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The oxygen evolution reaction has an important role in many alternative-energy schemes because it supplies the protons and electrons required for converting renewable electricity into chemical fuels 1 – 3 . Electrocatalysts accelerate the reaction by facilitating the required electron transfer 4 , as well as the formation and rupture of chemical bonds 5 . This involvement in fundamentally different processes results in complex electrochemical kinetics that can be challenging to understand and control, and that typically depends exponentially on overpotential 1 , 2 , 6 , 7 . Such behaviour emerges when the applied bias drives the reaction in line with the phenomenological Butler–Volmer theory, which focuses on electron transfer 8 , enabling the use of Tafel analysis to gain mechanistic insight under quasi-equilibrium 9 – 11 or steady-state assumptions 12 . However, the charging of catalyst surfaces under bias also affects bond formation and rupture 13 – 15 , the effect of which on the electrocatalytic rate is not accounted for by the phenomenological Tafel analysis 8 and is often unknown. Here we report pulse voltammetry and operando X-ray absorption spectroscopy measurements on iridium oxide to show that the applied bias does not act directly on the reaction coordinate, but affects the electrocatalytically generated current through charge accumulation in the catalyst. We find that the activation free energy decreases linearly with the amount of oxidative charge stored, and show that this relationship underlies electrocatalytic performance and can be evaluated using measurement and computation. We anticipate that these findings and our methodology will help to better understand other electrocatalytic materials and design systems with improved performance. Spectroscopic studies and theoretical calculations of the electrocatalytic oxygen evolution reaction establish that reaction rates depend on the amount of charge stored in the electrocatalyst, and not on the applied potential.

Solar-to-fuel energy conversion relies on the invention of efficient catalysts enabling water oxidation through low-energy pathways. Our aerobic life is based on this strategy, mastered by the natural Photosystem II enzyme, using a tetranuclear Mn–oxo complex as oxygen evolving center. Within artificial devices, water can be oxidized efficiently on tailored metal-oxide surfaces such as RuO ₂. The quest for catalyst optimization in vitro is plagued by the elusive description of the active sites on bulk oxides. Although molecular mimics of the natural catalyst have been proposed, they generally suffer from oxidative degradation under multiturnover regime. Here we investigate a nano-sized Ru ₄–polyoxometalate standing as an efficient artificial catalyst featuring a totally inorganic molecular structure with enhanced stability. Experimental and computational evidence reported herein indicates that this is a unique molecular species mimicking oxygenic RuO ₂ surfaces. Ru ₄–polyoxometalate bridges the gap between homogeneous and heterogeneous water oxidation catalysis, leading to a breakthrough system. Density functional theory calculations show that the catalytic efficiency stems from the optimal distribution of the free energy cost to form reaction intermediates, in analogy with metal-oxide catalysts, thus providing a unifying picture for the two realms of water oxidation catalysis. These correlations among the mechanism of reaction, thermodynamic efficiency, and local structure of the active sites provide the key guidelines for the rational design of superior molecular catalysts and composite materials designed with a bottom–up approach and atomic control.

Water oxidation is efficiently catalyzed by several Ru-based polyoxometalate (POM) molecular catalysts differing in the number, local atomistic environment and oxidation state of the Ru sites. We employ density functional theory calculations to rationalize the dependency of the reaction overpotential on the main structural and electronic molecular properties. In particular, we compare the thermodynamics of the water oxidation cycle for single-site Ru-POM and multiple-site Ru4-POM complexes. For the Ru-POM case, we also investigate the reaction free energy as a function of the Ru oxidation state. We find that the overpotential of these molecular catalysts is primarily determined by the oxidation state of the metal center and is minimum for Ru(IV). In solution, the number of active sites is shown to play a minor role on the reaction energetics. The results are rationalized and discussed in terms of the local structure around the active sites and of the electrostatic screening due to the molecular structure or the solvent.

The oxygen evolution reaction (OER) plays a crucial role in (photo)electrochemical devices that use renewable energy to produce synthetic fuels. Recent measurements on semiconducting oxides have found a power law dependence of the OER rate on surface hole density, suggesting a multihole mechanism. In this study, using transient photocurrent measurements, density functional theory simulations and microkinetic modelling, we have uncovered the origin of this behaviour in haematite. We show here that the OER rate has a third-order dependence on the surface hole density. We propose a mechanism wherein the reaction proceeds by accumulating oxidizing equivalents through a sequence of one-electron oxidations of surface hydroxy groups. The key O–O bond formation step occurs by the dissociative chemisorption of a hydroxide ion involving three oxyl sites. At variance with the case of metallic oxides, the activation energy of this step is weakly dependent on the surface hole coverage, leading to the observed power law. The multihole mechanism of the oxygen evolution reaction on semiconductor electrodes has been hard to elucidate due to a lack of atomic-scale structural characterization of the material interface. Using pulse voltammetry and simulations of α-Fe 2 O 3 photoanodes, this study predicts the chemical origin of the third-order rate dependence on holes.

A Correction to this paper has been published: https://doi.org/10.1038/s41586-020-03101-x.

The oxygen evolution reaction has an important role in many alternative-energy schemes because it supplies the protons and electrons required for converting renewable electricity into chemical fuels.sup.1-3. Electrocatalysts accelerate the reaction by facilitating the required electron transfer.sup.4, as well as the formation and rupture of chemical bonds.sup.5. This involvement in fundamentally different processes results in complex electrochemical kinetics that can be challenging to understand and control, and that typically depends exponentially on overpotential.sup.1,2,6,7. Such behaviour emerges when the applied bias drives the reaction in line with the phenomenological Butler-Volmer theory, which focuses on electron transfer.sup.8, enabling the use of Tafel analysis to gain mechanistic insight under quasi-equilibrium.sup.9-11 or steady-state assumptions.sup.12. However, the charging of catalyst surfaces under bias also affects bond formation and rupture.sup.13-15, the effect of which on the electrocatalytic rate is not accounted for by the phenomenological Tafel analysis.sup.8 and is often unknown. Here we report pulse voltammetry and operando X-ray absorption spectroscopy measurements on iridium oxide to show that the applied bias does not act directly on the reaction coordinate, but affects the electrocatalytically generated current through charge accumulation in the catalyst. We find that the activation free energy decreases linearly with the amount of oxidative charge stored, and show that this relationship underlies electrocatalytic performance and can be evaluated using measurement and computation. We anticipate that these findings and our methodology will help to better understand other electrocatalytic materials and design systems with improved performance.

In this thesis a novel approach for simulating electronic transport in nanoscale structures is introduced. We consider an open quantum system (the electrons of structure) accelerated by an external electromotive force and dissipating energy through inelastic scattering with a heat bath (phonons) acting on the electrons. This method can be regarded as a quantum-mechanical extension of the semi-classical Boltzmann transport equation. We use periodic boundary conditions and employ Density Functional Theory to recast the many-particle problem in an effective single-particle mean-field problem. By explicitly treating the dissipation in the electrodes, the behavior of the potential is an outcome of our method, at variance with the scattering approaches based on the Landauer formalism. We study the self-consistent steady-state solution, analyzing the out-of-equilibrium electron distribution, the electrical characteristics, the behavior of the self-consistent potential and the density of states of the system. We apply the method to the study of electronic transport in several molecular devices, consisting of small organic molecules or atomic wires sandwiched between gold surfaces. For gold wires we recover the experimental evidence that transport in short wires is ballistic, independent of the length of the wire and with conductance of one quantum. In benzene-1,4-dithiol we find that the delocalization of the frontier orbitals of the molecule is responsible for the high value of conductance and that, by inserting methylene groups to decouple the sulfur atoms from the carbon ring, the current is reduced, in agreement with the experimental measurements. We study the effect a geometrical distortion in a molecular device, namely the relative rotation of the carbon rings in a biphenyl-4,4'-dithiol molecule. We find that the reduced coupling between π orbitals of the rings induced by the rotation leads to a reduction of the conductance and that this behavior is captured by a simple two level model. Finally the transport properties of alkanethiol monolayers are analyzed by means of the local density of states at the Fermi energy: we find an exponential dependence of the current on the length of the chain, in quantitative agreement with the corresponding experiments.

This chapter contains sections titled: Introduction Predicting Surface Structures and Phase Transitions Surface Phase Diagrams from Ab Initio Atomistic Thermodynamics Catalysis and Diffusion from Ab Initio Kinetic Monte Carlo Simulations Summary References

Recent experiments on model catalysts have shown that Ag-Cu alloys have improved selectivity with respect to pure silver for ethylene epoxidation. In this paper we review our first-principles investigations on the (111) surface of this alloy and present new findings on other low index surfaces. We find that, for every surface orientation, the presence of oxygen leads to copper segregation to the surface. Considering the alloy to be in equilibrium with an oxygen atmosphere and accounting for the effect of temperature and pressure, we compute the surface free energy and study the stability of several surface structures. Investigating the dependence of the surface free energy on the surface composition, we construct the phase diagram of the alloy for every surface orientation. Around the temperature, pressure and composition of interest for practical applications, we find that a limited number of structures can be present, including a thin layer of copper oxide on top of the silver surface and copper-free structures. Different surface orientations show a very similar behavior and in particular a single layer with CuO stoichiometry, significantly distorted when compared to a layer of bulk CuO, has a wide range of stability for all orientations. Our results are consistent with, and help explain, recent experimental measurements.

In this paper we investigate by means of first-principles density functional theory calculations the (111) surface of the Ag-Cu alloy under varying conditions of pressure of the surrounding oxygen atmosphere and temperature. This alloy has been recently proposed as a catalyst with improved selectivity for ethylene epoxidation with respect to pure silver, the catalyst commonly used in industrial applications. Here we show that the presence of oxygen leads to copper segregation to the surface. Considering the surface free energy as a function of the surface composition, we construct the convex hull to investigate the stability of various surface structures. By including the dependence of the free surface energy on the oxygen chemical potential, we are able compute the phase diagram of the alloy as a function of temperature, pressure and surface composition. We find that, at temperature and pressure typically used in ethylene epoxidation, a number of structures can be present on the surface of the alloy, including clean Ag(111), thin layers of copper oxide and thick oxide-like structures. These results are consistent with, and help explain, recent experimental results.