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In the last decade, trends for competing electrocatalytic processes have been largely captured by volcano plots, which can be constructed by the analysis of adsorption free energies as derived from electronic structure theory in the density functional theory approximation. One prototypical example refers to the four-electron and two-electron oxygen reduction reactions (ORRs), resulting in the formation of water and hydrogen peroxide, respectively. The conventional thermodynamic volcano curve illustrates that the four-electron and two-electron ORRs reveal the same slopes at the volcano legs. This finding is related to two facts, namely, that only a single mechanistic description is considered in the model, and electrocatalytic activity is assessed by the concept of the limiting potential, a simple thermodynamic descriptor evaluated at the equilibrium potential. In the present contribution, the selectivity challenge of the four-electron and two-electron ORRs is analyzed, thereby accounting for two major expansions. First, different reaction mechanisms are included into the analysis, and second, Gmₐₓ(U), a potential-dependent activity measure that factors overpotential and kinetic effects into the evaluation of adsorption free energies, is applied for approximation of electrocatalytic activity. It is illustrated that the slope of the four-electron ORR is not constant at the volcano legs but rather is prone to change as soon as another mechanistic pathway is energetically preferred or another elementary step becomes the limiting one. Due to the varying slope of the four-electron ORR volcano, a trade-off between activity and selectivity for hydrogen peroxide formation is observed. It is demonstrated that the two-electron ORR is energetically preferred at the left and right volcano legs, thus opening a new strategy for the selective formation of H₂O₂ by an environmentally benign route. CA Exner

The apparent activation energy, Eₐpp, is a common measure in thermal catalysis to discuss the activity and limiting steps of catalytic processes on solid-state materials. Recently, the electrocatalysis community adopted the concept of Eₐpp and combined it with the Butler-Volmer theory. Certain observations though, such as potential-dependent fluctuations of Eₐpp, are yet surprising because they conflict with the proposed linear decrease in Eₐpp with increasing overpotential. The most common explanation for this finding refers to coverage changes upon alterations in the temperature or the applied electrode potential. In the present contribution, it is demonstrated that the modulation of surface coverages cannot entirely explain potential-dependent oscillations of Eₐpp, and rather the impact of entropic contributions of the transition states has been overlooked so far. In the case of a nearly constant surface coverage, these entropic contributions can be extracted by a dedicated combination of Tafel plots and temperature-dependent experiments.

The anodic four-electron oxygen evolution reaction (OER) corresponds to the limiting process in acidic or alkaline electrolyzers to produce gaseous hydrogen at the cathode of the device. In the last decade, tremendous efforts have been dedicated to the identification of active OER materials by electronic structure calculations in the density functional theory approximation. Most of these works rely on the assumption that the mononuclear mechanism, comprising the *OH, *O, and *OOH intermediates, is operative under OER conditions, and that a single elementary reaction step (most likely *OOH formation) governs the kinetics. In the present manuscript, six different OER mechanisms are analyzed, and potential-dependent volcano curves are constructed to comprehend the electrocatalytic activity of these pathways in the approximation of the descriptor Gmₐₓ(U), a potential-dependent activity measure based on the notion of the free-energy span model. While the mononuclear description mainly describes the legs of the volcano plot, corresponding to electrocatalysts with low intrinsic activity, it is demonstrated that the preferred pathway at the volcano apex is a strong function of the applied electrode potential. The observed mechanistic complexity including a switch of the favored pathway with increasing overpotential sets previous investigations aiming at the identification of reaction mechanisms and limiting steps into question since the entire breadth of OER pathways was not accounted for. A prerequisite for future atomic-scale studies on highly active OER catalysts refers to the evaluation of several mechanistic pathways so that neither important mechanistic features are overlooked nor limiting steps are incorrectly determined. in press

While metal-air batteries (MABs) are considered to outperform lithium-ion batteries for energy-storage applications, the sluggish bifunctional oxygen electrocatalysis at the cathode of MABs still represents a major bottleneck that severely limits efficiency. Recently, it was motivated by means of electronic structure calculations to replace the oxygen redox chemistry at the cathode of MABs by the redox chemistry of peroxide, considering that the latter is governed by kinetically facile two-electron processes. Herein, two different concepts of rechargeable metal-hydrogen peroxide batteries are investigated, consisting of either the peroxide reduction (PRR) and peroxide formation (PFR) reactions or the two-electron oxygen reduction (ORR) and two-electron oxygen evolution (OER) reactions at the cathode. Applying a dedicated thermodynamic framework in the spirit of the descriptor Gmₐₓ(U), a potential-dependent activity measure that factors overpotential and kinetic effects into the evaluation of adsorption free energies, generalized volcano plots for the PRR, PFR, two-electron ORR, and two-electron OER as well as their competing side reactions are derived. It is illustrated that for the PFR/PRR, selectivity can be steered toward the desired product without loss in activity whereas for the two-electron ORR/OER, a trade-off between activity and selectivity is encountered. The derived volcano models in this contribution may aid the search for potential material motifs for the PFR/PRR and the two-electron ORR/OER by calculations in the framework of electronic structure theory. CA Exner

Oxygen reduction reaction (ORR) corresponds to the limiting process in fuel cells to convert gaseous hydrogen and oxygen from the air into electricity. Most commonly, electronic structure calculations in the density functional theory (DFT) approximation are applied to comprehend the elementary reaction steps on the atomic scale, including the identification of limiting reaction steps and approximation of electrocatalytic activity. A major challenge in the modeling of the ORR refers to the complexity of the mechanistic pathways given that a plethora of different descriptions, ranging from the mononuclear to OOH dissociation mechanisms, dissociative and oxide pathways, have been reported in the literature. In the present work, the adsorption free energy of the *OH intermediate, ΔG₁, is introduced as an effective descriptor for rapid screening of ORR mechanisms. By applying a rigorous thermodynamic analysis in conjunction with a descriptor-based approach, it is demonstrated how the calculation of a single binding energy in terms of ΔG₁ can be used to identify the energetically favored mechanistic description for any ORR catalyst by analyzing the location of the material in the volcano plot. The introduced procedure may support future DFT-based studies in that the preferred pathway is not missed when modeling the four-electron ORR by a binding-energy approach.

Summary In the last decade, tremendous efforts have been dedicated to the breaking of the OOH versus OH scaling relation, which is recognized as the bottleneck for electrocatalysts in the oxygen evolution reaction (OER), the anodic process in water electrolyzers. Breaking the OER scaling relation is seen as a universal remedy to enhance electrocatalytic activity, yet no major progress has so far been achieved in the design of improved OER materials according to this strategy. Introducing kinetics into the thermodynamics-based concept of scaling relations illustrates that the breaking of the OER scaling relation could be accompanied by decreased electrocatalytic activity. As a consequence, it appears imperative to progress the theoretical description of the OER in different directions other than the breaking of this scaling relation. This could include the investigation of competing mechanistic pathways, concerted and decoupled proton-electron transfer steps, or microkinetic considerations in conjunction with machine-learning approaches.

MXenes, a rather new family of 2D carbides and nitrides, have shown to be promising materials in many technological applications, particularly in electrocatalysis. The as-synthesized MXenes exhibit a variety of surface terminations involving mixtures of O, OH, H, or F surface groups. These terminations play a crucial role in the electrocatalytic performance of these materials as these may change depending on the reaction conditions. The Pourbaix diagrams have long being used to provide the thermodynamically stable surface under certain conditions of pH and potential, U. However, experimental determination of Pourbaix diagrams may be quite challenging while first-principles studies, considering the most likely terminations, allow deriving reliable insights. Here, Pourbaix diagrams for a series of representative MXenes are provided; the Ti2C, Ti3C2, V2C, and Mo2C MXenes, with the novelty of considering single and several double mixed terminations. The possible implications of the obtained results are discussed, especially for a proper choice of models in theoretical electrocatalysis studies, including the water splitting related hydrogen evolution reaction (HER), or the oxygen reduction reaction (ORR), but also serving as a guide to any further computational studies and also to electrocatalytic experiments.

Electrochemical nitrogen reduction reaction (NRR) is mainly hampered by two facts. On the one hand, the hydrogen evolution reaction competes with the NRR under cathodic reaction conditions. On the other hand, the sluggish reaction kinetics of the NRR, due to the transfer of six proton-electron pairs in the reaction mechanism, causes large overpotentials, and thus results in humble intrinsic activity for ammonia formation. Optimization strategies for NRR electrocatalysts are ultimately called for to overcome these issues. While breaking scaling relation is considered as a universal remedy to enhance turnover for any electrocatalytic process, recently, the concept of catalytic resonance theory has been put forth as a second option to obtain reaction rates beyond the limiting Sabatier volcano. Yet, a comparison of these two concepts is missing but urgently needed to comprehend design principles for electrocatalyst optimization on the atomic scale. In the present work, breaking scaling relation and catalytic resonance by programmable catalysis are compared on the example of the NRR over transition-metal oxides. It is demonstrated that a fine tuning rather than a full breaking of nitrogen-containing scaling relations is required to enhance electrocatalytic activity of electrocatalysts at the volcano apex. The success of catalytic resonance theory is based on the occurrence of negative scaling correlations whereas in the case of positive scaling correlations, the impact of this approach on the optimization of electrocatalysts strongly depends on the location of the material in the volcano plot. The obtained insight may spur the development of NRR electrocatalysts with enhanced intrinsic activity by following the outlined design principles. in press

Efficient transport of pharmaceuticals to malignant cells in the human body often requires the application of drug-delivery systems (DDSs) consisting of several building blocks, each of them bearing a specific function. While nanoparticles are promising as potential carrier moieties, biomolecules may add to the efficient delivery by binding several drug molecules simultaneously. In this contribution, we apply a combination of atomistic molecular dynamics simulations and density functional theory calculations to characterize a multi-component DDS for the transport of the anthracycline antibiotic doxorubicin (DOX), comprising a gold nanoparticle (NP) and a drug-binding peptide (DBP) grafted on the NP surface. We have shown previously that the DDS can stabilize one DOX per DBP. However, by increasing the drug load to a 2 : 1 DOX : DBP ratio the two drug molecules compete for the available adsorption sites, which may cause spontaneous dissociation of one DOX molecule. We identify the chain length of the DBP as a limiting factor for the drug-loading capacity and provide important guidelines for further optimization of multi-component functionalized DDSs.

Metal-air batteries are encountered as a promising solution for energy storage due to their high energy density, cost effectiveness, and environmental benefits. Yet, the application of metal-air batteries in practice is still not mature, which is also related to the bifunctional oxygen electrocatalysis at the cathode, comprising the oxygen reduction (ORR) and oxygen evolution (OER) reactions during discharge and charge of the battery, respectively. Experimentally, the performance of electrocatalysts in the OER and ORR is described by bifunctional index (BI), but, so far, there is no direct approach to capture the BI on the atomic scale. Herein, we present a method to ascertain the BI from ab initio theory, thereby combining a data-driven methodology with thermodynamic considerations and microkinetic modeling as a function of the applied overpotential. Our approach allows deriving the BI from simple adsorption free energies, which are easily accessible to electronic structure theory in the density functional theory (DFT) approximation. We outline how our methodology may steer the design of efficient bifunctional catalysts on the atomic scale.

Computational approaches to describe catalysts under electrochemical conditions are steadily increasing. Yet, particularly the theoretical description of nanostructured catalysts, which have the advantage of a high surface area or unique electronic properties through refined synthetic protocols, is still hampered by the occurrence of pitfalls that need to be circumvented. In this perspective, we aim to introduce the reader to common pitfalls in the modeling of nanostructured catalysts with applications in energy conversion and storage, and we discuss the application of machine learning techniques as a potential solution to overcome the associated gaps.

Identification of active electrocatalysts for the oxygen evolution reaction (OER), corresponding to the bottleneck in electrolyzers to produce gaseous hydrogen as energy vector, by electronic structure calculations relies on the assumption of the mononuclear mechanism, comprising the *OH, *O, and *OOH intermediates. This mechanistic description is thermodynamically hampered by a scaling relation between the *OH and *OOH adsorbates, which may serve as an explanation why OER catalysts commonly require large overpotentials to reach sufficient current densities. Recently, an alternate OER pathway was proposed that, in contrast to the mononuclear description, consists of the formation of two adjacent *OO adsorbates, and gaseous oxygen is produced by chemical recombination of the neighboring *OO intermediates. In the present manuscript, a data-driven model based on a dedicated assessment of the elementary reaction steps is deduced, which enables evaluating the mononuclear and *OO pathways by the same set of parameters. Potential-dependent volcano plots are constructed to comprehend the energetics of the competing mechanisms. It is demonstrated that the alternate OER pathway consisting of the *OO∙∙*OO recombination step may excel the mononuclear description at overpotentials corresponding to typical OER conditions. Consequently, it is suggested that future studies, aiming at the identification of OER materials, may not omit the *OO∙∙*OO recombination mechanism when using concepts of materials screening in a heuristic fashion or multiscale modeling.

Material screening in electrocatalysis has been spurred by the concept of volcano plots, which rely on analyzing binding energies at zero overpotential. Recently, a unifying material-screening appr...

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Electrochemical water splitting is a key technology for moving toward a promising energy scenario based on renewable (regenerative) energy resources in that wind and solar energy can be stored and ...

The computational hydrogen electrode (CHE) approach has spurred ab initio investigations in the field of electrocatalysis, since the underlying concept enables to quantify free energy changes, ΔG (...

OA Förderung 2021 Binding energies of reaction intermediates are largely used to comprehend activity trends in a class of electrode materials. For a two-electron process, such as the hydrogen evolution reaction (HER), it is a well-established paradigm that the optimum electrocatalyst binds adsorbed hydrogen thermoneutrally at zero overpotential. While this picture was challenged recently by means of density functional theory (DFT) calculations and microkinetic considerations, reporting a shift of the optimum binding energy to strong or weak bonding with increasing overpotential, now experiments show further evidence for this theory. This perspective article juxtaposes the different views of the optimum binding energy for the HER by means of the Sabatier principle, microkinetic considerations, DFT calculations, and experiments, and provides an outlook of potential future investigations by the combination of experiments with DFT aiming at sustainable materials development for the hydrogen electrocatalysis.

Knowledge of the relation between electrocatalytic activity and the rate-determining step or the surface coverage of reaction intermediates is crucial to design next-generation electrocatalysts that may contribute to the sustainability of our society. Commonly, microkinetic models making use of the quasi-equilibrium or steady-state assumptions are applied to correlate potential mechanistic descriptions to experimental data, which are usually depicted in the form of a Tafel plot. Yet, there is a discrepancy in the literature on the utility of the quasi-equilibrium and steady-state conditions, both of which are approximations per se. This inconsistency is the starting point of the present work, which compares the quasi-equilibrium and steady-state approaches for the analysis of a Tafel plot by the concept of free-energy diagram for a two-electron process. A correlation between the two frameworks is deduced and important guidelines for the application of the quasi-equilibrium and steady-state assumptions are obtained. While the quasi-equilibrium approach is a suitable approximation for the analysis of a linear Tafel line without change in the Tafel slope, it may fail in the evaluation of a Tafel plot with two linear Tafel regimes. There, the binding energy of the reaction intermediate governs whether the quasi-equilibrium model is justified, or the steady-state approach is needed. This implies that density functional theory calculations are indispensably required as a supplement to analyze a Tafel plot with two different Tafel slopes, a situation that is particularly observed for highly active electrocatalysts. CA Exner

Understanding the complex interactions of different building blocks within a sophisticated drug-delivery system (DDS), aimed at targeted transport of the drug to malignant cells, requires modeling techniques on different time and length scales. On the example of the anthracycline antibiotic doxorubicin (DOX), we investigate a potential DDS component, consisting of a gold nanoparticle and a short peptide sequence as carriers of DOX. The combination of atomistic molecular dynamics simulations and density functional theory calculations facilitates compiling a volcano plot, which allows deriving general conclusions on DDS constituents for chemotherapeutic agents within the class of anthracycline antibiotics: the nanoparticle and peptide carrier moieties need to be chosen in such a way that the anthracycline body of the drug is able to intercalate between both entities or between two (π-stacking) residues of the peptide. Using the popular volcano framework as a guideline, the present article connects the catalysis and biosimulation communities, thereby identifying a strategy to overcome the limiting volcano relation by tuning the coordination number of the drug in the DDS component.

In this article, we study the competing oxygen evolution and hydrogen peroxide (H2O2) formation reactions for periodic models of graphene with different active-site concentrations by means of densi...

Hydrogen electrocatalysis has been spurred by theoretical predictions, using simple ab initio thermodynamic considerations, in that the free-binding energy of adsorbed hydrogen has been applied in a heuristic fashion to search for sustainable electrocatalysts as a replacement for scarce platinum in electrolyzers and fuel cells. The original volcano model of Norskov et al. is given in [14] purports that the optimum hydrogen-evolution catalyst binds adsorbed hydrogen thermoneutrally at zero overpotential, a paradigm based on pure thermodynamic considerations. Recently, the Sabatier principle was revisited by factoring the applied overpotential and kinetics into the analysis. The extended Sabatier principle suggests that the optimum hydrogen-evolution catalyst binds adsorbed hydrogen weakly rather than thermoneutrally. This notion is corroborated by the fact that the most active hydrogen-evolution catalysts, Pt, MoS2, or Mo2C, indeed bind hydrogen weakly by about (100–200) meV rather than thermoneutrally at zero overpotential.

The oxygen evolution reaction (OER) is often designated as the enigma in water electrolysis because the development of active and stable OER catalysts is a challenging and formidable task. While ab initio theory in the density functional theory approximation initially focused on the mechanistic description via the OH, O, and OOH adsorbates, in recent years the lattice oxygen evolution reaction (LOER) mechanism attracted increasing attention, given that the LOER is seen as the main reason for catalyst instability under anodic potential conditions. The present concept article critically analyzes the LOER and indicates pitfalls in the interpretation of this mechanistic pathway. A method to assess the energetics of the LOER in relation to conventional OER mechanisms by the compilation of free-energy diagrams is introduced, which may contribute to enhance our understanding of the competing LOER and OER on the atomic scale. Further works are urgently needed to comprehend the interrelationship for the evolution of gaseous oxygen from the electrolyte or the crystal lattice.

The development of oxygen evolution reaction (OER) electrocatalysts has been spurred by thermodynamic considerations on the free-energy landscape. It is a common paradigm that the optimum thermodynamic free-energy landscape reveals a symmetric shape in that all reaction intermediates are stabilized at the equilibrium potential of the reaction. However, so far, no OER electrocatalyst has been reported that corresponds to the thermodynamic ideal because of the presence of a linear scaling relationship. Therefore, the common approach builds on the breaking of the scaling relations to establish a catalytic material that is close to the symmetric picture, yet, with minor successes. Relating to the simple two-electron hydrogen evolution reaction (HER), it was recently reported that the optimum thermodynamic free-energy landscape reveals an asymmetric shape rather than a symmetric form as soon as overpotential and kinetic effects are factored in the analysis. This finding motivates scrutinizing whether the symmetric free-energy landscape as the thermodynamic ideal in the OER is justified. Transferring the knowledge from the HER to the OER results in the introduction of the electrochemical-step asymmetry index (ESAI), representing the concept of the asymmetric thermodynamic free-energy diagram. By comparing the ESAI to the symmetric picture in terms of the electrochemical-step symmetry index (ESSI), it is demonstrated herein that the asymmetric rather than the symmetric free-energy landscape corresponds to the thermodynamic ideal. This outcome suggests changing the mindset when applying the concept of free-energy diagrams for the discovery of OER materials by heuristic material-screening techniques.

The formation of gaseous chlorine within chlor-alkali electrolysis is accompanied by a selectivity problem, as the evolution of gaseous oxygen constitutes a detrimental side reaction in the same potential range. As such, the development of electrode materials with high selectivity toward the chlorine evolution reaction is of particular importance to the chemical industry. Insight into the elementary reaction steps is ultimately required to comprehend chlorine selectivity on a molecular level. Commonly, linear scaling relationships are analyzed by the construction of a volcano plot, using the binding energy of oxygen, ΔEO, as a descriptor in the analysis. The present article reinvestigates the selectivity problem of the competing chlorine and oxygen evolution reactions by applying a different strategy compared to previous literature studies. On the one hand, a unifying material-screening framework that, besides binding energies, also includes the applied overpotential, kinetics, and the electrochemical-step symmetry index is used to comprehend trends in this selectivity issue for transition-metal oxide-based electrodes. On the other hand, the free-energy difference between the adsorbed oxygen and adsorbed hydroxide, ΔG2, rather than ΔEO is used as a descriptor in the analysis. It is demonstrated that the formation of the OCl adsorbate within the chlorine evolution reaction inherently limits chlorine selectivity, whereas, in the optimum case, the formation of the Cl intermediate can result in significantly higher chlorine selectivity. This finding is used to derive the design criteria for highly selective chlorine evolution electrocatalysts, which can be used in the future to search for potential electrode compositions by material-screening techniques.

The application of proton exchange membrane electrolyzers in practice to produce gaseous hydrogen as energy vector is majorly hampered by the sluggish oxygen evolution reaction (OER) at the anode. On the atomic scale, a scaling relation between the OH and OOH intermediates has been recognized as main limitation for the development of highly active OER catalysts. Breaking scaling relation is considered as a universal remedy to obtain OER materials with enhanced electrocatalytic activity. While it is a well-accepted paradigm that the optimum OER catalyst reveals a symmetric thermodynamic free-energy landscape, recently, it was suggested that the thermodynamic ideal may correspond to a free-energy landscape with asymmetric shape, allowing thermoneutral stabilization of the key intermediate at the target overpotential. In the present manuscript, we analyze breaking scaling relation in the OER to the symmetric and asymmetric thermodynamic free-energy landscapes by statistical methods at different applied overpotentials. Our analysis reveals that breaking scaling relation to the asymmetric rather than to the symmetric picture is statistically more significant as soon as an overpotential is applied, calling for a change in mindset when thermodynamic considerations are used for catalyst optimization.

Extended Tafel plots at various temperatures for an electrocatalyzed reaction and (possibly) its reversed reaction on single-crystalline model electrodes allow for constructing the (essential part of the) free energy surface, in particular the free energies of the transition states (TS). Free energies of the reaction intermediates (RIs) including the chemical nature of active surface sites (S) are hardly accessible to experiment and need therefore to be taken from constrained ab initio thermodynamics calculations. The compact compilation of experimental kinetic data in the form of a free energy diagram enables a critical assessment and validation of theoretical free energy landscapes based on first-principles kinetics. For three prototypical electrocatalyzed reactions, namely the chlorine evolution reaction (CER) and oxygen evolution reaction (OER) over RuO2(110) as well as hydrogen evolution reaction (HER) on Pt(111), we exemplify this universal approach and discuss potential benefits for theoretical mod...

Ultrathin single-crystalline RuO 2(110) films supported on Ru(0001) are employed as model electrodes to extract kinetic information about the industrially important chlorine evolution reaction (CER) in a 5M concentrated NaCl solution under well-defined electrochemical conditions and variable temperatures. A combination of chronoamperometry (CA) and online electrochemical mass spectrometry (OLEMS) experiments provides insight into the selectivity issue: At pH = 0.9, the CER dominates over oxygen evolution, whereas at pH = 3.5, oxygen evolution and other parasitic side reactions contribute mostly to the total current density. From temperature-dependent CA data for pH = 0.9, we determine the apparent free activation energy of the CER over RuO 2(110) to be 0.91 eV, which compares reasonably well with the theoretical value of 0.79 eV derived from first-principles microkinetics. The experimentally determined apparent free activation energy of 0.91 eV is considered as a benchmark for assessing future improved theoretical modeling from first principles.

Efficient drug delivery to malignant cells in the human organism requires the application of drug-delivery systems (DDS) that consist of several building blocks, such as a biomolecule to bind the drug as well as a carrier for transport. In the present study, we investigate a potential DDS component for the cytostatic doxorubicin (DOX) that consists of a gold nanoparticle (Au-NP) and a short drug-binding peptide sequence. Combining molecular dynamics simulations with density functional theory calculations allows resolving the adsorption configurations of DOX at simulated physiological conditions as well as the interaction energies between the building blocks of the DDS. Interestingly, it turns out that the task of the Au-NP is not limited to being a passive carrier. The nanoparticle is directly involved in the stabilization of the drug by intercalating DOX together with a tryptophan residue from the peptide. Another favored adsorption configuration corresponds to an intercalation complex of DOX with two tryptophan residues, reminiscent of the intercalation of DOX between DNA bases. The insights gained in the present study allow deriving general conclusions about the surface chemistry of DOX: its tendency to intercalate seems not to depend on its π-stacking partners (organic or inorganic), as long as they can be properly arranged around the drug. Hence, DOX may be stabilized sufficiently during its delivery if intercalation within the carrier moieties is possible. This finding may assist the construction of a more complex DDS for DOX in the future, for which the investigated drug-peptide-nanoparticle conjugate may serve as a prototype.