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.

Heterogeneous Catalyst as a Functional Substrate Governing the Shape of Electrochemical Precipitates in Oxygen-Fueled Rechargeable Batteries.

Lithium-oxygen batteries have the potential to become the most eminent solution for future energy storage with their theoretical energy density exceeding all existing batteries. However, the insulating and insoluble discharge product (lithium peroxide; Li2O2) impairs practical application. Conventional catalyst designs based on the electronic structure and interfacial charge transfer descriptors have not been able to overcome these limitations due to Li2O2. Herein, we revisit the role of heterogeneous catalysts as substrates to regulate Li2O2 growth and the formation of solid/solid reaction interfaces. We demonstrate that controlled solid/solid interfacial structure design is a critical performance parameter beyond the inherent electronic structure. In particular, the Cu2O substrate in this study induces a homogeneous deposition of Pd atoms, which leads to well-controlled growth of Li2O2 resolving mass and charge transport limits (i.e., the bottleneck of oxygen reduction/evolution reactions), thus improving reversibility, capacity, and durability of the cells by dissipating electrochemical and mechanical stress. We thus verified the essential role of solid/solid interfaces to regulate the nucleation and growth process of Li2O2 in lithium-oxygen batteries.

An implicit electrolyte model for plane wave density functional theory exhibiting nonlinear response and a nonlocal cavity definition.

We have developed and implemented an implicit electrolyte model in the Vienna Ab initio Simulation Package (VASP) that includes nonlinear dielectric and ionic responses as well as a nonlocal definition of the cavities defining the spatial regions where these responses can occur. The implementation into the existing VASPsol code is numerically efficient and exhibits robust convergence, requiring computational effort only slightly higher than the original linear polarizable continuum model. The nonlinear + nonlocal model is able to reproduce the characteristic "double hump" shape observed experimentally for the differential capacitance of an electrified metal interface while preventing "leakage" of the electrolyte into regions of space too small to contain a single water molecule or solvated ion. The model also gives a reasonable prediction of molecular solvation free energies as well as the self-ionization free energy of water and the absolute electron chemical potential of the standard hydrogen electrode. All of this, combined with the additional ability to run constant potential density functional theory calculations, should enable the routine computation of activation barriers for electrocatalytic processes.

A Two-Dimensional MoS2 Catalysis Transistor by Solid-State Ion Gating Manipulation and Adjustment (SIGMA).

A variety of methods including tuning chemical compositions, structures, crystallinity, defects and strain, and electrochemical intercalation have been demonstrated to enhance the catalytic activity. However, none of these tuning methods provide direct dynamical control during catalytic reactions. Here we propose a new method to tune the activity of catalysts through solid-state ion gating manipulation and adjustment (SIGMA) using a catalysis transistor. SIGMA can electrostatically dope the surface of catalysts with a high electron concentration over 5 × 1013 cm-2 and thus modulate both the chemical potential of the reaction intermediates and their electrical conductivity. The hydrogen evolution reaction (HER) on both pristine and defective MoS2 were investigated as model reactions. Our theoretical and experimental results show that the overpotential at 10 mA/cm2 and Tafel slope can be in situ, continuously, dynamically, and reversibly tuned over 100 mV and around 100 mV/dec, respectively.

Practical Considerations for Continuum Models Applied to Surface Electrochemistry.

Modelling the electrolyte at the electrochemical interface remains a major challenge in ab initio simulations of charge transfer processes at surfaces. Recently, the development of hybrid polarizable continuum models/ab initio models have allowed for the treatment of solvation and electrolyte charge in a computationally efficient way. However, challenges remain in its application. Recent literature has reported that large cell heights are required to reach convergence, which presents a serious computational cost. Furthermore, calculations of reaction energetics require costly iterations to tune the surface charge to the desired potential. In this work, we present a simple capacitor model of the interface that illuminates how to circumvent both of these challenges. We derive a correction to the energy for finite cell heights to obtain the large cell energies at no additional computational expense. We furthermore demonstrate that the reaction energetics determined at constant charge are easily mapped to those at constant potential, which eliminates the need to apply iterative schemes to tune the system to a constant potential. These developments together represent more than an order of magnitude reduction of the computational overhead required for the application of polarizable continuum models to surface electrochemistry.

Generalized molecular solvation in non-aqueous solutions by a single parameter implicit solvation scheme.

In computer simulations of solvation effects on chemical reactions, continuum modeling techniques regain popularity as a way to efficiently circumvent an otherwise costly sampling of solvent degrees of freedom. As effective techniques, such implicit solvation models always depend on a number of parameters that need to be determined earlier. In the past, the focus lay mostly on an accurate parametrization of water models. Yet, non-aqueous solvents have recently attracted increasing attention, in particular, for the design of battery materials. To this end, we present a systematic parametrization protocol for the Self-Consistent Continuum Solvation (SCCS) model resulting in optimized parameters for 67 non-aqueous solvents. Our parametrization is based on a collection of ≈6000 experimentally measured partition coefficients, which we collected in the Solv@TUM database presented here. The accuracy of our optimized SCCS model is comparable to the well-known universal continuum solvation model (SMx) family of methods, while relying on only a single fit parameter and thereby largely reducing statistical noise. Furthermore, slightly modifying the non-electrostatic terms of the model, we present the SCCS-P solvation model as a more accurate alternative, in particular, for aromatic solutes. Finally, we show that SCCS parameters can, to a good degree of accuracy, also be predicted for solvents outside the database using merely the dielectric bulk permittivity of the solvent of choice.

Transferable ionic parameters for first-principles Poisson-Boltzmann solvation calculations: Neutral solutes in aqueous monovalent salt solutions.

Implicit solvation calculations based on a Stern-layer corrected size-modified Poisson-Boltzmann (SMPB) model are an effective approach to capture electrolytic effects in first-principles electronic structure calculations. For a given salt solution, they require a range of ion-specific parameters, which describe the size of the dissolved ions as well as thickness and shape of the Stern layer. Out of this defined parameter space, we show that the Stern layer thickness expressed in terms of the solute's electron density and the resulting ionic cavity volume completely determine ion effects on the stability of neutral solutes. Using the efficient SMPB functionality of the full-potential density-functional theory package FHI-aims, we derive optimized such Stern layer parameters for neutral solutes in various aqueous monovalent electrolytes. The parametrization protocol relies on fitting to reference Setschenow coefficients that describe solvation free energy changes with ionic strength at low to medium concentrations. The availability of such data for NaCl solutions yields a highly predictive SMPB model that allows to recover the measured Setschenow coefficients with an accuracy that is comparable to prevalent quantitative regression models. Correspondingly derived SMPB parameters for other salts suffer from a much scarcer experimental data base but lead to Stern layer properties that follow a physically reasonable trend with ionic hydration numbers.

Elucidating Solvatochromic Shifts in Two-Dimensional Photocatalysts by Solving the Bethe-Salpeter Equation Coupled with Implicit Solvation Method.

Many studies have focused on tailoring the photophysical properties of two-dimensional (2D) materials for photocatalytic (PC) or photoelectrochemical (PEC) applications. To understand the optical properties of 2D materials in solution, we established a computational method that combined the Bethe-Salpeter equation (BSE) calculations with our GW-GPE method, allowing for GW/BSE-level calculations with implicit solvation described using the generalized Poisson equation (GPE). We applied this method to MoS2, phosphorene (PP), and g-C3N4 and found that when the solvent dielectric increased, it reduced the exciton binding energy and quasiparticle bandgap, resulting in almost no solvatochromic shift in the excitonic peaks of MoS2 and PP, which is consistent with previous experiments. However, our calculations predicted that the solvent dielectric had a significant impact on the excitonic properties of g-C3N4, exhibiting a large solvatochromic shift. We expect that our GW/BSE-GPE method will offer insights into the design of 2D materials for PC and PEC applications.

The importance of a charge transfer descriptor for screening potential CO2 reduction electrocatalysts.

It has been over twenty years since the linear scaling of reaction intermediate adsorption energies started to coin the fields of heterogeneous and electrocatalysis as a blessing and a curse at the same time. It has established the possibility to construct activity volcano plots as a function of a single or two readily accessible adsorption energies as descriptors, but also limited the maximal catalytic conversion rate. In this work, it is found that these established adsorption energy-based descriptor spaces are not applicable to electrochemistry, because they are lacking an important additional dimension, the potential of zero charge. This extra dimension arises from the interaction of the electric double layer with reaction intermediates which does not scale with adsorption energies. At the example of the electrochemical reduction of CO2 it is shown that the addition of this descriptor breaks the scaling relations, opening up a huge chemical space that is readily accessible via potential of zero charge-based material design. The potential of zero charge also explains product selectivity trends of electrochemical CO2 reduction in close agreement with reported experimental data highlighting its importance for electrocatalyst design.

Tuning the C1 /C2 Selectivity of Electrochemical CO2 Reduction on Cu-CeO2 Nanorods by Oxidation State Control.

Ceria (CeO2 ) is one of the most extensively used rare earth oxides. Recently, it has been used as a support material for metal catalysts for electrochemical energy conversion. However, to date, the nature of metal/CeO2 interfaces and their impact on electrochemical processes remains unclear. Here, a Cu-CeO2 nanorod electrochemical CO2 reduction catalyst is presented. Using operando analysis and computational techniques, it is found that, on the application of a reductive electrochemical potential, Cu undergoes an abrupt change in solubility in the ceria matrix converting from less stable randomly dissolved single atomic Cu2+ ions to (Cu0 ,Cu1+ ) nanoclusters. Unlike single atomic Cu, which produces C1 products as the main product during electrochemical CO2 reduction, the coexistence of (Cu0 ,Cu1+ ) clusters lowers the energy barrier for C-C coupling and enables the selective production of C2+ hydrocarbons. As a result, the coexistence of (Cu0 ,Cu1+ ) in the clusters at the Cu-ceria interface results in a C2+ partial current density/unit Cu weight 27 times that of a corresponding Cu-carbon catalyst under the same conditions.

GW Quasiparticle Energies and Bandgaps of Two-Dimensional Materials Immersed in Water.

Computational simulations have become of major interest to screen potential photocatalysts for optimal band edge positions which straddle the redox potentials. Unfortunately, these methods suffer from a difficulty in resolving the dynamic solvent response on the band edge positions. We have developed a computational method based on the GW approximation coupled with an implicit solvation model that solves a generalized Poisson equation (GPE), that is, GW-GPE. Using GW-GPE, we have investigated the band edge locations of (quasi) 2D materials immersed in water and found a good agreement with experimental data. We identify two contributions of the solvent effect, termed a "polarization-field effect" and an "environmental screening effect", which are found to be highly sensitive to the atomic and charge distribution of the 2D materials. We believe that the GW-GPE scheme can pave the way to predict band edge positions in solvents, enabling design of 2D material-based photocatalysts and energy systems.

Strained Pt(221) Facet in a PtCo@Pt-Rich Catalyst Boosts Oxygen Reduction and Hydrogen Evolution Activity.

Over the last years, the development of highly active and durable Pt-based electrocatalysts has been identified as the main target for a large-scale industrial application of fuel cells. In this work, we make a significant step ahead in this direction by preparing a high-performance electrocatalyst and suggesting new structure-activity design concepts which could shape the future of oxygen reduction reaction (ORR) catalyst design. For this, we present a new one-dimensional nanowire catalyst consisting of a L10 ordered intermetallic PtCo alloy core and compressively strained high-index facets in the Pt-rich shell. We find the nanoscale PtCo catalyst to provide an excellent turnover for the ORR and hydrogen evolution reaction (HER), which we explain from high-resolution transmission electron microscopy and density functional theory calculations to be due to the high ratio of Pt(221) facets. These facets include highly active ORR and HER sites surprisingly on the terraces which are activated by a combination of sub-surface Co-induced high Miller index-related strain and oxygen coverage on the step sites. The low dimensionality of the catalyst provides a cost-efficient use of Pt. In addition, the high catalytic activity and durability are found during both half-cell and proton exchange membrane fuel cell (PEMFC) operations for both ORR and HER. We believe the revealed design concepts for generating active sites on the Pt-based catalyst can open up a new pathway toward the development of high-performance cathode catalysts for PEMFCs and other catalytic systems.

On the importance of the electric double layer structure in aqueous electrocatalysis.

To design electrochemical interfaces for efficient electric-chemical energy interconversion, it is critical to reveal the electric double layer (EDL) structure and relate it with electrochemical activity; nonetheless, this has been a long-standing challenge. Of particular, no molecular-level theories have fully explained the characteristic two peaks arising in the potential-dependence of the EDL capacitance, which is sensitively dependent on the EDL structure. We herein demonstrate that our first-principles-based molecular simulation reproduces the experimental capacitance peaks. The origin of two peaks emerging at anodic and cathodic potentials is unveiled to be an electrosorption of ions and a structural phase transition, respectively. We further find a cation complexation gradually modifies the EDL structure and the field strength, which linearly scales the carbon dioxide reduction activity. This study deciphers the complex structural response of the EDL and highlights its catalytic importance, which bridges the mechanistic gap between the EDL structure and electrocatalysis.

A unifying mechanism for cation effect modulating C1 and C2 productions from CO2 electroreduction.

Electrocatalysis, whose reaction venue locates at the catalyst-electrolyte interface, is controlled by the electron transfer across the electric double layer, envisaging a mechanistic link between the electron transfer rate and the electric double layer structure. A fine example is in the CO2 reduction reaction, of which rate shows a strong dependence on the alkali metal cation (M+) identity, but there is yet to be a unified molecular picture for that. Using quantum-mechanics-based atom-scale simulation, we herein scrutinize the M+-coupling capability to possible intermediates, and establish H+- and M+-associated ET mechanisms for CH4 and CO/C2H4 formations, respectively. These theoretical scenarios are successfully underpinned by Nernstian shifts of polarization curves with the H+ or M+ concentrations and the first-order kinetics of CO/C2H4 formation on the electrode surface charge density. Our finding further rationalizes the merit of using Nafion-coated electrode for enhanced C2 production in terms of enhanced surface charge density.

Tunable Product Selectivity in Electrochemical CO2 Reduction on Well-Mixed Ni-Cu Alloys.

Electrochemical reduction of CO2 on copper-based catalysts has become a promising strategy to mitigate greenhouse gas emissions and gain valuable chemicals and fuels. Unfortunately, however, the generally low product selectivity of the process decreases the industrial competitiveness compared to the established large-scale chemical processes. Here, we present random solid solution Cu1-xNix alloy catalysts that, due to their full miscibility, enable a systematic modulation of adsorption energies. In particular, we find that these catalysts lead to an increase of hydrogen evolution with the Ni content, which correlates with a significant increase of the selectivity for methane formation relative to C2 products such as ethylene and ethanol. From experimental and theoretical insights, we find the increased hydrogen atom coverage to facilitate Langmuir-Hinshelwood-like hydrogenation of surface intermediates, giving an impressive almost 2 orders of magnitude increase in the CH4 to C2H4 + C2H5OH selectivity on Cu0.87Ni0.13 at -300 mA cm-2. This study provides important insights and design concepts for the tunability of product selectivity for electrochemical CO2 reduction that will help to pave the way toward industrially competitive electrocatalyst materials.

Selective electrochemical reduction of nitric oxide to hydroxylamine by atomically dispersed iron catalyst.

Electrocatalytic conversion of nitrogen oxides to value-added chemicals is a promising strategy for mitigating the human-caused unbalance of the global nitrogen-cycle, but controlling product selectivity remains a great challenge. Here we show iron-nitrogen-doped carbon as an efficient and durable electrocatalyst for selective nitric oxide reduction into hydroxylamine. Using in operando spectroscopic techniques, the catalytic site is identified as isolated ferrous moieties, at which the rate for hydroxylamine production increases in a super-Nernstian way upon pH decrease. Computational multiscale modelling attributes the origin of unconventional pH dependence to the redox active (non-innocent) property of NO. This makes the rate-limiting NO adsorbate state more sensitive to surface charge which varies with the pH-dependent overpotential. Guided by these fundamental insights, we achieve a Faradaic efficiency of 71% and an unprecedented production rate of 215 µmol cm-2 h-1 at a short-circuit mode in a flow-type fuel cell without significant catalytic deactivation over 50 h operation.

Double layer charging driven carbon dioxide adsorption limits the rate of electrochemical carbon dioxide reduction on Gold.

Electrochemical CO[Formula: see text] reduction is a potential route to the sustainable production of valuable fuels and chemicals. Here, we perform CO[Formula: see text] reduction experiments on Gold at neutral to acidic pH values to elucidate the long-standing controversy surrounding the rate-limiting step. We find the CO production rate to be invariant with pH on a Standard Hydrogen Electrode scale and conclude that it is limited by the CO[Formula: see text] adsorption step. We present a new multi-scale modeling scheme that integrates ab initio reaction kinetics with mass transport simulations, explicitly considering the charged electric double layer. The model reproduces the experimental CO polarization curve and reveals the rate-limiting step to be *COOH to *CO at low overpotentials, CO[Formula: see text] adsorption at intermediate ones, and CO[Formula: see text] mass transport at high overpotentials. Finally, we show the Tafel slope to arise from the electrostatic interaction between the dipole of *CO[Formula: see text] and the interfacial field. This work highlights the importance of surface charging for electrochemical kinetics and mass transport.

Unified Approach to Implicit and Explicit Solvent Simulations of Electrochemical Reaction Energetics.

One of the major open challenges in ab initio simulations of the electrochemical interface is the determination of electrochemical barriers under a constant driving force. Existing methods to do so include extrapolation techniques based on fully explicit treatments of the electrolyte, as well as implicit solvent models which allow for a continuous variation in electrolyte charge. Emerging hybrid continuum models have the potential to revolutionize the field, since they account for the electrolyte with little computational cost while retaining some explicit electrolyte, representing a "best of both worlds" method. In this work, we present a unified approach to determine reaction energetics from fully explicit, implicit, and hybrid treatments of the electrolyte based on a new multicapacitor model of the electrochemical interface. A given electrode potential can be achieved by a variety of interfacial structures; a crucial insight from this work is that the effective surface charge gives a good proxy of the local potential, the true driving force of electrochemical processes. In contrast, we show that the traditionally considered work function gives rise to multivalued functions depending on the simulation cell size. Furthermore, we show that the reaction energetics are largely insensitive to the countercharge distribution chosen in hybrid implicit/explicit models, which means that any of the myriad implicit electrolyte models can be equivalently applied. This work thus paves the way for the accurate treatment of ab initio reaction energetics of general surface electrochemical processes using both implicit and explicit electrolytes.

pH effects on the electrochemical reduction of CO(2) towards C2 products on stepped copper.

We present a microkinetic model for CO(2) reduction (CO(2)R) on Cu(211) towards C2 products, based on energetics estimated from an explicit solvent model. We show that the differences in both Tafel slopes and pH dependence for C1 vs C2 activity arise from differences in their multi-step mechanisms. We find the depletion in C2 products observed at high overpotential and high pH to arise from the 2nd order dependence of C-C coupling on CO coverage, which decreases due to competition from the C1 pathway. We further demonstrate that CO(2) reduction at a fixed pH yield similar activities, due to the facile kinetics for CO2 reduction to CO on Cu, which suggests C2 products to be favored for CO2R under alkaline conditions. The mechanistic insights of this work elucidate how reaction conditions can lead to significant enhancements in selectivity and activity towards higher value C2 products.

Function-Space-Based Solution Scheme for the Size-Modified Poisson-Boltzmann Equation in Full-Potential DFT.

The size-modified Poisson-Boltzmann (MPB) equation is an efficient implicit solvation model which also captures electrolytic solvent effects. It combines an account of the dielectric solvent response with a mean-field description of solvated finite-sized ions. We present a general solution scheme for the MPB equation based on a fast function-space-oriented Newton method and a Green's function preconditioned iterative linear solver. In contrast to popular multigrid solvers, this approach allows us to fully exploit specialized integration grids and optimized integration schemes. We describe a corresponding numerically efficient implementation for the full-potential density-functional theory (DFT) code FHI-aims. We show that together with an additional Stern layer correction the DFT+MPB approach can describe the mean activity coefficient of a KCl aqueous solution over a wide range of concentrations. The high sensitivity of the calculated activity coefficient on the employed ionic parameters thereby suggests to use extensively tabulated experimental activity coefficients of salt solutions for a systematic parametrization protocol.