Constant potential energetics of metallic and semiconducting electrodes: A benchmark study on 2D materials.

Grand-canonical (GC) constant-potential methods within an implicit solvent environment provide a general approach to compute the potential-dependent energetics at electrified solid-liquid interfaces with first-principles density-functional theory. Here, we use a mindfully chosen set of 27 isostructural 2D metal halides MX2 to analyze the variation of this energetics when the electronic structure changes from metallic to semiconducting and insulating state. Apart from expectable changes due to the opening up of the electronic bandgap, the calculations also show an increasing sensitivity to the numerical Brillouin zone integration and electronic smearing, which imposes computational burdens in practice. We rationalize these findings within the picture of the total interfacial capacitance arising from a series connection of the electrochemical double-layer capacitance and the so-called quantum capacitance resulting from the filling of electronic states inside the electrode. For metals, the electrochemical double-layer capacitance dominates at all potentials, and the entire potential drop takes place in the electrolyte. For semiconductors, the potential drop occurs instead fully or partially inside the electrode at potentials within or just outside the bandgap. For 2D semiconductors, the increased sensitivity to numerical parameters then results from the concomitantly increased contribution of the quantum capacitance that is harder to converge. Fortunately, this understanding motivates a simple extension of the CHE + DL approximation for metals, which provides the approximate GC energetics of 2D semiconductors using only quantities that can be obtained from computationally undemanding calculations at the point of zero charge and a generic double-layer capacitance.

Ab Initio-Based Modeling of Thermodynamic Cyclic Voltammograms: A Benchmark Study on Ag(100) in Bromide Solutions.

Experimental cyclic voltammograms (CVs) measured in the slow scan rate limit can be entirely described in terms of the thermodynamic equilibrium quantities of the electrified solid-liquid interface. They correspondingly serve as an important benchmark for the quality of first-principles calculations of interfacial thermodynamics. Here, we investigate the partially drastic approximations made presently in computationally efficient calculations for the well-defined showcase of an Ag(100) model electrode in Br-containing electrolytes, where the nontrivial part of the CV stems from the electrosorption of Br ions. We specifically study the entanglement of common approximations in the treatment of solvation and field effects, as well as in the way macroscopic averages of the two key quantities, namely, the potential-dependent adsorbate coverage and electrosorption valency, are derived from the first-principles energetics. We demonstrate that the combination of energetics obtained within an implicit solvation model and a perturbative second order account of capacitive double layer effects with a constant-potential grand-canonical Monte Carlo sampling of the adsorbate layer provides an accurate description of the experimental CV. However, our analysis also shows that error cancellation at lower levels of theory may equally lead to good descriptions even though key underlying physics such as the disorder-order transition of the Br adlayer at increasing coverages is inadequately treated.

Cavity formation at metal-water interfaces.

The free energy cost of forming a cavity in a solvent is a fundamental concept in rationalizing the solvation of molecules and ions. A detailed understanding of the factors governing cavity formation in bulk solutions has inter alia enabled the formulation of models that account for this contribution in coarse-grained implicit solvation methods. Here, we employ classical molecular dynamics simulations and multistate Bennett acceptance ratio free energy sampling to systematically study cavity formation at a wide range of metal-water interfaces. We demonstrate that the obtained size- and position-dependence of cavitation energies can be fully rationalized by a geometric Gibbs model, which considers that the creation of the metal-cavity interface necessarily involves the removal of interfacial solvent. This so-called competitive adsorption effect introduces a substrate dependence to the interfacial cavity formation energy that is missed in existing bulk cavitation models. Using expressions from scaled particle theory, this substrate dependence is quantitatively reproduced by the Gibbs model through simple linear relations with the adsorption energy of a single water molecule. Besides providing a better general understanding of interfacial solvation, this paves the way for the derivation and efficient parametrization of more accurate interface-aware implicit solvation models needed for reliable high-throughput calculations toward improved electrocatalysts.

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.

Electroreduction of CO2 in a Non-aqueous Electrolyte-The Generic Role of Acetonitrile.

Transition metal carbides, especially Mo2C, are praised to be efficient electrocatalysts to reduce CO2 to valuable hydrocarbons. However, on Mo2C in an aqueous electrolyte, exclusively the competing hydrogen evolution reaction takes place, and this discrepancy to theory was traced back to the formation of a thin oxide layer at the electrode surface. Here, we study the CO2 reduction activity at Mo2C in a non-aqueous electrolyte to avoid such passivation and to determine products and the CO2 reduction reaction pathway. We find a tendency of CO2 to reduce to carbon monoxide. This process is inevitably coupled with the decomposition of acetonitrile to a 3-aminocrotonitrile anion. Furthermore, a unique behavior of the non-aqueous acetonitrile electrolyte is found, where the electrolyte, instead of the electrocatalyst, governs the catalytic selectivity of the CO2 reduction. This is evidenced by in situ electrochemical infrared spectroscopy on different electrocatalysts as well as by density functional theory calculations.

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.

Static and dynamic water structures at interfaces: A case study with focus on Pt(111).

An accurate atomistic treatment of aqueous solid-liquid interfaces necessitates the explicit description of interfacial water ideally via ab initio molecular dynamics simulations. Many applications, however, still rely on static interfacial water models, e.g., for the computation of (electro)chemical reaction barriers and focus on a single, prototypical structure. In this work, we systematically study the relation between density functional theory-derived static and dynamic interfacial water models with specific focus on the water-Pt(111) interface. We first introduce a general construction protocol for static 2D water layers on any substrate, which we apply to the low index surfaces of Pt. Subsequently, we compare these with structures from a broad selection of reference works based on the Smooth Overlap of Atomic Positions descriptor. The analysis reveals some structural overlap between static and dynamic water ensembles; however, static structures tend to overemphasize the in-plane hydrogen bonding network. This feature is especially pronounced for the widely used low-temperature hexagonal ice-like structure. In addition, a complex relation between structure, work function, and adsorption energy is observed, which suggests that the concentration on single, static water models might introduce systematic biases that are likely reduced by averaging over consistently created structural ensembles, as introduced here.

Thermodynamic cyclic voltammograms: peak positions and shapes.

Based on a mean-field description of thermodynamic cyclic voltammograms (CVs), we analyze here in full generality, how CV peak positions and shapes are related to the underlying interface energetics, in particular when also including electrostatic double layer (DL) effects. We show in particular, how non-Nernstian behaviour is related to capacitive DL charging, and how this relates to common adsorbate-centered interpretations such as a changed adsorption energetics due to dipole-field interactions and the electrosorption valency - the number of exchanged electrons upon electrosorption per adsorbate. Using Ag(111) in halide-containing solutions as test case, we demonstrate that DL effects can introduce peak shifts that are already explained by rationalizing the interaction of isolated adsorbates with the interfacial fields, while alterations of the peak shape are mainly driven by the coverage-dependence of the adsorbate dipoles. In addition, we analyze in detail how changing the experimental conditions such as the ion concentrations in the solvent but also of the background electrolyte can affect the CV peaks via their impact on the potential drop in the DL and the DL capacitance, respectively. These results suggest new routes to analyze experimental CVs and use of those for a detailed assessment of the accuracy of atomistic models of electrified interfaces e.g. with and without explicitly treated interfacial solvent and/or approximate implicit solvent models.

Thermodynamic Cyclic Voltammograms Based on Ab Initio Calculations: Ag(111) in Halide-Containing Solutions.

Cyclic voltammograms (CVs) are a central experimental tool for assessing the structure and activity of electrochemical interfaces. Based on a mean-field ansatz for the interface energetics under applied potential conditions, we here derive an ab initio thermodynamics approach to efficiently simulate thermodynamic CVs. All unknown parameters are determined from density functional theory (DFT) calculations coupled to an implicit solvent model. For the showcased CVs of Ag(111) electrodes in halide-anion-containing solutions, these simulations demonstrate the relevance of double-layer contributions to explain experimentally observed differences in peak shapes over the halide series. Only the appropriate account of interfacial charging allows us to capture the differences in equilibrium coverage and total electronic surface charge that cause the varying peak shapes. As a case in point, this analysis demonstrates that prominent features in CVs do not only derive from changes in adsorbate structure or coverage but can also be related to variations of the electrosorption valency. Such double-layer effects are proportional to adsorbate-induced changes in the work function and/or interfacial capacitance. They are thus especially pronounced for electronegative halides and other adsorbates that affect these interface properties. In addition, the analysis allows us to draw conclusions on how the possible inaccuracy of implicit solvation models can indirectly affect the accuracy of other predicted quantities such as CVs.

Grand canonical simulations of electrochemical interfaces in implicit solvation models.

We discuss grand canonical simulations based on density-functional theory to study the thermodynamic properties of electrochemical interfaces of metallic electrodes in aqueous environments. Water is represented using implicit solvation, here via the self-consistent continuum solvation (SCCS) model, providing a charge-density dependent dielectric boundary. The electrochemical double layer is accounted for in terms of a phenomenological continuum description. It is shown that the experimental potentials of zero charge and interfacial capacitances can be reproduced for an optimized SCCS parameter set [ρmin = 0.0013, ρmax = 0.010 25]. By performing a detailed derivation and analysis of the interface energetics for selected electrochemical systems, we are able to relate the widely used approach of the computational hydrogen electrode (CHE) to a general grand canonical description of electrified interfaces. In particular, charge-neutral CHE results are shown to be an upper-boundary estimate for the grand canonical interfacial free energies. In order to demonstrate the differences between the CHE and full grand canonical calculations, we study the pristine (100), (110), and (111) surfaces for Pt, Au, Cu, and Ag, and H or Cl electrosorbed on Pt. The calculations support the known surface reconstructions in the aqueous solution for Pt and Au. Furthermore, the predicted potential-pH dependence of proton coverage, surface charge, and interfacial pseudocapacitance for Pt is found to be in close agreement with experimental or other theoretical data as well as the predicted equilibrium shapes for Pt nanoparticles. Finally, Cl is found to interact more strongly than H with the interfacial fields, leading to significantly altered interface energetics and structure upon explicit application of an electrode potential. This work underscores the strengths and eventual limits of the CHE approach and might guide further understanding of the thermodynamics of electrified interfaces.

Solvent-Aware Interfaces in Continuum Solvation.

Continuum models to handle solvent and electrolyte effects in an effective way have a long tradition in quantum-chemistry simulations and are nowadays also being introduced in computational condensed-matter and materials simulations. A key ingredient of continuum models is the choice of the solute cavity, i.e., the definition of the sharp or smooth boundary between the regions of space occupied by the quantum-mechanical (QM) system and the continuum embedding environment. The cavity, which should really reflect the region of space accessible to the degrees of freedom of the environmental components (the solvent), is usually defined by an exclusion approach in terms of the degrees of freedom of the system (the solute), typically, the atomic position of the QM system or its electronic density. Although most of the solute-based approaches developed lead to models with comparable and high accuracy when applied to small organic molecules, they can introduce significant artifacts when complex systems are considered. As an example, condensed-matter simulations often deal with supports that present open structures, i.e., low-density materials that have regions of space in which a continuum environment could penetrate, while a real solvent would not be able to. Similarly, unphysical pockets of continuum solvent may appear in systems featuring multiple molecular components, e.g., when dealing with hybrid QM/continuum approaches to solvation that involve introducing explicit solvent molecules around the solvated system. Here, we introduce a solvent-aware approach to eliminate the unphysical effects where regions of space smaller than the size of a single solvent molecule could still be filled with a continuum environment. We do this by defining a smoothly varying solute cavity that overcomes several of the limitations of straightforward solute-based definitions. This new approach applies to any smooth local definition of the continuum interface, it being based on the electronic density or the atomic positions of the QM system. It produces boundaries that are continuously differentiable with respect to the QM degrees of freedom, leading to accurate forces and/or Kohn-Sham potentials. The additional parameters involved in the solvent-aware interfaces can be set according to geometrical principles or can be converged to improve accuracy in complex multicomponent systems. Benchmarks on semiconductor substrates and on explicit water substrates confirm the flexibility and the accuracy of the approach and provide a general set of parameters for condensed-matter systems featuring open structures and/or explicit liquid components.

Potential-induced nanoclustering of metallic catalysts during electrochemical CO2 reduction.

In catalysis science stability is as crucial as activity and selectivity. Understanding the degradation pathways occurring during operation and developing mitigation strategies will eventually improve catalyst design, thus facilitating the translation of basic science to technological applications. Herein, we reveal the unique and general degradation mechanism of metallic nanocatalysts during electrochemical CO2 reduction, exemplified by different sized copper nanocubes. We follow their morphological evolution during operation and correlate it with the electrocatalytic performance. In contrast with the most common coalescence and dissolution/precipitation mechanisms, we find a potential-driven nanoclustering to be the predominant degradation pathway. Grand-potential density functional theory calculations confirm the role of the negative potential applied to reduce CO2 as the main driving force for the clustering. This study offers a novel outlook on future investigations of stability and degradation reaction mechanisms of nanocatalysts in electrochemical CO2 reduction and, more generally, in electroreduction reactions.

Semiconductor-metal transition induced by nanoscale stabilization.

The structure of tin (Sn) nanoparticles as function of size and temperature has been studied using density functional theory and thermodynamic considerations. It is known that bulk Sn undergoes a transition from the semiconducting α-phase to the metallic ß-phase at temperatures higher than 13.2 °C under atmospheric pressure. Here we show that, independent of temperature, Sn nanoparticles smaller than 8 nm diameter always crystallize in the ß-phase structure in thermodynamic equilibrium, and up to a size of 40 nm of the Sn nanoparticles this metallic phase is stable at all reasonable ambient temperatures (≳-40 °C). The transition to the metallic phase is caused by nanoscale stabilization due to the lower surface energies of the ß phase. This study suggests that the atomic structure and conductivity of nanostructured Sn anodes can change dramatically with size and temperature. This finding has implication for understanding the performance of future Li-based batteries since Sn nanostructures are considered as one of the most promising anode materials, but the mechanism of nanoscale stabilization might be used as a design strategy for other materials.

Polar surface energies of iono-covalent materials: implications of a charge-transfer model tested on Li2FeSiO4 surfaces.

The ionic compounds that are used as electrode materials in Li-based rechargeable batteries can exhibit polar surfaces that in general have high surface energies. We derive an analytical estimate for the surface energy of such polar surfaces assuming charge redistribution as a polarity compensating mechanism. The polar contribution to the converged surface energy is found to be proportional to the bandgap multiplied by the surface charge necessary to compensate for the depolarization field, and some higher order correction terms that depend on the specific surface. Other features, such as convergence behavior, coincide with published results. General conclusions are drawn on how to perform polar surface energy calculations in a slab configuration and upper boundaries of "purely" polar surface energies are estimated. Furthermore, we compare these findings with results obtained in a density functional theory study of Li(2)FeSiO(4) surfaces. We show that typical polar features are observed and provide a decomposition of surface energies into polar and local bond-cutting contributions for 29 different surfaces. We show that the model is able to explain subtle differences of GGA and GGA+U surface energy calculations.

E(1)(A) electronic band gap in wurtzite InAs nanowires studied by resonant Raman scattering.

We report on resonant Raman experiments carried out on wurtzite InAs nanowires. Resonant conditions have been obtained by tuning either the excitation energy or the band gap through external high pressure at fixed excitation energy. A complete azimuthal study of the Raman spectra with two laser excitation lines (2.41 and 1.92 eV) has also been performed on a single wire. The measured E2(H) mode resonance indicates that the E1(A) gap is about 2.4 eV, which is considerably reduced with respect to the zinc-blende InAs E1 gap. These findings confirm recent theoretical calculations of crystal phase induced bandstructure modifications.