Implicit Solvation Methods for Catalysis at Electrified Interfaces

Cation Effects on the Adsorbed Intermediates of CO2 Electroreduction Are Systematic and Predictable

The electrode-electrolyte interface, and in particular the nature of the cation, has considerable effects on the activity and product selectivity of the electrochemical reduction of CO2. Therefore, to improve the electrocatalysis of this challenging reaction, it is paramount to ascertain whether cation effects on adsorbed intermediates are systematic. Here, DFT calculations are used to show that the effects of K+, Na+, and Mg2+, on single carbon CO2 reduction intermediates can either be stabilizing or destabilizing depending on the metal and the adsorbate. Because systematic trends are observed, cation effects can be accurately predicted in simple terms for a wide variety of metals, cations and adsorbed species. These results are then applied to the reduction of CO2 to CO on four different catalytic surfaces (Au, Ag, Cu, Pd) and activation of weak-binding metals is consistently observed by virtue of the stabilization of the key intermediate *COOH.

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.

On the Thermodynamic Equivalence of Grand Canonical, Infinite-Size, and Capacitor-Based Models in First-Principle Electrochemistry

First principles-based computational and theoretical methods are constantly evolving trying to overcome the many obstacles towards a comprehensive understanding of electrochemical processes on an atomistic level. One of the major challenges has been the determination of reaction energetics under a constant potential. Here, a theoretical framework was proposed applying standard electronic structure methods and extrapolating to the infinite-cell size limit where reactions do not alter the potential. Today, electronically grand canonical modifications to electronic structure methods, holding the potential constant by varying the number of electrons in a finite simulation cell, become increasingly popular. In this perspective, we show that these two schemes are thermodynamically equivalent. Further, we link these methods to capacitive models of the interface, in the limit that the capacitance of the charging components (whether continuum or atomistic) are equal and invariant along the reaction pathway. We benchmark the three approaches with an example of alkali cation adsorption on Pt(111) showing that all three approaches converge in the cases of Li, Na and K. For Cs, however, strong deviation from the ideal conditions leads to a spread in the respective results. We discuss the latter by highlighting the cases of broken equivalence and assumptions among the approaches.

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.

Soft-sphere continuum solvation models for nonaqueous solvents

Solvation effects profoundly influence the characteristics and behavior of chemical systems in liquid solutions. The interaction between solute and solvent molecules intricately impacts solubility, reactivity, stability, and various chemical processes. Continuum solvation models gained prominence in quantum chemistry by implicitly capturing these interactions and enabling efficient investigations of diverse chemical systems in solution. In comparison, continuum solvation models in condensed matter simulation are very recent. Among these, the self-consistent continuum solvation (SCCS) and the soft-sphere continuum solvation models (SSCS) have been among the first to be successfully parameterized and extended to model periodic systems in aqueous solutions and electrolytes. As most continuum approaches, these models depend on a number of parameters that are linked to experimental or theoretical properties of the solvent, or that can be tuned based on reference data. Here, we present a systematic parameterization of the SSCS model for over 100 nonaqueous solvents. We validate the model's efficacy across diverse solvent environments by leveraging experimental solvation-free energies and partition coefficients from comprehensive databases. The average root means square error over all the solvents was calculated as 0.85 kcal/mol which is below the chemical accuracy (1 kcal/mol). Similarly to what has been reported by Hille et al. (J. Chem. Phys. 2019, 150, 041710.) for the SCCS model, a single-parameter model accurately reproduces experimental solvation energies, showcasing the transferability and predictive power of these continuum approaches. Our findings underscore the potential for a unified approach to predict solvation properties, paving the way for enhanced computational studies across various chemical environments.

Comparative analysis of surface phase diagrams in aqueous environment: Implicit vs explicit solvation models

Identifying the stable surface phases under a given electrochemical conditions serves as the basis for studying the atomistic mechanism of reactions at solid/water interfaces. In this work, we systematically compare the performance of the two main approaches that are used to capture the impact of an aqueous environment, implicit and explicit solvent, on surface energies and phase diagrams. As a model system, we consider the magnesium/water interface with (i) Ca substitution and (ii) proton and hydroxyl adsorption. We show that while the implicit solvent model is computationally very efficient, it suffers from two shortcomings. First, the choice of the implicit solvent parameters significantly influences the energy landscape in the vicinity of the surface. The default parameters benchmarked on solvation in water underestimate the energy of the dissolved Mg ion and lead to spontaneous dissolution of the surface atom, resulting in large differences in the surface energetics. Second, in systems containing a charged surface and a solvated ion, the implicit solvent model may not converge to the energetically stable ionic charge state but remain in a high-energy metastable configuration, representing the neutral charge state of the ion. When these two issues are addressed, surface phase diagrams that closely match the explicit water results can be obtained. This makes the implicit solvent model highly attractive as a computationally-efficient surrogate model to compute surface energies and phase diagrams.

Improving the reliability of machine learned potentials for modeling inhomogeneous liquids

The atomic-scale response of inhomogeneous fluids at interfaces and surrounding solute particles plays a critical role in governing chemical, electrochemical, and biological processes. Classical molecular dynamics simulations have been applied extensively to simulate the response of fluids to inhomogeneities directly, but are limited by the accuracy of the underlying interatomic potentials. Here, we use neural network potentials (NNPs) trained to ab initio simulations to accurately predict the inhomogeneous responses of two distinct fluids: liquid water and molten NaCl. Although NNPs can be readily trained to model complex bulk systems across a range of state points, we show that to appropriately model a fluid's response at an interface, relevant inhomogeneous configurations must be included in the training data. In order to sufficiently sample appropriate configurations of such inhomogeneous fluids, we develop protocols based on molecular dynamics simulations in the presence of external potentials. We demonstrate that NNPs trained on inhomogeneous fluid configurations can more accurately predict several key properties of fluids-including the density response, surface tension and size-dependent cavitation free energies-for liquid water and molten NaCl, compared to both empirical interatomic potentials and NNPs that are not trained on such inhomogeneous configurations. This work therefore provides a first demonstration and framework to extract the response of inhomogeneous fluids from first principles for classical density-functional treatment of fluids free from empirical potentials.

Hybrid quantum-classical polarizability model for single molecule biosensing

Optical whispering gallery mode biosensors are able to detect single molecules through effects of their polarizability. We address the factors that affect the polarizability of amino acids, which are the building blocks of life, via electronic structure theory. Amino acids are detected in aqueous environments, where their polarizability is different compared to the gasphase due to solvent effects. Solvent effects include structural changes, protonation and the local field enhancement through the solvent (water). We analyse the impact of these effects and find that all contribute to an increased effective polarizability in the solvent. We also address the excess polarizability relative to the displaced water cavity and develop a hybrid quantum-classical model that is in good agreement with self-consistent calculations. We apply our model to calculate the excess polarizability of 20 proteinogenic amino acids and determine the minimum resolution required to distinguish the different molecules and their ionised conformers based on their polarizability.

Activation Energies of Heterogeneous Electrocatalysis: A Theoretical Perspective

Heterogeneous electrochemistry is important for various applications. However, currently, there is limited information about activation energies. In this invited review, we review the challenges associated with calculating these activation energies. Specifically, we highlight three key difficulties in atomistic modeling: liquid structure, electrode potential, and electrolyte ions, along with state-of-the-art methods to address them. We aim to inspire more studies in the field of activation energies to better understand and design heterogeneous electrocatalysts.

GPAW: An open Python package for electronic structure calculations

We review the GPAW open-source Python package for electronic structure calculations. GPAW is based on the projector-augmented wave method and can solve the self-consistent density functional theory (DFT) equations using three different wave-function representations, namely real-space grids, plane waves, and numerical atomic orbitals. The three representations are complementary and mutually independent and can be connected by transformations via the real-space grid. This multi-basis feature renders GPAW highly versatile and unique among similar codes. By virtue of its modular structure, the GPAW code constitutes an ideal platform for the implementation of new features and methodologies. Moreover, it is well integrated with the Atomic Simulation Environment (ASE), providing a flexible and dynamic user interface. In addition to ground-state DFT calculations, GPAW supports many-body GW band structures, optical excitations from the Bethe-Salpeter Equation, variational calculations of excited states in molecules and solids via direct optimization, and real-time propagation of the Kohn-Sham equations within time-dependent DFT. A range of more advanced methods to describe magnetic excitations and non-collinear magnetism in solids are also now available. In addition, GPAW can calculate non-linear optical tensors of solids, charged crystal point defects, and much more. Recently, support for graphics processing unit (GPU) acceleration has been achieved with minor modifications to the GPAW code thanks to the CuPy library. We end the review with an outlook, describing some future plans for GPAW.

Understanding the Adiabatic Evolution of Surface States in Tetradymite Topological Insulators under Electrochemical Conditions

Nontrivial surface states in topological materials have emerged as exciting targets for surface chemistry research. In particular, topological insulators have been used as electrodes in electrocatalytic reactions. Herein, we investigate the robustness of the topological surface states and band topology under electrochemical conditions, specifically in the presence of an electric double layer. First-principles band structure calculations are performed on the electrified (111) surfaces of Bi2Te3, Bi2Se3, and Sb2Te3 using an implicit electrolyte model. Our results demonstrate the adiabatic evolution of the surface states upon surface charging. Under oxidizing potentials, the surface states are shifted upward in energy, preserving the Dirac point on the surface and the band inversion in the bulk. Conversely, under reduced potentials, hybridization is observed between the surface and bulk states, suggesting a likely breakdown of topological protection. The position of the Fermi level, which dictates the working states in catalytic reactions, should ideally be confined within the bulk bandgap. This requirement defines a potential window for the effective application of topological electrocatalysis.

Incorporating Electrolyte Correlation Effects into Variational Models of Electrochemical Interfaces

We propose a way for obtaining a classical free energy density functional for electrolytes based on a first-principle many-body partition function. Via a one-loop expansion, we include coulombic correlations beyond the conventional mean-field approximation. To examine electrochemical interfaces, we integrate the electrolyte free energy functional into a hybrid quantum-classical model. This scheme self-consistently couples electronic, ionic, and solvent degrees of freedom and incorporates electrolyte correlation effects. The derived free energy functional causes a correlation-induced enhancement in interfacial counterion density and leads to an overall increase in capacitance. This effect is partially compensated by a reduction of the dielectric permittivity of interfacial water. At larger surface charge densities, ion crowding at the interface stifles these correlation effects. While scientifically intriguing already at planar interfaces, we anticipate these correlation effects to play an essential role for electrolytes in nanoconfinement.

Recent developments and applications of reference interaction site model self-consistent field with constrained spatial electron density (RISM-SCF-cSED): A hybrid model of quantum chemistry and integral equation theory of molecular liquids

The significance of solvent effects in electronic structure calculations has long been noted, and various methods have been developed to consider this effect. The reference interaction site model self-consistent field with constrained spatial electron density (RISM-SCF-cSED) is a hybrid model that combines the integral equation theory of molecular liquids with quantum chemistry. This method can consider the statistically convergent solvent distribution at a significantly lower cost than molecular dynamics simulations. Because the RISM theory explicitly considers the solvent structure, it performs well for systems where hydrogen bonds are formed between the solute and solvent molecules, which is a challenge for continuum solvent models. Taking advantage of being founded on the variational principle, theoretical developments have been made in calculating various properties and incorporating electron correlation effects. In this review, we organize the theoretical aspects of RISM-SCF-cSED and its distinctions from other hybrid methods involving integral equation theories. Furthermore, we carefully present its progress in terms of theoretical developments and recent applications.

Multiscale Modeling of Aqueous Electric Double Layers

From the stability of colloidal suspensions to the charging of electrodes, electric double layers play a pivotal role in aqueous systems. The interactions between interfaces, water molecules, ions and other solutes making up the electrical double layer span length scales from Ångströms to micrometers and are notoriously complex. Therefore, explaining experimental observations in terms of the double layer's molecular structure has been a long-standing challenge in physical chemistry, yet recent advances in simulations techniques and computational power have led to tremendous progress. In particular, the past decades have seen the development of a multiscale theoretical framework based on the combination of quantum density functional theory, force-field based simulations and continuum theory. In this Review, we discuss these theoretical developments and make quantitative comparisons to experimental results from, among other techniques, sum-frequency generation, atomic-force microscopy, and electrokinetics. Starting from the vapor/water interface, we treat a range of qualitatively different types of surfaces, varying from soft to solid, from hydrophilic to hydrophobic, and from charged to uncharged.

Interfacial Electron Transfer in Chemical and Biological Transformation of Pollutants in Environmental Catalysis

Interfacial electron transfer (IET) is essential for chemical and biological transformation of pollutants, operative across diverse lengths and time scales. This Perspective presents an array of multiscale molecular simulation methodologies, supplemented by in situ monitoring and imaging techniques, serving as robust tools to decode IET enhancement mechanisms such as interface molecular modification, catalyst coordination mode, and atomic composition regulation. In addition, three IET-based pollutant transformation systems, an electrocatalytic oxidation system, a bioelectrochemical spatial coupling system, and an enzyme-inspired electrocatalytic system, were developed, demonstrating a high effect in transforming and degrading pollutants. To improve the effectiveness and scalability of IET-based strategies, the refinement of these systems is necessitated through rigorous research and theoretical exploration, particularly in the context of practical wastewater treatment scenarios. Future endeavors aim to elucidate the synergy between biological and chemical modules, edit the environmental functional microorganisms, and harness machine learning for designing advanced environmental catalysts to boost efficiency. This Perspective highlights the powerful potential of IET-focused environmental remediation strategies, emphasizing the critical role of interdisciplinary research in addressing the urgent global challenge of water pollution.

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.

Non-Noble Metal Incorporated Transition Metal Dichalcogenide Monolayers for Electrochemical CO2 Reduction: A First-Principles Study

Using non-noble metal atoms as catalysts is attractive for decreasing the cost of the CO2 reduction reaction (CO2RR). By screening first-row transition metals and noble metals through extensive first-principles calculations, non-noble Sc and Ti single atoms binding on vacancy-defected transition metal dichalcogenide (TMD) monolayers exhibit better catalytic performance and selectivity for electrochemical CO2RR than noble metal single atoms. The overpotentials of Sc and Ti atoms for the CO2RR can be reduced lower than 0.09 V after applying suitable biaxial tensile strains on vacancy-defected TMDs, which are approximately 1 order of magnitude lower than that of most reported metal atom catalysts. The vacancy defects of TMDs and charge transfer to metal atoms induced by tensile strain play a key role in improving the catalytic activity of non-noble metal single atoms. These results highlight a possible way to design new single atom catalysts for electrochemical CO2RR by utilizing the combination of non-noble metal atoms, defected TMDs, and strain engineering.

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.

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.

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.

The concerted proton-electron transfer mechanism of proton migration in the electrochemical interface

The proton migration in the electrochemical interface is a fundamental electrochemical processes in proton involved reactions. We find fractional electron transfer, which is inversely proportional to the distance between the proton and electrode, during the proton migration under constant potential. The electrical energy carried by the transferred charge facilitates the proton to overcome the chemical barrier in the migration pathway, which is accounting for more than half electrical energy in the proton involved reactions. Consequently, less charge transfer and energy exchange take place in the reduction process. Therefore, the proton migration in the electrochemical interface is an essential component of the electrochemical reaction in terms of electron transfer and energy conversation, and are worthy of more attention in the rational design and optimization of electrochemical systems.

Finding Infinities in Nanoconfined Geothermal Electrolyte Static Dielectric Properties and Implications on Ion Adsorption/Pairing

Infinities should naturally occur in the dielectric responses of ionic solutions relevant to many geochemical, energy storage, and electrochemical applications at a strictly zero frequency. Using molecular dynamics simulations cross-referenced with coarse-grained Monte Carlo models, using nanoslit pore models at hydrothermal conditions, and treating confined mobile charges as polarization, we demonstrate the far reaching consequences. The dielectric permittivity profile perpendicular to the slit (ϵ⊥(z)) increases, not decreases, with ionic concentration, unlike in the more widely studied megahertz-to-gigahertz frequency range. In confined electrolytes, the divergences in ϵ⊥(z) correctly describe crossovers between bulk- and surface-dominated dielectric behavior. Nanoconfinement at low ionic concentrations changes monovalent ion energetics by 1-2 kJ/mol, but no dielectric property studied so far is universally correlated to ion adsorption or ion-ion interactions. We caution that infinities signal violation of the "electrical insulator" dielectric assumption.

Automated, Consistent, and Even-Handed Selection of Active Orbital Spaces for Quantum Embedding

A widely used strategy to reduce the computational cost of quantum-chemical calculations is to partition the system into an active subsystem, which is the focus of the computational efforts, and an environment that is treated at a lower computational level. The system partitioning is mostly based on localized molecular orbitals. When reaction paths or energy differences are to be calculated, it is crucial to keep the orbital space consistent for all structures. Inconsistencies in orbital space can lead to unpredictable errors on the potential energy surface. While successful strategies to ensure this consistency have been established for organic and even metal-organic systems, these methods often fail for metal clusters or nanoparticles with a high density of near-degenerate and delocalized molecular orbitals. However, such systems are highly relevant for catalysis. Accurate yet feasible quantum-mechanical ab initio calculations are therefore highly desired. In this work, we present an approach based on the subsystem projected atomic orbital decomposition algorithm that allows us to ensure automated and consistent partitioning even for systems with delocalized and near-degenerate molecular orbitals and demonstrate the validity of this method for the binding energies of small molecules on transition-metal clusters.

Cation-π mechanism promotes the adsorption of humic acid on polystyrene nanoplastics to differently affect their aggregation: Evidence from experimental characterization and DFT calculation

Multiple water-chemistry factors determine nanoplastics aggregation and thus change their bioavailability and ecological risks in natural aquatic environments. However, the dominant factors and their interactive mechanisms remain elusive. In this study, polystyrene nanoplastics (PSNPs) showed greater colloidal stability in Li Lake water compared to ultrapure water. The RDA and PARAFAC results suggested that dissolved organic carbon, humic acid (HA) in particular, Ca2+, and pH are critical factors influencing PSNPs aggregation. Batch experiments showed that the critical coagulation concentration (CCC) of PSNPs was increased with pH increase; HA increased the CCC of PSNPs in NaCl by 2.6-fold but decreased that in CaCl2 by 1.8-fold. Moreover, cations increased the adsorption of HA on PSNPs. The DFT results suggested that HA-cations complexes (EAE = -1.10 eV and -0.51 eV for HA-Ca2+ and HA-Na+, respectively) but not HA alone (EAE = -0.33 eV) are the main scenarios for their adsorption on PSNPs, and a cation-π mechanism between PSNPs and HA-cations complexes dominates PSNPs aggregation in this scenario. The findings are significant for better understanding the environmental process and fate of nanoplastics in aquatic environments. ENVIRONMENTAL IMPLICATION: Nanoplastics are kinds of emerging contaminants. Nanoplastic aggregation determines their bioavailability and toxic risks to ecological health. Herein, the hydrodynamic sizes of PSNPs in local Li Lake water was tested and a redundancy analysis was performed to examine the key water-chemistry factors driving PSNPs aggregation. Moreover, the mechanisms in PSNPs aggregation driven by multiple dominant water-chemistry factors including cations, pH, and DOC were firstly unveiled by combining experimental characterization and theoretical computations. This work improves our understanding of the environmental fate of nanoplastics and provides a theoretical basis for the risk assessment and control of nanoplastics in real aquatic environments.

Thermodynamic and kinetic modeling of electrocatalytic reactions using a first-principles approach

The computational modeling of electrochemical interfaces and their applications in electrocatalysis has attracted great attention in recent years. While tremendous progress has been made in this area, however, the accurate atomistic descriptions at the electrode/electrolyte interfaces remain a great challenge. The Computational Hydrogen Electrode (CHE) method and continuum modeling of the solvent and electrolyte interactions form the basis for most of these methodological developments. Several posterior corrections have been added to the CHE method to improve its accuracy and widen its applications. The most recently developed grand canonical potential approaches with the embedded diffuse layer models have shown considerable improvement in defining interfacial interactions at electrode/electrolyte interfaces over the state-of-the-art computational models for electrocatalysis. In this Review, we present an overview of these different computational models developed over the years to quantitatively probe the thermodynamics and kinetics of electrochemical reactions in the presence of an electrified catalyst surface under various electrochemical environments. We begin our discussion by giving a brief picture of the different continuum solvation approaches, implemented within the ab initio method to effectively model the solvent and electrolyte interactions. Next, we present the thermodynamic and kinetic modeling approaches to determine the activity and stability of the electrocatalysts. A few applications to these approaches are also discussed. We conclude by giving an outlook on the different machine learning models that have been integrated with the thermodynamic approaches to improve their efficiency and widen their applicability.

Electric-Field-Induced Assembly of an Ionic Liquid-Water Interphase Enables Efficient Heavy Metal Electrosorption

Controlling ion desolvation, transport, and charge transfer at the electrode-electrolyte interface (EEI) is critical to enable the rational design of the efficient and selective separation of targeted heavy metals and the decontamination of industrial wastewater. The main challenge is to sufficiently resolve and interrogate the desolvation of solvated metal ions and their subsequent electroreduction at the EEI and establish pathways to modulate these intermediate steps to achieve efficient energy transfer for targeted reactive separations. Herein, we obtained a predictive understanding of modulating the desolvation and electrosorption of Pb2+ cations using the hydrophobic ionic liquid 1-ethyl-3-methylimidazolium chloride (EMIMCl) in aqueous electrolyte. We revealed the formation of a compact interphase layer consisting of EMIMCl-Pb complexes under an applied electric field using operando electrochemical Raman spectroscopy, atomic force microscopy, and electrochemical impedance spectroscopy measurements combined with classical molecular dynamics simulations. A lower negative potential was shown to result in the formation of a well-oriented layer with the positive imidazolium ring of EMIMCl lying perpendicular to the electrode and the hydrophobic alkyl chain extending into the bulk electrolyte. This oriented layer, which formed from a dilute concentration of EMIMCl added to the electrolyte, was demonstrated to facilitate desolvation of incoming solvated Pb2+ cations and decrease the charge transfer resistance for Pb electrodeposition, which has important implications for the selective removal of Pb from contaminated mixtures. Overall, our findings open up new opportunities to modulate ion desolvation using hydrophobic ionic liquids in aqueous electrolytes for efficient heavy-metal separation.

Theoretical understanding of the effect of specifically adsorbed halide anions on Cu-catalyzed CO2 electroreduction activity and product selectivity

Initial CO2 electroreduction into CO and its subsequent electroreduction pathways were selected to study the effect of specifically adsorbed halide anions X- (X = F, Cl, Br, I) on CO2 electroreduction activity and product selectivity at Cu(111)/H2O interfaces via DFT calculations. The calculated results show that the presence of halide anions can exert a notable effect on the CO2 adsorption characteristics and that chemically adsorbed CO2 molecules can be formed. Furthermore, the halide-anion-modified Cu(111)/H2O interfaces could significantly enhance the initial CO2 electroreduction into CO activity, which is regarded as the rate-determining step during CO2 electroreduction at clean Cu(111)/H2O interfaces. Analysis of the initial CO2 electroreduction and Volmer reaction pathways showed that the halide-anion-modified Cu(111)/H2O interfaces could suppress the HER and thus improve the CO2 electroreduction activity and product selectivity. It is speculated that the enhanced initial CO2 electroreduction activity at the F--, Cl--, Br--, and I--modified Cu(111)/H2O interfaces may originate from the decreased work functions and anion radical ·CO2- formations. Simultaneously, we concluded that dimer OCCO formations in the presence of halide anions were more favorable than CHO during CO electroreduction according to the order of I- > Br- > Cl- > F- and could result in the production of C2 product, suggesting an improved CO2 electroreduction product selectivity. The present analyses of electronic structure may explain the more favorable OCCO formations in the order of I- > Br- > Cl- > F-. The present understanding of this effect will provide an improved scientific guideline for the control of CO2 electroreduction pathways and design of more efficient electrocatalysts.

An Electrostatically Embedded QM/MM Scheme for Electrified Interfaces

Atomistic modeling of electrified interfaces remains a major issue for detailed insights in electrocatalysis, corrosion, electrodeposition, batteries, and related devices such as pseudocapacitors. In these domains, the use of grand-canonical density functional theory (GC-DFT) in combination with implicit solvation models has become popular. GC-DFT can be conveniently applied not only to metallic surfaces but also to semiconducting oxides and sulfides and is, furthermore, sufficiently robust to achieve a consistent description of reaction pathways. However, the accuracy of implicit solvation models for solvation effects at interfaces is in general unknown. One promising way to overcome the limitations of implicit solvents is going toward hybrid quantum mechanical (QM)/molecular mechanics (MM) models. For capturing the electrochemical potential dependence, the key quantity is the capacitance, i.e., the relation between the surface charge and the electrochemical potential. In order to retrieve the electrochemical potential from a QM/MM hybrid scheme, an electrostatic embedding is required. Furthermore, the charge of the surface and of the solvent regions has to be strictly opposite in order to consistently simulate charge-neutral unit cells in MM and in QM. To achieve such a QM/MM scheme, we present the implementation of electrostatic embedding in the VASP code. This scheme is broadly applicable to any neutral or charged solid/liquid interface. Here, we demonstrate its use in the context of GC-DFT for the hydrogen evolution reaction (HER) over a noble-metal-free electrocatalyst, MoS₂. We investigate the effect of electrostatic embedding compared to the implicit solvent model for three contrasting active sites on MoS₂: (i) the sulfur vacancy defect, which is rather apolar; (ii) a Mo antisite defect, where the active site is a surface bound highly polar OH group; and (iii) a reconstructed edge site, which is generally believed to be responsible for most of the catalytic activity. According to our results, the electrostatic embedding leads to almost indistinguishable results compared to the implicit solvent for the apolar system but has a significant effect on polar sites. This demonstrates the reliability of the hybrid QM/MM, electrostatically embedded solvation model for electrified interfaces.

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.

The ABC of Generalized Coordination Numbers and Their Use as a Descriptor in Electrocatalysis

The quest for enhanced electrocatalysts can be boosted by descriptor-based analyses. Because adsorption energies are the most common descriptors, electrocatalyst design is largely based on brute-force routines that comb materials databases until an energetic criterion is verified. In this review, it is shown that an alternative is provided by generalized coordination numbers (denoted by CN ¯ $\overline {{\rm{CN}}} $ or GCN), an inexpensive geometric descriptor for strained and unstrained transition metals and some alloys. CN ¯ $\overline {{\rm{CN}}} $ captures trends in adsorption energies on both extended surfaces and nanoparticles and is used to elaborate structure-sensitive electrocatalytic activity plots and selectivity maps. Importantly, CN ¯ $\overline {{\rm{CN}}} $ outlines the geometric configuration of the active sites, thereby enabling an atom-by-atom design, which is not possible using energetic descriptors. Specific examples for various adsorbates (e.g., *OH, *OOH, *CO, and *H), metals (e.g., Pt and Cu), and electrocatalytic reactions (e.g., O₂  reduction, H₂  evolution, CO oxidation, and reduction) are presented, and comparisons are made against other descriptors.

Theory of Anisotropic Metal Nanostructures

A significant challenge in the development of functional materials is understanding the growth and transformations of anisotropic colloidal metal nanocrystals. Theory and simulations can aid in the development and understanding of anisotropic nanocrystal syntheses. The focus of this review is on how results from first-principles calculations and classical techniques, such as Monte Carlo and molecular dynamics simulations, have been integrated into multiscale theoretical predictions useful in understanding shape-selective nanocrystal syntheses. Also, examples are discussed in which machine learning has been useful in this field. There are many areas at the frontier in condensed matter theory and simulation that are or could be beneficial in this area and these prospects for future progress are discussed.

Thickness-dependent catalytic activity of hydrogen evolution based on single atomic catalyst of Pt above MXene

Hydrogen as the cleanest energy carrier is a promising alternative renewable resource to fossil fuels. There is an ever-increasing interest in exploring efficient and cost-effective approaches of hydrogen production. Recent experiments have shown that single platinum atom immobilized on the metal vacancies of MXenes allows a high-efficient hydrogen evolution reaction (HER). Here usingab initiocalculations, we design a series of substitutional Pt-doped Ti_{n+ 1}C_nT_x(Ti_{n+ 1}C_nT_x-Pt_SA) with different thicknesses and terminations (n= 1, 2 and 3, T_x= O, F and OH), and investigate the quantum-confinement effect on the HER catalytic performance. Surprisingly, we reveal a strong thickness effect of the MXene layer on the HER performance. Among the various surface-terminated derivatives, Ti₂CF₂-Pt_SAand Ti₂CH₂O₂-Pt_SAare found to be the best HER catalysts with the change of Gibbs free energy ΔG_H*∼ 0 eV, complying with the thermoneutral condition. Theab initiomolecular dynamics simulations reveal that Ti₂CF₂-Pt_SAand Ti₂CH₂O₂-Pt_SApossess a good thermodynamic stability. The present work shows that the HER catalytic activity of the MXene is not solely governed by the local environment of the surface such as Pt single atom. We point out the critical role of thickness control and surface decoration of substrate in achieving a high-performance HER catalytical activity.

A Statistical Perspective on Microsolvation

The lack of a procedure to determine equilibrium thermodynamic properties of a small system interacting with a bath is frequently seen as a weakness of conventional statistical mechanics. A typical example for such a small system is a solute surrounded by an explicit solvation shell. One way to approach this problem is to enclose the small system of interest in a large bath of explicit solvent molecules, considerably larger than the system itself. The explicit inclusion of the solvent degrees of freedom is obviously limited by the available computational resources. A potential remedy to this problem is a microsolvation approach where only a few explicit solvent molecules are considered and surrounded by an implicit solvent bath. Still, the sampling of the solvent degrees of freedom is challenging with conventional grand canonical Monte Carlo methods, since no single chemical potential for the solvent molecules can be defined in the realm of small-system thermodynamics. In this work, a statistical thermodynamic model based on the grand canonical ensemble is proposed that avoids the conventional system size limitations and accurately characterizes the properties of the system of interest subject to the thermodynamic constraints of the bath. We extend an existing microsolvation approach to a generalized multibath "microstatistical" model and show that the previously derived approaches result as a limit of our model. The framework described here is universal and we validate our method numerically for a Lennard-Jones model fluid.

Comparing Ab Initio Molecular Dynamics and a Semiclassical Grand Canonical Scheme for the Electric Double Layer of the Pt(111)/Water Interface

The theoretical modeling of metal/water interfaces centers on an appropriate configuration of the electric double layer (EDL) under grand canonical conditions. In principle, ab initio molecular dynamics (AIMD) simulations would be the appropriate choice for treating the competing water-water and water-metal interactions and explicitly considering the atomic and electronic degrees of freedom. However, this approach only allows simulations of relatively small canonical ensembles over a limited period (shorter than 100 ps). On the other hand, computationally efficient semiclassical approaches can treat the EDL model based on a grand canonical scheme by averaging the microscopic details. Thus, an improved description of the EDL can be obtained by combining AIMD simulations and semiclassical methods based on a grand canonical scheme. By taking the Pt(111)/water interface as an example, we compare these approaches in terms of the electric field, water configuration, and double-layer capacitance. Furthermore, we discuss how the combined merits of the approaches can contribute to advances in EDL theory.

Dielectric Properties of Nanoconfined Water from Ab Initio Thermopotentiostat Molecular Dynamics

We discuss how to include our recently proposed thermopotentiostat technique [Deissenbeck et al. Phys. Rev. Lett. 2021, 126, 136803] into any existing ab initio molecular dynamics (AIMD) package. Using thermopotentiostat AIMD simulations in the canonical NVTΦ ensemble at a constant electrode potential, we compute the polarization bound charge and dielectric response of interfacial water from first principles.

Density-Potential Functional Theory of Electrochemical Double Layers: Calibration on the Ag(111)-KPF6 System and Parametric Analysis

The density-potential functional theory (DPFT) of electrochemical double layer (EDL) is upgraded by adopting (generalized) gradient approximations for kinetic, exchange, and correlation functionals of metal electrons. A new numerical scheme that is more stable and converges faster is proposed to solve the DPFT model. The DPFT model is calibrated with existing differential double-layer capacitance (C_dl) data of the EDL at Ag(111)-KPF₆ aqueous interface at five concentrations at room temperature. Metal electronic effects are essential to explain why the two peaks of the camel-shaped C_dl curves are almost symmetric in spite of the size difference of the hydrated cations and anions. A systematic parametric analysis is then conducted in terms of key EDL properties, including the potential of zero charge and the differential capacitance. The parametric analysis, on the one hand, elucidates how quantum mechanical behaviors of metal electrons as well as interactions between metal electrons and the electrolyte solution impact the EDL properties and, on the other hand, identifies key parameters of the DPFT model, which should be calibrated using first-principles calculations and/or advanced experiments in the future.

Materials Screening by the Descriptor G max(η): The Free-Energy Span Model in Electrocatalysis

To move from fossil-based energy resources to a society based on renewables, electrode materials free of precious noble metals are required to efficiently catalyze electrochemical processes in fuel cells, batteries, or electrolyzers. Materials screening operating at minimal computational cost is a powerful method to assess the performance of potential electrode compositions based on heuristic concepts. While the thermodynamic overpotential in combination with the volcano concept refers to the most popular descriptor-based analysis in the literature, this notion cannot reproduce experimental trends reasonably well. About two years ago, the concept of G _max(η), based on the idea of the free-energy span model, has been proposed as a universal approach for the screening of electrocatalysts. In contrast to other available descriptor-based methods, G _max(η) factors overpotential and kinetic effects by a dedicated evacuation scheme of adsorption free energies into an analysis of trends. In the present perspective, we discuss the application of G _max(η) to different electrocatalytic processes, including the oxygen evolution and reduction reactions, the nitrogen reduction reaction, and the selectivity problem of the competing oxygen evolution and peroxide formation reactions, and we outline the advantages of this screening approach over previous investigations.

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.

Epitaxial Core-Shell Oxide Nanoparticles: First-Principles Evidence for Increased Activity and Stability of Rutile Catalysts for Acidic Oxygen Evolution

Due to their high activity and favorable stability in acidic electrolytes, Ir and Ru oxides are primary catalysts for the oxygen evolution reaction (OER) in proton-exchange membrane (PEM) electrolyzers. For a future large-scale application, core-shell nanoparticles are an appealing route to minimize the demand for these precious oxides. Here, we employ first-principles density-functional theory (DFT) and ab initio thermodynamics to assess the feasibility of encapsulating a cheap rutile-structured TiO₂ core with coherent, monolayer-thin IrO₂ or RuO₂ films. Resulting from a strong directional dependence of adhesion and strain, a wetting tendency is only obtained for some low-index facets under typical gas-phase synthesis conditions. Thermodynamic stability in particular of lattice-matched RuO₂ films is instead indicated for more oxidizing conditions. Intriguingly, the calculations also predict an enhanced activity and stability of such epitaxial RuO₂ /TiO₂ core-shell particles under OER operation.

Improving the Accuracy of Atomistic Simulations of the Electrochemical Interface

Atomistic simulation of the electrochemical double layer is an ambitious undertaking, requiring quantum mechanical description of electrons, phase space sampling of liquid electrolytes, and equilibration of electrolytes over nanosecond time scales. All models of electrochemistry make different trade-offs in the approximation of electrons and atomic configurations, from the extremes of classical molecular dynamics of a complete interface with point-charge atoms to correlated electronic structure methods of a single electrode configuration with no dynamics or electrolyte. Here, we review the spectrum of simulation techniques suitable for electrochemistry, focusing on the key approximations and accuracy considerations for each technique. We discuss promising approaches, such as enhanced sampling techniques for atomic configurations and computationally efficient beyond density functional theory (DFT) electronic methods, that will push electrochemical simulations beyond the present frontier.

Modeling Operando Electrochemical CO2 Reduction

Since the seminal works on the application of density functional theory and the computational hydrogen electrode to electrochemical CO₂ reduction (eCO₂R) and hydrogen evolution (HER), the modeling of both reactions has quickly evolved for the last two decades. Formulation of thermodynamic and kinetic linear scaling relationships for key intermediates on crystalline materials have led to the definition of activity volcano plots, overpotential diagrams, and full exploitation of these theoretical outcomes at laboratory scale. However, recent studies hint at the role of morphological changes and short-lived intermediates in ruling the catalytic performance under operating conditions, further raising the bar for the modeling of electrocatalytic systems. Here, we highlight some novel methodological approaches employed to address eCO₂R and HER reactions. Moving from the atomic scale to the bulk electrolyte, we first show how ab initio and machine learning methodologies can partially reproduce surface reconstruction under operation, thus identifying active sites and reaction mechanisms if coupled with microkinetic modeling. Later, we introduce the potential of density functional theory and machine learning to interpret data from Operando spectroelectrochemical techniques, such as Raman spectroscopy and extended X-ray absorption fine structure characterization. Next, we review the role of electrolyte and mass transport effects. Finally, we suggest further challenges for computational modeling in the near future as well as our perspective on the directions to follow.