Grand Canonical Ensemble Modeling of Electrochemical Interfaces Made Simple

Toward Realistic Models of the Electrocatalytic Oxygen Evolution Reaction

The electrocatalytic oxygen evolution reaction (OER) supplies the protons and electrons needed to transform renewable electricity into chemicals and fuels. However, the OER is kinetically sluggish; it operates at significant rates only when the applied potential far exceeds the reversible voltage. The origin of this overpotential is hidden in a complex mechanism involving multiple electron transfers and chemical bond making/breaking steps. Our desire to improve catalytic performance has then made mechanistic studies of the OER an area of major scientific inquiry, though the complexity of the reaction has made understanding difficult. While historically, mechanistic studies have relied solely on experiment and phenomenological models, over the past twenty years ab initio simulation has been playing an increasingly important role in developing our understanding of the electrocatalytic OER and its reaction mechanisms. In this Review we cover advances in our mechanistic understanding of the OER, organized by increasing complexity in the way through which the OER is modeled. We begin with phenomenological models built using experimental data before reviewing early efforts to incorporate ab initio methods into mechanistic studies. We go on to cover how the assumptions in these early ab initio simulations─no electric field, electrolyte, or explicit kinetics─have been relaxed. Through comparison with experimental literature, we explore the veracity of these different assumptions. We summarize by discussing the most critical open challenges in developing models to understand the mechanisms of the OER.

Revealing the Size and Potential Dependent D2O Microkinetics on Pt Nanoparticles Using Grand Canonical Ensemble Modeling

Revealing the potential and nanoparticle size effect is significant for understanding the electrochemical microkinetic behaviors under real reaction conditions. Herein, an efficient strategy of combining the robust fully converged constant potential (FCP) algorithm and the size dependent site distribution rule assumption was proposed. A simple reaction of isotopic D2O/H2O adsorption and dissociation on Pt nanoparticles was set as the model reaction. The results show that the cathodic negative potential and the anodic positive potential would result in the D2O orientation of the D-down/O-down physisorption configuration. Microkinetic simulations by this strategy obtained electrochemical widows for D2O/H2O dissociation, and the optimal Pt nanoparticle diameter was predicted to be 1.8 nm, which agrees well with the experimental observation of ∼2 nm threshold. The kinetic isotope effect (KIE) rate constant ratio at the optimal potential of -0.80 V vs SHE was calculated to be ∼1.83. This work provides a guideline in studying electrochemical electrode-electrolyte interactions on nanoparticles.

Emerging Atomistic Modeling Methods for Heterogeneous Electrocatalysis

Heterogeneous electrocatalysis lies at the center of various technologies that could help enable a sustainable future. However, its complexity makes it challenging to accurately and efficiently model at an atomic level. Here, we review emerging atomistic methods to simulate the electrocatalytic interface with special attention devoted to the components/effects that have been challenging to model, such as solvation, electrolyte ions, electrode potential, reaction kinetics, and pH. Additionally, we review relevant computational spectroscopy methods. Then, we showcase several examples of applying these methods to understand and design catalysts relevant to green hydrogen. We also offer experimental views on how to bridge the gap between theory and experiments. Finally, we provide some perspectives on opportunities to advance the field.

Strain-induced catalytic enhancement in Co-BTA and Rh-BTA for efficient 2e- oxygen reduction: a DFT study

Here we design TM-BTA catalysts for the electrochemical synthesis of hydrogen peroxide (H2O2), focusing on the efficient two-electron (2e-) oxygen reduction pathway. Employing density functional theory (DFT), we screened 17 transition metals, identifying Co-BTA and Rh-BTA as outstanding candidates based on their low overpotentials and superior catalytic activity. A key innovation is the application of mechanical strain to these catalysts, significantly optimizing their performance by modulating the d-band center. This approach enhances the adsorption of oxygen-containing intermediates, crucial for the 2e- ORR process. Our findings demonstrate that a tensile strain of 1.95% optimally enhances catalytic efficiency in both Co-BTA and Rh-BTA, substantially reducing overpotential. This research not only highlights the potential of TM-BTA catalysts in H2O2 production but also underscores the importance of strain modulation as a cost-effective and efficient method to improve the selectivity and activity of electrocatalysts, offering a novel perspective in the field of sustainable chemical synthesis.

Activation Energies of Heterogeneous Electrocatalysis: A Theoretical Perspective

Heterogeneous electrochemistry is important for various applications. However, currently, there is limited information about activation energies. In this invited review, we review the challenges associated with calculating these activation energies. Specifically, we highlight three key difficulties in atomistic modeling: liquid structure, electrode potential, and electrolyte ions, along with state-of-the-art methods to address them. We aim to inspire more studies in the field of activation energies to better understand and design heterogeneous electrocatalysts.

Constant Potential Thermodynamic Integration for Obtaining the Free Energy Profile of Electrochemical Reaction

In this work, we advanced an efficient free energy sampling method based on constrained ab initio molecular dynamics (cAIMD) with a fully explicit solvent layer to depict the electrochemical reaction process at constant surface charge density, named the "Constant-Potential Thermodynamic Integration (CPTI)" method. For automatically adjusting surface charge density at different states, we built an "on-the-fly" procedure which is capable of managing all the necessary steps during cAIMD simulations, including the system pre-equilibrium, surface charge density updating, and force sampling. We applied it to predict the potential-dependent free energy profiles of CO2 adsorption on a single-atom catalyst. The results show that our method can not only account for changes in electrostatic potential energy associated with potential but also consider the potential-induced solvation effects. Our approach enables the accurate simulation of electrochemical environment by presenting the complete solid-liquid interface and efficient computation of electrocatalytic reaction energetics based on a robust potential descriptor.

Controlled Electrochemical Barrier Calculations without Potential Control

The knowledge of electrochemical activation energies under applied potential conditions is a prerequisite for understanding catalytic activity at electrochemical interfaces. Here, we present a new set of methods that can compute electrochemical barriers with accuracy comparable to that of constant potential grand canonical approaches, without the explicit need for a potentiostat. Instead, we Legendre transform a set of constant charge, canonical reaction paths. Additional straightforward approximations offer the possibility to compute electrochemical barriers at a fraction of computational cost and complexity, and the analytical inclusion of geometric response highlights the importance of incorporating electronic as well as the geometric degrees of freedom when evaluating electrochemical barriers.

Realistic Modeling of the Electrocatalytic Process at Complex Solid-Liquid Interface

The rational design of electrocatalysis has emerged as one of the most thriving means for mitigating energy and environmental crises. The key to this effort is the understanding of the complex electrochemical interface, wherein the electrode potential as well as various internal factors such as H-bond network, adsorbate coverage, and dynamic behavior of the interface collectively contribute to the electrocatalytic activity and selectivity. In this context, the authors have reviewed recent theoretical advances, and especially, the contributions to modeling the realistic electrocatalytic processes at complex electrochemical interfaces,  and illustrated the challenges and fundamental problems in this field. Specifically, the significance of the inclusion of explicit solvation and electrode potential as well as the strategies toward the design of highly efficient electrocatalysts are discussed. The structure-activity relationships and their dynamic responses to the environment and catalytic functionality under working conditions are illustrated to be crucial factors for understanding the complexed interface and the electrocatalytic activities. It is hoped that this review can help spark new research passion and ultimately bring a step closer to a realistic and systematic modeling method for electrocatalysis.

Electric Double Layer Effects in Electrocatalysis: Insights from Ab Initio Simulation and Hierarchical Continuum Modeling

Structures of the electric double layer (EDL) at electrocatalytic interfaces, which are modulated by the material properties, the electrolyte characteristics (e.g., the pH, the types and concentrations of ions), and the electrode potential, play crucial roles in the reaction kinetics. Understanding the EDL effects in electrocatalysis has attracted substantial research interest in recent years. However, the intrinsic relationships between the specific EDL structures and electrocatalytic kinetics remain poorly understood, especially on the atomic scale. In this Perspective, we briefly review the recent advances in deciphering the EDL effects mainly in hydrogen and oxygen electrocatalysis through a multiscale approach, spanning from the atomistic scale simulated by ab initio methods to the macroscale by a hierarchical approach. We highlight the importance of resolving the local reaction environment, especially the local hydrogen bond network, in understanding EDL effects. Finally, some of the remaining challenges are outlined, and an outlook for future developments in these exciting frontiers is provided.