Benchmarking water adsorption on metal surfaces with ab initio molecular dynamics.

Solid-water interfaces are ubiquitous in nature and technology. In particular, technologies evolving in the green transition, such as electrocatalysis, heavily rely on the junction of an electrolyte and an electrode as a central part of the device. For the understanding of atomic-scale processes taking place at the electrolyte-electrode interface, density functional theory (DFT) has become the de facto standard. The validation of DFT's ability to simulate the interfacial solid/water interaction is crucial, and ideal simulation setups need to be identified in order to prevent avoidable systematic errors. Here, we develop a rigorous sampling protocol for benchmarking the adsorption/desorption energetics of water on metallic surfaces against experimental temperature programmed desorption, single crystal adsorption calorimetry, and thermal energy atom scattering. We screened DFT's quality on a series of transition metal surfaces, applying three of the most common exchange-correlation approximations: PBE-D3, RPBE-D3, and BEEF-vdW. We find that all three xc-functionals reflect the pseudo-zeroth order desorption of water rooted in the combination of attractive adsorbate-adsorbate interactions and their saturation at low and intermediate coverages, respectively. However, both RPBE-D3 and BEEF-vdW lead to more accurate water adsorption strengths, while PBE-D3 clearly overbinds near-surface water. We relate the variations in binding strength to specific variations in water-metal and water-water interactions, highlighting the structural consequences inherent in an uninformed choice of simulation parameters. Our study gives atomistic insight into water's complex adsorption equilibrium. Furthermore, it represents a guideline for future DFT-based simulations of solvated solid interfaces by providing an assessment of systematic errors in specific setups.

GPAW: An open Python package for electronic structure calculations.

We review the GPAW open-source Python package for electronic structure calculations. GPAW is based on the projector-augmented wave method and can solve the self-consistent density functional theory (DFT) equations using three different wave-function representations, namely real-space grids, plane waves, and numerical atomic orbitals. The three representations are complementary and mutually independent and can be connected by transformations via the real-space grid. This multi-basis feature renders GPAW highly versatile and unique among similar codes. By virtue of its modular structure, the GPAW code constitutes an ideal platform for the implementation of new features and methodologies. Moreover, it is well integrated with the Atomic Simulation Environment (ASE), providing a flexible and dynamic user interface. In addition to ground-state DFT calculations, GPAW supports many-body GW band structures, optical excitations from the Bethe-Salpeter Equation, variational calculations of excited states in molecules and solids via direct optimization, and real-time propagation of the Kohn-Sham equations within time-dependent DFT. A range of more advanced methods to describe magnetic excitations and non-collinear magnetism in solids are also now available. In addition, GPAW can calculate non-linear optical tensors of solids, charged crystal point defects, and much more. Recently, support for graphics processing unit (GPU) acceleration has been achieved with minor modifications to the GPAW code thanks to the CuPy library. We end the review with an outlook, describing some future plans for GPAW.

On the Thermodynamic Equivalence of Grand Canonical, Infinite-Size, and Capacitor-Based Models in First-Principle Electrochemistry.

First principles-based computational and theoretical methods are constantly evolving trying to overcome the many obstacles towards a comprehensive understanding of electrochemical processes on an atomistic level. One of the major challenges has been the determination of reaction energetics under a constant potential. Here, a theoretical framework was proposed applying standard electronic structure methods and extrapolating to the infinite-cell size limit where reactions do not alter the potential. Today, electronically grand canonical modifications to electronic structure methods, holding the potential constant by varying the number of electrons in a finite simulation cell, become increasingly popular. In this perspective, we show that these two schemes are thermodynamically equivalent. Further, we link these methods to capacitive models of the interface, in the limit that the capacitance of the charging components (whether continuum or atomistic) are equal and invariant along the reaction pathway. We benchmark the three approaches with an example of alkali cation adsorption on Pt(111) showing that all three approaches converge in the cases of Li, Na and K. For Cs, however, strong deviation from the ideal conditions leads to a spread in the respective results. We discuss the latter by highlighting the cases of broken equivalence and assumptions among the approaches.

Unraveling the rate-determining step of C2+ products during electrochemical CO reduction.

The electrochemical reduction of CO has drawn a large amount of attention due to its potential to produce sustainable fuels and chemicals by using renewable energy. However, the reaction's mechanism is not yet well understood. A major debate is whether the rate-determining step for the generation of multi-carbon products is C-C coupling or CO hydrogenation. This paper conducts an experimental analysis of the rate-determining step, exploring pH dependency, kinetic isotope effects, and the impact of CO partial pressure on multi-carbon product activity. Results reveal constant multi-carbon product activity with pH or electrolyte deuteration changes, and CO partial pressure data aligns with the theoretical formula derived from *CO-*CO coupling as the rate-determining step. These findings establish the dimerization of two *CO as the rate-determining step for multi-carbon product formation. Extending the study to commercial copper nanoparticles and oxide-derived copper catalysts shows their rate-determining step also involves *CO-*CO coupling. This investigation provides vital kinetic data and a theoretical foundation for enhancing multi-carbon product production.

Impact of palladium/palladium hydride conversion on electrochemical CO2 reduction via in-situ transmission electron microscopy and diffraction.

Electrochemical conversion of CO2 offers a sustainable route for producing fuels and chemicals. Pd-based catalysts are effective for converting CO2 into formate at low overpotentials and CO/H2 at high overpotentials, while undergoing poorly understood morphology and phase structure transformations under reaction conditions that impact performance. Herein, in-situ liquid-phase transmission electron microscopy and select area diffraction measurements are applied to track the morphology and Pd/PdHx phase interconversion under reaction conditions as a function of electrode potential. These studies identify the degradation mechanisms, including poisoning and physical structure changes, occurring in PdHx/Pd electrodes. Constant potential density functional theory calculations are used to probe the reaction mechanisms occurring on the PdHx structures observed under reaction conditions. Microkinetic modeling reveals that the intercalation of *H into Pd is essential for formate production. However, the change in electrochemical CO2 conversion selectivity away from formate and towards CO/H2 at increasing overpotentials is due to electrode potential dependent changes in the reaction energetics and not a consequence of morphology or phase structure changes.

Impact of Anodic Oxidation Reactions in the Performance Evaluation of High-Rate CO2 /CO Electrolysis.

The membrane-electrode assembly (MEA) approach appears to be the most promising technique to realize the high-rate CO2 /CO electrolysis, however there are major challenges related to the crossover of ions and liquid products from cathode to anode via the membrane and the concomitant anodic oxidation reactions (AORs). In this perspective, by combining experimental and theoretical analyses, several impacts of anodic oxidation of liquid products in terms of performance evaluation are investigated. First, the crossover behavior of several typical liquid products through an anion-exchange membrane is analyzed. Subsequently, two instructive examples (introducing formate or ethanol oxidation during electrolysis) reveals that the dynamic change of the anolyte (i.e., pH and composition) not only brings a slight shift of anodic potentials (i.e., change of competing reactions), but also affects the chemical stability of the anode catalyst. Anodic oxidation of liquid products can also cause either over- or under-estimation of the Faradaic efficiency, leading to an inaccurate assessment of overall performance. To comprehensively understand fundamentals of AORs, a theoretical guideline with hierarchical indicators is further developed to predict and regulate the possible AORs in an electrolyzer. The perspective concludes by giving some suggestions on rigorous performance evaluations for high-rate CO2 /CO electrolysis in an MEA-based setup.

Fundamental Drivers of Electrochemical Barriers.

We find that ion creation and destruction dominate the behavior of electrochemical reaction barriers, through grand-canonical electronic structure calculations of proton deposition on transition metal surfaces. We show that barriers respond to potential in a nonlinear manner and trace this to the continuous degree of electron transfer as an ion is created or destroyed. This explains both Marcus-like curvature and Hammond-like shifts. Across materials, we find the barrier energy to be driven primarily by the charge presented on the surface, which, in turn, is dictated by the native work function, a fundamentally different driving force than in nonelectrochemical systems.

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.

Solvation of furfural at metal-water interfaces: Implications for aqueous phase hydrogenation reactions.

Metal-water interfaces are central to understanding aqueous-phase heterogeneous catalytic processes. However, the explicit modeling of the interface is still challenging as it necessitates extensive sampling of the interfaces' degrees of freedom. Herein, we use ab initio molecular dynamics (AIMD) simulations to study the adsorption of furfural, a platform biomass chemical on several catalytically relevant metal-water interfaces (Pt, Rh, Pd, Cu, and Au) at low coverages. We find that furfural adsorption is destabilized on all the metal-water interfaces compared to the metal-gas interfaces considered in this work. This destabilization is a result of the energetic penalty associated with the displacement of water molecules near the surface upon adsorption of furfural, further evidenced by a linear correlation between solvation energy and the change in surface water coverage. To predict solvation energies without the need for computationally expensive AIMD simulations, we demonstrate OH binding energy as a good descriptor to estimate the solvation energies of furfural. Using microkinetic modeling, we further explain the origin of the activity for furfural hydrogenation on intrinsically strong-binding metals under aqueous conditions, i.e., the endothermic solvation energies for furfural adsorption prevent surface poisoning. Our work sheds light on the development of active aqueous-phase catalytic systems via rationally tuning the solvation energies of reaction intermediates.

Unraveling the reaction mechanisms for furfural electroreduction on copper.

Electrochemical routes for the valorization of biomass-derived feedstock molecules offer sustainable pathways to produce chemicals and fuels. However, the underlying reaction mechanisms for their electrochemical conversion remain elusive. In particular, the exact role of proton-electron coupled transfer and electrocatalytic hydrogenation in the reaction mechanisms for biomass electroreduction are disputed. In this work, we study the reaction mechanism underlying the electroreduction of furfural, an important biomass-derived platform chemical, combining grand-canonical (constant-potential) density functional theory-based microkinetic simulations and pH dependent experiments on Cu under acidic conditions. Our simulations indicate the second PCET step in the reaction pathway to be the rate- and selectivity-determining step for the production of the two main products of furfural electroreduction on Cu, i.e., furfuryl alcohol and 2-methyl furan, at moderate overpotentials. We further identify the source of Cu's ability to produce both products with comparable activity in their nearly equal activation energies. Furthermore, our microkinetic simulations suggest that surface hydrogenation steps play a minor role in determining the overall activity of furfural electroreduction compared to PCET steps due to the low steady-state hydrogen coverage predicted under reaction conditions, the high activation barriers for surface hydrogenation and the observed pH dependence of the reaction. As a theoretical guideline, low pH (<1.5) and moderate potential (ca. -0.5 V vs. SHE) conditions are suggested for selective 2-MF production.

Electrochemistry from the atomic scale, in the electronically grand-canonical ensemble.

The ability to simulate electrochemical reactions from first-principles has advanced significantly in recent years. Here, we discuss the atomistic interpretation of electrochemistry at three scales: from the electronic structure to elementary processes to constant-potential reactions. At each scale, we highlight the importance of the grand-canonical nature of the process and show that the grand-canonical energy is the natural thermodynamic state variable, which has the additional benefit of simplifying calculations. We show that atomic forces are the derivative of the grand-potential energy when the potential is fixed. We further examine the meaning of potential at the atomic scale and its link to the chemical potential and discuss the link between charge transfer and potential in several situations.

Limits to scaling relations between adsorption energies?

Linear scaling relations have led to an understanding of trends in catalytic activity and selectivity of many reactions in heterogeneous and electro-catalysis. However, linear scaling between the chemisorption energies of any two small molecule adsorbates is not guaranteed. A prominent example is the lack of scaling between the chemisorption energies of carbon and oxygen on transition metal surfaces. In this work, we show that this lack of scaling originates from different re-normalized adsorbate valence energies of lower-lying oxygen vs higher-lying carbon. We develop a model for chemisorption of small molecule adsorbates within the d-band model by combining a modified form of the Newns-Anderson hybridization energy with an effective orthogonalization term. We develop a general descriptor to a priori determine if two adsorbates are likely to scale with each other.

Force-Based Method to Determine the Potential Dependence in Electrochemical Barriers.

Determining ab initio potential-dependent energetics is critical to the investigation of mechanisms for electrochemical reactions. While methodology for evaluating reaction thermodynamics is established, simulation techniques for the corresponding kinetics is still a major challenge owing to a lack of potential control, finite cell size effects, or computational expense. In this work, we develop a model that allows for computing electrochemical activation energies from just a handful of density functional theory (DFT) calculations. The sole input into the model are the atom-centered forces obtained from DFT calculations performed on a homogeneous grid composed of varying field strengths. We show that the activation energies as a function of the potential obtained from our model are consistent for different supercell sizes and proton concentrations for a range of electrochemical reactions.

Theories for Electrolyte Effects in CO2 Electroreduction.

Electrochemical CO2 reduction (eCO2R) enables the conversion of waste CO2 to high-value fuels and commodity chemicals powered by renewable electricity, thereby offering a viable strategy for reaching the goal of net-zero carbon emissions. Research in the past few decades has focused both on the optimization of the catalyst (electrode) and the electrolyte environment. Surface-area normalized current densities show that the latter can affect the CO2 reduction activity by up to a few orders of magnitude.In this Account, we review theories of the mechanisms behind the effects of the electrolyte (cations, anions, and the electrolyte pH) on eCO2R. As summarized in the conspectus graphic, the electrolyte influences eCO2R activity via a field (ε) effect on dipolar (µ) reaction intermediates, changing the proton donor for the multi-step proton-electron transfer reaction, specifically adsorbed anions on the catalyst surface to block active sites, and tuning the local environment by homogeneous reactions. To be specific, alkali metal cations (M+) can stabilize reaction intermediates via electrostatic interactions with dipolar intermediates or buffer the interfacial pH via hydrolysis reactions, thereby promoting the eCO2R activity with the following trend in hydrated size (corresponding to the local field strength ε)/hydrolysis ability: Cs+ > K+ > Na+ > Li+. The effect of the electrolyte pH can give a change in eCO2R activity of up to several orders of magnitude, arising from linearly shifting the absolute interfacial field via the relationship USHE = URHE - (2.3kBT)pH, homogeneous reactions between OH- and desorbed intermediates, or changing the proton donor from hydronium to water along with increasing pH. Anions have been suggested to affect the eCO2R reaction process by solution-phase reactions (e.g., buffer reactions to tune local pH), acting as proton donors or as a surface poison.So far, the existing models of electrolyte effects have been used to rationalize various experimentally observed trends, having yet to demonstrate general predictive capabilities. The major challenges in our understanding of the electrolyte effect in eCO2R are (i) the long time scale associated with a dynamic ab initio picture of the catalyst|electrolyte interface and (ii) the overall activity determined by the length-scale interplay of intrinsic microkinetics, homogeneous reactions, and mass transport limitations. New developments in ab initio dynamic models and coupling the effects of mass transport can provide a more accurate view of the structure and intrinsic functions of the electrode-electrolyte interface and the corresponding reaction energetics toward comprehensive and predictive models for electrolyte design.

Computational Screening of Single and Di-Atom Catalysts for Electrochemical CO2 Reduction.

Supported single atom catalysts on defected graphene show great potential for electrochemical reduction of CO2 to CO. In this study, we perform a computational screening of single and di-atom catalysts (MNCs and FeMNC respectively) with M varying from Sc to Zn on nitrogen-doped graphene for CO2 reduction using hybrid-density functional theory and potential dependent micro-kinetic modeling. The formation energy calculations reveal several stable single and di-atom doping site motifs. We consider the kinetics of CO2 using the binding energies of CO2* and COOH* intermediates as the descriptors to analyze the activity of these catalysts. In comparison to (211) transition metal (TM) surfaces, both MNCs and FeMNCs show a variety of binding motifs of the reaction intermediates on different metal dopants. We find four MNCs as CrNC, MnNC, FeNC, and CoNC with high catalytic efficiency for CO2R. Among the different FeMNCs with varying doping geometry and surrounding N-coordination, we have identified 11 candidates having high TOF for CO production and lower selectivity for the hydrogen evolution reaction. FeMnNC shows the highest activity for CO2R. Large CO2* dipole-field interactions in both the MNCs and FeMNCs give rise to deviations in scaling from TM surfaces.

Generalizable Trends in Electrochemical Protonation Barriers.

Predicting activation energies for reaction steps is essential for modeling catalytic processes, but accurate barrier simulations often require considerable computational expense, especially for electrochemical reactions. Given the challenges of barrier computations and the growing promise of electrochemical routes for various processes, generalizable energetic trends in electrochemistry can significantly aid in analyzing reaction networks and building microkinetic models. Herein, we employ density functional theory and machine learning nudged elastic band models to simulate electrochemical protonation of *C, *N, and *O monatomic adsorbates from hydronium on a series of transition metal surfaces. We observe a consistent trend of decreasing protonation reaction energies yet increasing activation barriers from *O to *N to *C. Analysis of bond orders and reaction pathways provides insight into the origin of the observed trends in protonation energetics. We hypothesize that these results are relevant for polyatomic adsorbates, which can simplify analysis of reaction mechanisms and inform catalyst design.

Long-lived charged states of single porphyrin-tape junctions under ambient conditions.

The ability to control the charge state of individual molecules wired in two-terminal single-molecule junctions is a key challenge in molecular electronics, particularly in relation to the development of molecular memory and other computational componentry. Here we demonstrate that single porphyrin molecular junctions can be reversibly charged and discharged at elevated biases under ambient conditions due to the presence of a localised molecular eigenstate close to the Fermi edge of the electrodes. In particular, we can observe long-lived charge-states with lifetimes upwards of 1-10 seconds after returning to low bias and large changes in conductance, in excess of 100-fold at low bias. Our theoretical analysis finds charge-state lifetimes within the same time range as the experiments. The ambient operation demonstrates that special conditions such as low temperatures or ultra-high vacuum are not essential to observe hysteresis and stable charged molecular junctions.

Improving the intrinsic activity of electrocatalysts for sustainable energy conversion: where are we and where can we go?

As we are in the midst of a climate crisis, there is an urgent need to transition to the sustainable production of fuels and chemicals. A promising strategy towards this transition is to use renewable energy for the electrochemical conversion of abundant molecules present in the earth's atmosphere such as H2O, O2, N2 and CO2, to synthetic fuels and chemicals. A cornerstone to this strategy is the development of earth abundant electrocatalysts with high intrinsic activity towards the desired products. In this perspective, we discuss the importance and challenges involved in the estimation of intrinsic activity both from the experimental and theoretical front. Through a thorough analysis of published data, we find that only modest improvements in intrinsic activity of electrocatalysts have been achieved in the past two decades which necessitates the need for a paradigm shift in electrocatalyst design. To this end, we highlight opportunities offered by tuning three components of the electrochemical environment: cations, buffering anions and the electrolyte pH. These components can significantly alter catalytic activity as demonstrated using several examples, and bring us a step closer towards complete system level optimization of electrochemical routes to sustainable energy conversion.

On the Coupling of Electron Transfer to Proton Transfer at Electrified Interfaces.

Many electrochemical processes are governed by the transfer of protons to the surface, which can be coupled with electron transfer; this electron transfer is in general non-integer and unknown a priori, but is required to hold the potential constant. In this study, we employ a combination of surface spectroscopic techniques and grand-canonical electronic-structure calculations in order to rigorously understand the thermodynamics of this process. Specifically, we explore the protonation/deprotonation of 4-mercaptobenzoic acid as a function of the applied potential. Using grand-canonical electronic-structure calculations, we directly infer the coupled electron transfer, which we find to be on the order of 0.1 electron per proton; experimentally, we also access this quantity via the potential-dependence of the pKa. We show a striking agreement between the potential-dependence of the measured pKa and that calculated with electronic-structure calculations. We further employ a simple electrostatics-based model to show that this slope can equivalently be interpreted to provide information on the degree of coupled electron transfer or the potential change at the point of the charged species.

Scaled and Dynamic Optimizations of Nudged Elastic Bands.

We present a modified nudged elastic band routine that can reduce the number of force calls by more than 50% for bands with nonuniform convergence. The method, which we call "dyNEB", dynamically and selectively optimizes images on the basis of the perpendicular PES-derived forces and parallel spring forces acting on that region of the band. The convergence criteria are scaled to focus on the region of interest, i.e., the saddle point, while maintaining continuity of the band and avoiding truncation. We show that this method works well for solid state reaction barriers-nonelectrochemical in general and electrochemical in particular-and that the number of force calls can be significantly reduced without loss of resolution at the saddle point.