Simulating Electrochemical Systems by Combining the Finite Field Method with a Constant Potential Electrode

Modeling of Nanomaterials for Supercapacitors: Beyond Carbon Electrodes

Capacitive storage devices allow for fast charge and discharge cycles, making them the perfect complements to batteries for high power applications. Many materials display interesting capacitive properties when they are put in contact with ionic solutions despite their very different structures and (surface) reactivity. Among them, nanocarbons are the most important for practical applications, but many nanomaterials have recently emerged, such as conductive metal-organic frameworks, 2D materials, and a wide variety of metal oxides. These heterogeneous and complex electrode materials are difficult to model with conventional approaches. However, the development of computational methods, the incorporation of machine learning techniques, and the increasing power in high performance computing now allow us to tackle these types of systems. In this Review, we summarize the current efforts in this direction. We show that depending on the nature of the materials and of the charging mechanisms, different methods, or combinations of them, can provide desirable atomic-scale insight on the interactions at play. We mainly focus on two important aspects: (i) the study of ion adsorption in complex nanoporous materials, which require the extension of constant potential molecular dynamics to multicomponent systems, and (ii) the characterization of Faradaic processes in pseudocapacitors, that involves the use of electronic structure-based methods. We also discuss how recently developed simulation methods will allow bridges to be made between double-layer capacitors and pseudocapacitors for future high power electricity storage devices.

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.

Contrasting Views of the Electric Double Layer in Electrochemical CO2 Reduction: Continuum Models vs Molecular Dynamics

In the field of electrochemical CO2 reduction, both continuum models and molecular dynamics (MD) models have been used to understand the electric double layer (EDL). MD often focuses on the region within a few nm of the electrode, while continuum models can span up to the device level (cm). Still, both methods model the EDL, and for a cohesive picture of the CO2 electrolysis system, the two methods should agree in the regions where they overlap length scales. To this end, we make a direct comparison between state-of-the-art continuum models and classical MD simulations under the conditions of CO2 reduction on a Ag electrode. For continuum modeling, this includes the Poisson-Nernst-Planck formulation with steric (finite ion size) effects, and in MD the electrode is modeled with the constant potential method. The comparison yields numerous differences between the two modeling methods. MD shows cations forming two adsorbed layers, including a fully hydrated outer layer and a partial hydration layer closer to the electrode surface. The strength of the inner adsorbed layer increases with cation size (Li+ < Na+ < K+ < Cs+) and with more negative applied potentials. Continuum models that include steric effects predict CO2 to be mostly excluded within 1 nm of the cathode due to tightly packed cations, yet we find little evidence to support these predictions from the MD results. In fact, MD shows that the concentration of CO2 increases within a few Å of the cathode surface due to interactions with the Ag electrode, a factor not included in continuum models. The EDL capacitance is computed from the MD results, showing values in the range of 7-9 μF cm-2, irrespective of the electrolyte concentration, cation identity, or applied potential. The direct comparison between the two modeling methods is meant to show the areas of agreement and disagreement between the two views of the EDL, so as to improve and better align these models.

Impedance of nanocapacitors from molecular simulations to understand the dynamics of confined electrolytes

Nanoelectrochemical devices have become a promising candidate technology across various applications, including sensing and energy storage, and provide new platforms for studying fundamental properties of electrode/electrolyte interfaces. In this work, we employ constant-potential molecular dynamics simulations to investigate the impedance of gold-aqueous electrolyte nanocapacitors, exploiting a recently introduced fluctuation-dissipation relation. In particular, we relate the frequency-dependent impedance of these nanocapacitors to the complex conductivity of the bulk electrolyte in different regimes, and use this connection to design simple but accurate equivalent circuit models. We show that the electrode/electrolyte interfacial contribution is essentially capacitive and that the electrolyte response is bulk-like even when the interelectrode distance is only a few nanometers, provided that the latter is sufficiently large compared to the Debye screening length. We extensively compare our simulation results with spectroscopy experiments and predictions from analytical theories. In contrast to experiments, direct access in simulations to the ionic and solvent contributions to the polarization allows us to highlight their significant and persistent anticorrelation and to investigate the microscopic origin of the timescales observed in the impedance spectrum. This work opens avenues for the molecular interpretation of impedance measurements, and offers valuable contributions for future developments of accurate coarse-grained representations of confined electrolytes.

Charging and discharging a supercapacitor in molecular simulations

As the world moves more toward unpredictable renewable energy sources, better energy storage devices are required. Supercapacitors are a promising technology to meet the demand for short-term, high-power energy storage. Clearly, understanding their charging and discharging behaviors is essential to improving the technology. Molecular Dynamics (MD) simulations provide microscopic insights into the complex interplay between the dynamics of the ions in the electrolyte and the evolution of the charge distributions on the electrodes. Traditional MD simulations of (dis)charging supercapacitors impose a pre-determined evolving voltage difference between the electrodes, using the Constant Potential Method (CPM). Here, we present an alternative method that explicitly simulates the charge flow to and from the electrodes. For a disconnected capacitor, i.e., an open circuit, the charges are allowed to redistribute within each electrode while the sum charges on both electrodes remain constant. We demonstrate, for a model capacitor containing an aqueous salt solution, that this method recovers the charge-potential curve of CPM simulations. The equilibrium voltage fluctuations are related to the differential capacitance. We next simulate a closed circuit by introducing equations of motion for the sum charges, by explicitly accounting for the external circuit element(s). Charging and discharging of the model supercapacitor via a resistance proceed by double exponential processes, supplementing the usual time scale set by the electrolyte dynamics with a novel time scale set by the external circuit. Finally, we propose a simple equivalent circuit that reproduces the main characteristics of this supercapacitor.

In Situ Spectroscopic Elucidation of the Electrochemical Potential Drop at Polyelectrolytes/Au Interfaces

Polyelectrolytes have been widely applied in electrochemical devices. Understanding the polyelectrolyte/electrode interfaces is pivotal for polyelectrolyte-based applications. Here, we measured the electrochemical potential drop and the local activity of the mobile ion of H+ or OH- at the polyelectrolytes/Au interfaces by in situ electrochemical surface-enhanced Raman spectroscopy and voltammetry in three-electrode cells. We found that the potential dependences of the electrochemical potential drop in polyelectrolytes were smaller than that in conventional electrolyte solutions. The interfacial activity of H+ or OH- was much lower than that of bulk polyelectrolytes. The potential-dependent molecular dynamics simulations showed that the mobility of ionomers of polyelectrolytes in an electrostatic field was limited by a polymer matrix. These results suggested a characteristically thicker compact layer in the electrical double layer of a polyelectrolyte/electrode interface due to the accumulation of mobile H+ or OH- with a thicker hydration layer and immobile ionomers.

PiNNwall: Heterogeneous Electrode Models from Integrating Machine Learning and Atomistic Simulation

Electrochemical energy storage always involves the capacitive process. The prevailing electrode model used in the molecular simulation of polarizable electrode-electrolyte systems is the Siepmann-Sprik model developed for perfect metal electrodes. This model has been recently extended to study the metallicity in the electrode by including the Thomas-Fermi screening length. Nevertheless, a further extension to heterogeneous electrode models requires introducing chemical specificity, which does not have any analytical recipes. Here, we address this challenge by integrating the atomistic machine learning code (PiNN) for generating the base charge and response kernel and the classical molecular dynamics code (MetalWalls) dedicated to the modeling of electrochemical systems, and this leads to the development of the PiNNwall interface. Apart from the cases of chemically doped graphene and graphene oxide electrodes as shown in this study, the PiNNwall interface also allows us to probe polarized oxide surfaces in which both the proton charge and the electronic charge can coexist. Therefore, this work opens the door for modeling heterogeneous and complex electrode materials often found in energy storage systems.

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.

Frequency-Dependent Impedance of Nanocapacitors from Electrode Charge Fluctuations as a Probe of Electrolyte Dynamics

The frequency-dependent impedance is a fundamental property of electrical components. We show that it can be determined from the equilibrium dynamical fluctuations of the electrode charge in constant-potential molecular simulations, extending in particular a fluctuation-dissipation relation for the capacitance recovered in the low-frequency limit and provide an illustration on water-gold nanocapacitors. This Letter opens the way to the interpretation of electrochemical impedance measurements in terms of microscopic mechanisms, directly from the dynamics of the electrolyte, or indirectly via equivalent circuit models as in experiments.

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.

Predictive Molecular Models for Charged Materials Systems: From Energy Materials to Biomacromolecules

Electrostatic interactions play a dominant role in charged materials systems. Understanding the complex correlation between macroscopic properties with microscopic structures is of critical importance to develop rational design strategies for advanced materials. But the complexity of this challenging task is augmented by interfaces present in the charged materials systems, such as electrode-electrolyte interfaces or biological membranes. Over the last decades, predictive molecular simulations that are founded in fundamental physics and optimized for charged interfacial systems have proven their value in providing molecular understanding of physicochemical properties and functional mechanisms for diverse materials. Novel design strategies utilizing predictive models have been suggested as promising route for the rational design of materials with tailored properties. Here, an overview of recent advances in the understanding of charged interfacial systems aided by predictive molecular simulations is presented. Focusing on three types of charged interfaces found in energy materials and biomacromolecules, how the molecular models characterize ion structure, charge transport, morphology relation to the environment, and the thermodynamics/kinetics of molecular binding at the interfaces is discussed. The critical analysis brings two prominent field of energy materials and biological science under common perspective, to stimulate crossover in both research field that have been largely separated.

ELECTRODE: An electrochemistry package for atomistic simulations

Constant potential methods (CPM) enable computationally efficient simulations of the solid-liquid interface at conducting electrodes in molecular dynamics (MD). They have been successfully used, for example, to realistically model the behavior of ionic liquids or water-in-salt electrolytes in supercapacitors and batteries. The CPM models conductive electrodes by updating charges of individual electrode atoms according to the applied electric potential and the (time-dependent) local electrolyte structure. Here we present a feature-rich CPM implementation, called ELECTRODE, for the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS), which includes a constrained charge method and a thermo-potentiostat. The ELECTRODE package also contains a finite-field approach, multiple corrections for non-periodic boundary conditions of the particle-particle particle-mesh solver, and a Thomas-Fermi model for using non-ideal metals as electrodes. We demonstrate the capabilities of this implementation for a parallel-plate electrical double-layer capacitor, for which we have investigated the charging times with the different implemented methods and found an interesting relationship between water and ionic dipole relaxations. To prove the validity of the one-dimensional correction for the long-range electrostatics, we estimated the vacuum capacitance of two co-axial carbon nanotubes and compared it to structureless cylinders, for which an analytical expression exists. In summary, the ELECTRODE package enables efficient electrochemical simulations using state-of-the-art methods, allowing one to simulate even heterogeneous electrodes. Moreover, it allows unveiling more rigorously how electrode curvature affects the capacitance with the one-dimensional correction.

Unified polarizable electrode models for open and closed circuits: Revisiting the effects of electrode polarization and different circuit conditions on electrode-electrolyte interfaces

A precise understanding of the interfacial structure and dynamics is essential for the optimal design of various electrochemical devices. Herein, we propose a method for classical molecular dynamics simulations to deal with electrochemical interfaces with polarizable electrodes under the open circuit condition. Less attention has been paid to electrochemical circuit conditions in computation despite being often essential for a proper assessment, especially comparison between different models. The present method is based on the chemical potential equalization principle, as is a method developed previously to deal with systems under the closed circuit condition. These two methods can be interconverted through the Legendre transformation, so that the difference in the circuit conditions can be compared on the same footing. Furthermore, the electrode polarization effect can be correctly studied by comparing the present method with the conventional simulations with the electrodes represented by fixed charges, since both of the methods describe systems under the open circuit condition. The method is applied to a parallel-plate capacitor composed of platinum electrodes and an aqueous electrolyte solution. The electrode polarization effects have an impact on the interfacial structure of the electrolyte solution. We found that the difference in the circuit conditions significantly affects the dynamics of the electrolyte solution. The electric field at the charged electrode surface is poorly screened by the nonequilibrium solution structure in the open circuit condition, which accelerates the motion of the electrolyte solution.

Fully periodic, computationally efficient constant potential molecular dynamics simulations of ionic liquid supercapacitors

Molecular dynamics (MD) simulations of complex electrochemical systems, such as ionic liquid supercapacitors, are increasingly including the constant potential method (CPM) to model conductive electrodes at a specified potential difference, but the inclusion of CPM can be computationally expensive. We demonstrate the computational savings available in CPM MD simulations of ionic liquid supercapacitors when the usual non-periodic slab geometry is replaced with fully periodic boundary conditions. We show how a doubled cell approach, previously used in non-CPM MD simulations of charged interfaces, can be used to enable fully periodic CPM MD simulations. Using either a doubled cell approach or a finite field approach previously reported by others, fully periodic CPM MD simulations produce comparable results to the traditional slab geometry simulations with a nearly double speedup in computational time. Indeed, these savings can offset the additional cost of the CPM algorithm, resulting in periodic CPM MD simulations that are computationally competitive with the non-periodic, fixed charge equivalent simulations for the ionic liquid supercapacitors studied here.

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.

Microscopic Simulations of Electrochemical Double-Layer Capacitors

Electrochemical double-layer capacitors (EDLCs) are devices allowing the storage or production of electricity. They function through the adsorption of ions from an electrolyte on high-surface-area electrodes and are characterized by short charging/discharging times and long cycle-life compared to batteries. Microscopic simulations are now widely used to characterize the structural, dynamical, and adsorption properties of these devices, complementing electrochemical experiments and in situ spectroscopic analyses. In this review, we discuss the main families of simulation methods that have been developed and their application to the main family of EDLCs, which include nanoporous carbon electrodes. We focus on the adsorption of organic ions for electricity storage applications as well as aqueous systems in the context of blue energy harvesting and desalination. We finally provide perspectives for further improvement of the predictive power of simulations, in particular for future devices with complex electrode compositions.

Chemistry Dissolved in Ionic Liquids. A Theoretical Perspective

The theoretical treatment of ionic liquids must focus now on more realistic models while at the same time keeping an accurate methodology when following recent ionic liquids research trends or allowing predictability to come to the foreground. In this Perspective, we summarize in three cases of advanced ionic liquid research what methodological progress has been made and point out difficulties that need to be overcome. As particular examples to discuss we choose reactions, chirality, and radicals in ionic liquids. All these topics have in common that an explicit or accurate treatment of the electronic structure and/or intermolecular interactions is required (accurate methodology), while at the same time system size and complexity as well as simulation time (realistic model) play an important role and must be covered as well.

Multifunctional Electrocatalysis on Single-Site Metal Catalysts: A Computational Perspective

Multifunctional electrocatalysts are vastly sought for their applications in water splitting electrolyzers, metal-air batteries, and regenerative fuel cells because of their ability to catalyze multiple reactions such as hydrogen evolution, oxygen evolution, and oxygen reduction reactions. More specifically, the application of single-atom electrocatalyst in multifunctional catalysis is a promising approach to ensure good atomic efficiency, tunability and additionally benefits simple theoretical treatment. In this review, we provide insights into the variety of single-site metal catalysts and their identification. We also summarize the recent advancements in computational modeling of multifunctional electrocatalysis on single-site catalysts. Furthermore, we explain each modeling step with open-source-based working examples of a standard computational approach.

Constant potential simulations on a mesh

Molecular dynamics simulations in a constant potential ensemble are an increasingly important tool to investigate charging mechanisms in next-generation energy storage devices. We present a highly efficient approach to compute electrostatic interactions in simulations employing a constant potential method (CPM) by introducing a particle-particle particle-mesh solver specifically designed for treating long-range interactions in a CPM. Moreover, we present evidence that a dipole correction term-commonly used in simulations with a slab-like geometry-must be used with caution if it is also to be used within a CPM. It is demonstrated that artifacts arising from the usage of the dipole correction term can be circumvented by enforcing a charge neutrality condition in the evaluation of the electrode charges at a given external potential.

Electrochemistry from first-principles in the grand canonical ensemble

Progress in electrochemical technologies, such as automotive batteries, supercapacitors, and fuel cells, depends greatly on developing improved charged interfaces between electrodes and electrolytes. The rational development of such interfaces can benefit from the atomistic understanding of the materials involved by first-principles quantum mechanical simulations with Density Functional Theory (DFT). However, such simulations are typically performed on the electrode surface in the absence of its electrolyte environment and at constant charge. We have developed a new hybrid computational method combining DFT and the Poisson-Boltzmann equation (P-BE) capable of simulating experimental electrochemistry under potential control in the presence of a solvent and an electrolyte. The charged electrode is represented quantum-mechanically via linear-scaling DFT, which can model nanoscale systems with thousands of atoms and is neutralized by a counter electrolyte charge via the solution of a modified P-BE. Our approach works with the total free energy of the combined multiscale system in a grand canonical ensemble of electrons subject to a constant electrochemical potential. It is calibrated with respect to the reduction potential of common reference electrodes, such as the standard hydrogen electrode and the Li metal electrode, which is used as a reference electrode in Li-ion batteries. Our new method can be used to predict electrochemical properties under constant potential, and we demonstrate this in exemplar simulations of the differential capacitance of few-layer graphene electrodes and the charging of a graphene electrode coupled to a Li metal electrode at different voltages.

Advanced Materials for Energy-Water Systems: The Central Role of Water/Solid Interfaces in Adsorption, Reactivity, and Transport

The structure, chemistry, and charge of interfaces between materials and aqueous fluids play a central role in determining properties and performance of numerous water systems. Sensors, membranes, sorbents, and heterogeneous catalysts almost uniformly rely on specific interactions between their surfaces and components dissolved or suspended in the water-and often the water molecules themselves-to detect and mitigate contaminants. Deleterious processes in these systems such as fouling, scaling (inorganic deposits), and corrosion are also governed by interfacial phenomena. Despite the importance of these interfaces, much remains to be learned about their multiscale interactions. Developing a deeper understanding of the molecular- and mesoscale phenomena at water/solid interfaces will be essential to driving innovation to address grand challenges in supplying sufficient fit-for-purpose water in the future. In this Review, we examine the current state of knowledge surrounding adsorption, reactivity, and transport in several key classes of water/solid interfaces, drawing on a synergistic combination of theory, simulation, and experiments, and provide an outlook for prioritizing strategic research directions.

Computational Amperometry of Nanoscale Capacitors in Molecular Simulations

In recent years, constant applied potential molecular dynamics has allowed researchers to study the structure and dynamics of the electrochemical double-layer of a large variety of nanoscale capacitors. Nevertheless, it has remained impossible to simulate polarized electrodes at fixed total charge. Here, we show that combining a constant potential electrode with a finite electric displacement fills this gap by allowing us to simulate open-circuit conditions. The method can be extended by applying an electric displacement ramp to perform computational amperometry experiments at different current intensities. As in experiments, the full capacitance of the system is obtained at low intensity, but this quantity decreases when the applied ramp becomes too fast with respect to the microscopic dynamics of the liquid.

Molecular Simulation of Electrode-Solution Interfaces

Many key industrial processes, from electricity production, conversion, and storage to electrocatalysis or electrochemistry in general, rely on physical mechanisms occurring at the interface between a metallic electrode and an electrolyte solution, summarized by the concept of an electric double layer, with the accumulation/depletion of electrons on the metal side and of ions on the liquid side. While electrostatic interactions play an essential role in the structure, thermodynamics, dynamics, and reactivity of electrode-electrolyte interfaces, these properties also crucially depend on the nature of the ions and solvent, as well as that of the metal itself. Such interfaces pose many challenges for modeling because they are a place where quantum chemistry meets statistical physics. In the present review, we explore the recent advances in the description and understanding of electrode-electrolyte interfaces with classical molecular simulations, with a focus on planar interfaces and solvent-based liquids, from pure solvent to water-in-salt electrolytes.

Controlling potential difference between electrodes based on self-consistent-charge density functional tight binding

A proper understanding and description of the electronic response of the electrode surfaces in electrochemical systems are quite important because the interactions between the electrode surface and electrolyte give rise to unique and useful interfacial properties. Atomistic modeling of the electrodes requires not only an accurate description of the electronic response under a constant-potential condition but also computational efficiency in order to deal with systems large enough to investigate the interfacial electrolyte structures. We thus develop a self-consistent-charge density functional tight binding based method to model a pair of electrodes in electrochemical cells under the constant-potential condition. The method is more efficient than the (ab initio) density functional theory calculations so that it can treat systems as large as those studied in classical atomistic simulations. It can also describe the electronic response of electrodes quantum mechanically and more accurately than the classical counterparts. The constant-potential condition is introduced through a Legendre transformation of the electronic energy with respect to the difference in the number of electrons in the two electrodes and their electrochemical potential difference, through which the Kohn-Sham equations for each electrode are variationally derived. The method is applied to platinum electrodes faced parallel to each other under an applied voltage. The electronic response to the voltage and a charged particle is compared with the result of a classical constant-potential method based on the chemical potential equalization principle.

Multi-scale approach for the prediction of atomic scale properties

Electronic nearsightedness is one of the fundamental principles that governs the behavior of condensed matter and supports its description in terms of local entities such as chemical bonds. Locality also underlies the tremendous success of machine-learning schemes that predict quantum mechanical observables - such as the cohesive energy, the electron density, or a variety of response properties - as a sum of atom-centred contributions, based on a short-range representation of atomic environments. One of the main shortcomings of these approaches is their inability to capture physical effects ranging from electrostatic interactions to quantum delocalization, which have a long-range nature. Here we show how to build a multi-scale scheme that combines in the same framework local and non-local information, overcoming such limitations. We show that the simplest version of such features can be put in formal correspondence with a multipole expansion of permanent electrostatics. The data-driven nature of the model construction, however, makes this simple form suitable to tackle also different types of delocalized and collective effects. We present several examples that range from molecular physics to surface science and biophysics, demonstrating the ability of this multi-scale approach to model interactions driven by electrostatics, polarization and dispersion, as well as the cooperative behavior of dielectric response functions.

Macroscopic surface charges from microscopic simulations

Attaining accurate average structural properties in a molecular simulation should be considered a prerequisite if one aims to elicit meaningful insights into a system's behavior. For charged surfaces in contact with an electrolyte solution, an obvious example is the density profile of ions along the direction normal to the surface. Here, we demonstrate that, in the slab geometry typically used in simulations, imposing an electric displacement field D determines the integrated surface charge density of adsorbed ions at charged interfaces. This allows us to obtain macroscopic surface charge densities irrespective of the slab thickness used in our simulations. We also show that the commonly used Yeh-Berkowitz method and the "mirrored slab" geometry both impose vanishing integrated surface charge densities. We present results both for relatively simple rocksalt (1 1 1) interfaces and the more complex case of kaolinite's basal faces in contact with an aqueous electrolyte solution.

Frontiers in molecular simulation of solvated ions, molecules and interfaces

This themed collection is a collection of articles on frontiers in molecular simulation of solvated ions, molecules and interfaces.

Modeling interfacial electrochemistry: concepts and tools

This paper presents a grand canonical formalism and provides tools to investigate electrochemical effects at interfaces.

DFT modelling of explicit solid–solid interfaces in batteries: methods and challenges

Density Functional Theory (DFT) calculations of electrode material properties in high energy density storage devices like lithium batteries have been standard practice for decades.