (GC-DFT) in combination with implicit solvation models has become popular. GC-DFT can be conveniently applied not only to metallic surfaces but also to semiconducting oxides and sulfides and is, furthermore, sufficiently robust to achieve a consistent description of reaction pathways. However, the accuracy of implicit solvation models for solvation effects at interfaces is in general unknown. One promising way to overcome the limitations of implicit solvents is going toward hybrid quantum mechanical (QM)/molecular mechanics (MM) models. For capturing the electrochemical potential dependence, the key quantity is the capacitance, i.e., the relation between the surface charge and the electrochemical potential. In order to retrieve the electrochemical potential from a QM/MM hybrid scheme, an electrostatic embedding is required. Furthermore, the charge of the surface and of the solvent regions has to be strictly opposite in order to consistently simulate charge-neutral unit cells in MM and in QM. To achieve such a QM/MM scheme, we present the implementation of electrostatic embedding in the VASP code. This scheme is broadly applicable to any neutral or charged solid/liquid interface. Here, we demonstrate its use in the context of GC-DFT for the hydrogen evolution reaction (HER) over a noble-metal-free electrocatalyst, MoS₂. We investigate the effect of electrostatic embedding compared to the implicit solvent model for three contrasting active sites on MoS₂: (i) the sulfur vacancy defect, which is rather apolar; (ii) a Mo antisite defect, where the active site is a surface bound highly polar OH group; and (iii) a reconstructed edge site, which is generally believed to be responsible for most of the catalytic activity. According to our results, the electrostatic embedding leads to almost indistinguishable results compared to the implicit solvent for the apolar system but has a significant effect on polar sites. This demonstrates the reliability of the hybrid QM/MM, electrostatically embedded solvation model for electrified interfaces.

Implicit Solvation Methods for Catalysis at Electrified Interfaces

Implicit solvation is an effective, highly coarse-grained approach in atomic-scale simulations to account for a surrounding liquid electrolyte on the level of a continuous polarizable medium. Originating in molecular chemistry with finite solutes, implicit solvation techniques are now increasingly used in the context of first-principles modeling of electrochemistry and electrocatalysis at extended (often metallic) electrodes. The prevalent ansatz to model the latter electrodes and the reactive surface chemistry at them through slabs in periodic boundary condition supercells brings its specific challenges. Foremost this concerns the difficulty of describing the entire double layer forming at the electrified solid–liquid interface (SLI) within supercell sizes tractable by commonly employed density functional theory (DFT). We review liquid solvation methodology from this specific application angle, highlighting in particular its use in the widespread ab initio thermodynamics approach to surface catalysis. Notably, implicit solvation can be employed to mimic a polarization of the electrode’s electronic density under the applied potential and the concomitant capacitive charging of the entire double layer beyond the limitations of the employed DFT supercell. Most critical for continuing advances of this effective methodology for the SLI context is the lack of pertinent (experimental or high-level theoretical) reference data needed for parametrization.

Role of OH Intermediates during the Au Oxide Electro-Reduction at Low pH Elucidated by Electrochemical Surface-Enhanced Raman Spectroscopy and Implicit Solvent Density Functional Theory

Molecular understanding of the electrochemical oxidation of metals and the electro-reduction of metal oxides is of pivotal importance for the rational design of catalyst-based devices where metal(oxide) electrodes play a crucial role. Operando monitoring and reliable identification of reacting species, however, are challenging tasks because they require surface-molecular sensitive and specific experiments under reaction conditions and sophisticated theoretical calculations. The lack of molecular insight under operating conditions is largely due to the limited availability of operando tools and to date still hinders a quick technological advancement of electrocatalytic devices. Here, we present a combination of advanced density functional theory (DFT) calculations considering implicit solvent contributions and time-resolved electrochemical surface-enhanced Raman spectroscopy (EC-SERS) to identify short-lived reaction intermediates during the showcase electro-reduction of Au oxide (AuOx) in sulfuric acid over several tens of seconds. The EC-SER spectra provide evidence for temporary Au-OH formation and for the asynchronous adsorption of (bi)sulfate ions at the surface during the reduction process. Spectral intensity fluctuations indicate an OH/(bi)sulfate turnover period of 4 s. As such, the presented EC-SERS potential jump approach combined with implicit solvent DFT simulations allows us to propose a reaction mechanism and prove that short-lived Au-OH intermediates also play an active role during the AuOx electro-reduction in acidic media, implying their potential relevance also for other electrocatalytic systems operating at low pH, like metal corrosion, the oxidation of CO, HCOOH, and other small organic molecules, and the oxygen evolution reaction.

The electrochemical interface in first-principles calculations

First-principles predictions play an important role in understanding chemistry at the electrochemical interface. Electronic structure calculations are straightforward for vacuum interfaces, but do not easily account for the interfacial fields and solvation that fundamentally change the nature of electrochemical reactions. Prevalent techniques for first-principles prediction of electrochemical processes range from expensive explicit solvation using ab initio molecular dynamics, through a hierarchy of continuum solvation techniques, to neglecting solvation and interfacial field effects entirely. Currently, no single approach reliably captures all relevant effects of the electrochemical double layer in first-principles calculations. This review systematically lays out the relation between all major approaches to first-principles electrochemistry, including the key approximations and their consequences for accuracy and computational cost. Focusing on ab initio methods for thermodynamic properties of aqueous interfaces, we first outline general considerations for modeling electrochemical interfaces, including solvent and electrolyte dynamics and electrification. We then present the specifics of various explicit and implicit models of the solvent and electrolyte. Finally, we discuss the compromise between computational efficiency and accuracy, and identify key outstanding challenges and future opportunities in the wide range of techniques for first-principles electrochemistry.

Effects of surface charge and cluster size on the electrochemical dissolution of platinum nanoparticles using COMB3 and continuum electrolyte models

We study the site-dependent dissolution of platinum nanoparticles under electrochemical conditions to assess their thermodynamic stability as a function of shape and size using empirical molecular dynamics and electronic-structure models. The third-generation charge optimized many-body potential is employed to determine the validity of uniform spherical representations of the nanoparticles in predicting dissolution potentials (the Kelvin model). To understand the early stages of catalyst dissolution, implicit solvation techniques based on the self-consistent continuum solvation method are applied. It is demonstrated that interfacial charge and polarization can shift the dissolution energies by amounts on the order of 0.74 eV depending on the surface site and nanoparticle shape, leading to the unexpected preferential removal of platinum cations from highly coordinated sites in some cases.