The nanoscale structure of the Pt-water double layer under bias revealed

Revealing the molecular interplay of coverage, wettability, and capacitive response at the Pt(111)-water solution interface under bias

While electrified interfaces are crucial for electrocatalysis and corrosion, their molecular morphology remains largely unknown. Through highly realistic ab initio molecular dynamics simulations of the Pt(111)-water solution interface in reducing conditions, we reveal a deep interconnection among electrode coverage, wettability, capacitive response, and catalytic activity. We identify computationally the experimentally hypothesised states for adsorbed hydrogen on Pt, HUPD and HOPD, revealing their role in governing interfacial water reorientation and hydrogen evolution. The transition between these two H states with increasing potential, induces a shift from a hydrophobic to a hydrophilic interface and correlates with a change in the primary electrode screening mechanism. This results in a slope change in differential capacitance, marking the onset of the experimentally observed peak around the potential of zero charge. Our work produces crucial insights for advancing electrocatalytic energy conversion, developing deep understanding of electrified interfaces.

Electronic Response and Charge Inversion at Polarized Gold Electrode

We have studied polarized Au(100) and Au(111) electrodes immersed in electrolyte solution by implementing finite-field methods in density functional theory-based molecular dynamics simulations. This allows us to directly compute the Helmholtz capacitance of electric double layer by including both electronic and ionic degrees of freedom, and the results turn out to be in excellent agreement with experiments. It is found that the electronic response of Au electrode makes a crucial contribution to the high Helmholtz capacitance and the instantaneous adsorption of Cl can lead to a charge inversion on the anodic polarized Au(100) surface. These findings point out ways to improve popular semi-classical models for simulating electrified solid-liquid interfaces and to identify the nature of surface charges therein which are difficult to access in experiments.

How to Assess and Predict Electrical Double Layer Properties. Implications for Electrocatalysis

The electrical double layer (EDL) plays a central role in electrochemical energy systems, impacting charge transfer mechanisms and reaction rates. The fundamental importance of the EDL in interfacial electrochemistry has motivated researchers to develop theoretical and experimental approaches to assess EDL properties. In this contribution, we review recent progress in evaluating EDL characteristics such as the double-layer capacitance, highlighting some discrepancies between theory and experiment and discussing strategies for their reconciliation. We further discuss the merits and challenges of various experimental techniques and theoretical approaches having important implications for aqueous electrocatalysis. A strong emphasis is placed on the substantial impact of the electrode composition and structure and the electrolyte chemistry on the double-layer properties. In addition, we review the effects of temperature and pressure and compare solid-liquid interfaces to solid-solid interfaces.

Grand Canonical Ensemble Approaches in CP2K for Modeling Electrochemistry at Constant Electrode Potentials

In electrochemical experiments, the number of electrons of the electrode immersed in the electrolyte is usually variable. Additionally, the numbers of adsorbed substances on the surface of the electrode, the solvent molecules, and counter charge ions in the near-surface region can also vary. Treating electrochemical solid-liquid interfaces with the typical fixed electron number density functional theory (DFT) approach tends to be a challenge. This can be addressed by using grand canonical ensemble approaches. We present the implementation of two grand canonical ensemble approaches in the open-source computational chemistry software CP2K that go beyond the existing canonical ensemble paradigm. The first approach is based on implicit solvent models and explicit atomistic solute (electrode with/without adsorbed species) models, and includes two recent developments: (a) grand canonical self-consistent field (GC-SCF) method (J. Chem. Phys. 2017, 146, 114104) allowing the electron number of the system to fluctuate naturally and accordingly with the experimental electrode potential, (b) planar counter charge (J. Chem. Phys. 2019, 150, 041722, Phys. Rev. B 2003, 68, 245416) salt model completely screening the net charge of the electrode model. In contrast with previous studies, in our implementation, the work function (WF) (absolute electrode potential if the potential drop at the electrolyte-vacuum interface is omitted) is the constrained quantity during an SCF optimization instead of the Fermi energy. The chemical potential of electrons (negative WF) is a natural variable of the grand potential in the GC ensemble of electronic states, and this method can easily achieve stable SCF convergence and obtain an electronic structure that precisely corresponds to a user-specified WF. The second approach referred to as the GC DFT molecular dynamics (DFT-MD) simulation scheme (Phys. Rev. Lett. 2002, 88, 213002, J. Chem. Phys. 2005, 122, 234505, J. Am. Chem. Soc. 2004, 126 (12), 3928-3938) is based on fully explicit modeling the solvent molecules and the ions and is used to calculate the electron chemical potential corresponding to an equilibrium electrochemical half-reaction (M(n+m)+ + ne- ⇌ Mm+) which involves DFT-MD, by allowing the number of electrons to vary during the DFT-MD simulation process. This opens the way for forefront electrochemical calculations in CP2K for a broad range of systems.

Enabling Ab Initio Molecular Dynamics under Bias: The CP2K+SMEAGOL Interface for Integrating Density Functional Theory and Non-Equilibrium Green Functions

Density functional theory (DFT) combined with non-equilibrium Green's functions (NEGF) is a powerful approach to model quantum transport under external bias potentials at reasonable computational cost. In this work, we present a new interface between the popular mixed Gaussian/plane waves electronic structure package, CP2K, and the NEGF, code SMEAGOL, the most feature-rich implementation of DFT-NEGF available for CP2K to date. The CP2K+SMEAGOL interface includes the implementation of current induced forces. We verify this implementation for a variety of systems: an infinite 1D Au wire, a parallel-plate capacitor, and a Au-H2-Au junction. We find good agreement with SMEAGOL calculations performed with SIESTA for the same systems and with the example of a solvated Au wire demonstrating for the first time that DFT-NEGF can be used to perform molecular dynamics simulations under bias of large-scale condensed phase systems under realistic operating conditions.

Emerging Atomistic Modeling Methods for Heterogeneous Electrocatalysis

Heterogeneous electrocatalysis lies at the center of various technologies that could help enable a sustainable future. However, its complexity makes it challenging to accurately and efficiently model at an atomic level. Here, we review emerging atomistic methods to simulate the electrocatalytic interface with special attention devoted to the components/effects that have been challenging to model, such as solvation, electrolyte ions, electrode potential, reaction kinetics, and pH. Additionally, we review relevant computational spectroscopy methods. Then, we showcase several examples of applying these methods to understand and design catalysts relevant to green hydrogen. We also offer experimental views on how to bridge the gap between theory and experiments. Finally, we provide some perspectives on opportunities to advance the field.

Accelerating QM/MM simulations of electrochemical interfaces through machine learning of electronic charge densities

A crucial aspect in the simulation of electrochemical interfaces consists in treating the distribution of electronic charge of electrode materials that are put in contact with an electrolyte solution. Recently, it has been shown how a machine-learning method that specifically targets the electronic charge density, also known as SALTED, can be used to predict the long-range response of metal electrodes in model electrochemical cells. In this work, we provide a full integration of SALTED with MetalWalls, a program for performing classical simulations of electrochemical systems. We do so by deriving a spherical harmonics extension of the Ewald summation method, which allows us to efficiently compute the electric field originated by the predicted electrode charge distribution. We show how to use this method to drive the molecular dynamics of an aqueous electrolyte solution under the quantum electric field of a gold electrode, which is matched to the accuracy of density-functional theory. Notably, we find that the resulting atomic forces present a small error of the order of 1 meV/Å, demonstrating the great effectiveness of adopting an electron-density path in predicting the electrostatics of the system. Upon running the data-driven dynamics over about 3 ns, we observe qualitative differences in the interfacial distribution of the electrolyte with respect to the results of a classical simulation. By greatly accelerating quantum-mechanics/molecular-mechanics approaches applied to electrochemical systems, our method opens the door to nanosecond timescales in the accurate atomistic description of the electrical double layer.

Revealing Interface Polarization Effects on the Electrical Double Layer with Efficient Open Boundary Simulations under Potential Control

A major challenge in modeling interfacial processes in electrochemical (EC) devices is performing simulations at constant potential. This requires an open-boundary description of the electrons, so that they can enter and leave the computational cell. To enable realistic modeling of EC processes under potential control we have interfaced density functional theory with the hairy probe method in the weak coupling limit (Zauchner et al. Phys. Rev. B 2018, 97, 045116). Our implementation was systematically tested using simple parallel-plate capacitor models with pristine surfaces and a single layer of adsorbed water molecules. Remarkably, our code's efficiency is comparable with a standard DFT calculation. We reveal that local field effects at the electrical double layer induced by the change of applied potential can significantly affect the energies of chemical steps in heterogeneous electrocatalysis. Our results demonstrate the importance of an explicit modeling of the applied potential in a simulation and provide an efficient tool to control this critical parameter.

S.O.S: Shape, orientation, and size tune solvation in electrocatalysis

Current models to understand the reactivity of metal/aqueous interfaces in electrochemistry, e.g., volcano plots, are based on the adsorption free energies of reactants and products, which are often small hydrophobic molecules (such as in CO2 and N2 reduction). Calculations played a major role in the quantification and comprehension of these free energies in terms of the interactions that the reactive species form with the surface. However, solvation free energies also come into play in two ways: (i) by modulating the adsorption free energy together with solute-surface interactions, as the solute has to penetrate the water adlayer in contact with the surface and get partially desolvated (which costs free energy); (ii) by regulating transport across the interface, i.e., the free energy profile from the bulk to the interface, which is strongly non-monotonic due to the unique nature of metal/aqueous interfaces. Here, we use constant potential molecular dynamics to study the solvation contributions, and we uncover huge effects of the shape and orientation (on top of the already known size effect) of small hydrophobic and amphiphilic solutes on their adsorption free energy. We propose a minimal theoretical model, the S.O.S. model, that accounts for size, orientation, and shape effects. These novel aspects are rationalized by recasting the concepts at the base of the Lum-Chandler-Weeks theory of hydrophobic solvation (for small solutes in the so-called volume-dominated regime) into a layer-by-layer form, where the properties of each interfacial region close to the metal are explicitly taken into account.

Enhanced interfacial water dissociation on a hydrated iron porphyrin single-atom catalyst in graphene

Single Atom Catalysis (SAC) is an expanding field of heterogeneous catalysis in which single metallic atoms embedded in different materials catalyze a chemical reaction, but these new catalytic materials still lack fundamental understanding when used in electrochemical environments. Recent characterizations of non-noble metals like Fe deposited on N-doped graphitic materials have evidenced two types of Fe-N4 fourfold coordination, either of pyridine type or of porphyrin type. Here, we study these defects embedded in a graphene sheet and immersed in an explicit aqueous medium at the quantum level. While the Fe-pyridine SAC model is clear cut and widely studied, it is not the case for the Fe-porphyrin SAC that remains ill-defined, because of the necessary embedding of odd-membered rings in graphene. We first propose an atomistic model for the Fe-porphyrin SAC. Using spin-polarized ab initio molecular dynamics, we show that both Fe SACs spontaneously adsorb two interfacial water molecules from the solvent on opposite sides. Interestingly, we unveil a different catalytic reactivity of the two hydrated SAC motives: while the Fe-porphyrin defect eventually dissociates an adsorbed water molecule under a moderate external electric field, the Fe-pyridine defect does not convey water dissociation.

Ab initio study of water dissociation on a charged Pd(111) surface

The interactions between molecules and electrode surfaces play a key role in electrochemical processes and are a subject of extensive research, both experimental and theoretical. In this paper, we address the water dissociation reaction on a Pd(111) electrode surface, modeled as a slab embedded in an external electric field. We aim at unraveling the relationship between surface charge and zero-point energy in aiding or hindering this reaction. We calculate the energy barriers with dispersion-corrected density-functional theory and an efficient parallel implementation of the nudged-elastic-band method. We show that the lowest dissociation barrier and consequently the highest reaction rate take place when the field reaches a strength where two different geometries of the water molecule in the reactant state are equally stable. The zero-point energy contributions to this reaction, on the other hand, remain nearly constant across a wide range of electric field strengths, despite significant changes in the reactant state. Interestingly, we show that the application of electric fields that induce a negative charge on the surface can make nuclear tunneling more significant for these reactions.

Dynamically Formed Surfactant Assembly at the Electrified Electrode-Electrolyte Interface Boosting CO2 Electroreduction

Electrocatalytic reactions occur in the nanoscale space at the electrified electrode-electrolyte interface. It is well known that the electrode-electrolyte interface, also called as interfacial microenvironment, is difficult to investigate due to the interference of bulk electrolytes and its dynamic evolution in response to applied bias potential. Here, we employ electrochemical co-reduction of CO₂ and H₂O on commercial Ag electrodes as a model system, in conjunction with quaternary ammonium cationic surfactants as electrolyte additives. We probe bias-potential-driven dynamic response of the interfacial microenvironment as well as the mechanistic origin of catalytic selectivity. By virtue of comprehensive in situ vibrational spectroscopy, electrochemical impedance spectroscopy, and molecular dynamics simulations, it is revealed that the structure of surfactants is dynamically changed from a random distribution to a nearly ordered assembly with increasing bias potential. The nearly ordered surfactant assembly regulates the interfacial water environment by repelling isolated water and suppressing water orientation into an ordered structure as well as promotes CO₂ enrichment at the electrified interface. Eventually, the formed hydrophobic-aerophilic interface microenvironment reduces the activity of water dissociation and increases the selectivity of CO₂ electroreduction to CO. These results highlight the importance of regulating the interfacial microenvironment by organic additives as a means of boosting the electrochemical performance in electrosynthesis and beyond.

Realistic Modelling of Dynamics at Nanostructured Interfaces Relevant to Heterogeneous Catalysis

The focus of this short review is directed towards investigations of the dynamics of nanostructured metallic heterogeneous catalysts and the evolution of interfaces during reaction—namely, the metal–gas, metal–liquid, and metal–support interfaces. Indeed, it is of considerable interest to know how a metal catalyst surface responds to gas or liquid adsorption under reaction conditions, and how its structure and catalytic properties evolve as a function of its interaction with the support. This short review aims to offer the reader a birds-eye view of state-of-the-art methods that enable more realistic simulation of dynamical phenomena at nanostructured interfaces by exploiting resource-efficient methods and/or the development of computational hardware and software.

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.

Is the water/Pt(111) interface ordered at room temperature?

The structure of the water/Pt(111) interface has been a subject of debate over the past decades. Here, we report the results of a room temperature molecular dynamics study based on neural network potentials, which allow us to access long time scale simulations while retaining ab initio accuracy. We find that the water/Pt(111) interface is characterized by a double layer composed of a primary, strongly bound adsorption layer with a coverage of ∼0.15 ML, which is coupled to a secondary, weakly bound adsorption layer with a coverage of ∼0.58 ML. By studying the order of the primary adsorption layer, we find that there is an effective repulsion between the adsorbed water molecules, which gives rise to a dynamically changing, semi-ordered interfacial structure, where the water molecules in the primary adsorption layer are distributed homogeneously across the interface, forming frequent hydrogen bonds to water molecules in the secondary adsorption layer. We further show that these conclusions are beyond the time scales accessible to ab initio molecular dynamics.

The role of hydrophobic hydration in the free energy of chemical reactions at the gold/water interface: Size and position effects

Metal/water interfaces catalyze a large variety of chemical reactions, which often involve small hydrophobic molecules. In the present theoretical study, we show that hydrophobic hydration at the Au(100)/water interface actively contributes to the reaction free energy by up to several hundreds of meV. This occurs either in adsorption/desorption reaction steps, where the vertical distance from the surface changes in going from reactants to products, or in addition and elimination reaction steps, where two small reactants merge into a larger product and vice versa. We find that size and position effects cannot be captured by treating them as independent variables. Instead, their simultaneous evaluation allows us to map the important contributions, and we provide examples of their combinations for which interfacial reactions can be either favored or disfavored. By taking a N₂ and a CO₂ reduction pathway as test cases, we show that explicitly considering hydrophobic effects is important for the selectivity and rate of these relevant interfacial processes.