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Chao Zhang, Jun Cheng, Yiming Chen, Maria K Y Chan, Qiong Cai, Rodrigo P Carvalho, Cleber F N Marchiori, Daniel Brandell, C Moyses Araujo, Ming Chen, Xiangyu Ji, Guang Feng, Kateryna Goloviznina, Alessandra Serva, Mathieu Salanne, [Toshihiko Mandai](https://orcid.org/0000-0002-2403-7794), Tomooki Hosaka, Mirna Alhanash, Patrik Johansson, Yun-Ze Qiu, Hai Xiao, Michael Eikerling, Ryosuke Jinnouchi, Marko M Melander, Georg Kastlunger, Assil Bouzid, Alfredo Pasquarello, Seung-Jae Shin, Minho M Kim, Hyungjun Kim, Kathleen Schwarz, Ravishankar Sundararaman

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2023 Roadmap on molecular modelling of electrochemical energy materialsJ. Phys. Energy 5 (2023) 041501 https://doi.org/10.1088/2515-7655/acfe9bJournal of Physics: EnergyOPEN ACCESSRECEIVED19 April 2023REVISED1 September 2023ACCEPTED FOR PUBLICATION29 September 2023PUBLISHED30 October 2023Original content fromthis work may be usedunder the terms of theCreative CommonsAttribution 4.0 licence.Any further distributionof this work mustmaintain attribution tothe author(s) and the titleof the work, journalcitation and DOI.ROADMAP2023 Roadmap on molecular modelling of electrochemicalenergy materialsChao Zhang1,2,27,∗, Jun Cheng3,27,∗, Yiming Chen4, Maria K Y Chan4, Qiong Cai5,6,Rodrigo P Carvalho1,7, Cleber F NMarchiori8, Daniel Brandell1, C Moyses Araujo7,8, Ming Chen9,Xiangyu Ji9, Guang Feng9, Kateryna Goloviznina10, Alessandra Serva10, Mathieu Salanne10,11,Toshihiko Mandai12, Tomooki Hosaka13, Mirna Alhanash14, Patrik Johansson14,15, Yun-Ze Qiu16,Hai Xiao16, Michael Eikerling17, Ryosuke Jinnouchi18, Marko MMelander19, Georg Kastlunger20,Assil Bouzid21, Alfredo Pasquarello22, Seung-Jae Shin23,24, Minho M Kim23, Hyungjun Kim23,Kathleen Schwarz25 and Ravishankar Sundararaman261 Department of Chemistry—Ångström Laboratory, Uppsala University, Box 538, 75121 Uppsala, Sweden2 Wallenberg Initiative Materials Science for Sustainability, Uppsala University, 75121 Uppsala, Sweden3 State Key Laboratory of Physical Chemistry of Solid Surfaces, iChEM, College of Chemistry and Chemical Engineering, XiamenUniversity, Xiamen 361005, People’s Republic of China4 Center for Nanoscale Materials, Argonne National Laboratory, 9700 Cass Ave, Lemont, IL 60439, United States of America5 School of Chemistry and Chemical Engineering, Faculty of Engineering and Physical Sciences, University of Surrey, Guildford GU27XH, United Kingdom6 The Faraday Institution, Quad One, Harwell Campus, Didcot, OX11 0RA, United Kingdom7 Materials Theory Division, Department of Physics and Astronomy, Uppsala University, Box 516, 75120 Uppsala, Sweden8 Department of Engineering and Physics, Karlstad University, 65188 Karlstad, Sweden9 State Key Laboratory of Coal Combustion, School of Energy and Power Engineering, Huazhong University of Science andTechnology, Wuhan 430074, People’s Republic of China10 Sorbonne Université, CNRS, Physico-chimie des Électrolytes et Nanosystèmes Interfaciaux, PHENIX, F-75005 Paris, France11 Institut Universitaire de France (IUF), 75231 Paris, France12 Center for Green Research on Energy and Environmental Materials, National Institute for Materials Science, 1-1 Namiki, Tsukuba,Ibaraki 305-0044, Japan13 Department of Applied Chemistry, Tokyo University of Science, 1-3 Kagurazaka, Shinjuku, Tokyo, Japan14 Department of Physics, Chalmers University of Technology, 412 96 Göteborg, Sweden15 Alistore-ERI, CNRS FR 3104, 15 Rue Baudelocque, 80039 Amiens, France16 Department of Chemistry, Tsinghua University, Beijing 100084, People’s Republic of China17 Forschungszentrum Jülich GmbH and RWTH Aachen University, Jülich, Germany18 Toyota Central R&D Labs., Inc., 41-1 Yokomichi, Nagakute, Aichi 480-1192, Japan19 Department of Chemistry, University of Jyväskylä, Jyväskylä, Finland20 Department of Physics, Technical University of Denmark, Lyngby, Denmark21 Institut de Recherche sur les Céramiques (IRCER), Centre Européen de la Céramique, 12 Rue Atlantis, Limoges, 87068, France22 Chaire de Simulation à l’Echelle Atomique (CSEA), Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne,Switzerland23 Department of Chemistry, Korea Advanced Institute of Science and Technology, Daejeon 34141, Republic of Korea24 Department of Materials Science and Engineering, Yonsei University, Seoul 03722, Republic of Korea25 National Institute of Standards and Technology, Gaithersburg, MD, United States of America26 Rensselaer Polytechnic Institute, Troy, NY, United States of America27 Guest editors of the Roadmap.∗ Authors to whom any correspondence should be addressed.E-mail: chao.zhang@kemi.uu.se and chengjun@xmu.edu.cnKeywords: electrochemical interfaces, density-functional theory, molecular dynamics simulation, electrochemical energy storage,machine learning, electrocatalysisAbstractNew materials for electrochemical energy storage and conversion are the key to the electrificationand sustainable development of our modern societies. Molecular modelling based on the principlesof quantum mechanics and statistical mechanics as well as empowered by machine learningtechniques can help us to understand, control and design electrochemical energy materials atatomistic precision. Therefore, this roadmap, which is a collection of authoritative opinions, servesas a gateway for both the experts and the beginners to have a quick overview of the current statusand corresponding challenges in molecular modelling of electrochemical energy materials forbatteries, supercapacitors, CO2 reduction reaction, and fuel cell applications.© 2023 The Author(s). Published by IOP Publishing Ltdhttps://doi.org/10.1088/2515-7655/acfe9bhttps://crossmark.crossref.org/dialog/?doi=10.1088/2515-7655/acfe9b&domain=pdf&date_stamp=2023-10-30https://creativecommons.org/licenses/by/4.0/https://creativecommons.org/licenses/by/4.0/https://orcid.org/0000-0002-7167-0840https://orcid.org/0000-0001-6971-0797https://orcid.org/0000-0002-1501-5550https://orcid.org/0000-0003-0922-1363https://orcid.org/0000-0002-1677-0515https://orcid.org/0000-0003-3895-6529https://orcid.org/0000-0003-0377-3669https://orcid.org/0000-0002-8019-2801https://orcid.org/0000-0001-5192-0016https://orcid.org/0000-0001-6659-9181https://orcid.org/0000-0001-9913-4938https://orcid.org/0000-0002-7525-2494https://orcid.org/0000-0002-1753-491Xhttps://orcid.org/0000-0002-2403-7794https://orcid.org/0000-0002-9907-117Xhttps://orcid.org/0000-0001-9399-1584https://orcid.org/0000-0002-0822-1161https://orcid.org/0000-0002-9363-7240https://orcid.org/0000-0002-9142-2799https://orcid.org/0000-0002-3960-8908https://orcid.org/0000-0002-1539-4511https://orcid.org/0000-0002-0625-4592mailto:chao.zhang@kemi.uu.semailto:chengjun@xmu.edu.cnJ. Phys. Energy 5 (2023) 041501 C Zhang et alContents1. Introduction—where are we heading in computational electrochemistry? 32. Modelling and characterization of transition metal oxide electrodes 53. Metal anodes for rechargeable next-generation batteries 84. Organic electrode materials 115. MOF-based supercapacitors 156. Ionic liquids and carbon-based supercapacitors 197. Liquid electrolytes for multivalent batteries 228. Theoretical understanding of single-atom electrocatalysis 259. Theory and computation of the local reaction environment in electrocatalytic media 2810. Modelling and machine learning of fuel cell 3211. Modelling electrochemical interfaces and reactions with GPAW: grand canonical ensemble DFTapproaches 3512. Constant Fermi-level molecular dynamics: recent achievements and future challenges 3813. Density functional theory in classical explicit solvents (DFT-CES): efforts towards understandingthe unseen, buried electric double layer 4114. Implicit solvation models for electrochemical interfaces 45Data availability statement 47References 482J. Phys. Energy 5 (2023) 041501 C Zhang et al1. Introduction—where are we heading in computational electrochemistry?Chao Zhang1,2,4 and Jun Cheng3,41 Department of Chemistry—Ångström Laboratory, Uppsala University, Box 538, 75121 Uppsala, Sweden2Wallenberg Initiative Materials Science for Sustainability, Uppsala University, 75121 Uppsala, Sweden3 State Key Laboratory of Physical Chemistry of Solid Surfaces, iChEM, College of Chemistry and ChemicalEngineering, Xiamen University, Xiamen 361005, People’s Republic of China4 Guest editors of the Roadmap.E-mail: chao.zhang@kemi.uu.se and chengjun@xmu.edu.cnOn the very first pages of his Lecture (notes) on Physics, Richard Feynman already said that the single mostimportant scientific knowledge is ‘all things are made of atoms’ [1]. Indeed, materials are the foundation ofour modern societies. In particular, new materials related to electrochemical energy storage and conversionare the key to electrification and sustainable development of our world. That is why different initiatives havebeen taken place across the globe, e.g. Energy Frontier Research Centres in the US, the CollaborativeInnovation Centre of Chemistry for Energy Materials in China, and the Wallenberg Initiative MaterialsScience for Sustainability in Sweden.These new and large initiatives come in sharp contrast with the fact that electrochemistry on its own is arather old discipline, even just counting from the era of Michael Faraday (1791–1867) instead of trackingback to its origin in physiology. This contrast highlights the motivation and the ambition behind thesecollaborative efforts, which is to understand, control and design electrochemical energy materials atatomistic precision. In fact, one of the grand challenges is to establish the quantitative relationship betweenthe macroscopic observables such as current and voltage measured in electrochemical experiments, and thestructural, dynamical, and compositional evolutions of corresponding bulk materials and interfaces(interphases) at the microscopic scales. In this regard, molecular modelling based on the principles ofquantum mechanics and statistical mechanics as well as empowered by machine learning techniques canprovide both new physical insights and predictive solutions to this outstanding problem.When the field first started about 40 years ago, Woods Halley as one of the pioneers wrote that‘Electrochemistry is not widely regarded as a forefront area for the condensed matter theorist. Here we willtry to show with two examples that the charged solid-liquid interface at which all the basic phenomena ofelectrochemistry take place is a promising area for research for condensed matter theory’ [2]. Today, we nolonger need to convince young theoreticians that molecular modelling of electrochemical energy materials isan exciting field to work on. Nevertheless, the key phrase ‘charged solid-liquid interface’ does reveal the focusand the uniqueness of our research area.Electrochemistry involves the interface between electrode and electrolyte, in which the transitionbetween ionic current and electronic current happens [3]. This transition involves the fluctuation ofelectronic levels and the solvent (electrolyte) molecules. Therefore, it is crucial to have a molecular anddynamical understanding of both electrode and electrolyte materials. In this roadmap, Chan and her teamprovide a succinct overview of integrating materials modelling, characterization techniques, and machinelearning approaches for the development of transition metal oxide-based cathode materials. This is followedby an up-to-date report from Cai on her account of the current status and challenges of modelling metalanodes for rechargeable batteries. To explore the low-cost and sustainable electrode materials, Araujo and hiscollaborators present a snapshot of the molecular modelling-assisted design of organic electrode materialsusing both the density functional theory (DFT) calculations and the surrogate models based on machinelearning (ML). Similarly, organic materials can also be used as electrode materials for supercapacitors andthe recent advances in molecular dynamics (MD) simulations of metal-organic frameworks with theconstant potential method are summarized by Feng’s group. On the electrolyte side, we have twocontributions focusing on liquid electrolytes, in which the ion solvation and its dynamics are crucial forsolving the conundrum. The PHENIX team focuses on ionic liquids and carbon-based supercapacitors withan emphasis on the polarizable force fields used in the MD simulations. The joint piece from the Swedish andJapanese teams highlights the difference in the development and the modelling of liquid electrolytes formultivalent batteries as compared to more matured lithium-ion batteries.As distinguished from energy storage systems, the focus of electrochemical interface modelling in energyconversions, such as CO2 reduction reaction (CO2RR) and fuel cell reactions, lies on local reactivity. This isparticularly true for single-atom electrocatalysis, as laid out and discussed by Xiao’s group, where the strongstatic correlation plays an important role and high-level wavefunction methods are often necessary forquantitative predictions. On a similar note, Eikerling provides a holistic view of the role of theory andcomputation in describing the local reaction environment within the context of the oxygen reduction3https://mailto:chao.zhang@kemi.uu.sehttps://mailto:chengjun@xmu.edu.cnJ. Phys. Energy 5 (2023) 041501 C Zhang et alreaction in polymer electrolyte fuel cells. This comes together nicely with a multi-scale perspective on fuelcell modelling from Jinnouchi, in which ML-based simulation techniques are anticipated to bridge thefirst-principles method and the coarse-grained MD simulations.In addition to the central position of solid–liquid interfaces in computational electrochemistry regardlessof whether it is for energy storage or conversion applications, the second aspect of the key phase mentionedabove is ‘charged’ or electrified (interfaces). This is the core difference in molecular modelling ofelectrochemical energy materials, as compared to other branches of computational (theoretical) chemistry ormaterials modelling. The boundary condition matters in computational electrochemistry as much as it doesin potentiostatic, galvanostatic, or coulostatic measurements in electrochemical experiments. In this regard,we have two contributions to the method developments of grand canonical DFT and DFTMD fromMelander with Kastlunger and Bouzid with Pasquarello respectively. This comes hand-in-hand withperspectives on how to reduce the computational cost of describing the solvent (electrolyte) degrees offreedom from Kim’s group with a quantum mechanics/molecular mechanics approach and from Schwarzand Sundararaman on implicit solvation models.Overall, this roadmap originating from 20 groups in 11 countries serves as a gateway for both the expertsand the beginners to have a quick overview of the current status and corresponding challenges in molecularmodelling of electrochemical energy materials for batteries, supercapacitors, CO2RR, and fuel cellapplications. It is not intended to be a comprehensive review, rather they are opinions of leading experts intheir respective domains. Therefore, topics such as solid electrolytes (both ceramic and polymer), descriptorengineering of electrocatalysts and their ML discovery, are not included in this collection and can be foundelsewhere [4–8].Looking into the future, we are optimistic about the acceleration brought by ML techniques to molecularmodelling. Being hopeful about ML techniques, it is also clear that the physics-based approaches will stillplay a central role in tackling unconventional systems (e.g. non-pristine electrode surfaces in the double layermodelling) [9] and generating new inspirations (e.g. the connections between different types of constantpotential simulation techniques used in molecular simulation and electronic structure calculationcommunities) [10]. Keeping these in mind, our field will contribute more significantly to the R&D of newmaterials for electrochemical applications; the common physical chemistry principles behind a plethora ofseemingly different experimental phenomena can be revealed and understood; and the gap between theoryand experiment will be further narrowed down with collaborative efforts at both national and internationallevels.AcknowledgmentsThis project has received funding from the European Research Council (ERC) under the European UnionsHorizon 2020 research and innovation programme (Grant Agreement No. 949012). This work was partiallysupported by the Wallenberg Initiative Materials Science for Sustainability (WISE) funded by the Knut andAlice Wallenberg Foundation (KAW). J C is grateful for the funding support from the National NaturalScience Foundation of China (Grant Nos. 21861132015, 21991151, 21991150 and 22021001).4J. Phys. Energy 5 (2023) 041501 C Zhang et al2. Modelling and characterization of transitionmetal oxide electrodesYiming Chen and Maria K Y ChanCenter for Nanoscale Materials, Argonne National Laboratory, 9700 Cass Ave, Lemont, IL 60439, UnitedStates of AmericaE-mail: mchan@anl.govStatusTransition metal oxides (TMOs) have been playing crucial roles in the family of Li-ion battery cathodes sincethe 1980s when layered LiCoO2 was developed [11]. As its name indicates, TMO is a group of materials thatadopt a general formula of LixMyOz where M indicates single or multiple TM elements. There are threemajor structural prototypes for TMO cathode materials: layered, spinel, and disordered rocksalt (DRX).Layered TMOs usually possess alternating layers of TM-O2 octahedra and Li along the c-axis. Spinelmaterials, such as well-investigated LiMn2O4, mostly have a cubic lattice symmetry where oxygen anionsform a face-centred cubic lattice. DRX which has Li and TMmixing in its cation site has attracted significantattention in recent years.In addition to electrochemical experiments, modelling and characterization are vital to explain thematerial properties of TMO electrodes (as shown in figure 1). Modelling methodologies, including firstprinciples density functional theory (DFT) calculations, molecular dynamics or Monte Carlo simulations,and continuum approaches, have been proven to be reliable and versatile tools to understand theseproperties. For example, DFT calculations are widely applied to predict the voltage profiles, structurestability, and diffusion barriers based on thermodynamics and kinetics [12]. Molecular dynamics and MonteCarlo simulations are used to understand lithium diffusion dynamics and thermodynamic ground states.Characterization techniques, including microscopy and spectroscopy, have become indispensable toidentifying materials properties and explaining mechanisms. In-situ and operandomeasurements allowresearchers to identify dynamic evolution during cycling and synthesis. In recent years, simulatedcharacterization techniques have emerged as a valuable complement to experimental ones to explain dataand identify mechanisms [13–15].With those tools, the investigation of TMO electrodes has gained substantial progress towardcommercialization. For instance, LiNixMnyCo1−x−yO2 (NMC) was first discovered in 2001 [16, 17] and isnow one of the prevailing cathode materials in high-energy applications such as electric vehicles. Yet, therestill exists considerable room for improved understanding and performance with the help of modelling andcharacterization techniques.Current and future challengesAn ideal cathode for lithium-ion batteries needs to satisfy the following requirements: high gravimetricand/or volumetric energy density for the appropriate storage application, high rate capability to allow fastcharging, low cost of production for large-scale commercialization, and stability for safety and long-termcyclability. Unfortunately, there exists no single material that can satisfy all requirements. In the family ofTMOs, spinel materials have excellent rate performance because of the 3D percolating diffusion channels.However, its low energy density makes it less appealing to high-energy applications. DRX has the highestenergy density among all TMOs [18] but it also suffers from materials degradation. On the other hand,layered TMOs have high energy density and good stability, explaining its popularity in the industry. Thecommon problem for layered TMOs lies in their usage of Co, which is becoming increasingly expensive andraises ethical issues during Co mining processes.One of the biggest obstacles for TMO cathode improvement is understanding their degradationmechanisms. In NMC in particular, with an increasing effort to replace costly Co with cheaper and moreabundant Ni, NMC gains structural instability that leads to defects and performance decrease. Althoughdefects in NMC are well-observed in experiments, its formation mechanism and how it impacts batteryperformance remain inconclusive. In addition to experimental efforts, computational material scientists havebeen solving this problem using first principles calculations [19, 20]. Both studies unveiled the relevance ofthe lithiation state to the degradation of NMC cathodes during electrochemical cycling. One study explicitlyexplored its impact on mechanical properties, such as elastic modulus and hardness, while the other oneinvestigated how the formation of defects can be related to delithiation. First principles calculations revealedthat Jahn–Teller distortion, depletion of electrostatic interactions of Li–O, and weak ionic TM–O bondingcontribute to the change in mechanical properties as Li is extracted from NMCmaterials. Simultaneously,the reduction in Li content also diminishes the formation energy of defects, including oxygen vacancy,5https://mailto:mchan@anl.govJ. Phys. Energy 5 (2023) 041501 C Zhang et alFigure 1. Schematic diagram for modelling and characterization of TMOs. The top panel represents a few typical properties thatcan be solved with modelling tools. The middle panel showcases the crystal structure of a typical TMO, NMC material. Thebottom panel exemplifies several characterization techniques that are widely used for TMO studies.thereby increasing the likelihood of defect formation. In particular, the role of oxygen instability was foundby DFT to be particularly enhanced at grain boundaries [21].Another challenge lies in the oxidation state change during electrochemical cycling. With advancedcharacterization techniques such as x-ray absorption spectroscopy, researchers can qualitatively determinethe oxidation states of TM in different states of charge [22, 23]. However, such changes are not alwaysstraightforward to interpret from spectral data. Scientists are interested in the complex interplay between TMredox and oxygen redox [24], details of the atomistic processes involving degradation and oxygen instability,the role of defects, and the effect of stoichiometry on the above.Advances in science and technology to meet challengesAdvances in modelling, in concert with advances in advanced characterization, are needed to tackle theabove challenges. In modelling, the need to model larger simulation cells due to cation order and disorder aswell as grain boundaries, and to dynamic simulations covering ion diffusion and degradation time scales,requires the use of efficient interatomic potentials such as those trained using machine learning methods.The use of high throughput simulations together with ML will also allow the discovery of new compositionswith desired properties. On the characterization side, the development of spatially and temporally resolveddiffraction and spectroscopy (x-ray and electron) will allow the simultaneous, multi-modal characterizationof TMO cathode materials. For instance, Quilty et al demonstrated the necessity to use multiplecharacterization techniques to unveil the full picture of the capacity fade of NMC in real time [25].Moreover, with an increasing trend to embrace open-source data and code, data sharing will significantlyenrich both the data quality and quantity available to the public, spurring the usage of machine learningmethods in the electrochemistry field. Researchers can not only train more reliable machine learning modelsbut also can develop novel machine learning architectures that are limited by the data size beforehand. Forinstance, a recent work by Chen et al employed random forest models to discern the fundamental drivingforces of battery aging modes, achieving an accuracy of 86% in classifying aging modes. This investigationrevealed that a combination of active materials loss and a reduction in Li inventory predominately governsthe aging behaviours observed across diverse NMC compositions [26]. Such machine learning applicationswill pave the way to understanding materials aging and diminishing performance degradation of NMCmaterials.The most exciting future developments involve the intersection of modelling, characterization, and ML.Using computational spectroscopy and microscopy, ML models and iterative learning approaches will allowreal time inference on experimental characterization data [27], allowing understanding of redox reaction anddegradation mechanisms, and even spatial inhomogeneity of these mechanisms with mapping techniques.6J. Phys. Energy 5 (2023) 041501 C Zhang et alConcluding remarksThe computational materials science field has come a long way towards predictive modelling of TMOcathode materials. The semi-quantitative prediction of voltages and stability of cathode materials from DFTcalculations is now a matter of routine. The frontier has moved towards the discovery, understanding, andimprovement of existing and yet-to-be-discovered classes of TMO, aided by advanced characterization,computational microscopy and spectroscopy, as well as machine learning approaches.AcknowledgmentsThis work is supported by the U.S. Department of Energy (DOE) Office of Science Scientific User Facilitiesproject titled ‘Integrated Platform for Multimodal Data Capture, Exploration and Discovery Driven by AITools’. M C acknowledges the support from the BES SUFD Early Career award. Work performed at theCenter for Nanoscale Materials, a U.S. Department of Energy Office of Science User Facility, was supportedby the U.S. DOE, Office of Basic Energy Sciences, under Contract No. DE-AC02-06CH11357.7J. Phys. Energy 5 (2023) 041501 C Zhang et al3. Metal anodes for rechargeable next-generation batteriesQiong CaiSchool of Chemistry and Chemical Engineering, Faculty of Engineering and Physical Sciences, University ofSurrey, Guildford GU2 7XH, United KingdomThe Faraday Institution, Quad One, Harwell Campus, Didcot, OX11 0RA, United KingdomE-mail: q.cai@surrey.ac.ukStatusUtilizing metals as anodes is an ultimate solution towards achieving high energy density rechargeablebatteries, due to their high storage capacities and low electrochemical potentials. Among the studied metals(Li, Na, K, Zn, Mg, Ca, Al), Li metal anode (LMA) is considered as the most promising due to the extremelyhigh theoretical capacity and low reduction potential (see figure 2), for next-generation batteries such asLi-metal batteries, Li–oxygen batteries, and Li–sulphur batteries. LMAs started in 1970s but were mainlyused for primary Li metal batteries. The roadblocks for the application of LMAs in researchable Li batteriescome from the formation and growth of Li dendrite, the loss of active Li, and the huge volume change duringthe repeated charge and discharge process, causing breakage of solid electrolyte interface (SEI), significantcapacity fade, piercing of separator, short circuit, and fatal failure of batteries [28]. Therefore, Li-ion batteriesutilizing stable graphite as anodes have been dominant in practical applications.Nevertheless, the promises and challenges of LMAs have attracted significant research interest andespecially extensive research efforts over the past decade, driven by the desire to improve the energy densityof Li batteries for longer driving range of electric vehicles. Through intensive research, four strategies havebeen proposed to enable longer cycle life for LMAs: (1) novel electrolyte additives to regulate the Li mobilityand suppress the Li dendrite growth [29]; (2) novel separators/solid electrolyte with high mechanicalmodulus and flexibility to suppress Li dendrite and accommodate the big volume change [30, 31]; (3)interface engineering to design protective layers at the metal surface [31, 32] hosting structures to stabilizeLMAs [32]. These strategies have prolonged the cycle life to above 100 cycles; longer cycle life of 500–1000cycles might be achievable with continuous research and breakthrough.Recently, Na metal anodes (NMAs) [33] and K metal anodes (KMAs) [34] have gained increasing interestdue to their abundance, low cost, and sustainability. NMAs and KMAs are still in their infancy, showing evenmore severe capacity fade with more un-controlled dendrite growth and different dendrite morphology/properties. More research efforts are needed for developing NMAs and KMAs, with the anticipation that thestrategies for LMAs would also be effective but different materials solutions might be required for each metalanode. Although multi-valent metals (i.e. Zn, Al) have achieved much longer cycle life than alkali metals[35, 36], it lacks a good understanding on their exact working mechanisms during the charge/dischargeprocess and why they behave differently from alkali metals.Current and future challengesTo design high-performance metal anodes, it is pivotal to understand the fundamental mechanisms ofdendrite formation and growth. However, the high reactiveness of metals (especially alkali metals) and theinterfacial process at the anode–electrolyte interface present great challenges for experimental techniques[37]. Microscopy techniques (e.g. optical microscopy, cryogenic electron microscopy) can directly observethe meso-scale dendrite growth process during battery operation, whilst electrochemical measurement (e.g.electrochemical impedance spectroscopy, galvanostatic intermittent titration technique) can be used tointerpret the likely processes at metal anodes [38]. The atomic-scale mechanisms, which are difficult to probeusing experimental techniques, have been poorly understood.Atomistic modelling using density functional theory (DFT), molecular dynamics (MD), and ab initiomolecular dynamics (AIMD) simulations can provide insights into atomic-scale mechanisms (see figure 3).So far, atomistic modelling activities are centred around the following areas: (1) classical DFT calculations todetermine bulk and surface properties of metal anodes, surface energies and thermodynamic stability ofcrystal faces, adsorption energies on the crystal surfaces [39], diffusion pathways and diffusion barriers ofmetal ions on crystal faces, Young’s moduli and shear moduli of crystalline metals, the impact of Cu currentcollectors on the surface diffusion barriers of Li, the formation of coordinated clusters as nucleation seeds onLi and Cu surfaces, the nucleation barriers and nucleation overpotentials [40]; (2) potential-dependentgrand canonical DFT simulations to investigate the thermodynamic origin of different dendrite growthregimes (e.g. epitaxial, mossy, fractal) and SEI formation, linking with intrinsic metal surface properties [41];(3) MD simulations to study the grain boundary (GB) structures of the polycrystalline metal anodes, Lidiffusion through the GB structures, atomic-scale structure mismatch between Li metal and Cu current8https://mailto:q.cai@surrey.ac.ukJ. Phys. Energy 5 (2023) 041501 C Zhang et alFigure 2. The theoretical capacity and reduction potential of different metal anodes.Figure 3. Schematic illustrating the complex processes happening at metal anodes.collectors, generation of vacancies [42]; (4) large-scale MD simulations to study the defects and poreformation within Li metals at the Li metal-solid state electrolyte [43]; (5) AIMD simulations to study thereactions of metal anodes with electrolyte and the formation of SEIs [44, 45].Most of the atomistic modelling work has been on LMA systems, with very limited work on Na and K,and multivalent metals. A systematic approach is needed to compare different metals which will provideinsights in how the chemical and physical nature of different metals dictates different behaviours of metalanodes. To better understand dendrite formation and growth process, bigger nucleation clusters beyond tensof atoms need to be simulated to identify the critical nucleation size and track the initial dendritemorphology change. Furthermore, the model systems need to explicitly include the influence of the realisticbattery environment (e.g. presence of electrolytes, potential SEI layers, potential defects, charge/dischargeprocesses). However, such systematic and thorough studies are computational demanding and require hugecomputational power and time.Advances in science and technology to meet challengesSignificant development and improvement of computational power and atomistic modelling methods (e.g.involvement of smart machines or robotic techniques to automate the simulation processes) are required, toallow: (1) systematic investigations of different metal anodes to shed lights on fundamental mechanisms of9J. Phys. Energy 5 (2023) 041501 C Zhang et althe different behaviours of metal anodes; (2) implementation of model systems that include the fluences ofthe realistic battery environment with the presence of electrolyte, SEI and defects, battery operationtemperatures, charge/discharge process; (3) capture of long-range or time-dependent phenomena such assmall to larger nucleation clusters and continuous growth of dendrite during battery operation. With AIMDsimulations, it is now possible to study the time-dependent breakdown of electrolyte and formation of SEI atthe metal–electrolyte interfaces. The ability to link the SEI with metal dendrite formation and growth willaccelerate systematic materials design and simulations of realistic phenomenon.Correlating atomistic modelling with advanced operando measurements is important to verify the modelsystems and enhance our understanding of the metal anodes at atomic scale. This calls for development ofoperando techniques that can probe atomic or nano-scale chemical and morphological information andprocesses in 3D space as a function of time. At the other hand, atomistic modelling could also be used to helpdesign materials for high performance metal anodes. For example, atomistic modelling could be used todesign highly effective 3D host materials for metal anodes to stabilize the plating/striping process duringbattery operation, and provide fundamental insights into the underlying mechanisms.The conventional atomistic modelling studies using DFT, MD, and AIMD are computationally intensiveand time consuming as they normally involve the examination of a large number of structures andcalculations. Machine learning methods could help speed up the atomistic modelling by reducing andoptimizing the number of structures and simulations needed, thereby boosting the predictive capabilitiesand expanding the boundaries of atomistic simulations. Machine learning methods could also help developforce fields based on DFT calculations and experimental inputs, to enable simulations of larger metal anodesystems (e.g. metals with grain boundaries, systems containing both metal anodes and SEI layers) [46]. Forexample, neural network potentials and inverse generative network have been developed for Li-ion batteriesand could be adapted for batteries based on metal anodes [44, 46].Concluding remarksAtomistic computational research based on DFT, MD, and AIMD simulations provides atomic-scalefundamental understanding of metal anodes and critical processes such as dendrite formation and growth,which cannot be obtained with meso- and macro-scale approaches. The atomic-scale understanding of metalanodes is still limited and patchy, with current studies focusing on small and partial metal anode systems. Thefull potential of atomistic computational research is yet to be unleashed, for systematic and thorough studiesof metal anodes to understand the underlying mechanisms of different metal behaviours. Development ofmachine learning methods are required to speed up such atomistic simulations. Machine learning methodswill be useful in assisting DFT calculations by reducing and optimizing the number of structures andcalculations, enabling fast screening. Machine learning methods will also be helpful in developing force fieldsfor large-scale MD simulations of metal anode systems considering more complex and realistic batteryenvironment surrounding metal anodes. Atomistic modelling is foreseen to play a crucial role in helpingdesign high-performance metal anodes systems and providing insights in fundamental mechanisms.AcknowledgmentsQiong Cai would like to acknowledge financial support by the Faraday Institution through the LiSTARprogramme (Grants FIRG014, FIRG058) and Horizon Europe through the OPERA consortium (GrantsNumber 101103834).10J. Phys. Energy 5 (2023) 041501 C Zhang et al4. Organic electrode materialsRodrigo P Carvalho1,2, Cleber F N Marchiori3, Daniel Brandell2 and C Moyses Araujo1,31 Materials Theory Division, Department of Physics and Astronomy, Uppsala University, Box 516, 75120Uppsala, Sweden2 Department of Chemistry—Ångström Laboratory, Uppsala University, Box 538, 75121 Uppsala, Sweden3 Department of Engineering and Physics, Karlstad University, 65188 Karlstad, SwedenE-mail: rodrigo.carvalho@physics.uu.se, Cleber.Marchiori@kau.se, daniel.brandell@kemi.uu.seand Moyses.Araujo@kau.seStatusOrganic electrode materials (OEMs) are arising as promising alternatives to enable next generation batterytechnologies thanks to a unique combination of key sustainability aspects (e.g. green chemistry syntheticroutes, renewable resources and easier end-of-life treatments) and molecular versatility (a large possiblevariation of chemical compositions and structures) [47–50]. While such materials have been explored for along time [51], the success of the inorganic counterparts has to some degree hampered the investigation andfurther development of OEMs. Now, with the enormous increase in the demand for sustainable batteries, theresearch on OEMs has been revitalized, and is emerging as a subfield within battery research and technology.Due to limitations in volumetric energy density, these are primarily targeting cells for large-scale energystorage, while using printed electronics and other cost-efficient techniques.OEMs are usually grouped as p-, n- or bipolar-type materials depending on their charge state in theredox reactions [48]. For instance, during battery cycling the n-type redox units will change reversiblybetween the negatively charged (O−) and neutral (O) states while the p-type ones change between neutral(O) and positively charged (O+) states. The direction of such reactions will determine whether they becomeanode or cathode active materials. These definitions and the most common chemistries are displayed infigures 4(a) and (b), respectively. OEMs are generally not very ion-specific, so that progress achieved forLi-ion battery materials would generally also impact other battery chemistries, e.g. Na-ion batteries [48].The most straight-forward OEMs are based on low-Mw crystalline compounds with differentredox-active groups incorporated. Since this gives rise to molecular packing and a high concentration ofelectrochemically active sites, the capacity is comparatively high. In fact, exceptionally high levels of reversibleion insertion have been reported for unsaturated compounds for a phenomenon called ‘superlithiation’ [52].Furthermore, they display fairly stable electrochemical potentials spanning between 0 and 4 V vs. Li+/Lidepending on the used electroactive moiety, and thus rendering it possible to construct high-voltage full cells.The major issue plaguing the development of low-Mw OEMs are their easy dissolution in most commonelectrolyte systems, rendering significant capacity fade of the corresponding cells. One apparent compromiseis thereby to copolymerize organic redox-active unit by attaching it to a polymer backbone [53, 54] or turnthe conjugated backbone itself redox-active [55–58]. The polymer-based electrodes bring also otheradvantages concerning mechanical flexibility, easy casting and film formation and eventually electrochemicalstability. However, this renders a significant compromise with the energy density.The fundamental understanding of the underlying electrochemistry taking place during the charge anddischarging of OEMs is still lacking. Advanced atomic-scale modelling approaches are here playing aprominent role. However, these are still limited considering the relevance of the research field. Earlier workshave employed molecular modelling within density functional theory (DFT) to investigate thethermodynamics of redox process, and has provided some relevant insights [59–63]. However, the need for aproper modelling of the crystalline environment has prompted a combination of DFT with crystal structureprediction approaches (e.g. evolutionary algorithms) in a number of studies [64–67]. Moreover, recentstudies have been exploring artificial intelligence methodologies to accelerate the discovery of novel OEMs[68–70].Current and future challengesThere are still fundamental issues related to energy density, rate capability and cycling stability that need tobe resolved for OEMs to become a competitive technology. Such drawbacks are intrinsically connected to thelow concentration of redox-active units, low electronic and ionic conductivity and high reactivity duringbattery cycling.Rational design methodologies need to be developed to explore the huge chemical space provided by theorganic realm [71] in order to accelerate the discovery of suitable OEMs. This could only be achievedthrough a fundamental understanding of the electrochemical reactions at molecular level, which remains as achallenge. The nature of the organic compounds makes it difficult to employ the standard experimental11https://mailto:rodrigo.carvalho@physics.uu.sehttps://mailto:Cleber.Marchiori@kau.sehttps://mailto:daniel.brandell@kemi.uu.sehttps://mailto:Moyses.Araujo@kau.seJ. Phys. Energy 5 (2023) 041501 C Zhang et alFigure 4. (a) Definition of p- and n-type materials ([48] John Wiley & Sons. © 2018 WILEY-VCH Verlag GmbH & Co. KGaA,Weinheim) and (b) most common redox chemistry in organic materials (reprinted (adapted) with permission from [52].Copyright 2016 American Chemical Society).techniques used for inorganic battery electrodes, e.g. operando-XRD or XPS to explore the bulk structure andsolid electrolyte interphase, respectively. The different elements (dominated by C, N, O) can be difficult todistinguish from each other with electron scattering techniques, the crystallinity is often incomplete, and theelements are similar to those used in the electrolytes and electrode additives. Moreover, synthesis andcharacterization of the huge amounts of organic materials theoretically available, to fully explore allpossibilities, would certainly be unfeasible.There are several problems to resolve for the critical understanding of the bulk properties of OEMsduring battery operation. This is at present a bottle-neck for materials development, since the interplaybetween chemical composition, OEM structure and electrode morphology and the resulting electrochemicalproperties are far less developed than for inorganic counterparts. Key issues regard reaction kinetics andenergetics of the OEMs, mass transport and structural chemistry. The operating voltage is controlled boththrough the electroactive moiety in the compound and its chemical surrounding, while the rate performanceis controlled by ionic and electronic transport. Their interrelations are far from being properly elucidated.Yet one property that requires considerably more attention are the interfacial properties of OEMs inbattery cells. These will control the possible decomposition reactions of both electrolyte (as for solidelectrolyte interface (SEI) layer formation for inorganic counterparts) and the electrode materialsthemselves, while they will also strongly affect the dissolution of active material into the electrolyte. Suchinterfacial chemistry of OEMs has only started to be mapped, and only for a few selected systems. The field isdecades behind that of inorganic counterparts. There is thus a great opportunity here for the development ofmodelling approaches at different scales in space and time.An important development was the implementation of evolutionary algorithms interplayed with DFTcalculations to resolve the crystal structure (without need of experimental inputs), which allowed a morefundamental understanding of the solid-state electrochemistry of OEMs [64–67]. However, this constitutes acomputational demanding strategy that hinders its use for more extended high-throughput screeningpurposes. In this sense, there is a need for alternative methodologies to explore the vast number of possiblecandidates. Surrogate models to fast and efficient prediction of the materials properties, based on artificialneural networks, have been developed [68–71]; but it is still a challenge to achieve accurate results with smalltraining datasets. Another great challenge in this field is the development of multiscale models to assess theelectrochemical properties of the amorphous and crystalline polymeric electrodes. This is in fact muchneeded as it is known that organic materials can display polymorphism [72], be completely amorphous as isthe case of polymeric materials, and even lose crystallinity upon cycling.Advances in science and technology to meet challengesThe interplay between first-principles modelling (based on DFT) and artificial intelligence techniques (e.g.machine learning and evolutionary algorithms) is opening new horizons in materials science by accelerating12J. Phys. Energy 5 (2023) 041501 C Zhang et alFigure 5.Workflow for the AI-driven in-silicon design of novel OEMS (reproduced from [68]. CC BY 4.0). Two datasets aredeveloped (crystals and molecules) to train the AI-kernel including linear and neural models, which in turn facilitate thehigh-throughput screening of millions of molecules.the discovery of novel compounds. These data-driven methodologies are already having an impact on thedesign of novel OEMs and they will continue playing an important role in the consolidation of thesetechnologies. Figure 5 displays a workflow of such computational materials design approach that we haverecently proposed [68]. This AI-driven design was extended to post-lithium chemistries and also to providean initial assessment of the materials redox stability [69].In a first assessment, the gas-phase molecular modelling has given important insights about thestructure-properties relationships. For instance, it successfully described the thermodynamics trend forsuperlithiation process in dilithium benzene-dipropiolate (Li2BDP) [52]. In a broader context it has alsobeen employed to assess lithiation limits of high-capacity organic battery anodes in combination withso-called atomic charge derivative analysis [73]. The molecular modelling will certainly continue beingdeveloped to acquire knowledge on the electrochemical trends using cheaper computational methods.The evolutionary algorithms in connection with DFT calculations will be further explored as a powerfultool to determine the crystal structure when having only the chemical composition as input. Here, by startingwith an initial set of randomly generated crystal structures, the geometry optimization is performed usingDFT calculation and the free energy of each structure is computed. The energetically most favourablestructures are selected to form the first population of individuals. With those individuals, a series ofevolutionary inspired operations are performed to form the next generation of individuals. This is followedby another round of DFT based geometry optimization and energy evaluations. This procedure is repeateduntil the halt criteria, e.g. variation of free energy, is reached. Such methodology must be connected with lesscostly computational methods like tight-binding DFT to explore more complex systems and larger materialslibraries. Novel solid-state approaches allowing the investigation of metastable structures may also be furtheradvanced [74].Molecular dynamics (MD) simulations will also be critical to understand both the interplay betweenatomic-scale structure and dynamics in these complex systems, as well as elucidating transport processes inelectrodes and in the active materials itself, which is largely unexplored today. There is plenty of force fielddevelopment made for organic compounds from simulations of biological systems which are adequate to usefor OEMs, while AI-developed force fields could also provide useful solutions in the near future. Thesimulation of interfacial chemistry could be especially rewarding, where a rapid methodology improvementhas been seen for inorganic counterparts in recent years, but should be transferred also to OEM-basedsystems.Concluding remarksThe great demand for the development of sustainable battery technologies has revitalized the research onorganic electrode materials. It is in turn prompting the development of novel molecular modellingapproaches not only to achieve the fundamental understanding of their electrochemistry but also to13https://creativecommons.org/licenses/by/4.0/J. Phys. Energy 5 (2023) 041501 C Zhang et alaccelerate the discovery of new materials. For instance, DFT based calculations have been interplayed withevolutionary algorithms to resolve the crystal structures at different Li-ion insertion stages while surrogatemodels, based on artificial neural networks, have been developed to predict materials properties at muchlower computational costs. The latter has made it feasible to explore a vast materials library and it has beenintegrated in a novel computational materials design platform for OEMs. Molecular modelling is foreseen tocontinue playing an important role in the consolidation of these technologies. Multiscale approaches shouldbe further developed to investigate the morphology effects establishing the structure-propertiesrelationships. Furthermore, the interfacial modelling of OEMs in battery cells is also very important tounderstand the possible decomposition reactions of both electrolyte and the electrode materials themselves,which may lead to formation of SEI. Finally, MD simulations, using AI-developed force fields, will be criticalto understand ion transport mechanism in these complex systems.AcknowledgmentsThe authors acknowledge support from the Swedish Research Council (Grant Numbers 2018-04506 and2020-05223), the Swedish Energy Agency (Grant Number. 45420-1) and STandUP for Energy.14J. Phys. Energy 5 (2023) 041501 C Zhang et al5. MOF-based supercapacitorsMing Chen, Xiangyu Ji and Guang FengState Key Laboratory of Coal Combustion, School of Energy and Power Engineering, Huazhong Universityof Science and Technology, Wuhan 430074, People’s Republic of ChinaE-mail: gfeng@hust.edu.cnStatusElectrical double layer capacitors (EDLCs), also called supercapacitors, have played an increasing role in theenergy storage community, because they bridge the gap between batteries and conventional capacitors [75].With the significant progress over the last decades, commercial EDLCs can provide a high power density ofapproximately 30 kW kg−1 but a moderate energy density (∼10 Wh kg−1), which is noticeably lower thanthat of lithium-ion batteries (∼300 Wh kg−1) [76, 77]. Therefore, the primary focus of current research anddevelopment in the field of supercapacitors is to improve their energy density while maintaining high powerdensity.Metal-organic frameworks (MOFs), characterized as a class of crystalline sponge-like materials with aperiodic network structure formed by metal nodes and organic ligands, have been identified as a type ofpromising electrode candidates for supercapacitors, on account of their exceptional specific surface area,controllable pore size, and tuneable chemical functional groups [78–80]. As shown in figure 6, owing to thesuccessful synthesis of exceptionally stable and highly porous MOFs in the 1990s [81, 82], tens of thousandsof MOFs have been reported and developed [78–80]. However, the majority of these MOFs werecharacterized as electrical insulators with low charge mobility. Consequently, MOFs have traditionally beenemployed as sacrificial templates or precursors to yield MOF derivatives as electrode materials [80]. Despitecertain advantages (e.g. high conductivity or high specific capacity) obtained from such modification, it canalso cause an inadvertent collapse of some unstrengthened MOF-derived electrodes during charging anddischarging, deteriorating their electrochemical performance [83, 84].The first conductive MOF (c-MOF), named Cu[Cu(pdt)2] (pdt= 2,3-pyrazinedithiolate), was reportedin 2009, delivering an electrical conductivity of 6× 10−4 S cm−1 [85]. Since then, many c-MOFs withdistinctive electronic structures have begun to sprout [86]. In particular, a 2D c-MOF, Ni3(HITP)2(HITP= 2,3,6,7,10,11-hexaiminotriphenylene) was developed to show high conductivity with bulk and filmvalues up to 2 and 40 S cm−1, respectively [87]. When this 2D pristine c-MOF was used as a sole electrodewithout any binders and additivities, it demonstrated excellent capacitive performance with a specificcapacitance of up to 111 F g−1 in organic electrolytes, indicating that pristine c-MOFs can be employed assupercapacitor electrodes without any modifications [88]. This landmark work has opened up a newopportunity for using the pristine MOF as supercapacitor electrodes. Subsequently, c-MOFs with organicligands formed by triphenylene or hexaaminobenzene have been successfully employed as electrodes withextraordinary capacitive performance in aqueous electrolytes [89, 90]. Meanwhile, the structure and energystorage performance of c-MOF immersed in ionic liquid electrolyte were described quantitatively for the firsttime through a joint work of molecular dynamic (MD) simulation and experiment [91]. Future advances inthis field could potentially see the realization of appropriate c-MOF electrodes in EDLC applications.Current and future challengesDespite recent significant advances in research to enhance the capacitive performance of supercapacitorswith pristine c-MOF electrodes, their practical realization with high energy storage performance is still in itsearly stages [92, 93]. The major challenge of c-MOF-based EDLCs lies in the lack of fundamentalunderstanding of the EDL structure formed by the MOF electrode and the electrolyte at the nanoscale andthe behaviour of ions confined in complex nanopores, making it intolerable to sift out pleasing c-MOFelectrodes through the standard trial and error methods.Specifically, various combinations of metal nodes and organic ligands would generate dramaticallydiverse c-MOFs topologies, presenting different pore sizes and pore shapes. The non-ideal pore shape canhave a significant effect on the distribution of electrolyte ions inside the pore. Meanwhile, the classical theorybased on the ideal-solution model (e.g. Poisson–Nernst–Planck equation) fails to describe the charge storageand ion transport inside nanopores [75, 94]. MD simulations are useful to elucidate the mechanism of thecapacitance performance of energy storage properties of the c-MOFs by monitoring the fluxes andelectrosorption of the ion in nanopores during the charging and discharging process [80, 94].In the past decade, the majority of EDLC modelling has been done with the constant-charge method,which can provide a qualitative comprehension of the EDL structure on the ideal surface [95]. However, thisapproach is limited in its ability to properly reproduce the behaviour of ions within the polarized c-MOF15https://mailto:gfeng@hust.edu.cnJ. Phys. Energy 5 (2023) 041501 C Zhang et alFigure 6. The timeline of MOFs for supercapacitors [81, 84, 85, 88, 89, 91]. Adapted from [81], with permission from SpringerNature. Reprinted (adapted) with permission from [84]. Copyright 2008 American Chemical Society. Reprinted (adapted) withpermission from [85]. Copyright 2009 American Chemical Society. Adapted from [88], with permission from Springer Nature.[89] John Wiley & Sons. © 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim. Reproduced with permission from [91].Copyright © 2020, The Author(s), under exclusive licence to Springer Nature Limited.systems, as the partial charges of the c-MOF atoms remain static during the simulation in an unphysical way[91]. The MD simulations with the constant potential method (CPM), where the electrons of the metallicsurface respond to the motion of nearby ions to maintain a constant potential at the surface by dynamicallyadjusting an electrostatic field and in turn affects the behaviour of ions, are required to gain a deeperunderstanding of the energy storage mechanism in c-MOF-based EDLCs. However, molecular simulationson c-MOF-based EDLCs are still scarce [91]. Moreover, current CPM studies have been limited to thepotentiostatic mode, which does not accurately reflect the galvanostatic charge–discharge (GCD) modewidely used in experimental settings. CPM simulations on c-MOF EDLCs with more realistic chargingconditions are required for future advances [96, 97].In addition, the electrochemical stability of c-MOF, as another crucial factor in determining thecapacitive performance, has been investigated based on the electronic structure of pure c-MOF via densityfunctional theory (DFT) [86]. However, the effect of electrolytes on the physicochemical properties ofc-MOF electrodes under polarization cannot be ignored. An accurate prediction on the electrochemicalwindow of c-MOF-based EDLC remains a virgin area.Despite the ability of CPM simulations to capture the interfacial structure and ion transport innanopores of c-MOF electrodes clearly, there is still a gap between the microscopic details of ion transportand the macroscale patterns underlying the charging dynamics. In particular, the time constant of chargingobtained fromMD simulation deviates significantly from that observed in experiments. This highlights anurgent request to develop multiscale theory or modelling to link microdynamics to macroscopicalcharging-discharging performance quantitatively.Advances in science and technology to meet challengesUnderstanding capacitive behaviour in c-MOF hosts in favour of the design of innovative electrode materialsand constructing sophisticated c-MOF-based EDLC systems. As shown in figure 7, the first atomic-levelperception of the EDL structure and ion transport inside c-MOF electrodes has been unravelled via CPMsimulation [91]. A quantitative agreement has been achieved between the MD-predicted capacitance andexperimental measurements, establishing a link between the EDL structure and energy storage performanceto some extent [91]. Besides, on the basis of the conventional CPMmethod, a GCD-aimed CPM wasdeveloped to physically control the electric current and maintain a constant potential across each electrodeatom [96]. Further investigation with this advanced MD simulation method (figure 7) is required to furtherimprove the understanding of ion transport behaviour in c-MOF under more realistic charging-dischargingconditions, such as the hysteresis in ion adsorption–desorption dynamics during charging and dischargingwhich has been observed in nanoporous electrode experimentally but not observed in c-MOF electrodes yet[96].Moreover, the physicochemical properties of c-MOF have been extensively investigated via DFTcalculation [86]. However, the influence of the electrolytes on the c-MOF electrode was not taken intoaccount. To accurately describe the electrical structure of c-MOF electrodes under charging conditions, aninteractive MD-DFT model within the EDL should be developed (figure 7). Specifically, advanced CPMsimulations based on a fine-tuned force field are carried out to capture the structures and statistics in the16J. Phys. Energy 5 (2023) 041501 C Zhang et alFigure 7. Advances in science and technology to meet challenges of electrochemical interface modelling of c-MOF-basedsupercapacitors. Reproduced with permission from [91]. Copyright © 2020, The Author(s), under exclusive licence to SpringerNature Limited. Reprinted (adapted) with permission from [102]. Copyright 2020 American Chemical Society.EDL. Then, DFT calculations are employed to extract the physicochemical properties of c-MOF and thecorresponding reduction potentials of the representative species in the EDL. In addition to the previouslypostulated models, an alternative approach involving the amalgamation of quantum mechanical/molecularmechanical (QM/MM) principles can be employed to achieve commensurate functionality [98, 99]. Thismodel elucidates the interface by DFT, while solvent effects are captured through molecular mechanicalframeworks [98, 99]. Currently, research on MOFs via QM/MMmodels predominantly fixates upon theintrinsic properties of MOF materials, such as reaction mechanisms [100, 101]. There is still a lack ofresearch on MOF-based EDLCs via QM/MMmodels.To make up for the gap between the charging and discharging characteristics at the nanoscale and powerdensity at the macroscale, rationalizing the MD-obtained charging dynamics is required (figure 7) [94]. Oneapproach to interpreting the charging process is multiscale modelling with an equivalent circuit model,which includes the transmission line model, where the circuit properties are assumed to be distributedcontinuously throughout the material [91]. Establishing a bridge from the micro to macro level viadimensionless is another feasible method [96].Although the relationship between structure and performance can be established to a certain degreethrough the aforementioned MD simulations, DFT calculations, and multiscale analyses, it becomesinefficient to exhaust all possible combinations and to perform effective analysis to identify a few c-MOFswith glorious performance. As an emerging computer technology to train and analyse input data to disclosepreviously hidden trends, machine learning could offer a promising research direction to speed up thediscovery and design processes for the c-MOF electrodes (figure) [80, 102]. It is worth highlighting that afundamental grasp of the physics and chemistry of these systems is crucial, since decisions cannot behaphazardly left to artificial intelligence.Concluding remarksIn the pursuit of high energy density and power density of EDLC technologies, c-MOFs with uniqueproperties show emerging potential in supercapacitors as promising electrode candidates. The orderednanostructure with well-controlled atomistic architectures serves as a platform to establish structure-function relationships and reliably predict their performance. However, modelling electrochemical interfaceof c-MOF-based supercapacitors is still a challenging task. Further developments in simulation methods,such as the constant potential method with more realistic charging conditions, and MD-DFT model on theelectrochemical properties of MOFs, as well as the multiscale modelling are required to advance theunderstanding of the electrochemical behaviour of MOF-based supercapacitors. Additionally, machinelearning is an auspicious tool to accelerate the discovery and design of c-MOF supercapacitors. Therefore,further in-depth and systematic research with the aforementioned methodologies is essential to bridge thegap between the c-MOF laboratory studies and commercial applications.17J. Phys. Energy 5 (2023) 041501 C Zhang et alAcknowledgmentsThe authors acknowledge the funding support from the National Natural Science Foundation of China(52106090 and 52161135104) and the Program for HUST Academic Frontier Youth Team. M C also thanksto China Postdoctoral Science Foundation (No. 2022T150228).18J. Phys. Energy 5 (2023) 041501 C Zhang et al6. Ionic liquids and carbon-based supercapacitorsKateryna Goloviznina1, Alessandra Serva1 and Mathieu Salanne1,21 Sorbonne Université, CNRS, Physico-chimie des Électrolytes et Nanosystèmes Interfaciaux, PHENIX,F-75005 Paris, France2 Institut Universitaire de France (IUF), 75231 Paris, FranceE-mail: kateryna.goloviznina@sorbonne-universite.fr, alessandra.serva@sorbonne-universite.frand mathieu.salanne@sorbonne-universite.frStatusSupercapacitors are energy storage devices characterized by fast charging/discharging times. This is enabledby a mechanism based on the adsorption of ions from a liquid electrolyte at the surface of high surface areaelectrodes. Unlike Li-ion batteries, the operation is not slowed down by the diffusion of ions inside the bulkof solid materials. In addition, supercapacitors display larger cycle life. In the absence of Faradaic reactions,and due to the small volume change during operations, the chemical and mechanical stresses are limited.Within a cycle, their performance depends on three characteristic properties, the capacitance, the appliedvoltage and the total resistance: the two formers have to be maximized while the latter should be kept as smallas possible.For the electrode, carbon-based materials are the best candidates due to their highly accessible surfacearea, low cost, and good electrical conductivity. The liquid electrolyte is traditionally made of organic ions(e.g. tetraethylammonium tetrafluoroborate) dissolved in acetonitrile, which displays a much largerelectrochemical stability window (ESW) than water. When ionic liquids (ILs) were ‘rediscovered’,supercapacitors appeared quickly as one of the most promising applications. The main advantage of ILs istheir wide ESW, which leads to a substantial increase of the applied voltage [103]. In addition, since ILs aremade of ions only, they were expected to maximize the charge accumulated at the surface of the electrode,hence the capacitance.However, the main weakness of ILs is their low fluidity. This is all the more important since it wasdiscovered that carbon materials with narrow pores, of dimension similar to ionic species, yielded muchlarger capacitances due to the adsorption of desolvated ions [104]. Over the past two decades, most of theexperimental work aimed at formulating ILs with optimized properties [105]. In parallel, the chargingmechanisms inside carbon nanopores were studied by combining many techniques. In this context,molecular dynamics (MD) plays a prominent role together with in situ spectroscopic and diffractiontechniques [106].Current and future challengesThe theoretical study of bulk ILs has now become routine, yielding accurate structural and dynamicproperties, but the study of electrochemical interfaces revealed much more challenging. Conventionaldouble-layer theories were shown to lack many ingredients linked to the highly concentrated characters ofthese liquids [107]. Introducing them lead to a deeper understanding of the phenomenon at play, and inparticular to the discovery of a ‘superionic state’ in which ions of the same sign pack together insideelectrified nanopores [108].In MD studies, electrodes were first treated as homogeneously charged surfaces and model nanoporousmaterials such as carbon nanotubes could be studied, yielding a qualitative view on the ion de-coordinationmechanisms [109]. To reach quantitative agreements with the experimental capacitances, it was necessary todevelop a method in which the electrodes are held at the constant potential to account for the chargepolarization at the surface of the electrodes and to use realistic representations of the disordered nanoporouscarbons as shown on figure 8(a) [110]. The charging mechanisms of nanopores were shown to be dominatedby ion exchange with the bulk, the adsorbed ions being partly decoordinated due to confinement(figure 8(b)). The confirmation of the existence of a superionic state was further validated by in situdiffraction studies [111]. The impact of pore size, geometry, and roughness were also investigated [112, 113]as illustrated in figure 8(c). Concerning the dynamics, the confinement effects lead to a sluggish diffusion ofthe ions which is enhanced by crowding effects [114]. Efficient charging protocols were proposed toovercome this difficulty [115].In complement to recent experiments, MD simulations have recently focused on systems made offunctionalized ILs. For example, surface-active ILs with amphiphilic structures were proposed for increasingthe charge accumulation at the interface (figure 8(d)) [116]. MD simulations showed that this effect was dueto the exclusion of the non-polar alkyl tails from the electrode surface. In another work, redox-active ILswere used (figure 8(e)), leading to a two-fold increase of the capacitance [117]. In these systems, the charge is19https://mailto:kateryna.goloviznina@sorbonne-universite.frhttps://mailto:alessandra.serva@sorbonne-universite.frhttps://mailto:mathieu.salanne@sorbonne-universite.frJ. Phys. Energy 5 (2023) 041501 C Zhang et alFigure 8. (a) Example of a supercapacitor consisting of the [Emim][TFSI] ionic liquid between two porous electrodes(CDC-1200) held at constant potential. (b) Typical structure of the [Bmim][PF6] ionic liquid inside electrified pores of theCDC-1200 material from coarse-grained molecular dynamics. Reproduced from [110], with permission from Springer Nature.(c) Integral capacitances for atomically flat and rough slit pores as a function of pore dimensions for [Emim][TFSI] ionic liquid.The corresponding simulation snapshots are also shown. Reprinted with permission from [112]. Copyright 2015 AmericanChemical Society. (d) Schematics of hypothesized ion arrangements for the [Bmim][AOT] surface active ionic liquid at anegatively charged interface held at=−2 V. Adapted from [116], with permission from Springer Nature. (e) Structural formulaof the [MIm–TEMPO][AQ-PFS] bi-redox ionic liquid. The ionic liquid moieties are highlighted in red and blue, while the redoxmoieties in orange and green.stored inside the ionic species through electron transfer reactions in addition to the charge accumulated onthe carbon surface. Here also, simulations could provide insight into the peculiar structure of the ILs: due tothe large concentration of ions, and thus of redox groups, the latter adopt a percolating structure throughoutthe whole liquid that could favour electron transfers beyond the first adsorbed layer [118].Advances in science and technology to meet challengesDespite the recent advances, several effects remain only partially addressed in current MD studies, preventingquantitative description of complex ILs at electrochemical interfaces. On the electrolyte side, the interactionpotentials were often based on a coarse-grained representation at first, before the advances in computationalpower and in software efficiency allowed for the use of all-atom force fields. However, polarization effects areknown to have a strong impact on the dynamics properties of these systems. In the case of interfaces, theycan also change the adsorption properties of the ions, hence the capacitive properties of the devices. It is onlyrecently that an approach allowing to account for the coupling of electrolyte and electrode polarization wasintroduced in the framework of the Ewald summation method, and implemented in a public software [119].The next challenge consists in the development of adequate force fields for interfaces. A recipe forparametrizing polarizable potentials is now available, which is based on the most popular force field for ILs[120]. It is now necessary to extend it to the carbonaceous materials used for supercapacitor electrodes. Thiswill require performing careful electronic structure calculations since it was shown using highly accuratereference quantumMonte-Carlo calculations that the various density functional approximations yield verydifferent results for the interaction between a liquid and carbon nanostructures [121]. This is due to theimportance of the van der Waals interactions in these systems. Accounting for the flexibility of the carbonmaterials would also be a significant step forward. Although supercapacitor electrodes do not undergo as20J. Phys. Energy 5 (2023) 041501 C Zhang et alsignificant structural changes as Li-ion batteries ones, the small changes may have consequences on the ionadsorption properties.An interesting alternative to the polarizable interaction potentials is the use of machine-learning forcefields. These have proven very useful for modelling systems, and the case of electrolytes was recently putforward [122]. However, the electrochemical interfaces are a particularly challenging case since electrostaticinteractions play a key role, and due to the necessity to account for the electrode potential. Machine-learningforce fields often have a short-ranged character, but physics inspired approaches combining them withconventional Coulomb potentials provide an interesting lead [123, 124]. It is very likely that many researchefforts will be put in this field over the next years.Concluding remarksThe modelling of IL-based supercapacitors has certainly played an important role on the improvements ofthe devices over the years. By providing a more and more precise picture of the structure and dynamics of theions at electrified interfaces, simulations have provided experimentalists the necessary mechanistic insight todesign electrode structures with better performances. The recent advances in the models, as well as thepotentialities opened by machine learning, can bring the field even forward, in particular by allowing thesimulation of complex functionalized ILs. In addition, the work performed on this topic has benefited otherfields, such as the study of electrocatalytic surfaces or of battery interfaces, for which MD is emerging as anew tool to understand the impact of the electrolyte composition and structure on the overall performances.AcknowledgmentsThis project has received funding from the European Research Council (ERC) under the European Union’sHorizon 2020 research and innovation programme (Grant Agreement No. 771294). It was supported by theFrench National Research Agency (Labex STORE-EX, Grant No. ANR-10-LABX-0076).21J. Phys. Energy 5 (2023) 041501 C Zhang et al7. Liquid electrolytes for multivalent batteriesToshihiko Mandai1, Tomooki Hosaka2, Mirna Alhanash3 and Patrik Johansson3,41 Center for Green Research on Energy and Environmental Materials, National Institute for MaterialsScience, 1-1 Namiki, Tsukuba, Ibaraki 305-0044, Japan2 Department of Applied Chemistry, Tokyo University of Science, 1-3 Kagurazaka, Shinjuku, Tokyo, Japan3 Department of Physics, Chalmers University of Technology, 412 96 Göteborg, Sweden4 Alistore-ERI, CNRS FR 3104, 15 Rue Baudelocque, 80039 Amiens, FranceE-mail: mandai.toshihiko@nims.go.jp, hosaka@rs.tus.ac.jp, mirna.alhanash@chalmers.seand patrik.johansson@chalmers.seStatusMultivalent batteries come in different designs and with different promises; less dependent on scarce metals,enabling higher capacities and energy densities, lower price-tags, etc. Here we focus on magnesium (Mg),calcium (Ca), and aluminium (Al) battery electrolytes (figure 9) [125, 126]. Compared to mature batterytechnologies, i.e. lithium-ion batteries (LIBs), the role of molecular modelling concerning liquid electrolyteR&D is here more diverse. It is used to interpret experimental data, design the molecules to be used—bothsalts and solvents, address electrolytes for conceptual issues and promises with respect to the cell designs, andscreen possible electrolyte materials prior to experimental efforts. While bulk electrolyte studies mostly usestrategies and modelling protocols developed for LIBs, metal plating and stripping are fundamentalelectrochemical reactions of uttermost importance for multivalent batteries. Thus, much modelling effortshould be devoted to understanding these mechanisms, especially for the often very special electrolytesemployed.To date, experimental efforts have clearly paved the way for electrolyte development and therefore theinterpretation assistance from molecular modelling to understand mechanisms at the electrolyte/electrodeinterfaces has been a major focus. For Mg batteries, the electrolytes are often still ‘classical’ organo-haloaluminate based, and the modelling focuses on the speciation in the bulk electrolyte [127, 128], withsome notable and recent exceptions focusing on the role of Cl− anions at the electrolyte/electrodeinterface—i.e. for improved plating (and stripping) [129, 130]. More recently, borate and aluminate anionshave been addressed [131], expanding electrolyte composition options for Ca batteries using the very sameanions [132] together with the limited set of ‘conventional’ Ca-salts available [133–135]. For Al batteries, thesituation is quite different as plating and stripping is fundamentally less of a problem in conventional AlCl4−based systems [136]. Despite the large need for Cl− free electrolytes to reduce corrosion issues [137], veryfew novel electrolytes have been proposed experimentally and computationally. Looking at propertiestargeted by the molecular modelling, most are physico-chemical, including local structure/coordination(figure 10) [138], solvation [128], and dynamics [127], rather than electrochemical, but there are somenotable exceptions on e.g. electrochemical stability windows [130, 139] and electrode passivation [140].Current and future challengesGoing forward, it is important to move from basic physico-chemical, speciation and basic ion transport, etc,to more ‘real’ performance related modelling, including more realistic reactions, dynamics, and kinetics. Todo this, we must be able to calculate ion transport under the influence of electric field, include dynamic ioncorrelation, look at the electrolyte decomposition and passivation on the Mg, Ca and Al electrodesurfaces—which in turn demands detailed desolvation processes and activation energies and the kinetics ofeach of these processes. While we so far have not even mentioned the cathode side, there are also challengesas how to model the electrolyte (active) species both for organic and sulphur cathodes—popular choice is tomatch the high capacities of the metal anodes and to avoid the sluggish kinetics of hard cations in inorganicintercalation hosts. There are some recent approaches that seem promising in these aspects, such as thegrand-canonical DFT calculations for electrochemical reactions [130] and MD simulations with ML(reactive) force-fields (FFs) [141]. Moving from methodology to scientific challenges, the modelling shouldbe able to reveal how, and to some extent explain why, Cl− (Mg and Al) and B (Ca) seem to be ions/elementsso crucial for efficient plating & stripping of Mg/Ca/Al at their respective metal anodes. This has already beentouched upon by modelling efforts looking at how to prevent passivation [130, 139] and what role ion-pairsin the electrolyte have in the observed decreased overpotential [129, 130]. Another challenge is to usemodelling to create electrolyte compositional maps and correlate with the generated electrochemically activespecies, including equilibria formed species such as AlCl4−–Al2Cl7− [136]. Finally, there are also manyprospects for other liquid electrolyte designs than the ‘traditional’ salt-in-solvent. Concepts such as(localized) highly concentrated electrolytes ((L)HCEs) may both enhance functionality and safety, and have22https://mailto:mandai.toshihiko@nims.go.jphttps://mailto:hosaka@rs.tus.ac.jphttps://mailto:mirna.alhanash@chalmers.sehttps://mailto:patrik.johansson@chalmers.seJ. Phys. Energy 5 (2023) 041501 C Zhang et alFigure 9. A Venn diagram emphasizing the communalities between types of liquid electrolytes (targeted by molecularmodelling) for different multivalent battery technologies: A: Organo-haloaluminates, B: Organic solvent based, and C: Ionicliquid based.Figure 10. The most common cation 1st solvation shells modelled for Ca2+, Mg2+ and Al3+ electrolytes—showing theimportant role of Cl− anions for the two latter battery chemistries.recently been modelled for multivalent cation conductors [142]. Another possibility is electrolytes based ondeep eutectic solvents, to be further explored by modelling also for multivalent charge carriers [137].Advances in science and technology to meet challengesTo enable proper and accurate treatment of both structure and dynamics, including reactions at interfacesunder influence of electric field and phenomena such as Stern layer and inner and outer Helmholtz layers,better MD FFs are required, ideally also being able to handle and properly describe overpotentials. This isgeneral to the battery field, but due to the inherently slower dynamics and stronger electrostatic interactionscombined with the use of metal anodes, AIMD simulations are not feasible. This issue is even more pressingfor multivalent battery technologies. Alongside this, there is then need for much more experimental data inorder to train ML models and verify these classical FFs needed—all to enable faster simulations andeventually electrolyte design by ML. One route for this would be to do combined experimental andcomputational high-throughput screening—and ML approaches are indeed expected to both push the limitsof how much molecular modelling, especially MD simulations, can contribute as well as bridge the gap toactual electrochemical experiments. However, relying on ML means locking in on concepts where trainingdata is plentiful could prevent further realization of any revolutionary electrolyte designs—that aredesperately needed for the Mg, Ca, and Al batteries alike. Hence, other routes allowing unbiased treatment ofany kind of chemistry, such as today’s popular AIMD and DFT protocols and strategies, will still have a place,and advances in pure computational power may still be a large contributing factor for success.Concluding remarksMolecular modelling efforts of (liquid) electrolytes for multivalent battery technologies follow closely both inscope, concepts, and method development that of LIBs. The main notable differences originate in thecommon use of special counter-anions and metal anodes, and the need to accurately predict and understandthe plating & stripping phenomena. Recent advances in modelling methods and computational capabilitiesare steadily paving the way for modelling the complex electrochemical reactions that occur at the23J. Phys. Energy 5 (2023) 041501 C Zhang et alelectrode–electrolyte interface. Such advanced molecular modelling has deepened the understanding ofelectrolyte-dependent electrochemical reactions and has facilitated electrolyte design. However, theparadigm change of AI and modelling truly guiding experimental efforts—the goal of BIG-MAP [143] andthe Electrolyte Genome project [144]—is not (yet) a reality.AcknowledgmentsP J acknowledges the support from the Swedish Energy Agency (Grant P50638-1) to M A, the EuropeanUnion’s Horizon 2020 research and innovation programme under Grant Agreement 957189 (BIG-MAP), apart of Battery 2030+, his Swedish Research Council’s Distinguished Professor Grant, and Sweden’sInnovation Agency (VINNOVA) through Battery Alliance Sweden (BASE). T M acknowledges financialsupport from the NEXT Center of Innovation Program (COI-NEXT, Grant Number JPMJPF2016) of theJapan Science and Technology Agency and a Grant-in-Aid for Scientific Research (KAKENHI, GrantNumber 21K05263) of the Japan Society for the Promotion of Science (JSPS). T H thanks the JSPS for thesupport through Grant-in-Aid for Scientific Research (KAKENHI, Grant Number 22K14772).24J. Phys. Energy 5 (2023) 041501 C Zhang et al8. Theoretical understanding of single-atom electrocatalysisYun-Ze Qiu and Hai XiaoDepartment of Chemistry, Tsinghua University, Beijing 100084, People’s Republic of ChinaE-mail: haixiao@tsinghua.edu.cnStatusSince the concept of single-atom catalyst (SAC) was first coined in 2011 [145, 146], there has beentremendous progress on developing and implementing SACs for a wide spectrum of topics in heterogeneouscatalysis including electrocatalysis [147–149]. And the applications of SACs to electrocatalysis havedemonstrated great potentials toward industrial deployment for a few vital electrochemical reactionsincluding the hydrogen evolution reactions (HERs), oxygen evolution/reduction reactions (OER/ORR) andCO2 reduction reaction (CO2RR) [149], which compose promising technologies essential to energy andenvironmental engineering. The remarkable achievements of SAC are likely owing to its appealing meritsincluding high stability, activity, selectivity and atomic efficiency [150], as well as its precise tunability that isa key feature for the rational pursuit of optimal catalysts. The precise tunability of SAC arises from itsintrinsic nature by definition, i.e. its active centres are composed of singly dispersed single-atomic sites, sotheir structures are well-defined and uniform. This lays the very foundation for establishing explicitstructure-performance relationships and thus formulating guidelines and theories for designing andoptimizing the catalysts. Thus, the SAC presents an ideal design platform that can exploit the synergybetween experimental and theoretical investigations to deliver high-performing electrocatalysis that meetsthe requirements for practical implementations.In pursuit of the rational design of heterogeneous catalysts, theoretical investigations have been playingan indispensable role in elaborating the atomistic understanding of catalytic performances and formulatingdescriptor-based structure-performance relationships. This is perfectly illustrated by a dazzling line ofresearch, which paved a road from the scaling relations and Brønsted–Evans–Polanyi relation to the volcanoplot that quantifies the Sabatier principle to predict the optimal catalysts [151, 152]. In particular, densityfunctional theory (DFT) calculations were universally employed, and the descriptors from thewell-celebrated d-band theory [153] were widely adopted to rationalize the trends in catalytic performanceand found great success in predicting highly efficient novel electrocatalysts for HER, OER, ORR, and CO2RRwith volcano plots [152]. This research paradigm was seamlessly integrated into the studies of single-atomelectrocatalysts (SAECs), in which the theoretical understanding based on DFT calculations has become anecessary component that often covers identification of active site structures, investigation of reactionmechanisms underlying catalytic performance, and preferably descriptor-based guidelines [154]. Thisroutine, however, is confronted with challenges in every aspect from theoretical methods and catalyticmechanisms to formulations of understanding, which necessitate future endeavours (see figure 11).Current and future challengesThe unparalleled popularity of DFT calculations in computational electrocatalysis is rooted in the balancebetween computational cost and accuracy offered by the commonly used exchange–correlation (XC)functionals mostly at the level of generalized gradient approximation (GGA). Besides, DFT calculations areversatile to include empirical dispersion corrections and implicit solvation effects, as well as the appliedpotential in electrocatalysis using the implicit computational hydrogen electrode (CHE) approach [155] orthe explicit grand-canonical DFT method [156]. Explicit solvation and ions can be further included withDFT-based ab initiomolecular dynamics (AIMD) simulations [157]. However, conventional XC functionalsin DFT are plagued by the delocalization error and static correlation error [158]. The former may bealleviated with+U corrections or hybrid functionals, while the latter requires methods beyond thesingle-reference Kohn–Sham scheme. Unfortunately, the active sites of SAECs are often composed oftransition metal atoms with strong static correlation, and this may greatly compromise the reliability ofcommon DFT results. In quantum chemistry, there are standard high-level wavefunction theory (WFT)methods such as CASSCF and MRCI to tackle the static correlation error, but they are computationally tooexpensive to be practical in computational electrocatalysis. Therefore, there is a demand for new theoreticalmethods that are effective in describing static correlation while computationally viable.In elucidating electrochemical reaction mechanisms, theoretical investigations are often simplified withthe CHE approach that enables thermodynamics-only calculations to estimate the overpotentials and thusconnect to the catalytic performance. Recently, there have been a growing number of studies that furtherincluded kinetics, i.e., transition states and associated barriers, and employed the microkinetic modelling tocalculate the current densities that can be directly compared with experiments [154]. Complications in25https://mailto:haixiao@tsinghua.edu.cnJ. Phys. Energy 5 (2023) 041501 C Zhang et alFigure 11. Challenges in theoretical studies of single-atom electrocatalysis including methods to tackle the static correlation,approaches to explore potential-dependent dynamic reaction pathways, and strategies to formulate quantitative understanding.reaction mechanisms by participations of electrolyte species can also be examined with AIMD simulations.However, catalytic reactions at electrochemical interfaces are coupled with the applied potential, and a strongpotential-dependence may alter the mechanism underlying catalysis in a dramatic manner [159–165]. Astriking example is provided by operando characterizations that identify the reversible transformation ofactive sites in Cu SAEC from Cu single-atoms to metallic nanoparticles (clustering) under negative potentialsin CO2RR conditions, and it is the nanoparticle that is responsible for electrocatalysis [159]. This shakes thecommon assumption in theoretical studies of reaction mechanisms on SAECs that the single-atomic sites areresponsible for electrocatalysis, and calls particular attentions on the coupling between applied potentialsand catalytic mechanisms starting from the dynamic transformation of active site structure. This clusteringalso presents a possible channel for the degradation of SAECs, and future efforts may be necessary to developsystematic strategies/algorithms to generate potential-dependent reaction networks that include the activesite transformations, in order to understand both the catalytic activity and stability of SAECs.In regard of the ultimate goal to design the optimal SAECs, theoretical understanding should providequantitative guidelines in the form of mathematical functions of structure-performance relationship interms of descriptor-based variables. This likely requires establishing approximate theories like the d-bandtheory. However, there are intricacies in formulating such understandings of single-atom electrocatalysis. Arecent study showed that the symmetry of frontier orbitals in SACs can play a decisive role in catalysis andthis results in the failure of d-band theory in characterizing the catalytic performance of SACs [166]. It wasalso demonstrated that the electrostatic interactions arising from local atomic heterogeneity around theactive sites of SACs can play a significant role in delivering the catalysis [167]. Therefore, delicateconsiderations may be required in future endeavours to formulate design principles for SAECs.Advances in science and technology to meet challengesQuantum embedding methods present a promising approach to tackle the static correlation problem in acost-efficient manner [168]. The basic idea underlying these methods is to decompose the whole system intosubsystems that are treated with different levels of theories. This strategy may be a perfect match for thetheoretical modelling of SAEC, where the local structure around the transition metal single-atomic site canbe treated with high-level WFT methods, and the rest (support and environment) is described bycost-efficient methods such as DFT or even force fields. Very recently, there have emerged studies applyingquantum embedding methods to computational electrocatalysis. A notable case study is from Carter’s group[169], in which they applied the approach with embedded correlated wavefunction to study theelectrochemical CO2RR on Cu(111) surface. Developments along this line for the studies of SAECs aremuch-anticipated and should strengthen the synergy between computation and experiments inunderstanding and designing high-performing SAECs.26J. Phys. Energy 5 (2023) 041501 C Zhang et alAIMD simulations have seen rapidly increasing applications to investigate the dynamic catalysis onSAECs, and found great success in revealing the roles of electrolyte species in electrocatalysis. Nevertheless,exploration of reaction mechanisms by common AIMD simulations is limited to the chemical spacepredefined by the collective variables (CVs). Subtle complications like the dramatic transformation of activesite structures in SAECs might be easily overlooked and missed in CVs, and would not emerge naturally inAIMD simulations as they are rare events. These can be further complicated by the potential-dependences ofreaction mechanisms. Very recently, Bai et al [170] elucidated the dynamic evolution of active site structurein Cu SAECs from Cu single-atoms to clusters that is initiated by the adsorptions of H under negativepotentials. Future developments toward automatic and comprehensive exploration of potential-dependentreaction pathways can greatly facilitate the pursuit of a true picture underlying single-atom electrocatalysis.There is a rich toolbox accumulated so far for analysing and extracting intrinsic features in catalysis, aspartly showcased in the previous study [167]. Yet it remains challenging to compose relevant descriptors andthus formulate quantitative structure-performance relationships because of intertwined intricacies present insingle-atom electrocatalysis, and it relies highly on chemical intuitions. Nowadays, the surge of machinelearning (ML) techniques has made a thrilling impact on computational catalysis, and great progress hasbeen made on descriptor-based catalyst discovery with ML techniques [152]. With future advancementstoward systematic extraction of chemically intuitive descriptors and automatic formulation of quantitativestructure-performance relationships based on physical laws, ML techniques may spark a wave of trulybreakthrough studies in the rational design of SAECs.Concluding remarksTheoretical understanding of single-atom electrocatalysis constitutes a core element for the design ofhigh-performing SAECs that unleash their full potentials for industrial applications in energy andenvironment. Yet challenges are present in theoretical studies of single-atom electrocatalysis, from efficientmethods to tackle the static correlation, to comprehensive approaches to explore potential-dependentreaction mechanisms, and to systematic strategies to formulate quantitative and physically sensiblestructure-performance relationships. Nevertheless, there are promising directions to face up these challenges,and hopefully the field will be advancing rapidly.AcknowledgmentsWe are grateful to the financial support from National Natural Science Foundation of China (Nos. 22122304and 92261111), Tsinghua University Dushi Program, National Key Research and Development Project(2022YFA1503000) and Tsinghua University Initiative Scientific Research Program (20221080 065).27J. Phys. Energy 5 (2023) 041501 C Zhang et al9. Theory and computation of the local reaction environment in electrocatalytic mediaMichael EikerlingForschungszentrum Jülich GmbH and RWTH Aachen University, Jülich, GermanyE-mail: m.eikerling@fz-juelich.deStatusHydrogen fuel cells and water electrolysers will be enablers of the epochal green energy transition [171, 172].Among the materials and components that these technologies require to function, the electrocatalyticallyactive layers or catalyst layers (CLs), a type of porous composite electrode, are of critical importance [173].The most advanced CLs are those for the oxygen reduction reaction (ORR) in polymer electrolyte fuel cells(PEFCs). Their development history unveils important lessons, described in [171, 174], in order to speed upCL development for other technologies.Theory and computationTheory and computation provide multifarious approaches to understand, analyse, and predict relationsamong structure, properties and performance of CLs. Figure 12 comprehensively depicts the relevantphenomena, model systems, and approaches. Physical models can be devised to rationalize impacts onperformance, durability and economic viability that are exerted by (1) the catalyst material’s electronicstructure, (2) the catalyst surface atomic structure and chemisorption state, (3) the local reactionenvironment (LRE) at the catalyst–electrolyte interface, (4) catalyst–support interactions, (5) a near-surfaceionomer-skin layer [175], (6) pore size and contact angle distributions in the CL [175, 176], (7)percolation-controlled transport properties [177].Where to seek improvements?Major efforts in the scientific community exploring energy materials for hydrogen technology have beenfocusing on the discovery and design of novel electrocatalysts, relying on descriptors (or feature vectors) thatrepresent electronic structure effects, surface atom arrangement, and chemisorption properties [178, 179].However, the staggering increase in the mass-specific activity of platinum in PEFCs—by about a factor 103over the last 60 years has not been achieved primarily through modification of these properties but mostlythrough advanced engineering and optimization of the electrode medium that the catalyst is surroundedwith. This assertion and the hierarchy of effects in figure 12 imply that more complex features, beyond thosedirectly related to electronic structure and chemisorption properties of the electrocatalyst, must beconsidered.Current and future challengesThe utmost urgency and global dimension of the energy challenge demand a drastic acceleration of thematerials development process, from discovery and design to device level integration and deployment. Fromamong the influencing features, listed as 1–7 above, a minimal set of descriptors (or features) should bedevised to steer the selection and development of catalyst layer materials and guide materials integration,assembly, and fabrication towards CLs with optimal mass activity, power performance and stability. Thisminimal set should guarantee the most rapid and resource-efficient discovery and development process. Anew breed of future labs is emerging to accomplish this mission [180–182]. They are self-drivinglaboratories, comprising autonomous closed-loop discovery systems that blend robotic platforms forsynthesis, fabrication and characterization together with high-throughput screening (HTS), assisted bymachine learning [7], model-driven data analytics [183], as well as physics-aware modelling andhigh-performance computing (HPC).In the field of electrocatalysis, a crucial, albeit often overlooked aspect in this endeavour is that materialsshould be evaluated and compared (e.g. in HTS) under conditions, for which they are expected to performand last in the electrochemical device. This corresponds to closing the loop in figure 12 between modellingand diagnosis at the device level (top in figure 12) that provide the locally prevailing conditions andAI-enabled forays in HTS of materials (‘1 pm position’ in figure 12). In the context of electrocatalysis,knowledge of the local reaction environment (LRE) for a given materials combination under relevantoperating conditions is a crucial prerequisite for the rational selection and accelerated design ofelectrocatalyst materials and CLs. The LRE is the outcome of a complex interplay of electronic structureeffects, surface-transforming reactive processes, electrolyte phenomena, and transport processes thatdemands physical modelling and HPC to be used at various structural levels [184].28https://mailto:m.eikerling@fz-juelich.deJ. Phys. Energy 5 (2023) 041501 C Zhang et alFigure 12. Full-cycle integration of methods in theory and computation to rationalize how catalyst layers form and function, fadeand fail. The arrow that closes the loop from device modelling to ab initio simulations applied of atomistic structure anddynamics symbolizes the importance of knowing the real conditions that prevail at the surface of the catalysts, as a prerequisite ofAI-enabled materials design and development.Theory and computation of electrocatalytic interfaces must account, in a self-consistent manner, forcoupling and correlation effects among electronic, ionic, and solvent subsystems involved [185, 186]. As abasic capability, they should yield the relation between free surface charge density, σM, and electrodepotential, ϕM, not only close to the potential of zero charge but in the potential ranges that are relevant forreactions of interest, such as the reduction or evolution of oxygen or the reduction of CO2. Dependences ofthis fundamental charging relation on pH and electrolyte composition should be captured as well. What’smore, the interface response is dynamic; it involves charge transfer and polarization effects, coupled totransformations in chemisorption state and solvent configuration.Advances in theory and computation to meet challengesDeciphering the local reaction environmentThe ideally suited approach to tackle this challenge would be using first principles methods based onKohn–Sham density functional theory (KS-DFT) that should allow for the explicit control of ϕM, thusbeing grand-canonical [187–189]. Suitable approaches should yield self-consistent solutions for the(sub-)nanoscale distributions of electric potential, pH, and ion concentrations as well as chemisorption stateand solvent properties. Albeit, thus far approaches based on KS-DFT are not able to simulate systems, inparticular the dynamically fluctuating electrolyte side, at sufficient length and time scales [190]. However,molecular simulations are anticipated to receive a boost with further advances in hardware designs, e.g.,multi-GPU processing [191]. The transition to the era of exascale supercomputing [192, 193] might providemuch needed capabilities to expand the reach of quantum mechanical simulations to thermodynamicallyrelevant scales. Moreover, the emergence of machine learned interatomic potentials will help acceleratesimulations and more effectively bridge scales [194–196].To guide advances in simulations, self-consistent approaches with all subsystems accounted for butsimplifying assumptions made in their treatment will continue to be of great value. The first in the line ofdevelopment of such approaches revealed the non-monotonic surface charging behaviour of a platinumelectrode [197], and, thereby, solved an old experimental puzzle [198]. Guided by this development, asimulation approach was adopted that hybridizes KS-DFT for the metal region with the effective screeningmedium reference interaction site method for the electrolyte side [199]. Two very promising results wereobtained with this approach: (i) when correctly set up, especially when treating the near surface water layerexplicitly as part of the quantum region, it provides realistic electrolyte distribution functions in the interfaceand yields interfacial water density profiles that agree with AIMD simulations and (ii) it reproduces, as a firstamong simulation approaches, the non-monotonic metal charging relation of the partially oxidizedPt(111)/electrolyte interface, in agreement with the analytical theory and experiments. There is thusconvergence between theory and simulation to build on, but still a long way to go in terms of bringing realisminto simulations. As a major limitation, in either approach the control variable to define the interface state isnot the electrode potential, but the surface coverage by chemisorbed oxygen as a proxy variable. Due to theunique relation between electrode potential and oxygen coverage, this approach is viable for the Pt electrode.However, it is not generalizable to a wider range of interface problems, since proxy variables to replace theelectrode potential with are not a priori known. A reactive DFT-based approach is needed to close this gap.A further step on the theory side is the development of a hybrid density-potential functional [186].Variational analysis of this functional yields a grand-canonical model of the electrochemical double layer(EDL). It describes metal electrons at the level of Thomas–Fermi–Dirac–Wigner (TFDW) theory and treatsthe electrolyte solution classically at the mean-field level, taking into account electrostatic interactions, ion29J. Phys. Energy 5 (2023) 041501 C Zhang et alFigure 13. Heterogeneous and asymmetric nanostructure, account-ting for key structural features at interfaces in PEFCcatalyst layers.size effects, and nonlinear solvent polarization. The model uses parametrizable force relations to describe theshort-range forces between metal cationic cores, metal electrons, electrolyte ions, and solvent molecules.Partial charge transfer in the presence of ion specific adsorption is treated in Anderson–Newns theory. Withthese features, the model represents a viable framework to study EDLs under the constant potentialcondition, as needed for deciphering multifaceted EDL effects in electrocatalysis. The approach reproducesthe capacitive interface response of the Ag(111)–KPF6 system. Future refinements should account forfluctuation effects and correlations [200, 201]. Moreover, limitations of the simple TFDW theory need to beovercome with more advanced functionals [202].Accelerated computational protocol for extended simulation of interfacesIn the future, KS-DFT-based first principles simulations of electrochemical interfaces, microkinetic modelsparametrized with energy parameters from KS-DFT calculations, and machine learning (ML) will becombined to study reactive processes at extended time and length scales. ML models of interatomic potentialenergy and force fields based on deep neural networks have the potential to overcome the accuracy vs.efficiency dilemma molecular simulations [203]. Deep potential molecular dynamics (DPMD) simulationswith precision comparable to KS-DFT-based simulations increase the length and time scales of ab initiomolecular dynamics with a computational cost that scales linearly with system size [204]. DPMD simulationsare required to examine the influence of structural composition on the surface-controlled coupled dynamicsof water and ions. These elements can be combined together into multistep computational protocols fordetermining the structure and composition of the most stable interface structures for varying electrodepotential and pH, and then use those structures to conduct MD simulations of dynamic processes at theinterface.Infuse interface simulations with a sense of realismIn typical journal articles on CL structure and function, it can often be read that the ‘catalyst is in contactwith ionomer’. What does ‘contact with ionomer’ mean or imply? The wording as such is a problem and themisconception behind the wording is challenging to overcome. In a well-functioning CL under relevantoperating conditions, the catalyst is not in contact with ionomer, but with water in a confined region that isbound on one side by catalyst and support and on the other side by an ionomer skin layer, cf Figure 13. Thesewater-filled nanogap regions with width< 2 nm are asymmetric and heterogeneous. Supported nanoparticlesystems result in heterogeneous surface charging on the metal side of the gap. The ionomer skin exhibits ahigh charge density due to fixed but flexible anionic charges. Deep-potential MD simulations with propertreatment of surface charging, dipolar, and polarization effects can be used to determine the stability of sucha nanoprotonic gap. Compared to fixed interface and charge configurations considered in References [205,206], interface properties at the catalyst–support boundary can be continuously tuned by ϕM—the interfacewill ‘breath water in or out’, which should be exciting ‘to see’ in a future simulation! Potential and protondensity distributions and the electrocyclic activity in the gap will respond to these variations. Theoretical andDPMD-based studies will be of great value for studies of these phenomena.Concluding remarksCatalyst–electrolyte interfaces are ubiquitous in electrochemical energy science. Detailed assessment ofdynamic processes involved in desired and undesired electrocatalytic processes hinges on knowledge of thelocal reaction environment at these interfaces. Advanced self-consistent theoretical approaches andcomputational approaches accelerated with machine learning will be needed to decipher this environmentfor realistic interface configurations and in operando conditions. Understanding the conditions that prevail30J. Phys. Energy 5 (2023) 041501 C Zhang et alin the water-filled nanoprotonic gap region between catalyst/support and ionomer skin layer will be crucialto steer the design and rapid screening of catalyst layer materials and to guide their assembly into anoptimally functioning and stable electrode.AcknowledgmentsThe author acknowledges funding of research presented in this article from the Helmholtz-GemeinschaftDeutscher Forschungszentren e.V. (HGF), Program-oriented Funding (PoF IV), under the Research ProgramMaterials and Technologies for the Energy Transition (MTET).31J. Phys. Energy 5 (2023) 041501 C Zhang et al10. Modelling andmachine learning of fuel cellRyosuke JinnouchiToyota Central R&D Labs., Inc., 41-1 Yokomichi, Nagakute, Aichi 480-1192, JapanE-mail: e1262@mosk.tytlabs.co.jpStatusProton exchange membrane fuel cells (PEMFCs) are promising power sources for automobiles. Severalautomakers have commercialized fuel cell vehicles with the required power density and durability [207], andfurther extensions of applications are expected for heavy duty transportations, such as trucks, buses, trains,ships and so on [208]. For wider applications, however, higher energy conversion efficiency, longer durabilityand lower cost are desired [209]. These demands are demonstrated by the performance and cost target set byNew Energy and Industrial Technology Development Organization (NEDO) in Japan [210]. Figure 14 showsthe target current–voltage (IV) curve of a single cell for heavy duty transportations in 2030 and the curve ofthe second-generation Toyota MIRAI (Gen2-MIRAI). The NEDO roadmap reports that the applicationsrequire the significantly higher efficiency than Gen2-MIRAI as well as a higher maximum operationtemperature of 378 K and longer operation time of 50 000 h. The target IV curve was decomposed to thetarget properties of constituent materials by using a multi-physics simulation predicting an IV curve of asingle cell from properties of materials. The resulted target properties of the cathode catalyst for oxygenreduction reaction (ORR) and polymer electrolyte are shown in the same figure. The simulation indicatesthat the target IV requires the high catalytic activity, gas diffusivity of catalyst layer (CL), proton conductivityof electrolyte and durability. Accordingly, advanced electrode and electrolyte materials are necessary.Current and future challengesModelling and simulations have provided essential information on understandings and designs of PEMFCsand constituent materials. As illustrated by the NEDO roadmap [210], the multi-physics macroscopicsimulation [211] solving diffusions, conductions and reactions can determine the performance of the singlecell from the properties of materials and vice versa. To get ideas of high-performance materials, microscopicsimulations are necessary. The time- and length-scales of relevant reactions and transport phenomena spanover 0.1 nm to 1 m and 1 fs to days (or even years), and a single method cannot solve the problems. Thus, avariety of simulations suited to each scale have been developed as illustrated in figure 15. The continuumtheory simulation [212] is a powerful method to solve the heterogeneous reaction field in the 3D cathode CLthat is a porous medium composed of Pt nanoparticles supported on carbons and polymer electrolyte.Coarse-grained molecular dynamics (MD) simulations have been used to predict the mesoscale porousstructure [213], and full-atomistic classical MD simulations assuming empirical interatomic potentials [214]have been used to predict atomic scale structures and transport coefficients required for the continuumtheory. Potential-dependent catalytic rate constants of electron transfer reactions can be obtained byfirst-principles (FP)-based models of electrified interfaces [215] and can be used in the FP-basedmicrokinetic catalytic reaction models [216]. FP method is also a powerful tool to predict thermodynamicstability (Pourbaix diagram) of materials [217]. These FP methods have been used to clarify reactionmechanisms of advanced catalysts and to explore active and stable catalysts [216]. The growth ofmachine-learning (ML) technologies and databases have extended the applicability of these simulationmethods. The FP-database was, for example, used to identify acid-stable oxides in the cathode environment[218], and a convolutional neural network model was used to accelerate the screening of ternary Pt alloycatalysts [219]. ML-based image recognition technologies also enabled accurate reconstructions of CLstructures from microscopy images, which are required for the continuum theory simulations [220]. Thereare, however, a lot of challenges in simulations of complex practical materials. Difficulties mainly arise incomputations of distribution functions, transport coefficients, potential-dependent reaction rates andinteratomic potentials, which need to be transferred from one scale to the other in the multi-scale simulationframework. Empirical interparticle interactions of coarse-grained MD methods often involve significanterrors, and the resulted properties can be unreliable. The same problem also happens in interatomicpotentials of classical MD methods particularly for reactive systems. Although FP methods accurately predictthe atomic interactions, they are too expensive to realise sufficient statistics required for accurate predictionsof thermodynamics and kinetics.Advances in science and technology to meet challengesEmerging ML technologies are the key to surpass the previous limitations of the modelling and simulationstoward accurate and robust bottom-up approaches starting from FP methods. ML interatomic potentials32https://mailto:e1262@mosk.tytlabs.co.jpJ. Phys. Energy 5 (2023) 041501 C Zhang et alFigure 14. IV curves of the target in 2030 set by NEDO and Gen2-MIRAI. The table summarizes the target properties of thecathode catalyst layer (CL) and proton exchange membrane. Data were taken from [210].Figure 15.Multi-scale simulations of electrode and electrolyte materials. Thermodynamic and kinetic properties are transferredfrom one simulation to the other, enabling predictions of desired properties.(MLPs) were shown to realize orders of magnitude faster computations of interatomic interactions retainingnear FP-accuracy [221], and state-of-the-art active-learning schemes accelerated the time-consumingtrainings containing preparations of FP datasets [222]. Several MD simulations using MLPs were conductedon anhydrous electrolytes [223] and water/Pt interfaces [224, 225] and exhibited promising results.33J. Phys. Energy 5 (2023) 041501 C Zhang et alML-algorithms were also demonstrated to systematically construct interparticle interactions of coarse-grained model that can accurately compute free energies of solvated molecules [226]. Because MLPs forcomplex multi-element systems need large FP datasets, their applications are still limited to simple systems.In this rapidly growing field, however, many advanced MLP algorithms are investigated, and accuracy andefficiency continue to improve [227]. In addition to the MLP algorithms, efficient and robust statisticalsampling algorithms combined with MLPs are also necessary in order to accurately predict thethermodynamics and kinetics of electrolyte and electrode materials. Free energies of reaction intermediates,for example, are essential descriptors of the catalytic activity, but most of FP-based methods compute the freeenergies by assuming harmonic vibrations of atoms [216] although interfacial solvent molecular motions areanharmonic. The same difficulties also appear if one tries to compute potential-dependent activation freeenergies beyond the descriptor-based approach [228]. This severely limits the applicability of the FP methodto many significant electrolyte effects on the activity and durability of catalysts [229, 230]. Recent studies[231, 232] demonstrated that MLPs can be used as surrogate models that enable efficient thermodynamicintegrations to compute free energies of hydrated ions and adsorbates. Although the examined systems weresimple aqueous systems, the algorithm combined with accurate MLPs will provide quantitative predictionsof free energies of complex heterogeneous materials.Concluding remarksA wide variety of simulation methods have been developed and have provided indispensable information,such as breakdown of overpotentials of a single cell [211], volcano plot of ORR [216] and bottleneck oftransport phenomena in cathode CL [214], for designs of PEMFCs and advanced materials. The widedistribution of PEMFCs, however, demands further innovative materials. For the discoveries, unexploredmaterials and systems need to be examined by simulations as well as experiments. MLP-aided statisticalsampling of dynamically fluctuating electrode/electrolyte interfaces is expected to provide a platform of newdiscoveries because several experiments [228, 229] reported significant electrolyte effects and because thesystems have not been sufficiently examined owing to challenges in the conventional simulations. ML-aidedseamless connections from the FP method to the coarse-grained MD is also expected to provide a platformbecause the mesoscopic self-organization of porous cathode CL involves many unclarified questions. Webelieve that the new simulations will pave the way to discoveries of guiding principles for innovativematerials.34J. Phys. Energy 5 (2023) 041501 C Zhang et al11. Modelling electrochemical interfaces and reactions with GPAW: grand canonicalensemble DFT approachesMarko MMelander1 and Georg Kastlunger21 Department of Chemistry, University of Jyväskylä, Jyväskylä, Finland2 Department of Physics, Technical University of Denmark, Lyngby, DenmarkE-mail: marko.m.melander@jyu.fi and geokast@dtu.dkStatusGrand canonical ensemble density functional theory (GCE-DFT) is a theoretically rigorous way to simulateelectrochemical interfaces under constant electrode potential and electrolyte activity conditions directlymimicking experimental conditions as depicted in figure 16 [188]. GCE-DFT explicitly regards the electrodepotential in simulations and complements the widely adopted computational hydrogen electrode (CHE)method [155]. In particular and unlike CHE, GCE-DFT can be directly applied to simulate constantpotential reaction kinetics [233], decoupled electron proton transfer reactions and non-Nernstian pH shifts[234, 235]. Thus, a combination of CHE and GCE-DFT is able to describe any thermodynamically-stableand transition state within complex reaction mechanisms at arbitrary potentials and pH [236].In recent years, several practical realizations of GCE-DFT have been implemented in the GPAW code[237]. GPAW is an open-source, Python-based DFT code using the projector augmented wave (PAW)method and allows calculations within real-space grid (FD), LCAO [238] and plane wave (PW) basis sets.The Python environment together with Numpy [239] and Scipy [240] facilitates implementation, whilenumerical performance is guaranteed by external C/C++/Fortran libraries. Unlike PW-based GCE-DFTimplementations [241], GPAW works in real-space within FD and LCAO bases; this allows direct utilizationof natural 2D periodic boundary conditions (PBCs) for the electrode and electrostatic potential [188, 233,242] difficult to achieve with PW codes [243]. The 2D PBCs effectively build a reference electrode within thesimulation cell [188, 242] provide correct decay of the electrostatic potential needed for treating continuumelectrolytes, and allow the simulation of asymmetric slabs/electrodes. All these features combined makeGPAW a flexible environment for GCE-DFT development.Constant potential calculations can currently be performed either by iteratively fixing the work function[233], Fermi level or the electrode inner potential [242], following the algorithm outlined in figure 16. Cellcharge neutrality is maintained by the solvated jellium method [233] which offers a computationally stableand fast method with a correctly behaving electrostatic potential. Also Poisson–Boltzmann electrolytemodels have been implemented [188] but these are currently not available in the main branch because ofnumerical instabilities due to the underlying finite-difference Poisson solver. The solvent is treated as a lineardielectric continuum [244] although a classical DFT model of water is also available [245] but not yet testedfor electrodes. GPAW’s GCE- DFT methods automatically provide the Legendre-transformed total GCEenergies. Thus, they can directly be combined with e.g. nudged elastic band calculations to obtain constantpotential reaction kinetics or constrained DFT [246] to build GCE-DFT diabatic states [247] for thesimulation of Marcus-like electron and proton transfer kinetics.Current and future challengesGPAW already achieves out-of-the-box stable and efficient GCE-DFT calculations for a wide variety ofsystems and the main challenges are related to improving upon current numerical methods andapproximations. Like in most solid state codes, only a linear dielectric model is currently available and theparametrization is limited to aqueous systems and small molecules—there are no parameter sets for metallicor other electrode surfaces. Also going beyond the linear dielectric model is expected to improve the solventdescription and the surface capacitance in particular. Combining more general dielectric and electrolytemodels with improved parametrizations for surfaces would hopefully also enable the simulation of morecomplex solvents, including models for complex aqueous electrolytes [248] or the modelling the capacitanceand layering of ionic liquids [249]. Another challenge is going beyond the dielectric continuum models andtreat the electrolyte with more refined methods based on the statistical theory of classical liquids [250], suchas reference interaction site method (RISM) and classical DFT approaches.As mentioned above, the current dielectric continuum model uses the finite-difference Poisson solverwhich is known to perform badly for elongated system such as slabs with extend vacuum or dielectricregions. In default GPAW calculations this was recently resolved by implementing a Fourier and Fourier-sinetransform-based FastPoissonSolver, which not only makes slab calculations faster but also numerically morestable. In currently unpublished work, we have extended this solver to the dielectric continuum Poissonsolver and observed greatly improved performance. In the future, we expect this to stabilize the convergence35https://mailto:marko.m.melander@jyu.fihttps://mailto:geokast@dtu.dkJ. Phys. Energy 5 (2023) 041501 C Zhang et alFigure 16. Left: Illustration of a GCE-DFT simulation with a fixed electrochemical potential of electrons (µ̃n) and solvent (µ̃sol) tocontrol the electrode potential and solvent properties, respectively. Right: Simplified workflow of the current realization ofcalculating GCE-DFT energies within GPAW. Note that in contrast to fixed charge DFT calculations two convergence criteria needto be fulfilled, namely the convergence of the electronic workfunction (Φ e) and the maximal atomic forces in the DFT cell ( fmax).Reproduced from [242]. CC BY 4.0.of the generalized Poisson–Boltzmann electrolyte models. Further improvement in stability and efficiencycould be gained by moving from iterative fixed potential calculations to a scheme where the constantpotential condition is achieved within a single self-consistent field cycle. We expect this to be particularlyimportant for GCE constrained DFT calculations where an additional iterative loop is needed [247] as well asGCE-DFT molecular dynamics simulations.Advances in science and technology to meet challengesThe combination of (GCE-)DFT and classical liquid theories is well-documented but cur- rentimplementations [251–253] have typically been hard-coded in the DFT packages and require significantimplementation work. On the other hand, it was recently demonstrated [245] that GPAW can be directlyinterfaced with an external classical DFT code with minimal changes to both codes. We therefore proposethat GPAW could be rather naturally interfaced with already existing, open-source RISM [254] or classicalDFT implementations [255] rather than re- programming them; this task should be greatly facilitated byGPAW’s flexible and modular Pythonic structure.The Pythonic structure is also expected to facilitate interfacing GPAW with machine learning methodssuch as on-the-fly generation [256] of data-driven force fields. An outstanding challenge is treatment of theelectrode potential in machine learning methods and currently there are no schemes for achieving thisefficiently. A brute-force parametrization of explicitly potential-dependent force fields is readily achievableby reparametrizing at each potential, a substantial computational burden. More promising schemes could beachieved by learning e.g. the electrostatic potential [257], which is directly related to the electrode potential[242], or the charge response kernel [258].Finally, porting GPAW to support GPUs will make GCE-DFT calculations (and also machine learningintegration) significantly faster. While there is a legacy implementation supporting GPUs [259], this isoutdated and cannot be used with current versions of GPAW. There is, however, an active on-goingdevelopment to make GPAW work with CUDA and HIP architectures [260].Concluding remarksWe have provided an overview of simulating electrochemical systems with GCE-DFT as implemented inGPAW. We have highlighted the features which make GPAW a versatile and flexible platform for developingand using GCE-DFT methods. In general, the theoretical foundation of simulating the electrode–electrolyte interface under constant electrode potential is set and we can already address electrochemicalthermodynamics and kinetics as an explicit function of the electrode potential. In the future, focus should bedirected at developing better electrolyte and solvent models, improving efficiency and stability, andintegrating GCE-DFT with other simulation approaches, such as machine learning methods.36https://creativecommons.org/licenses/by/4.0/J. Phys. Energy 5 (2023) 041501 C Zhang et alAcknowledgmentsMMM acknowledges the funding by Academy of Finland (Project # 338228, CompEL). G K thanks theEuropean Union’s Horizon 2020 research and innovation program (Grant # 851441, SELECTCO2) and theVillum foundation (Grant # 9455, V-Sustain). Both authors acknowledge the GPAW developers for theircontinuous efforts to maintain and improve GPAW.37J. Phys. Energy 5 (2023) 041501 C Zhang et al12. Constant Fermi-level molecular dynamics: recent achievements and futurechallengesAssil Bouzid1 and Alfredo Pasquarello21 Institut de Recherche sur les Céramiques (IRCER), Centre Européen de la Céramique, 12 Rue Atlantis,Limoges, 87068, France2 Chaire de Simulation à l’Echelle Atomique (CSEA), Ecole Polytechnique Fédérale de Lausanne(EPFL),CH-1015 Lausanne, SwitzerlandE-mail: assil.bouzid@cnrs.fr and alfredo.pasquarello@epfl.chStatusAchieving a detailed understanding of the electrochemical processes occurring at solid/liquid interfaces is ofparamount importance towards the design of efficient and durable solar cells, energy conversion, and storagedevices. These processes are usually driven by an applied bias potential that determines the amount of excesscharge (electrons or protons) at the interface, which in turn influences the double layer structure and theelectrochemical properties of the interface. At this level, atomic-scale modelling provides powerful tools toaccess the intimate details of the interface structure in close correlation with its overall electrochemicalproperties. Several modelling schemes have been proposed to simulate metal/water interfaces through eitherimplicit [261–264] or explicit but static [265, 266] solvents, either at fixed excess charge [267, 268] or byvarying the bias potential [243, 269–273]. Among these modelling schemes, constant Fermi-level moleculardynamics (CFLMD), initially developed by Bonnet et al [270] and then further extended by the presentauthors [274–277], have enabled the study of electrochemical processes at metal/water interfaces under biaspotential. In practice, within the CFLMD scheme (see figure 17), the studied system is connected to anexternal potentiostat at fixed Fermi level that acts like an electron reservoir or a fictitious external electrode.The dynamical control of the Fermi level is ensured by considering the electronic charge of the system as afictitious dynamical variable subject to inertia such that the extended system is driven by a grand canonicalpotential. This technique is complemented with a proper alignment method that enables one to reference theapplied bias potential to the standard hydrogen electrode, thereby allowing for a direct comparison of themodelling results with experiments. In the case of the Pt(111)/water interface, CFLMD have enabled thestudy of the structural reorganization of the electrical double layer as a function of the applied bias potential,whereby a bias-dependent water organization has been demonstrated [274]. In addition, this scheme yields apotential of zero charge and a double layer capacitance in excellent agreement with experimentalmeasurements [274, 275]. Another interesting feature of CFLMD lies in its ability to spontaneously inducingchemical reactions when sufficiently strong bias potentials are applied. In the case of the oxygen evolutionreaction (OER) at the Pt(111)/water interface, CFLMD have enabled access to the organization of adsorbedspecies like H2Oads and OHads at the metal surface prior to the OER reaction providing a description inwhich they have been found to arrange in a hexagonal lattice with an irregular alternation. The OER reactionhas then been found to proceed through a hydrogen peroxide intermediate leading to a reduction of 0.2 eV ofthe reaction overpotential when compared to the conventional OER mechanism [276].Current and future challengesDespite the success of CFLMD in studying electrochemical processes at metal/water interfaces, its applicationto complex systems is still hindered by several intrinsic limitations. First, similar to all MD based simulations,long equilibration times are required to ensure equilibrium and to minimize the deviation from ergodicity.This comes with a considerable computational cost. In addition, the modelled physical system in the case ofmetal/water interface corresponds to a system of a single half electrode and does not account for the presenceof a counterelectrode as in experiments. Given that periodic boundary conditions are usually applied in thesimulation, a constant electric field across the water layer cannot be sustained and achieving a properdescription of the electrostatic potential becomes an issue. Furthermore, in experiments, the electric field inthe water region due to the extra charge at the metal surface is screened out by counterions of the electrolyte,but at present a proper treatment of such ions would require prohibitively large system sizes in thesimulation. In practice, a uniform neutralizing background is used, which effectively screens out thepotential evolution across the liquid region and artificially reduces the charge located on the electrode [274].Second, the CFLMD is currently mainly applied within standard semilocal density functional theory (DFT).While this framework provides a cost-effective tool for performing molecular dynamics simulations of themetal/liquid interfaces at fixed bias potential, it does not satisfy the piece-wise linearity condition of the totalenergy upon electron occupation as expected from exact DFT. Through the application of Janak’s theorem,one can see that this practically results in single-particle energy levels varying with electron occupation,38https://mailto:assil.bouzid@cnrs.frhttps://mailto:alfredo.pasquarello@epfl.chJ. Phys. Energy 5 (2023) 041501 C Zhang et alFigure 17. Applications of the CFLMD scheme. Central panel: schematic illustration of the CFLMD scheme. A system of particlesdescribed by a set of atomic positions ri and a total electronic charge ne is connected to an external potentiostat at a fixed Fermilevel ϵF acting like a fictitious external electrode. The electronic charge ne is considered as a dynamical variable with inertiaMe,and the extended system is driven by a grand canonical potential [270, 274]. The atomic degrees of freedom are coupled to athermostat set to a temperature T, and the charge dynamics are coupled to a separate thermostat set at a temperature TC [270,274]. Top (bottom) left panel: Representative snapshot illustrating the structure of the water double layer at Pt(111)/waterinterface when the electrode potential U is set at a negative (positive) value [274]. We note that in the case of negative bias, the Ptsurface was intentionally not covered by H (see [274]). Top right panel: Representative snapshot illustrating the product of theoxygen evolution reaction (OER) at Pt(111)/water interface (formation of O2) upon application a high positive potential [276].Bottom right panel: Double layer capacitance Cdl as a function of the applied electrode potential U [274]. Adapted withpermission from [274]. Copyright 2018 American Chemical Society.implying that resonances between adsorbate energy levels and the Fermi level are spuriously broadened uponvarying the bias potential [277]. The use of hybrid functionals could overcome such issues, but theirprohibitive computational cost currently prevents their systematic use in molecular dynamics simulations.Finally, modelling chemical reactions by varying the Fermi level within the CFLMD requires the use ofunrealistically high bias potentials [276] to overcome the energy barriers of the targeted reaction during theaccessible timespan of simulations. This requires the injection of large amounts of excess charge in thesystem, which then in turn undermines the comparison between the bias potential set for making thereaction viable in the simulation and the observed value in experiment.Advances in science and technology to meet challengesAlmost all grand canonical schemes currently employed to address solid/liquid interfacial properties atconstant electrode potential suffer from the same aforementioned limitations. Lifting these intrinsiclimitations would therefore represent a major step forward towards achieving a realistic and quantitativemodelling of electrochemical processes at solid/liquid interfaces. We here provide several possiblemethodological and technical advances that could contribute to the achievement of a successfulgrand-canonical scheme for modelling aqueous interfaces at constant bias potential. First, accounting for theoccurrence of counterions in the liquid solution could be achieved through auxiliary classical moleculardynamics. In fact, large-scale classical simulations of solid/liquid interfaces with counterions physicallypresent in the solution can be performed in order to determine the electrostatics induced by thesecounterions upon the charging of the electrode. This would then provide an average electrostatic potentialthat could be transferred to the ab-initiomodel. Hence, such a procedure would allow one to effectivelyaccount for the screening due to the counterions in the liquid solution during the ab-initiomoleculardynamics at fixed potential. This would imply that, prior to any first-principle simulation, one carries out aclassical MD simulation in the same conditions of excess charge in order to determine the electrostatics dueto the counterions. This procedure can be improved even further by resorting to machine-learning (ML)techniques. In particular, for a given system, several large-scale classical MD simulations at various excess39J. Phys. Energy 5 (2023) 041501 C Zhang et alcharges in the presence of counterions could be used to train a ML model able to predict the electrostatics ofcounterions at a given fixed bias potential. Such a model could then be coupled with the DFT description andprovide on the fly a correction of the average electrostatics in solution upon variation of the bias potential.Such an approach would be of particular interest for dealing with chemical reactions requiring the bias to bevaried in a continuous fashion. Second, to satisfy the piece-wise linearity condition, one could resort toDFT+ U schemes in which the parameter U is suitably set to comply with the generalized Koopmans’condition. For higher accuracy, one should assume the higher computational cost of hybrid functionals.Piece-wise linear hybrid functionals can be constructed in a cost-effective way by imposing the generalizedKoopmans’ condition on localized electronic states associated with defects or with hydrogenic-like potentialprobes [278]. Third, the last limitation related to the occurrence of high energy barriers when modellingchemical reactions could be overcome by combining grand-canonical schemes at constant bias withadvanced sampling methods to model rare events, such as the metadynamics scheme [279] or thethermodynamic integration method [280]. Finally, the implementation of the proposed extensions in anaccessible and efficient computer code is key towards their wide adoption by research communities.Concluding remarksIn summary, despite significant progress in modelling electrochemical processes at solid/liquid interfacesachieved in the last decade, substantial advances still lie ahead to reach a powerful and successfulmethodology. The advances suggested in the present roadmap contribution would enable a significant stepforward in that direction.40J. Phys. Energy 5 (2023) 041501 C Zhang et al13. Density functional theory in classical explicit solvents (DFT-CES): efforts towardsunderstanding the unseen, buried electric double layerSeung-Jae Shin1,2, Minho M Kim1 and Hyungjun Kim11 Department of Chemistry, Korea Advanced Institute of Science and Technology, Daejeon 34141, Republicof Korea2 Department of Materials Science and Engineering, Yonsei University, Seoul 03722, Republic of KoreaE-mail: linus16@kaist.ac.krStatusElectric double layer (EDL) is ubiquitously formed at electrochemical interfaces. Because an electrochemicalreaction is governed by electron transfer (ET) across the EDL region, one can deduce the intimateconnection between the EDL structure and electrochemical properties, although the details have not yet beenunravelled [281].A solid structure can be well-characterized by means of diffraction or surface-science experimentaltechniques. Whereas, it is extremely difficult to resolve the three-dimensional atomic arrangement of a liquidstructure such as that of an EDL. Therefore, to obtain the necessary atomic/electronic level information ofEDL structures, the need for a reliable and predictable molecular modelling method is emphasized.From the modelling viewpoint, it is always important to choose a simulation method with appropriatelength- and time-scales. As the Debye length spans from 0.3 nm to 3 nm at the conventional electrolyteconcentration (0.01 M–1 M), and the EDL relaxation time is measured to be in the order of nano-to-microseconds [282], one may argue that compared to the scales provided by classical molecular dynamics (MD),those provided by ab-initiomolecular dynamics (AIMD) may be insufficient to investigate the EDL structureand dynamics. However, a quantum mechanical (QM)-level of understanding on the electronic structure ofthe electrode, such as a location of the Fermi level for defining an electrochemical potential, is also essentialto predict the potentiodynamic polarization behaviour. Therefore, a multiscale approach combining aQM-level description for the electrode region and a classical MD-level description for the electrolyte regiondeems to be optimal.A conventional multiscale QM/MDmethod simultaneously propagates the dynamics of both regions.Consequently, the QM-region dynamics, as a bottleneck, strongly limits the achievable time scale.Particularly for the EDL system, the typical electrode in the QM region consists of numerous atoms andelectrons. Assuming a weak coupling between liquid electrolyte dynamics and electrode phonon, weemployed a mean-field coupling between these two regions—iterative QM optimizations and MD decoupletime-scales in these two regions (figure 18(a)), thus enabling a sufficiently lengthy dynamics simulation forthe electrolyte [99, 283, 284]. To ensure high fidelity, the interaction parameters across the two regions arefurther optimized based on QM energetics, which has been validated to reproduce a reliable interfacialtension [285] and water contact angle [286]. This first-principles-based multiscale simulation method,namely the density functional theory in classical explicit solvents (DFT-CES) has been developed by ourgroup to be applied to investigate in the structural investigation of EDL.Current and future challengesBy including a minimal number of counter ions to compensate the electrode charge, the DFT-CESsimulations succeeded to capture the key features of the camel-shaped behaviour of EDL capacitance(figure 18(b)), and elucidated their molecular origins [288]. The anodic hump originates due toelectrosorption of anions, and the cathodic hump is associated with an unprecedented phase transitionbehaviour [287]. This minimal counter-ion (MCI) description satisfies the electroneutral condition withinthe simulation cell by only including ions with one type of polarity. In this context, it corresponds to thedilute-limit concentration of the electrolyte, and can be compared with the Poisson-Boltzmann-typedescription of the Gouy–Chapman-type models. However, owing to the MD-description of the electrolyte, amean-field approximation is not required for handling the ion–ion interaction. It should be noted that theMCI description includes both Helmholtz and diffuse layers (figure 18(c)); thus, the predicted capacitanceshould be compared to the entire EDL capacitance.Despite of the success of MCI description in dilute limit cases, the EDL structure formed at a higherconcentration is more relevant to the actual electrochemical conditions. In the concentration regime of0.1 M–1 M, it is apparent that ions with both polarities coexist in the EDL region, and their concentration ismodulated by the bulk concentration. However, a complication arises as the local concentration of the ions atthe interface differs from the bulk concentration, and our understanding is typically limited to the latter.Mathematically, the electroneutral condition only determines the difference of cation and anion numbers,41https://mailto:linus16@kaist.ac.krJ. Phys. Energy 5 (2023) 041501 C Zhang et alFigure 18. Current status of DFT-CES in describing the EDL. (a) Iterative scheme of mean-field coupled DFT optimization andnanoseconds MD simulation. Reprinted with permission from [284]. Copyright 2018 American Chemical Society. (b) Theoreticalreproduction of camel-shaped behaviour of EDL capacitance using minimal counter-ion (MCI) description. DFT-CES predictsthe potential (E) dependent surface charge density (σ) shown in the left panel, and its derivative defines the differentialcapacitance (C = dσ/dE) shown in the right panel. (c) Full local density profiles of water (background colour), ion (blue andpale-yellow), and electrode charge (yellow) at cathodic interface (left panel) and anodic interface (right panel). Reproduced from[287]. CC BY 4.0.but excess number of ion pairs in the EDL region must change depending on the bulk ion concentration.Therefore, we need to develop a computational algorithm that can modulate ion-pair concentration in theEDL region depending on the bulk electrolyte conditions.Furthermore, a more advanced force-field (FF) is required. The DFT-CES employs the FF lacking theelectronic polarization effect with using fixed-charge model. In the case of water, although the dielectricscreening is mostly attributed to the orientational polarization of water dipoles, there still exists anon-negligible contribution from the electronic polarization. Also, it has been known that conventional FFcannot fully capture the interaction modes between the electrode and water [289]. Thus, a more advanced FFdescription that can model the complicate electrode-electrolyte interaction and possibly chemical reactions,will help increase the accuracy level and capability of DFT-CES.Lastly, the biggest challenge is related to how the electrochemical reaction can be modelled. As theQM-region structure can be optimized, DFT-CES, per se, can provide adsorbate binding energies and surface42https://creativecommons.org/licenses/by/4.0/J. Phys. Energy 5 (2023) 041501 C Zhang et alFigure 19. Future challenges to expand the functionality of current DFT-CES. (a) ‘Chemostatting’ method to control theelectrolyte concentration at the interface depending on the bulk concentration. (b) Advanced FFs (e.g. polarisable FFs) canimprove the accuracy level of electrolyte description. (c) To describe an ET process, quantum-dynamic behaviour needs to besimulated in a full or an approximated manner (e.g. Marcus theory).reaction energetics with including a full-atomic consideration of EDL structure [290]. More challengingquest will be related to how the ET rate can be simulated and linked with the electrochemical reactionproperties.Advances in science and technology to meet challengesFrom the thermodynamic viewpoint, the local ion concentration in the interface region can be considered tobe in equilibrium with the bulk electrolyte, i.e., an ion reservoir. Therefore, similar to various thermostattingmethods to couple the MD simulation cell with ‘heat reservoir’, we need to develop a computationalalgorithm to couple the interface simulation with ‘ion reservoir’, namely a ‘chemostatting’ method.By considering a grand canonical ensemble, one possible method is the hybrid Monte Carlo (MC)/MD,which incorporates MC steps during MD to create or annihilate ions according to the chemical potential ofion pairs in the reservoir [291]. However, here the simulation control parameter is the chemical potential,which cannot be directly dictated from the ion concentration value. Instead, a computational method todirectly modulate the ion concentration can be designed by including a sufficiently thick electrolyte slab thatcan include a bulk electrolyte region in the same simulation cell (figure 19(a)) [292].To include an electronic response of the electrolyte phase, an effort to couple advanced FF techniqueswith DFT-CES needs to be endeavoured. Polarizable FFs [293–295] can account for the electronicpolarization effect of molecules and ions in the electrolyte phase, which is missing in the current DFT-CES(figure 19(b)). It should be noted that coupling the reactive FFs [296, 297] with DFT-CES will help achieve amore realistic simulation. During aqueous electrochemical processes, water molecule is oftenmultifunctional—it serves not only as a dielectric solvent (which is the current description of DFT-CES), butalso as a reactant, proton donor/acceptor, reaction promotor, etc. By enabling the O–H bonddissociation/association of water, the simulation can provide means to explore and identify various roles ofwater during aqueous electrochemical reactions.ET process is fundamentally a quantum-dynamic phenomenon, occurring at a much shorter time scalethan the EDL relaxation (figure 19(c)). Therefore, to obtain an adequate computational description of ETprocess in the EDL, another scale of simulation must be integrated into the DFT-CES. Mixedquantum–classical techniques, such as a surface-hopping [298], are regarded as efficient and reliablemethods for simulating quantum dynamics. To enable such methods within the DFT-CES framework, weneed to develop a computational procedure for constructing potential energy surfaces and computinginterstate couplings, particularly using the solid-state wavefunctions [299]. Moreover, because the diabaticsurfaces are better suited for describing the ET process [300], development of a quantum dynamicsalgorithm based on diabatic representation might be required.43J. Phys. Energy 5 (2023) 041501 C Zhang et alConcluding remarksDespite its central importance in electrochemistry, structural investigation of the EDL is challenging for boththeoreticians and experimentalists due to its high complexity, system-heterogeneity, and concealment inburied space [301–304]. Being fully equipped with solid-state electronic structure theory and a reliableliquid-structure simulation, DFT-CES provides atomically resolved information of the EDL structure, and itsreliability is validated by comparing the predicted and experimental EDL capacitances. Compared to othermethods, DFT-CES is characterized by its ability to simulate full length- and time-scales of the electrolytephase (in comparison with the AIMD), and by all-atom-level accurate description of the EDL structure (incomparison with the continuum dielectric description). However, current DFT-CES is limited only for thedilute-limit concentration of the electrolyte, and it lacks some important quantum–mechanical phenomenathat occurs at the classically-described electrolyte region. Based on recent achievements in the computationalchemistry, e.g., computational statistical mechanical models and mixed quantum–classical simulations forquantum dynamics, we aim to develop novel computational methods for the DFT-CES in near future. Byovercoming the current limitations of DFT-CES using new methods, we expect to better understand themolecular grammar of EDL structure, which governs the complex electrochemical phenomena.AcknowledgmentsThis work was supported by the Samsung Science and Technology Foundation under Project NumberSSTF-BA2101-08.44J. Phys. Energy 5 (2023) 041501 C Zhang et al14. Implicit solvationmodels for electrochemical interfacesKathleen Schwarz1 and Ravishankar Sundararaman21 National Institute of Standards and Technology, Gaithersburg, MD, United States of America2 Rensselaer Polytechnic Institute, Troy, NY, United States of AmericaE-mail: kathleen.schwarz@nist.gov and sundar@rpi.eduStatusImplicit solvation modelling simplifies the simulation of liquid-containing systems relative to fully atomisticapproaches by eliminating the need to sample the space of all configurations of liquid molecules. Suchtechniques have a long history in liquid-phase solvation for predicting homogeneous catalysis [305]. Here,they can be parameterized to extensive solvation free energy data and approach the 0.04 eV (1 kcal mol−1)standard of chemical accuracy for solvation of neutral solutes in aqueous and several non-aqueous solvents[306]. Implicit solvation models have become increasingly prevalent for solid–liquid and electrochemicalinterfaces in the past two decades with the development of transferable models with few parameters [307,308], which is necessary due to the relative dearth of interfacial data to parameterize them. Combined withthe capability to perform electronic structure calculations at fixed electrode potential using grand-canonicaldensity functional theory [156], implicit solvation models have become the workhorse for first-principleselectrochemistry.The treatment of electrolytes using implicit solvation models has advanced rapidly to capture importanteffects at electrochemical interfaces, covered extensively in recent reviews [157, 241]. Specifically, solvationmodels to accurately predict the capacitance have been developed that are sensitive to both the sign andmagnitude of the solute electric field [309, 310]. These new solvation models (figure 20) include nonlinearityin both the dielectric and electrolyte response to the electric field, with separate solvent-only and electrolyteregions. As a surface charges, the solvation model cavities must also respond to the solute electric field,especially accounting for the sign of the electric field [311, 312]. However, a vast majority of currentfirst-principles electrochemistry calculations employ older and simpler solvation models missing many ofthese critical features of newer models, which need further software adoption and benchmarking.In parallel, advances in explicit solvation using ab initio and machine-learned-potential moleculardynamics present a unique opportunity for improving implicit solvation. (See [313] for a detailed review).Explicit interface simulations can provide critical data on interface energetics, missing from experiments, toimprove parametrization of implicit models [314]. Finally, while explicit solvation can be applied forbenchmarking and detailed studies of some systems, implicit solvation models for electrochemistry remainnecessary to facilitate systematic modelling of reaction mechanisms, to simulate larger/more complexinterfaces and to interpret and identify distinct physical effects within explicit solvation predictions.Current and future challengesWhile implicit solvation models have advanced to capture key aspects of idealized electrochemical interfaces,they typically do not account for many common effects at realistic interfaces (figure 20). Broadly, these canbe separated into limitations in the solvent structure, electron–solvent interactions and electronic structure.First, solvation models typically describe idealized non-adsorbing solvent and electrolyte, neglectingeffects like ion pairing in the bulk, ion packing effects near the interface at high charges, and ion and solventchemisorption at the interface. Future solvation models need to capture electrolyte-specific effects,potentially leveraging liquid-structure models that describe atomic-scale liquid structure [315, 316].The interaction between implicit solvation models and the electronic system is typically limited toelectrostatic interactions with energy corrections for secondary effects (e.g. dispersion) [305]. This imposes astrict and artificial partitioning between solute and solvent electrons, precluding effects such as the change ofelectron distribution at electrode surfaces from vacuum to electrochemical environments (figure 20). Inparticular, electron delocalization and charge transfer between the electrode and adjacent solvent moleculesmay play an important role in determining the capacitances of electrochemical interfaces, especially thoseinvolving hydrophilic electrodes such as Pt [317]; this is excluded in implicit solvation models byconstruction. Future solvation models may need to approximate such electronic effects, or work robustly inhybrid solvation schemes with explicit molecules in a first solvent shell.Finally, the accuracy of first-principles electrochemistry is not limited only by solvation models. While itis difficult to precisely pin down solvation errors for specific electrochemical predictions, table 1 providesorder of magnitude estimates for errors in solvation energies and the charging energy of interfaces based ontypical capacitance accuracy. Overall, these errors span the 0.04–0.4 eV (1–10 kcal mol−1) range. Incomparison, errors in surface and adsorption energies in electronic structure methods can be even larger,45https://mailto:kathleen.schwarz@nist.govhttps://mailto:sundar@rpi.eduJ. Phys. Energy 5 (2023) 041501 C Zhang et alFigure 20. Advanced implicit solvation models for the electrochemical interface approximate the charge response of solvent andelectrolyte ions outside the solvation cavity(ies). Describing electronic response in the electrode–electrolyte gap region, chargedelocalization with solvent molecules and chemisorption of ions requires improvements in implicit solvation models or reliablehybrid implicit-explicit approaches, while accurate energy level alignment and charge transfer at the interface require electronicstructure beyond density-functional theory.Table 1. Improving accuracy of first-principles electrochemistry requires advances in both solvation and electronic structure. Implicitsolvation errors in solvation energies and interface charging energies are comparable to electronic structure errors in adsorptionenergies in vacuum. (Surface energies and charging energy estimated for a∼ 1 nm2 area, to be comparable with adsorbate calculationsat typical coverages considered.).Quantity Typical accuracyImplicit solvationSolvation energy: neutralSolvation energy: ionsSurface charging energy0.04–0.1 eV [306, 311]0.1–0.4 eV [308, 311]0.04–0.1 eV [313]Electronic structurePBE adsorption energiesRPA adsorption energiesPBE surface energiesRPA surface energies0.4–0.8 eV [318]0.1–0.2 eV [318]0.2–0.3 eV [318]0.1–0.2 eV [318]especially for the most commonly-used semi-local density functional methods (such as with the PBEexchange–correlation functional reported in table 1). Higher-level electronic structure methods such as therandom-phase approximation (RPA) for correlation energies can substantially reduce these errors, but needto be more computationally efficient, robust and compatible with solvation models to become widespreadfor electrochemical predictions.Advances in science and technology to meet challengesImplicit solvation models remain vital in first-principles simulations of electrochemical systems, but theaccuracy of electrochemical predictions is limited by challenges in solvent structure, electron-solventinteractions and electronic structure, as outlined above. Recent advances in multiple fields have introducednew opportunities to address each of these areas, as we discuss next.46J. Phys. Energy 5 (2023) 041501 C Zhang et alFirst, advances in liquid-structure theory, based on classical density-functional theory as well as integralequation theory of liquids, hold the key to capturing electrolyte-specific effects in solvation [315, 316]. Earlydemonstrations of such approaches to electrochemical systems show promise in capturing non-trivialcharging and double-layer structure effects [316, 319], but require substantial benchmarking andimprovements in robustness and ease of use to supplant current implicit models. This necessarybenchmarking for liquid-structure theory, and more broadly for implicit solvation model development, hasbecome easier and faster with improvements in ab initio, classical and machine-learned-potential moleculardynamics.The interface between the electronic and implicit methods is arguably the most challenging area thatfuture solvation methods need to address. Capturing electron delocalization and charge transfer betweensolute and solvent requires fundamental modifications to the formulation of solvation methods. Forexample, this may require electronically-aware solvation models that are capable of exchanging electronswith the solute treated with a grand-canonical electronic structure method. Alternatively, hybrid approachescombining electronic structure, molecular dynamics and implicit solvation for different spatial regions couldalso capture such effects. Such hybrid methods need improvements in robustness and ease of use, potentiallyincluding automatic partitioning of the simulation between different methods [313].Finally, with increasing accuracy in the next-generation of solvation models, advances in electronicstructure methods that can be readily combined with such solvation models will also become necessary.Electronic structure methods such as RPA are promising alternatives to density functional theory (DFT), asthey can treat adsorbates and metals with comparable accuracy (in contrast to hybrid-functional DFT), andcorrectly predict their energy level alignment. However, these methods are still computationally veryexpensive, difficult to converge, and require more sophisticated interfacing [320] with implicit solvationmodels than addition of solvation energies from DFT-level calculations [321]. Their computational costmakes their application in explicit solvation prohibitive, underscoring the need to advancebeyond-DFT+ implicit solvation approaches. Recent developments in machine learning RPA energies usingDFT inputs [322] have the potential to make such techniques more accessible for application infirst-principles electrochemistry.Concluding remarksImplicit solvation models provide a computationally efficient way to describe the solvent and electrolyte insimulations of the electrochemical interface. Current electrochemical solvation models can accurately modelidealized electrochemical interfaces, but require advances to capture electrolyte-specific effects, liquidstructure and electronic interactions with the electrode. Opportunities also exist in extending solvationmodels to new environments, such as electrodes and non-aqueous solvents that are important for batteriesand electrosynthesis [306], and to treat the impact of solid environments such as surface films of metals[323]. In parallel, improvements in high-quality experimental data on the energetics of solvated and chargedinterfaces would be invaluable for further development of solvation models for electrochemistry. Finally, aconcerted improvement of beyond-DFT electronic structure methods interfaced with next-generationimplicit solvation models is necessary for robust and higher-accuracy prediction of electrochemical processes[313].Data availability statementAll data that support the findings of this study are included within the article (and any supplementary files).AcknowledgmentsRavishankar Sundararaman acknowledges support from the U.S. Department of Energy, Office of Science,Basic Energy Sciences, under Award #DE-SC0022247ORCID iDsChao Zhang https://orcid.org/0000-0002-7167-0840Jun Cheng https://orcid.org/0000-0001-6971-0797Yiming Chen https://orcid.org/0000-0002-1501-5550Maria K Y Chan https://orcid.org/0000-0003-0922-1363Qiong Cai https://orcid.org/0000-0002-1677-0515Rodrigo P Carvalho https://orcid.org/0000-0003-3895-6529Cleber F N Marchiori https://orcid.org/0000-0003-0377-366947https://orcid.org/0000-0002-7167-0840https://orcid.org/0000-0002-7167-0840https://orcid.org/0000-0001-6971-0797https://orcid.org/0000-0001-6971-0797https://orcid.org/0000-0002-1501-5550https://orcid.org/0000-0002-1501-5550https://orcid.org/0000-0003-0922-1363https://orcid.org/0000-0003-0922-1363https://orcid.org/0000-0002-1677-0515https://orcid.org/0000-0002-1677-0515https://orcid.org/0000-0003-3895-6529https://orcid.org/0000-0003-3895-6529https://orcid.org/0000-0003-0377-3669https://orcid.org/0000-0003-0377-3669J. Phys. Energy 5 (2023) 041501 C Zhang et alDaniel Brandell https://orcid.org/0000-0002-8019-2801C Moyses Araujo https://orcid.org/0000-0001-5192-0016Guang Feng https://orcid.org/0000-0001-6659-9181Kateryna Goloviznina https://orcid.org/0000-0001-9913-4938Alessandra Serva https://orcid.org/0000-0002-7525-2494Mathieu Salanne https://orcid.org/0000-0002-1753-491XToshihiko Mandai https://orcid.org/0000-0002-2403-7794Patrik Johansson https://orcid.org/0000-0002-9907-117XHai Xiao https://orcid.org/0000-0001-9399-1584Ryosuke Jinnouchi https://orcid.org/0000-0002-0822-1161Assil Bouzid https://orcid.org/0000-0002-9363-7240Alfredo Pasquarello https://orcid.org/0000-0002-9142-2799Minho M Kim https://orcid.org/0000-0002-3960-8908Kathleen Schwarz https://orcid.org/0000-0002-1539-4511Ravishankar Sundararaman https://orcid.org/0000-0002-0625-4592References[1] Feynman R P, Leighton R B and Sands M 2011 The Feynman Lectures on Physics vol I (Basic Books)[2] Halley J W 1986 Topics in the physics of electrochemistry Superlattices Microstruct. 2 165–72[3] Schmickler W and Santos E 2010 Interfacial Electrochemistry 2nd edn (Springer)[4] Famprikis T, Canepa P, Dawson J A, Islam M S and Masquelier C 2019 Fundamentals of inorganic solid-state electrolytes forbatteries Nat. Mater. 18 1278–91[5] Siegel D J, Nazar L, Chiang Y-M, Fang C and Balsara N P 2021 Establishing a unified framework for ion solvation and transportin liquid and solid electrolytes Trends Chem. 3 807–18[6] Margraf J T, Jung H, Scheurer C and Reuter K 2023 Exploring catalytic reaction networks with machine learning Nat. Catal.6 112–21[7] Steinmann S N, Wang Q and Seh Z W 2023 How machine learning can accelerate electrocatalysis discovery and optimizationMater. Horiz. 10 393–406[8] Exner K S 2020 A universal descriptor for the screening of electrode materials for multiple-electron processes: beyond thethermodynamic overpotential ACS Catal. 10 12607–17[9] Leung K, Merrill L C and Harrison K L 2022 Galvanic corrosion and electric field in lithium anode passivation films: effects onself-discharge J. Phys. Chem. C 126 8565–80[10] Andersson L and Zhang C 2023 Molecular dynamics simulations of metal-electrolyte interfaces under potential control Curr.Opin. Electrochem. 101407[11] Mizushima K, Jones P C, Wiseman P J and Goodenough J B 1981 LixCoO2 (0<x⩽1) : a new cathode material for batteries of highenergy density Solid State Ion. 15 783–9[12] Ong S P, Chevrier V L, Hautier G, Jain A, Moore C, Kim S, Xiaohua M and Ceder G 2011 Voltage, stability and diffusion barrierdifferences between sodium-ion and lithium-ion intercalation materials Energy Environ. Sci. 4 3680[13] Chen Y et al 2021 Database of ab initio L-edge x-ray absorption near edge structure Sci. Data 8 153[14] Schwenker E et al 2022 Ingrained: an automated framework for fusing atomic—scale image simulations into experiments Small18 2102960[15] Liang L, Lee E, Freeland J W, Fister T T, Thackeray MM and Chan M K Y 2019 Identifying the chemical origin of oxygen redoxactivity in Li-rich anti-fluorite lithium iron oxide by experimental and theoretical x-ray absorption spectroscopy J. Phys. Chem.Lett. 10 806–12[16] Zhonghua L, MacNeil D D and Dahn J R 2001 Layered Li[NixCo1−2xMnx]O2 cathode materials for lithium-ion batteriesElectrochem. Solid-State Lett. 4 A200[17] Ohzuku T and Makimura Y 2001 Layered lithium insertion material of LiCo 1/3 Ni 1/3 Mn 1/3 O 2 for lithium-ion batteries Chem.Lett. 30 642–3[18] Chen D, Ahn J and Chen G 2021 An overview of cation-disordered lithium-excess rocksalt cathodes ACS Energy Lett. 6 1358–76[19] Min K, Seo S-W, Song Y Y, Lee H S and Cho E 2017 A first-principles study of the preventive effects of Al and Mg doping on thedegradation in LiNi 0.8 Co 0.1 Mn0.1 O2 cathode materials Phys. Chem. Chem. Phys. 19 1762–9[20] Xu R, Sun H, de Vasconcelos L S and Zhao K 2017 Mechanical and structural degradation of LiNix Mny Coz O2 cathode in Li-ionbatteries: an experimental study J. Electrochem. Soc. 164 A3333–41[21] Liu X et al 2022 Origin and regulation of oxygen redox instability in high-voltage battery cathodes Nat. Energy 7 808–17[22] Tianyu L, Yuan X-Z, Zhang L, Song D, Shi K and Bock C 2019 Degradation mechanisms and mitigation strategies of nickel-richNMC-based lithium-ion batteries Electrochem. Energ. Rev. 3 43–80[23] Liu X, Wang D, Liu G, Srinivasan V, Liu Z, Hussain Z and Yang W 2013 Distinct charge dynamics in battery electrodes revealed byin situ and operando soft x-ray spectroscopy Nat. Commun. 4 2568[24] Liang L et al 2019 Probing electrochemically induced structural evolution and oxygen redox reactions in layered lithium iridateChem. Mater. 31 4341–52[25] Quilty C D et al 2022 Multimodal electrochemistry coupled microcalorimetric and x-ray probing of the capacity fademechanisms of Nickel rich NMC—progress and outlook Phys. Chem. Chem. Phys. 24 11471–85[26] Chen B-R, Walker C M, Kim S, Kunz M R, Tanim T R and Dufek E J 2022 Battery aging mode identification across NMCcompositions and designs using machine learning Joule 6 2776–93[27] Unruh D, Kolluru V S C, Baskaran A, Chen Y and Chan M K Y 2022 Theory+AI/ML for microscopy and spectroscopy:challenges and opportunitiesMRS Bull. 47 1024–35[28] Hatzell K B et al 2020 Challenges in lithium metal anodes for solid-state batteries ACS Energy Lett. 5 922–3448https://orcid.org/0000-0002-8019-2801https://orcid.org/0000-0002-8019-2801https://orcid.org/0000-0001-5192-0016https://orcid.org/0000-0001-5192-0016https://orcid.org/0000-0001-6659-9181https://orcid.org/0000-0001-6659-9181https://orcid.org/0000-0001-9913-4938https://orcid.org/0000-0001-9913-4938https://orcid.org/0000-0002-7525-2494https://orcid.org/0000-0002-7525-2494https://orcid.org/0000-0002-1753-491Xhttps://orcid.org/0000-0002-1753-491Xhttps://orcid.org/0000-0002-2403-7794https://orcid.org/0000-0002-2403-7794https://orcid.org/0000-0002-9907-117Xhttps://orcid.org/0000-0002-9907-117Xhttps://orcid.org/0000-0001-9399-1584https://orcid.org/0000-0001-9399-1584https://orcid.org/0000-0002-0822-1161https://orcid.org/0000-0002-0822-1161https://orcid.org/0000-0002-9363-7240https://orcid.org/0000-0002-9363-7240https://orcid.org/0000-0002-9142-2799https://orcid.org/0000-0002-9142-2799https://orcid.org/0000-0002-3960-8908https://orcid.org/0000-0002-3960-8908https://orcid.org/0000-0002-1539-4511https://orcid.org/0000-0002-1539-4511https://orcid.org/0000-0002-0625-4592https://orcid.org/0000-0002-0625-4592https://doi.org/10.1016/0749-6036(86)90082-0https://doi.org/10.1016/0749-6036(86)90082-0https://doi.org/10.1038/s41563-019-0431-3https://doi.org/10.1038/s41563-019-0431-3https://doi.org/10.1016/j.trechm.2021.06.004https://doi.org/10.1016/j.trechm.2021.06.004https://doi.org/10.1038/s41929-022-00896-yhttps://doi.org/10.1038/s41929-022-00896-yhttps://doi.org/10.1039/D2MH01279Khttps://doi.org/10.1039/D2MH01279Khttps://doi.org/10.1021/acscatal.0c03865https://doi.org/10.1021/acscatal.0c03865https://doi.org/10.1021/acs.jpcc.1c10602https://doi.org/10.1021/acs.jpcc.1c10602https://doi.org/10.1016/j.coelec.2023.101407https://doi.org/10.1039/c1ee01782ahttps://doi.org/10.1039/c1ee01782ahttps://doi.org/10.1038/s41597-021-00936-5https://doi.org/10.1038/s41597-021-00936-5https://doi.org/10.1002/smll.202102960https://doi.org/10.1002/smll.202102960https://doi.org/10.1021/acs.jpclett.8b03271https://doi.org/10.1021/acs.jpclett.8b03271https://doi.org/10.1246/cl.2001.642https://doi.org/10.1246/cl.2001.642https://doi.org/10.1021/acsenergylett.1c00203https://doi.org/10.1021/acsenergylett.1c00203https://doi.org/10.1039/C6CP06270Ahttps://doi.org/10.1039/C6CP06270Ahttps://doi.org/10.1149/2.1751713jeshttps://doi.org/10.1149/2.1751713jeshttps://doi.org/10.1038/s41560-022-01036-3https://doi.org/10.1038/s41560-022-01036-3https://doi.org/10.1007/s41918-019-00053-3https://doi.org/10.1007/s41918-019-00053-3https://doi.org/10.1038/ncomms3568https://doi.org/10.1038/ncomms3568https://doi.org/10.1021/acs.chemmater.8b04591https://doi.org/10.1021/acs.chemmater.8b04591https://doi.org/10.1039/D1CP05254Chttps://doi.org/10.1039/D1CP05254Chttps://doi.org/10.1016/j.joule.2022.10.016https://doi.org/10.1016/j.joule.2022.10.016https://doi.org/10.1557/s43577-022-00446-8https://doi.org/10.1557/s43577-022-00446-8https://doi.org/10.1021/acsenergylett.9b02668https://doi.org/10.1021/acsenergylett.9b02668J. Phys. Energy 5 (2023) 041501 C Zhang et al[29] Li X, Fu Z, Wang J, Zhao X, Zhang Y, Liu W, Cai Q and Hu C 2022 Dilithium phthalocyanine as electrolyte additive for theregulation of ion solvation and transport towards dendrite-free Li metal anodes Chem. Eng. J. 450 138112[30] Wang J et al 2022 Highly aligned lithiophilic electrospun nanofiber membrane for the multiscale suppression of Li dendritegrowth eScience 2 655–65[31] Sun S et al 2022 Thermally stable and dendrite-resistant separators toward highly robust lithium metal batteries Adv. EnergyMater. 12 2202206[32] Horstmann B et al 2021 Strategies towards enabling lithium metal in batteries: interphases and electrodes Energy Environ. Sci.14 5289[33] Zhao C, Lu Y, Yue J, Pan D, Qi Y, Hu Y-S and Chen L 2018 Advanced Na metal anodes J. Energy Chem. 27 1584–96[34] Liu P and Mitlin D 2020 Emerging potassiummetal anodes: perspectives on Ccontrol of the electrochemical interfaces Acc. Chem.Res. 53 1161–75[35] Shin J, Lee J, Park Y and Choi J W 2020 Aqueous zinc ion batteries: focus on zinc metal anodes Chem. Sci. 11 2028[36] Zhang J et al 2022 High-performance rechargeable aluminum-ion batteries enabled by composite FeF3 @ expanded graphitecathode and carbon nanotube-modified separator Adv. Energy Mater. 12 2200959[37] Chen X-R, Zhao B-C, Yan C and Zhang Q 2021 Review on Li deposition in working batteries: from nucleation to early growthAdv. Mater. 33 2004128[38] Paul P P et al 2021 A review of existing and emerging methods for lithium detection and characterization in Li-ion and Li-metalbatteries Adv. Energy Mater. 11 2100372[39] Fiesinger F, Gaissmaier D, van den Borg M and Jacob T 2022 First-principles studies on the atomistic properties of metallicmagnesium as anode material in magnesium-ion batteries ChemSusChem 15 e202200414[40] Røe I T and Schnell S K 2021 Slow surface diffusion on Cu substrates in Li metal batteries J. Mater. Chem. A 9 11042–8[41] Hagopian A, Doublet M-L and Filhol J-S 2020 Thermodynamic origin of dendrite growth in metal anode batteries EnergyEnviron. Sci. 13 5186–97[42] Sergeev A V, Rulev A A, Kondratyeva Y O and Yashina L V 2022 Computational insight into the grain boundary structure andatomic mobility in metallic lithium Acta Mater. 233 117988[43] Yang M, Liu Y, Nolan A M and Mo Y 2021 Interfacial atomistic mechanisms of lithium metal stripping and plating in solid-statebatteries Adv. Mater. 33 2008081[44] Wang J, Panchal A A, Gautam G S and Canep P 2022 The resistive nature of decomposing interfaces of solid electrolytes withalkali metal electrodes J. Mater. Chem. A 10 19732[45] Wu J, Ihsan-Ul-Haq M, Chen Y and Kim J-K 2021 Understanding solid electrolyte interphases: advanced characterizationtechniques and theoretical simulations Nano Energy 89 106489[46] Diddens D, Appiah W A, Mabrouk Y, Heuer A, Vegge T and Bhowmik A 2022 Modeling the solid electrolyte interphase: machinelearning as a game changer? Adv. Mater. Interfaces 9 2101734[47] Schon T B, McAllister B T, Li P and Seferos D S 2016 The rise of organic electrode materials for energy storage Chem. Soc. Rev.45 6345–404[48] Lee S, Kwon G, Ku K, Yoon K, Jung S-K, Lim H-D and Kang K 2018 Recent progress in organic electrodes for Li and Narechargeable batteries Adv. Mater. 30 1704682[49] Heiska J, Nisula M and Karppinen M 2019 Organic electrode materials with solid-state battery technology J. Mater. Chem. A7 18735[50] Zhao Q, Zhu Z and Chen J 2017 Molecular engineering with organic carbonyl electrode materials for advanced stationary andredox flow rechargeable batteries Adv. Mater. 29 1607007[51] Williams D L, Byrne J J and Driscoll J S J 1969 Electrochem. Soc. 116 2–4[52] Renault S, Oltean V A, Moyses Araujo C, Grigoriev A, Edström K and Brandell D 2016 Superlithiation of organic electrodematerials: the case of dilithium benzenedipropiolate Chem. Mater. 28 1920–6[53] Otteny F, Studer G, Kolek M, Bieker P, Winter M and Esser B 2020 Phenothiazine-functionalized poly(norbornene)s as high-ratecathode materials for organic batteries ChemSusChem 13 2232–8[54] Otteny F, Perner V, Wassy D, Kolek M, Bieker P, Winter M and Esser B 2020 Poly(vinylphenoxazine) as fast-charging cathodematerial for organic batteries ACS Sustain. Chem. Eng. 8 238–47[55] Acker P, Rzesny L, Marchiori C F N, Araujo C M and Esser B 2019 π-conjugation enables ultra-high rate capabilities and cyclingstabilities in phenothiazine copolymers as cathode-active battery materials Adv. Funct. Mater. 8 1906436[56] Casado N, Mantione D, Shanmukaraj D and Mecerreyes D 2020 Symmetric all-organic battery containing a dual redox-activepolymer as cathode and anode material ChemSusChem 13 2464–70[57] Xua S, Daia H, Zhu S, Wu Y, Sun M, Chen Y, Fan K, Zhang C, Wang C and HuW 2021 A branched dihydrophenazine-basedpolymer as a cathode material to achieve dual-ion batteries with high energy and power density eScience 1 60–68[58] Liu Y, Niu Z, Dai G, Chen Y, Li H, Huang L, Zhang X, Xu Y and Zhao Y 2021 Phenothiazine-based copolymer with redoxfunctional backbones for organic battery cathode materialsMater. Today Energy 21 100812[59] Yang S J, Qin X Y, He R, Shen W, Lia M and Zhao L B 2017 A density functional theory study on the thermodynamic and dynamicproperties of anthraquinone analogue cathode materials for rechargeable lithium ion batteries Phys. Chem. Chem. Phys.19 12480–9[60] Park J H, Liu T, Kim K C, Lee S W and Jang S S 2017 Systematic molecular design of ketone derivatives of aromatic molecules forlithium-ion batteries: first-principles DFT modeling ChemSusChem 10 1584–91[61] Bachman J E, Curtiss L A and Assary R S 2014 Investigation of the redox chemistry of anthraquinone derivatives using densityfunctional theory J. Phys. Chem. A 118 8852–60[62] Burkhardt S E, Bois J, Tarascon J M, Hennig R G and Abruña H D 2013 Li-carboxylate anode structure-property relationshipsfrom molecular modeling Chem. Mater. 25 132–41[63] Dardenne N, Blase X, Hautier G, Charlier J C and Rignanese G M 2015 Ab initio calculations of open-cell voltage in Li-Ionorganic radical batteries J. Phys. Chem. C 119 23373–8[64] Araujo R B, Banerjee A and Ahuja R 2018 Identifying the tuning key of disproportionation redox reaction in terephthalate: aLi-based anode for sustainable organic batteries Nano Energy 47 301–8[65] Marchiori C, Brandell D and Moyses Araujo C 2019 Predicting structure and electrochemistry of dilithiumthiophene-2,5-dicarboxylate electrodes by density functional theory and evolutionary algorithms J. Phys. Chem. C 123 4691–700[66] Carvalho R P, Marchiori C F N, Brandell D and Moyses Araujo C 2020 Tuning the electrochemical properties of organic batterycathode materials: insights from evolutionary algorithm DFT calculations ChemSusChem 13 2402–949https://doi.org/10.1016/j.cej.2022.138112https://doi.org/10.1016/j.cej.2022.138112https://doi.org/10.1016/j.esci.2022.09.001https://doi.org/10.1016/j.esci.2022.09.001https://doi.org/10.1002/aenm.202270172https://doi.org/10.1002/aenm.202270172https://doi.org/10.1039/d1ee00767jhttps://doi.org/10.1039/d1ee00767jhttps://doi.org/10.1016/j.jechem.2018.03.004https://doi.org/10.1016/j.jechem.2018.03.004https://doi.org/10.1021/acs.accounts.0c00099https://doi.org/10.1021/acs.accounts.0c00099https://doi.org/10.1039/d0sc00022ahttps://doi.org/10.1039/d0sc00022ahttps://doi.org/10.1002/aenm.202200959https://doi.org/10.1002/aenm.202200959https://doi.org/10.1002/adma.202004128https://doi.org/10.1002/adma.202004128https://doi.org/10.1002/aenm.202100372https://doi.org/10.1002/aenm.202100372https://doi.org/10.1002/cssc.202200414https://doi.org/10.1002/cssc.202200414https://doi.org/10.1039/D1TA02300Dhttps://doi.org/10.1039/D1TA02300Dhttps://doi.org/10.1039/d0ee02665dhttps://doi.org/10.1039/d0ee02665dhttps://doi.org/10.1016/j.actamat.2022.117988https://doi.org/10.1016/j.actamat.2022.117988https://doi.org/10.1002/adma.202008081https://doi.org/10.1002/adma.202008081https://doi.org/10.1039/d2ta02202hhttps://doi.org/10.1039/d2ta02202hhttps://doi.org/10.1016/j.nanoen.2021.106489https://doi.org/10.1016/j.nanoen.2021.106489https://doi.org/10.1002/admi.202101734https://doi.org/10.1002/admi.202101734https://doi.org/10.1039/C6CS00173Dhttps://doi.org/10.1039/C6CS00173Dhttps://doi.org/10.1002/adma.201704682https://doi.org/10.1002/adma.201704682https://doi.org/10.1039/C9TA04328Dhttps://doi.org/10.1039/C9TA04328Dhttps://doi.org/10.1002/adma.201607007https://doi.org/10.1002/adma.201607007https://doi.org/10.1149/1.2411755https://doi.org/10.1149/1.2411755https://doi.org/10.1021/acs.chemmater.6b00267https://doi.org/10.1021/acs.chemmater.6b00267https://doi.org/10.1002/cssc.201903168https://doi.org/10.1002/cssc.201903168https://doi.org/10.1021/acssuschemeng.9b05253https://doi.org/10.1021/acssuschemeng.9b05253https://doi.org/10.1002/adfm.201906436https://doi.org/10.1002/adfm.201906436https://doi.org/10.1002/cssc.201902856https://doi.org/10.1002/cssc.201902856https://doi.org/10.1016/j.esci.2021.08.002https://doi.org/10.1016/j.esci.2021.08.002https://doi.org/10.1016/j.mtener.2021.100812https://doi.org/10.1016/j.mtener.2021.100812https://doi.org/10.1039/C7CP01203Ahttps://doi.org/10.1039/C7CP01203Ahttps://doi.org/10.1002/cssc.201601730https://doi.org/10.1002/cssc.201601730https://doi.org/10.1021/jp5060777https://doi.org/10.1021/jp5060777https://doi.org/10.1021/cm302839zhttps://doi.org/10.1021/cm302839zhttps://doi.org/10.1021/acs.jpcc.5b07886https://doi.org/10.1021/acs.jpcc.5b07886https://doi.org/10.1016/j.nanoen.2018.02.038https://doi.org/10.1016/j.nanoen.2018.02.038https://doi.org/10.1021/acs.jpcc.8b11341https://doi.org/10.1021/acs.jpcc.8b11341https://doi.org/10.1002/cssc.201903450https://doi.org/10.1002/cssc.201903450J. Phys. Energy 5 (2023) 041501 C Zhang et al[67] Carvalho R P, Marchiori C, Oltean V, Renault S, Willhammar T, Gómez C P, Moyses Araujo C and Brandell D 2021Structure–property relationships in organic battery anode materials: exploring redox reactions in crystalline Na- and Li-benzenediacrylate using combined crystallography and density functional theory calculationsMater. Adv. 2 1024–34[68] Carvalho R P et al 2022 Artificial intelligence driven in-silico discovery of novel organic lithium-ion battery cathodes EnergyStorage Mater. 44 313–25[69] Carvalho R P, Brandell D and Moyses Araujo C 2023 An evolutionary-driven AI model discovering redox-stable organic electrodematerials for alkali-ion batteries Energy Storage Mater. 61 122865[70] Xu S, Liang J, Yu Y, Liu R, Xu Y, Zhu X and Zhao Y 2021 Machine learning-assisted discovery of high-voltage organic materials forrechargeable batteries J. Phys. Chem. C 125 21352–8[71] Ruddigkeit L, van Deursen R, Blum L C and Reymond J-L 2012 Enumeration of 166 billion organic small molecules in thechemical universe database GDB-17 J. Chem. Inf. Model. 52 2864–75[72] Melissen S T A G, Le Bahers T, Sautet P and Steinmann S N 2021 What does graphitic carbon nitride really look like? Phys. Chem.Chem. Phys. 23 2853–9[73] Carvalho R, Marchiori C, Brandell D and Moyses Araujo C 2022 Understanding the lithiation limits of high-capacity organicbattery anodes by atomic charge derivative analysis J. Chem. Phys. 157 181101[74] Carvalho R P, Alhanash M, Marchiori C F N, Brandell D and Araujo C M 2022 Exploring metastable phases during lithiation oforganic battery electrode materials ChemSusChem 15 e202200354[75] Simon P and Gogotsi Y 2020 Perspectives for electrochemical capacitors and related devices Nat. Mater. 19 1151–63[76] Wang K-B, Xun Q and Zhang Q 2020 Recent progress in metal-organic frameworks as active materials for supercapacitorsEnergyChem 2 100025[77] Liu L, Taberna P-L, Dunn B and Simon P 2021 Future directions for electrochemical capacitors ACS Energy Lett. 6 4311–6[78] Sun L, Campbell M G and Dincă M 2016 Electrically conductive porous metal–organic frameworks Angew. Chem., Int. Ed.55 3566–79[79] Liu J, Song X, Zhang T, Liu S, Wen H and Chen L 2021 2D conductive metal–organic frameworks: an emerging platform forelectrochemical energy storage Angew. Chem., Int. Ed. 60 5612–24[80] Niu L, Wu T, Chen M, Yang L, Yang J, Wang Z, Kornyshev A A, Jiang H, Bi S and Feng G 2022 Conductive metal–organicframeworks for supercapacitors Adv. Mater. 34 2200999[81] Yaghi O M, Li G and Li H 1995 Selective binding and removal of guests in a microporous metal–organic framework Nature378 703–6[82] Li H, Eddaoudi M, O’Keeffe M and Yaghi O M 1999 Design and synthesis of an exceptionally stable and highly porousmetal-organic framework Nature 402 276–9[83] Yue T, Xia C, Liu X, Wang Z, Qi K and Xia B Y 2021 Design and synthesis of conductive metal-organic frameworks and theircomposites for supercapacitors ChemElectroChem 8 1021–34[84] Liu B, Shioyama H, Akita T and Xu Q 2008 Metal-organic framework as a template for porous carbon synthesis J. Am. Chem. Soc.130 5390–1[85] Takaishi S, Hosoda M, Kajiwara T, Miyasaka H, Yamashita M, Nakanishi Y, Kitagawa Y, Yamaguchi K, Kobayashi A andKitagawa H 2009 Electroconductive porous coordination polymer Cu[Cu(Pdt)2] composed of donor and acceptor building unitsInorg. Chem. 48 9048–50[86] Xie L S, Skorupskii G and Dinca M 2020 Electrically conductive metal-organic frameworks Chem. Rev. 120 8536–80[87] Sheberla D, Sun L, Blood-Forsythe M A, Er S, Wade C R, Brozek C K, Aspuru-Guzik A and Dinca M 2014 High electricalconductivity in Ni(3)(2,3,6,7,10,11-hexaiminotriphenylene)(2), a semiconducting metal-organic graphene analogue J. Am.Chem. Soc. 136 8859–62[88] Sheberla D, Bachman J C, Elias J S, Sun C J, Shao-Horn Y and Dinca M 2017 Conductive MOF electrodes for stablesupercapacitors with high areal capacitance Nat. Mater. 16 220–4[89] Li W-H, Ding K, Tian H-R, Yao M-S, Nath B, Deng W-H, Wang Y and Xu G 2017 Conductive metal-organic frameworknanowire array electrodes for high-performance solid-state supercapacitors Adv. Funct. Mater. 27 1702067[90] Feng D et al 2018 Robust and conductive two-dimensional metal−organic frameworks with exceptionally high volumetric andareal capacitance Nat. Energy 3 30–36[91] Bi S et al 2020 Molecular understanding of charge storage and charging dynamics in supercapacitors with MOF electrodes andionic liquid electrolytes Nat. Mater. 19 552–8[92] Nguyen D K, Schepisi I M and Amir F Z 2019 Extraordinary cycling stability of Ni3(HITP)2 supercapacitors fabricated byelectrophoretic deposition: cycling at 100,000 cycles Chem. Eng. J. 378 122150[93] Díaz R, Orcajo M G, Botas J A, Calleja G and Palma J 2012 Co8-MOF-5 as electrode for supercapacitorsMater. Lett. 68 126–8[94] Wu J 2022 Understanding the electric double-layer structure, capacitance, and charging dynamics Chem. Rev. 122 10821–59[95] Scalfi L, Salanne M and Rotenberg B 2021 Molecular simulation of electrode-solution interfaces Annu. Rev. Phys. Chem.72 189–212[96] Zeng L, Wu T, Ye T, Mo T, Qiao R and Feng G 2021 Modeling galvanostatic charge–discharge of nanoporous supercapacitors Nat.Comput. Sci. 1 725–31[97] Bi S and Salanne M 2022 Co-ion desorption as the main charging mechanism in metallic 1T-MoS2 supercapacitors ACS Nano16 18658–66[98] Abidi N and Steinmann S N 2023 An electrostatically embedded QM/MM scheme for electrified interfaces ACS Appl. Mater.Interfaces 15 25009–17[99] Lim H-K, Lee H and Kim H 2016 A seamless grid-based interface for mean-field QM/MM Coupled with efficient solvation freeenergy calculations J. Chem. Theory Comput. 12 5088–99[100] Cui K and Schmidt J R 2020 Enabling efficient and accurate computational studies of MOF reactivity via QM/MM and QM/QMmethods J. Phys. Chem. C 124 10550–60[101] Yang B, Wu X-P, Gagliardi L and Truhlar D G 2021 Importance of lattice constants in QM/MM calculations on metal–organicframeworks J. Phys. Chem. B 125 5786–93[102] Zhang X, Zhang K and Lee Y 2020 Machine learning enabled tailor-made design of application-specific metal–organicFrameworks ACS Appl. Mater. Interfaces 12 734–43[103] McEwen A B, Ngo H L, LeCompte K and Goldman J L 1999 Electrochemical properties of imidazolium salt electrolytes forelectrochemical capacitor applications J. Electrochem. Soc. 146 168750https://doi.org/10.1039/D0MA00900Hhttps://doi.org/10.1039/D0MA00900Hhttps://doi.org/10.1016/j.ensm.2021.10.029https://doi.org/10.1016/j.ensm.2021.10.029https://doi.org/10.1016/j.ensm.2023.102865https://doi.org/10.1016/j.ensm.2023.102865https://doi.org/10.1021/acs.jpcc.1c06821https://doi.org/10.1021/acs.jpcc.1c06821https://doi.org/10.1021/ci300415dhttps://doi.org/10.1021/ci300415dhttps://doi.org/10.1039/D0CP06063Ahttps://doi.org/10.1039/D0CP06063Ahttps://doi.org/10.1063/5.0119904https://doi.org/10.1063/5.0119904https://doi.org/10.1002/cssc.202200354https://doi.org/10.1002/cssc.202200354https://doi.org/10.1038/s41563-020-0747-zhttps://doi.org/10.1038/s41563-020-0747-zhttps://doi.org/10.1016/j.enchem.2019.100025https://doi.org/10.1016/j.enchem.2019.100025https://doi.org/10.1021/acsenergylett.1c01981https://doi.org/10.1021/acsenergylett.1c01981https://doi.org/10.1002/anie.201506219https://doi.org/10.1002/anie.201506219https://doi.org/10.1002/anie.202006102https://doi.org/10.1002/anie.202006102https://doi.org/10.1002/adma.202200999https://doi.org/10.1002/adma.202200999https://doi.org/10.1038/378703a0https://doi.org/10.1038/378703a0https://doi.org/10.1038/46248https://doi.org/10.1038/46248https://doi.org/10.1002/celc.202001418https://doi.org/10.1002/celc.202001418https://doi.org/10.1021/ja7106146https://doi.org/10.1021/ja7106146https://doi.org/10.1021/ic802117qhttps://doi.org/10.1021/ic802117qhttps://doi.org/10.1021/acs.chemrev.9b00766https://doi.org/10.1021/acs.chemrev.9b00766https://doi.org/10.1021/ja502765nhttps://doi.org/10.1021/ja502765nhttps://doi.org/10.1038/nmat4766https://doi.org/10.1038/nmat4766https://doi.org/10.1002/adfm.201702067https://doi.org/10.1002/adfm.201702067https://doi.org/10.1038/s41560-017-0044-5https://doi.org/10.1038/s41560-017-0044-5https://doi.org/10.1038/s41563-019-0598-7https://doi.org/10.1038/s41563-019-0598-7https://doi.org/10.1016/j.cej.2019.122150https://doi.org/10.1016/j.cej.2019.122150https://doi.org/10.1016/j.matlet.2011.10.046https://doi.org/10.1016/j.matlet.2011.10.046https://doi.org/10.1021/acs.chemrev.2c00097https://doi.org/10.1021/acs.chemrev.2c00097https://doi.org/10.1146/annurev-physchem-090519-024042https://doi.org/10.1146/annurev-physchem-090519-024042https://doi.org/10.1038/s43588-021-00153-5https://doi.org/10.1038/s43588-021-00153-5https://doi.org/10.1021/acsnano.2c07272https://doi.org/10.1021/acsnano.2c07272https://doi.org/10.1021/acsami.3c01430https://doi.org/10.1021/acsami.3c01430https://doi.org/10.1021/acs.jctc.6b00469https://doi.org/10.1021/acs.jctc.6b00469https://doi.org/10.1021/acs.jpcc.0c01220https://doi.org/10.1021/acs.jpcc.0c01220https://doi.org/10.1021/acs.jpcb.1c02328https://doi.org/10.1021/acs.jpcb.1c02328https://doi.org/10.1021/acsami.9b17867https://doi.org/10.1021/acsami.9b17867https://doi.org/10.1149/1.1391827https://doi.org/10.1149/1.1391827J. Phys. Energy 5 (2023) 041501 C Zhang et al[104] Largeot C, Portet C, Chmiola J, Taberna P L, Gogotsi Y and Simon P 2008 Relation between the ion size and pore size for anelectric double-layer capacitor J. Am. Chem. Soc. 130 2730–1[105] Brandt A, Pohlmann S, Varzi A, Balducci A and Passerini S 2013 Ionic liquids in supercapacitorsMRS Bull. 38 554–9[106] Jeanmairet G, Rotenberg B and Salanne M 2022 Microscopic simulations of electrochemical double-layer capacitors Chem. Rev.122 10860–98[107] Kornyshev A 2007 Double-layer in ionic liquids: paradigm change? J. Phys. Chem. B 111 5545–57[108] Kondrat S and Kornyshev A A 2011 Superionic state in double-layer capacitors with nanoporous electrodes J. Phys.: Condens.Matter 23 022201[109] Shim Y and Kim H J 2010 Nanoporous carbon supercapacitors in an ionic liquid: a computer simulation study ACS Nano4 2345–55[110] Merlet C, Rotenberg B, Madden P A, Taberna P L, Simon P, Gogotsi Y and Salanne M 2012 On the molecular origin ofsupercapacitance in nanoporous carbon electrodes Nat. Mater. 11 306–10[111] Futamura R, Iiyama T, Takasaki Y, Gogotsi Y, Biggs M J, Salanne M, Ségalini J, Simon P and Kaneko K 2017 Partial breaking of theCoulombic ordering of ionic liquids confined in carbon nanopores Nat. Mater. 16 1225–32[112] Vatamanu J, Vatamanu M and Bedrov D 2015 Non-faradaic energy storage by room temperature ionic liquids in nanoporouselectrodes ACS Nano 9 5999–6017[113] Feng G and Cummings P T 2011 Supercapacitor capacitance exhibits oscillatory behavior as a function of nanopore size J. Phys.Chem. Lett. 2 2859–64[114] Pean C, Merlet C, Rotenberg B, Madden P A, Taberna P-L, Daffos B, Salanne M and Simon P 2014 On the dynamics of chargingin nanoporous carbon-based supercapacitors ACS Nano 8 1576–83[115] Breitsprecher K, Holm C and Kondrat S 2018 Charge Me Slowly, I Am in a Hurry: optimizing charge-discharge cycles innanoporous supercapacitors ACS Nano 12 9733–41[116] Mao X et al 2019 Self-assembled nanostructures in ionic liquids facilitate charge storage at electrified interfaces Nat. Mater.18 1350–7[117] Mourad E, Coustan L, Lannelongue P, Zigah D, Mehdi A, Vioux A, Freunberger S A, Favier F and Fontaine O 2016 Biredox ionicliquids with solid-like redox density in the liquid state for high-energy supercapacitors Nat. Mater. 16 446–53[118] Berthin R, Serva A, Fontaine O and Salanne M 2023 Nanostructural organization in a biredox ionic liquid J. Phys. Chem. Lett.14 101–6[119] Coretti A et al 2022 MetalWalls: simulating electrochemical interfaces between polarizable electrolytes and metallic electrodes J.Chem. Phys. 157 184801[120] Goloviznina K, Canongia Lopes J N, Costa Gomes M and Padua A 2019 Transferable, polarizable force fields for ionic liquids J.Chem. Theor. Comput. 15 5858–71[121] Brandenburg J G, Zen A, Alfè D and Michaelides A 2019 Interaction between water and carbon nanostructures: how good arecurrent density functional approximations? J. Chem. Phys. 151 164702[122] Shao Y, Knijff L, Dietrich F M, Hermansson K and Zhang C 2021 Modelling bulk electrolytes and electrolyte interfaces withatomistic machine learning Batter. Supercaps 4 585–95[123] Behler J 2021 Four generations of high-dimensional neural network potentials Chem. Rev. 121 10037–72[124] Grisafi A, Bussy A, Salanne M and Vuilleumier R 2023 Predicting the charge density response in metal electrodes(arXiv:2304.08966)[125] Ponrouch A, Bitenc J, Dominko R, Lindahl N, Johansson P and Palacin M R 2019 Multivalent rechargeable batteries EnergyStorage Mater. 20 253–62[126] Forero-Saboya J D, Tchitchekova D S, Johansson P, Palacín M R and Ponrouch A 2022 Interfaces and interphases in Ca and Mgbatteries Adv. Mater. Interfaces 9 2101578[127] Borodin O, Giffin G A, Moretti A, Haskins J B, Lawson J W, Henderson W A and Passerini S 2018 Insights into the structure andtransport of the lithium, sodium, magnesium, and Zinc Bis(trifluoromethansulfonyl)imide salts in ionic liquids J. Phys. Chem. C122 20108–21[128] Baskin A and Prendergast D 2020 Ion solvation engineering: how to manipulate the multiplicity of the coordination environmentof multivalent ions J. Phys. Chem. Lett. 11 9336–43[129] Canepa P, Gautam G S, Malik R, Jayaraman S, Rong Z, Zavadil K R, Persson K and Ceder G 2015 Understanding the initial stagesof reversible Mg deposition and stripping in inorganic nonaqueous electrolytes Chem. Mater. 27 3317–25[130] Kopač Lautar A, Bitenc J, Dominko R and Filhol J-S 2021 Building Ab Initio interface pourbaix diagrams to investigate electrolytestability in the electrochemical double layer: application to magnesium batteries ACS Appl. Mater. Interfaces 13 8263–73[131] Mandai T, Youn Y and Tateyama Y 2021 Remarkable electrochemical and ion-transport characteristics of magnesium-fluorinatedalkoxyaluminate–diglyme electrolytes for magnesium batteriesMater. Adv. 2 6283–96[132] Li Z, Fuhr O, Fichtner M and Zhao-Karger Z 2019 Towards stable and efficient electrolytes for room-temperature rechargeablecalcium batteries Energy Environ. Sci. 12 3496–501[133] Aurbach D, Skaletsky R and Gofer Y 1991 The electrochemical behavior of calcium electrodes in a few organic electrolytes J.Electrochem. Soc. 138 3536[134] Hou Z, Zhou R, Yao Y, Min Z, Lu Z, Zhu Y, Tarascon J-M and Zhang B 2022 Correlation between electrolyte chemistry and solidelectrolyte interphase for reversible Ca metal anodes Angew. Chem., Int. Ed. 61 e202214796[135] Forero-Saboya J D, Marchante E, Araujo R B, Monti D, Johansson P and Ponrouch A 2019 Cation solvation and physicochemicalproperties of Ca battery electrolytes J. Phys. Chem. C 123 29524–32[136] Kravchyk K V and Kovalenko M V 2020 Aluminum electrolytes for Al dual-ion batteries Commun. Chem. 3 1[137] Mandai T and Johansson P 2015 Al conductive haloaluminate-free non-aqueous room-temperature electrolytes J. Mater. Chem.A 3 12230–9[138] Hahn N T et al 2022 Concentration-dependent ion correlations impact the electrochemical behavior of calcium batteryelectrolytes Phys. Chem. Chem. Phys. 24 674–86[139] Yamijala S S R K C, Kwon H, Guo J and Wong B M 2021 Stability of calcium ion battery electrolytes: predictions from Ab Initiomolecular dynamics simulations ACS Appl. Mater. Interfaces 13 13114–22[140] Agarwal G, Howard J D, Prabhakaran V, Johnson G E, Murugesan V, Mueller K T, Curtiss L A and Assary R S 2021 Insights intospontaneous solid electrolyte interphase formation at magnesium metal anode surface from Ab Initiomolecular dynamicssimulations ACS Appl. Mater. Interfaces 13 38816–2551https://doi.org/10.1021/ja7106178https://doi.org/10.1021/ja7106178https://doi.org/10.1557/mrs.2013.151https://doi.org/10.1557/mrs.2013.151https://doi.org/10.1021/acs.chemrev.1c00925https://doi.org/10.1021/acs.chemrev.1c00925https://doi.org/10.1021/jp067857ohttps://doi.org/10.1021/jp067857ohttps://doi.org/10.1088/0953-8984/23/2/022201https://doi.org/10.1088/0953-8984/23/2/022201https://doi.org/10.1021/nn901916mhttps://doi.org/10.1021/nn901916mhttps://doi.org/10.1038/nmat3260https://doi.org/10.1038/nmat3260https://doi.org/10.1038/nmat4974https://doi.org/10.1038/nmat4974https://doi.org/10.1021/acsnano.5b00945https://doi.org/10.1021/acsnano.5b00945https://doi.org/10.1021/jz201312ehttps://doi.org/10.1021/jz201312ehttps://doi.org/10.1021/nn4058243https://doi.org/10.1021/nn4058243https://doi.org/10.1021/acsnano.8b04785https://doi.org/10.1021/acsnano.8b04785https://doi.org/10.1038/s41563-019-0449-6https://doi.org/10.1038/s41563-019-0449-6https://doi.org/10.1038/nmat4808https://doi.org/10.1038/nmat4808https://doi.org/10.1021/acs.jpclett.2c03330https://doi.org/10.1021/acs.jpclett.2c03330https://doi.org/10.1063/5.0101777https://doi.org/10.1063/5.0101777https://doi.org/10.1021/acs.jctc.9b00689https://doi.org/10.1021/acs.jctc.9b00689https://doi.org/10.1063/1.5121370https://doi.org/10.1063/1.5121370https://doi.org/10.1002/batt.202000262https://doi.org/10.1002/batt.202000262https://doi.org/10.1021/acs.chemrev.0c00868https://doi.org/10.1021/acs.chemrev.0c00868https://arxiv.org/abs/2304.08966https://doi.org/10.1016/j.ensm.2019.04.012https://doi.org/10.1016/j.ensm.2019.04.012https://doi.org/10.1002/admi.202101578https://doi.org/10.1002/admi.202101578https://doi.org/10.1021/acs.jpcc.8b05573https://doi.org/10.1021/acs.jpcc.8b05573https://doi.org/10.1021/acs.jpclett.0c02682https://doi.org/10.1021/acs.jpclett.0c02682https://doi.org/10.1021/acs.chemmater.5b00389https://doi.org/10.1021/acs.chemmater.5b00389https://doi.org/10.1021/acsami.0c19579https://doi.org/10.1021/acsami.0c19579https://doi.org/10.1039/D1MA00448Dhttps://doi.org/10.1039/D1MA00448Dhttps://doi.org/10.1039/C9EE01699Fhttps://doi.org/10.1039/C9EE01699Fhttps://doi.org/10.1149/1.2085455https://doi.org/10.1149/1.2085455https://doi.org/10.1002/anie.202214796https://doi.org/10.1002/anie.202214796https://doi.org/10.1021/acs.jpcc.9b07308https://doi.org/10.1021/acs.jpcc.9b07308https://doi.org/10.1038/s42004-020-00365-2https://doi.org/10.1038/s42004-020-00365-2https://doi.org/10.1039/C5TA01760Bhttps://doi.org/10.1039/C5TA01760Bhttps://doi.org/10.1039/D1CP04370Fhttps://doi.org/10.1039/D1CP04370Fhttps://doi.org/10.1021/acsami.0c21716https://doi.org/10.1021/acsami.0c21716https://doi.org/10.1021/acsami.1c07864https://doi.org/10.1021/acsami.1c07864J. Phys. Energy 5 (2023) 041501 C Zhang et al[141] Unke O T, Chmiela S, Sauceda H E, Gastegger M, Poltavsky I, Schütt K T, Tkatchenko A and Müller K-R 2021 Machine learningforce fields Chem. Rev. 121 10142–86[142] Martin P-A, Årén F and Johansson P 2023 (Localized) Highly concentrated electrolytes for calcium batter. Batter. Supercaps6 e202300003[143] Lombardo T et al 2021 Artificial intelligence applied to battery research: hype or reality? Chem. Rev. 122 10899–969[144] Qu X, Jain A, Rajput N N, Cheng L, Zhang Y, Ong S P, Brafman M, Maginn E, Curtiss L A and Persson K A 2015 The electrolytegenome project: a big data approach in battery materials discovery Comput. Mater. Sci. 103 56–67[145] Qiao B T, Wang A Q, Yang X F, Allard L F, Jiang Z, Cui Y T, Liu J Y, Li J and Zhang T 2011 Single-atom catalysis of CO oxidationusing Pt-1/FeOx Nat. Chem. 3 634–41[146] Yang X F, Wang A Q, Qiao B T, Li J, Liu J Y and Zhang T 2013 Single-atom catalysts: a new frontier in heterogeneous catalysis Acc.Chem. Res. 46 1740–8[147] Wang A Q, Li J and Zhang T 2018 Heterogeneous single-atom catalysis Nat. Rev. Chem. 2 65–81[148] Li J, Stephanopoulos M F and Xia Y N 2020 Introduction: heterogeneous single-atom catalysis Chem. Rev. 120 11699–702[149] Wang Y X et al 2020 Advanced electrocatalysts with single-metal-atom active sites Chem. Rev. 120 12217–314[150] Liu J C, Tang Y, Wang Y G, Zhang T and Li J 2018 Theoretical understanding of the stability of single-atom catalysts Natl Sci. Rev.5 638–41[151] Medford J, Vojvodic A, Hummelshoj J S, Voss J, Abild-Pedersen F, Studt F, Bligaard T, Nilsson A and Norskov J K 2015 From thesabatier principle to a predictive theory of transition-metal heterogeneous catalysis J. Catal. 328 36–42[152] Zhao Z J, Liu S H, Zha S J, Cheng D F, Studt F, Henkelman G and Gong J L 2019 Theory-guided design of catalytic materials usingscaling relationships and reactivity descriptors Nat. Rev. Mater. 4 792–804[153] Norskov J K, Abild-Pedersen F, Studt F and Bligaard T 2011 Density functional theory in surface chemistry and catalysis Proc.Natl Acad. Sci. USA 108 937–43[154] Resasco J, Abild-Pedersen F, Hahn C, Bao Z N, Koper M T M and Jaramillo T F 2022 Enhancing the connection betweencomputation and experiments in electrocatalysis Nat. Catal. 5 374–81[155] Norskov J K, Rossmeisl J, Logadottir A, Lindqvist L, Kitchin J R, Bligaard T and Jonsson H 2004 Origin of the overpotential foroxygen reduction at a fuel-cell cathode J. Phys. Chem. B 108 17886–92[156] Sundararaman R, Goddard W A and Arias T A 2017 Grand canonical electronic density-functional theory: algorithms andapplications to electrochemistry J. Chem. Phys. 146 114104[157] Schwarz K and Sundararaman R 2020 The electrochemical interface in first-principles calculations Surf. Sci. Rep. 75 100492[158] Cohen J, Mori-Sanchez P and Yang W T 2008 Insights into current limitations of density functional theory Science 321 792–4[159] Karapinar D et al 2019 Electroreduction of CO2 on single-site copper-nitrogen-doped carbon material: selective formation ofethanol and reversible restructuration of the metal sites Angew. Chem., Int. Ed. 58 15098–103[160] Shang R, Steinmann S N, Xu B Q and Sautet P 2020 Mononuclear Fe in N-doped carbon: computational elucidation of activesites for electrochemical oxygen reduction and oxygen evolution reactions Catal. Sci. Technol. 10 1006–14[161] Tan S, Ji Y and Li Y 2022 Single-atom electrocatalysis for hydrogen evolution based on the constant charge and constant potentialmodels J. Phys. Chem. Lett. 13 7036–42[162] Hutchison P, Rice P S, Warburton R E, Raugei S and Hammes-Schiffer S 2022 Multilevel computational studies reveal theimportance of axial ligand for oxygen reduction reaction on Fe–N–C materials J. Am. Chem. Soc. 144 16524–34[163] Brimle P, Almajed H, Alsunni Y, Alherz A W, Bare Z J L, Smith W A and Mursgrave C B 2022 Electrochemical CO2 reduction overmetal-/nitrogen-doped graphene single-atom catalysts modeled using the grand-canonical density functional theory ACS Catal.12 10161–71[164] Liu L and Xiao H 2023 Inverted region in electrochemical reduction of CO2 induced by potential-dependent pauli repulsion J.Am. Chem. Soc. 145 14267–75[165] Wang Z, Goddard W A and Xiao H 2023 Potential-dependent transition of reaction mechanisms for oxygen evolution on layereddouble hydroxides Nat. Commun. 14 4228[166] Fu Z M, Yang B W and Wu R Q 2020 Understanding the activity of single-atom catalysis from frontier orbitals Phys. Rev. Lett.125 156001[167] Zhang N N, Li J and Xiao H 2022 The key role of competition between orbital and electrostatic interactions in the adsorption ontransition metal single-atom catalysts anchored by N-doped graphene ChemCatChem 14 e202200275[168] Jones L O, Mosquera M A, Schatz G C and Ratner M A 2020 Embedding methods for quantum chemistry: applications frommaterials to life sciences J. Am. Chem. Soc. 142 3281–95[169] Zhao Q, Martirez J M P and Carter E A 2021 Revisiting understanding of electrochemical CO2 reduction on Cu(111): competingproton-coupled electron transfer reaction mechanisms revealed by embedded correlated wavefunction theory J. Am. Chem. Soc.143 6152–64[170] Bai X W, Zhao X H, Zhang Y H, Ling C Y, Zhou Y P, Wang J L and Liu Y Y 2022 Dynamic stability of copper single-atom catalystsunder working conditions J. Am. Chem. Soc. 144 17140–8[171] 2014 Polymer Electrolyte Fuel Cells: Physical Principles of Materials and Operation ed M Eikerling and A A Kulikovsky (CRC Press,Taylor & Francis Group)[172] Chatenet M et al 2022 Chem. Soc. Rev. 51 4583–762[173] Holdcroft S 2014 Chem. Mater. 26 381–93[174] Eslamibidgoli M J, Huang J, Kadyk T, Malek A and Eikerling M 2016 Nano Energy 29 334–61[175] Olbrich W, Kadyk T, Sauter U and Eikerling M 2022 J. Electrochem. Soc. 169 054521[176] Olbrich W, Kadyk T, Sauter U and Eikerling M 2022 Electrochim. Acta 431 140850[177] Eikerling M, Ioselevich A S and Kornyshev A A 2004 Fuel Cells 4 131[178] Seh Z W, Kibsgaard J, Dickens C F, Chorkendorff I, Nørskov J K and Jaramillo T F 2017 Science 355 eaad4998[179] Jiao S, Fu X and Huang H 2022 Adv. Funct. Mater. 32 2107651[180] Tabor D P et al 2018 Nat. Rev. Mater. 3 5–20[181] Tao H, Wu T, Kheiri S, Aldeghi M, Aspuru-Guzik A and Kumacheva E 2021 Adv. Funct. Mater. 31 2106725[182] Abolhasani M and Kumacheva E 2023 Nat. Synth. 2 483–92[183] Malek A, Wang Q, Baumann S, Guillon O, Eikerling M and Malek K 2021 Front. Energy Res. 9 52[184] Zhu X, Huang J and Eikerling M 2021 ACS Catal. 11 14521–32[185] Huang J, Li M, Eslamibidgoli M J, Eikerling M and Groß A 2021 JACS Au 1 1752–65[186] Huang J, Chen S and Eikerling M 2021 J. Chem. Theory Comput. 17 2417–3052https://doi.org/10.1021/acs.chemrev.0c01111https://doi.org/10.1021/acs.chemrev.0c01111https://doi.org/10.1002/batt.202300003https://doi.org/10.1002/batt.202300003https://doi.org/10.1021/acs.chemrev.1c00108https://doi.org/10.1021/acs.chemrev.1c00108https://doi.org/10.1016/j.commatsci.2015.02.050https://doi.org/10.1016/j.commatsci.2015.02.050https://doi.org/10.1038/nchem.1095https://doi.org/10.1038/nchem.1095https://doi.org/10.1021/ar300361mhttps://doi.org/10.1021/ar300361mhttps://doi.org/10.1038/s41570-018-0010-1https://doi.org/10.1038/s41570-018-0010-1https://doi.org/10.1021/acs.chemrev.0c01097https://doi.org/10.1021/acs.chemrev.0c01097https://doi.org/10.1021/acs.chemrev.0c00594https://doi.org/10.1021/acs.chemrev.0c00594https://doi.org/10.1093/nsr/nwy094https://doi.org/10.1093/nsr/nwy094https://doi.org/10.1016/j.jcat.2014.12.033https://doi.org/10.1016/j.jcat.2014.12.033https://doi.org/10.1038/s41578-019-0152-xhttps://doi.org/10.1038/s41578-019-0152-xhttps://doi.org/10.1073/pnas.1006652108https://doi.org/10.1073/pnas.1006652108https://doi.org/10.1038/s41929-022-00789-0https://doi.org/10.1038/s41929-022-00789-0https://doi.org/10.1021/jp047349jhttps://doi.org/10.1021/jp047349jhttps://doi.org/10.1063/1.4978411https://doi.org/10.1063/1.4978411https://doi.org/10.1016/j.surfrep.2020.100492https://doi.org/10.1016/j.surfrep.2020.100492https://doi.org/10.1126/science.1158722https://doi.org/10.1126/science.1158722https://doi.org/10.1002/anie.201907994https://doi.org/10.1002/anie.201907994https://doi.org/10.1039/C9CY01935Ahttps://doi.org/10.1039/C9CY01935Ahttps://doi.org/10.1021/acs.jpclett.2c01288https://doi.org/10.1021/acs.jpclett.2c01288https://doi.org/10.1021/jacs.2c05779https://doi.org/10.1021/jacs.2c05779https://doi.org/10.1021/acscatal.2c01832https://doi.org/10.1021/acscatal.2c01832https://doi.org/10.1021/jacs.3c02447https://doi.org/10.1021/jacs.3c02447https://doi.org/10.1038/s41467-023-40011-8https://doi.org/10.1038/s41467-023-40011-8https://doi.org/10.1103/PhysRevLett.125.156001https://doi.org/10.1103/PhysRevLett.125.156001https://doi.org/10.1002/cctc.202200275https://doi.org/10.1002/cctc.202200275https://doi.org/10.1021/jacs.9b10780https://doi.org/10.1021/jacs.9b10780https://doi.org/10.1021/jacs.1c00880https://doi.org/10.1021/jacs.1c00880https://doi.org/10.1021/jacs.2c07178https://doi.org/10.1021/jacs.2c07178https://doi.org/10.1039/d0cs01079khttps://doi.org/10.1039/d0cs01079khttps://doi.org/10.1021/cm401445hhttps://doi.org/10.1021/cm401445hhttps://doi.org/10.1016/j.nanoen.2016.06.004https://doi.org/10.1016/j.nanoen.2016.06.004https://doi.org/10.1149/1945-7111/ac6e8bhttps://doi.org/10.1149/1945-7111/ac6e8bhttps://doi.org/10.1016/j.electacta.2022.140850https://doi.org/10.1016/j.electacta.2022.140850https://doi.org/10.1002/fuce.200400029https://doi.org/10.1002/fuce.200400029https://doi.org/10.1126/science.aad4998https://doi.org/10.1126/science.aad4998https://doi.org/10.1002/adfm.202107651https://doi.org/10.1002/adfm.202107651https://doi.org/10.1038/s41578-018-0005-zhttps://doi.org/10.1038/s41578-018-0005-zhttps://doi.org/10.1002/adfm.202106725https://doi.org/10.1002/adfm.202106725https://doi.org/10.1038/s44160-022-00231-0https://doi.org/10.1038/s44160-022-00231-0https://doi.org/10.3389/fenrg.2021.609070https://doi.org/10.3389/fenrg.2021.609070https://doi.org/10.1021/acscatal.1c04791https://doi.org/10.1021/acscatal.1c04791https://doi.org/10.1021/jacsau.1c00315https://doi.org/10.1021/jacsau.1c00315https://doi.org/10.1021/acs.jctc.1c00098https://doi.org/10.1021/acs.jctc.1c00098J. Phys. Energy 5 (2023) 041501 C Zhang et al[187] Groß A 2021 Curr. Opin. Electrochem. 27 100684Cucinotta C S 2022 Curr. Opin. Electrochem. 36 101118[188] Melander M, Kuisma M, Christensen T E K and Honkala K 2019 Grand-canonical approach to density functional theory ofelectrocatalytic systems: thermodynamics of solid-liquid interfaces at constant ion and electrode potentials J. Chem. Phys.150 041706[189] Hörmann N G, Andreussi O and Marzari N 2019 J. Chem. Phys. 150 041730[190] Groß A, Gossenberger F, Lin X, Naderian M, Sakong S and Roman T 2014 J. Electrochem. Soc. 161 E3015–20[191] Dally W J, Turakhia Y and Han S 2020 Commun. ACM 63 48–57[192] Keal T W et al 2022 Comput. Sci. Eng. 24 36–45[193] Alexander F et al 2020 Exascale applications: skin in the game Phil. Trans. R. Soc. A 378 20190056[194] Bartók A P, Payne M C, Kondor R and Csányi G 2010 Phys. Rev. Lett. 104 136403[195] Behler J and Parrinello M 2007 Phys. Rev. Lett. 98 146401[196] Wang H, Zhang L and Han J 2018 Comput. Phys. Commun. 228 178–84[197] Huang J, Malek A, Zhang J and Eikerling M H 2016 J. Phys. Chem. C 120 13587–95[198] Frumkin A N and Petrii O A 1975 Electrochim. Acta 20 347–59[199] Tesch R, Kowalski P M and Eikerling M H 2021 J. Phys.: Condens. Matter 33 444004[200] Podgornik R 1989 J. Chem. Phys. 91 5840–9[201] Netz R R and Orland H 2000 Eur. Phys. J. E 1 203–14[202] Perdew J P, Burke K and Ernzerhof M 1996 Phys. Rev. Lett. 77 3865–8[203] Tiwary P et al 2016 Springer Series in Materials Science (Springer) p 195[204] Tsuchida E 2016 J. Phys. Soc. Japan 85 084801[205] Matej M and Netz R R 2015 Proc. Natl Acad. Sci. 112 12338–43[206] Kanduc M, Schlaich A, Schneck E and Netz R R 2016 Langmuir 32 8767–82[207] Yoshida T and Kojima K 2015 Toyota MIRAI fuel cell vehicle and progress toward a future hydrogen society Electrochem. Soc.Interface 24 45[208] Cullen D A, Neyerlin K C, Ahluwalia R K, Mukundan R, More K L, Borup R L, Weber A Z, Myers D J and Kusoglu A 2021 Newroads and challenges for fuel cells in heavy-duty transportation Nat. Energy 6 462–74[209] Kodama K, Nagai T, Kuwaki A, Jinnouchi R and Morimoto Y 2021 Challenges in applying highly active Pt-based nanostructuredcatalysts for oxygen reduction reactions to fuel cell vehicles Nat. Nanotechnol. 16 140–7[210] NEDO roadmap for fuel cells and hydrogen technologies (Japanese) (available at: www.nedo.go.jp/content/100871976.pdf)[211] Weber A Z and Newman J 2004 Modeling transport in polymer-electrolyte fuel cells Chem. Rev. 104 4679–726[212] Inoue G and Kawase M 2016 Effect of porous structure of catalyst layer on effective oxygen diffusion coefficient in polymerelectrolyte fuel cell J. Power Sources 327 1–10[213] Malek K, Eikerling M, Wang Q, Navessin T and Liu Z 2007 Self-organization in catalyst layers of polymer electrolyte fuel cells J.Phys. Chem. C 111 13627–34[214] Jinnouchi R, Kudo K, Kodama K, Kitano N, Suzuki T, Minami S, Shinozaki K, Hasegawa N and Shinohara A 2021 The role ofoxygen-permeable ionomer for polymer electrolyte fuel cells Nat. Commun. 12 4956[215] Jinnouchi R, Kodama K and Morimoto Y 2018 Electronic structure calculations on electrolyte–electrode interfaces: successes andlimitations Curr. Opin. Electrochem. 8 103–9[216] Kulkarni A, Siahrostami S, Patel A and Nørskov J K 2018 Understanding catalytic activity trends in the oxygen reduction reactionChem. Rev. 118 2302–12[217] Wang Z, Guo X, Montoya J and Nørskov J K 2020 Predicting aqueous stability of solid with computed Pourbaix diagram usingSCAN functional npj Comput. Mater. 6 160[218] Wang Z, Zheng Y-R, Chorkendorff I and Nørskov J K 2020 Acid-stable oxides for oxygen electrocatalysis ACS Energy Lett.5 2905–8[219] Lee J and Jinnouchi R 2021 Machine learning-based screening of highly stable and active ternary Pt alloys for oxygen reductionreaction J. Phys. Chem. C 125 16963–74[220] Niu Z, Pinfield V J, Wu B, Wang H, Jiao K, Leung D Y C and Xuan J 2021 Towards the digitalisation of porous energy materials:evolution of digital approaches for microstructural design Energy Environ. Sci. 14 2549–76[221] Deringer V L, Caro M A and Csányi G 2019 Machine learning interatomic potentials as emerging tools for materials science Adv.Mater. 31 1902765[222] Jinnouchi R, Miwa K, Karsai F, Kresse G and Asahi R 2020 On-the-fly active learning of interatomic potentials for large-scaleatomistic simulations J. Phys. Chem. Lett. 11 6946–55[223] Jinnouchi R 2022 Molecular dynamics simulations of proton conducting media containing phosphoric acid Phys. Chem. Chem.Phys. 24 15522–31[224] Mikkelsen A E G, Kristoffersen H H, Schiøtz J, Vegge T, Hansen H A and Jacobsen K W 2022 Structure and energetics of liquidwater–hydroxyl layers on Pt(111) Phys. Chem. Chem. Phys. 24 9885–90[225] Vandermause J, Xie Y, Lim J S, Owen C J and Kozinsky B 2022 Active learning of reactive Bayesian force fields applied toheterogeneous catalysis dynamics of H/Pt Nat. Commun. 13 5183[226] Wang J, Olsson S, Wehmeyer C, Pérez A, Charron N E, de Fabritiis G, Noé F and Clementi C 2019 Machine learning ofcoarse-grained molecular dynamics force fields ACS Cent. Sci. 5 755–67[227] Batzner S, Musaelian A, Sun L, Geiger M, Mailoa J P, Kornbluth M, Molinari N, Smidt T E and Kozinsky B 2022 E(3)-equivariantgraph neural networks for data-efficient and accurate interatomic potentials Nat. Commun. 13 2453[228] Abidi N and Steinman S N 2022 How are transition states modeled in heterogeneous electrocatalysis?Mol. Genet. Metab. Rep.33 100940[229] Daimon H, Yamazaki S-I, Asahi M, Ioroi T and Inaba M 2022 A strategy for drastic improvement in the durability of Pt/C andPtCo/C alloy catalysts for the oxygen reduction reaction by melamine surface modification ACS Catal. 12 8976–85[230] Wang T, Zhang Y, Huang B, Cai B, Rao R R, Giordano L, Sun S-G and Shao-Horn Y 2021 Enhancing oxygen reductionelectrocatalysis by tuning interfacial hydrogen bonds Nat. Catal. 4 753–62[231] Jinnouchi R, Karsai F and Kresse G 2020 Making free-energy calculations routine: combining first principles with machinelearning Phys. Rev. B 101 060201[232] Jinnouchi R, Karsai F, Verdi C and Kresse G 2021 First-principles hydration free energies of oxygenated species at water–platinuminterfaces J. Chem. Phys. 154 09410753https://doi.org/10.1016/j.coelec.2020.100684https://doi.org/10.1016/j.coelec.2020.100684https://doi.org/10.1063/1.5047829https://doi.org/10.1063/1.5047829https://doi.org/10.1063/1.5054580https://doi.org/10.1063/1.5054580https://doi.org/10.1149/2.003408jeshttps://doi.org/10.1149/2.003408jeshttps://doi.org/10.1145/3361682https://doi.org/10.1145/3361682https://doi.org/10.1109/MCSE.2022.3141328https://doi.org/10.1109/MCSE.2022.3141328https://doi.org/10.1098/rsta.2019.0056https://doi.org/10.1098/rsta.2019.0056https://doi.org/10.1103/PhysRevLett.104.136403https://doi.org/10.1103/PhysRevLett.104.136403https://doi.org/10.1103/PhysRevLett.98.146401https://doi.org/10.1103/PhysRevLett.98.146401https://doi.org/10.1016/j.cpc.2018.03.016https://doi.org/10.1016/j.cpc.2018.03.016https://doi.org/10.1021/acs.jpcc.6b03930https://doi.org/10.1021/acs.jpcc.6b03930https://doi.org/10.1016/0013-4686(75)90017-1https://doi.org/10.1016/0013-4686(75)90017-1https://doi.org/10.1088/1361-648X/ac1aa2https://doi.org/10.1088/1361-648X/ac1aa2https://doi.org/10.1063/1.457535https://doi.org/10.1063/1.457535https://doi.org/10.1007/s101890050023https://doi.org/10.1007/s101890050023https://doi.org/10.1103/PhysRevLett.77.3865https://doi.org/10.1103/PhysRevLett.77.3865https://doi.org/10.7566/JPSJ.85.084801https://doi.org/10.7566/JPSJ.85.084801https://doi.org/10.1073/pnas.1504919112https://doi.org/10.1073/pnas.1504919112https://doi.org/10.1021/acs.langmuir.6b01727https://doi.org/10.1021/acs.langmuir.6b01727https://doi.org/10.1149/2.F03152ifhttps://doi.org/10.1149/2.F03152ifhttps://doi.org/10.1038/s41560-021-00775-zhttps://doi.org/10.1038/s41560-021-00775-zhttps://doi.org/10.1038/s41565-020-00824-whttps://doi.org/10.1038/s41565-020-00824-whttps://www.nedo.go.jp/content/100871976.pdfhttps://doi.org/10.1021/cr020729lhttps://doi.org/10.1021/cr020729lhttps://doi.org/10.1016/j.jpowsour.2016.07.037https://doi.org/10.1016/j.jpowsour.2016.07.037https://doi.org/10.1021/jp072692khttps://doi.org/10.1021/jp072692khttps://doi.org/10.1038/s41467-021-25301-3https://doi.org/10.1038/s41467-021-25301-3https://doi.org/10.1016/j.coelec.2018.03.024https://doi.org/10.1016/j.coelec.2018.03.024https://doi.org/10.1021/acs.chemrev.7b00488https://doi.org/10.1021/acs.chemrev.7b00488https://doi.org/10.1038/s41524-020-00430-3https://doi.org/10.1038/s41524-020-00430-3https://doi.org/10.1021/acsenergylett.0c01625https://doi.org/10.1021/acsenergylett.0c01625https://doi.org/10.1021/acs.jpcc.1c02890https://doi.org/10.1021/acs.jpcc.1c02890https://doi.org/10.1039/D1EE00398Dhttps://doi.org/10.1039/D1EE00398Dhttps://doi.org/10.1002/adma.201902765https://doi.org/10.1002/adma.201902765https://doi.org/10.1021/acs.jpclett.0c01061https://doi.org/10.1021/acs.jpclett.0c01061https://doi.org/10.1039/D2CP00484Dhttps://doi.org/10.1039/D2CP00484Dhttps://doi.org/10.1039/D2CP00190Jhttps://doi.org/10.1039/D2CP00190Jhttps://doi.org/10.1038/s41467-022-32294-0https://doi.org/10.1038/s41467-022-32294-0https://doi.org/10.1021/acscentsci.8b00913https://doi.org/10.1021/acscentsci.8b00913https://doi.org/10.1038/s41467-022-29939-5https://doi.org/10.1038/s41467-022-29939-5https://doi.org/10.1016/j.ymgmr.2022.100940https://doi.org/10.1016/j.ymgmr.2022.100940https://doi.org/10.1021/acscatal.2c01942https://doi.org/10.1021/acscatal.2c01942https://doi.org/10.1038/s41929-021-00668-0https://doi.org/10.1038/s41929-021-00668-0https://doi.org/10.1103/PhysRevB.101.060201https://doi.org/10.1103/PhysRevB.101.060201https://doi.org/10.1063/5.0036097https://doi.org/10.1063/5.0036097J. Phys. Energy 5 (2023) 041501 C Zhang et al[233] Kastlunger G, Lindgren P and Peterson A A 2018 Controlled-potential simulation of elementary electrochemical reactions:proton discharge on metal surfaces J. Phys. Chem. C 122 12771–81[234] Verma AM, Laverdure L, Melander MM and Honkala K 2022 Mechanistic origins of the pH dependency in Au-catalyzed glycerolelectro-oxidation: insight from first- principles calculations ACS Catal. 12 662–75[235] Kastlunger G, Wang L, Govindarajan N, Heenen H H, Ringe S, Jaramillo T, Hahn C and Chan K 2022 Using pH dependence tounderstand mechanisms in electrochemical CO reduction ACS Catal. 12 4344–57[236] Lindgren P, Kastlunger G and Peterson A A 2022 Electrochemistry from the atomic scale, in the electronically grand-canonicalensemble J. Chem. Phys. 157 180902[237] Enkovaara J et al 2010 Electronic structure calculations with GPAW: a real-space implementation of the projectoraugmented-wave method J. Phys.: Condens. Matter 22 253202[238] Larsen A H, Vanin M, Mortensen J J, Thygesen K S and Jacobsen K W 2009 Localized atomic basis set in the projector augmentedwave method Phys. Rev. B 80 195112[239] Harris C R et al 2020 Array programming with NumPy Nature 585 357–62[240] Virtanen P et al 2020 SciPy 1.0: fundamental algorithms for scientific computing in python Nat. Methods 17 261–72[241] Ringe S, Hörmann N G, Oberhofer H and Reuter K 2022 Implicit solvation methods for catalysis at electrified interfaces Chem.Rev. 122 10777–820[242] Melander M, Wu T and Honkala K 2023 Constant inner potential DFT for modelling electrochemical systems under constantpotential and bias (https://doi.org/10.26434/chemrxiv-2021-r621x-v3)[243] Otani M and Sugino O 2006 First-principles calculations of charged surfaces and interfaces: a plane-wave nonrepeated slabapproach Phys. Rev. B 73 115407[244] Held A and Walter M 2014 Simplified continuum solvent model with a smooth cavity based on volumetric data J. Chem. Phys.141 174108[245] Jeanmairet G, Levesque M and Borgis D 2020 Tackling solvent effects by coupling electronic and molecular density functionaltheory J. Chem. Theory Comput. 16 7123–34[246] Melander M, Jónsson E Ö, Mortensen J J, Vegge T and García Lastra J M 2016 Implementation of constrained DFT for computingcharge transfer rates within the projector augmented wave method J. Chem. Theory Comput. 12 5367–78[247] Melander MM 2020 Grand canonical rate theory for electrochemical and electrocatalytic systems I: general formulation andproton-coupled electron transfer reactions J. Electrochem. Soc. 167 116518[248] de Souza J P, Kornyshev A A and Bazant M Z 2022 Polar liquids at charged interfaces: a dipolar shell theory J. Chem. Phys.156 244705[249] de Souza J P, Goodwin Z A H, McEldrew M, Kornyshev A A and Bazant M Z 2020 Interfacial layering in the electric double layerof ionic liquids Phys. Rev. Lett. 125 116001[250] Hansen J-P and McDonald I R (eds) 2013 Theory of Simple Liquids 4th edn (Academic)[251] Nishihara S and Otani M 2017 Hybrid solvation models for bulk, interface, and membrane: reference interaction site methodscoupled with density functional theory Phys. Rev. B 96 115429[252] Kovalenko A and Hirata F 1998 Three-dimensional density profiles of water in contact with a solute of arbitrary shape: a RISMapproach Chem. Phys. Lett. 290 237–44[253] Sundararaman R, Letchworth-Weaver K, Schwarz K A, Gunceler D, Ozhabes Y and Arias T 2017 JDFTx: software for jointdensity-functional theory SoftwareX 6 278–84[254] Cao S, Qiu Y, Unarta I C, Goonetilleke E C and Huang X 2022 The ion-dipole correction of the 3DRISM solvation model toaccurately compute water distributions around negatively charged biomolecules J. Phys. Chem. B 126 8632–45[255] Valiev M, Chuev G N and Fedotova M V 2022 CDFTPY: a python package for performing classical density functional theorycalculations for molecular liquids Comput. Phys. Commun. 276 108338[256] Jinnouchi R, Lahnsteiner J, Karsai F, Kresse G and BokdamM 2019 Phase transitions of hybrid perovskites simulated bymachine-learning force fields trained on the fly with bayesian inference Phys. Rev. Lett. 122 225701[257] Ko T W, Finkler J A, Goedecker S and Behler J 2021 A fourth-generation high- dimensional neural network potential withaccurate electrostatics including non-local charge transfer Nat. Commun. 12 398[258] Shao Y, Andersson L, Knijff L and Zhang C 2022 Finite-field coupling via learning the charge response kernel Electron. Struct.4 014012[259] Hakala S, Havu V, Enkovaara J and Nieminen R 2013 Parallel electronic structure calculations using multiple graphics processingunits (GPUs) Applied Parallel and Scientific Computing (Springer) pp 63–76[260] Louhivuori M GPAW, GPU, and LUMI (available at: https://members.cecam.org/storage/presentation/Martti_Louhivuori-1622790941.pdf) (Accessed 23 November 2022)[261] Jinnouchi R and Anderson A B 2008 Electronic structure calculations of liquid-solid interfaces: combination of density functionaltheory and modified poisson-boltzmann theory Phys. Rev. B 77 245417[262] Wang H-F and Liu Z-P 2009 Formic acid oxidation at Pt/H2O interface from periodic DFT calculations integrated with acontinuum solvation model J. Phys. Chem. C 113 17502–8[263] Bonnet N and Marzari N 2013 First-principles prediction of the equilibrium shape of nanoparticles under realisticelectrochemical conditions Phys. Rev. Lett. 110 086104[264] Sakong S, Naderian M, Mathew K, Hennig R G and Groß A 2015 Density functional theory study of the electrochemical interfacebetween a Pt electrode and an aqueous electrolyte using an implicit solvent method J. Chem. Phys. 142 234107[265] Tripkovic V, Björketun M E, Skúlason E and Rossmeisl J 2011 Standard hydrogen electrode and potential of zero charge in densityfunctional calculations Phys. Rev. B 84 115452[266] Skúlason E, Karlberg G S, Rossmeisl J, Bligaard T, Greeley J, Jónsson H and Nørskov J K 2007 Density functional theorycalculations for the hydrogen evolution reaction in an electrochemical double layer on the Pt (111) Phys. Chem. Chem. Phys.9 3241–50[267] Otani M, Hamada I, Sugino O, Morikawa Y, Okamoto Y and Ikeshoji T 2008 Structure of the water/platinum interface—a firstprinciples simulation under bias potential Phys. Chem. Chem. Phys. 10 3609–12[268] Otani M, Hamada I, Sugino O, Morikawa Y, Okamoto Y and Ikeshoji T 2008 Electrode dynamics from first principles J. Phys. Soc.Japan 77 024802[269] Lozovoi A Y, Alavi A, Kohanoff J and Lynden-Bell R M 2001 Ab-initio simulation of charged slabs at constant chemical potential J.Chem. Phys. 115 1661–954https://doi.org/10.1021/acs.jpcc.8b02465https://doi.org/10.1021/acs.jpcc.8b02465https://doi.org/10.1021/acscatal.1c03788https://doi.org/10.1021/acscatal.1c03788https://doi.org/10.1021/acscatal.1c05520https://doi.org/10.1021/acscatal.1c05520https://doi.org/10.1063/5.0123656https://doi.org/10.1063/5.0123656https://doi.org/10.1088/0953-8984/22/25/253202https://doi.org/10.1088/0953-8984/22/25/253202https://doi.org/10.1103/PhysRevB.80.195112https://doi.org/10.1103/PhysRevB.80.195112https://doi.org/10.1038/s41586-020-2649-2https://doi.org/10.1038/s41586-020-2649-2https://doi.org/10.1038/s41592-019-0686-2https://doi.org/10.1038/s41592-019-0686-2https://doi.org/10.1021/acs.chemrev.1c00675https://doi.org/10.1021/acs.chemrev.1c00675https://doi.org/10.26434/chemrxiv-2021-r621x-v3https://doi.org/10.1103/PhysRevB.73.115407https://doi.org/10.1103/PhysRevB.73.115407https://doi.org/10.1063/1.4900838https://doi.org/10.1063/1.4900838https://doi.org/10.1021/acs.jctc.0c00729https://doi.org/10.1021/acs.jctc.0c00729https://doi.org/10.1021/acs.jctc.6b00815https://doi.org/10.1021/acs.jctc.6b00815https://doi.org/10.1149/1945-7111/aba54bhttps://doi.org/10.1149/1945-7111/aba54bhttps://doi.org/10.1063/5.0096439https://doi.org/10.1063/5.0096439https://doi.org/10.1103/PhysRevLett.125.116001https://doi.org/10.1103/PhysRevLett.125.116001https://doi.org/10.1103/PhysRevB.96.115429https://doi.org/10.1103/PhysRevB.96.115429https://doi.org/10.1016/S0009-2614(98)00471-0https://doi.org/10.1016/S0009-2614(98)00471-0https://doi.org/10.1016/j.softx.2017.10.006https://doi.org/10.1016/j.softx.2017.10.006https://doi.org/10.1021/acs.jpcb.2c04431https://doi.org/10.1021/acs.jpcb.2c04431https://doi.org/10.1016/j.cpc.2022.108338https://doi.org/10.1016/j.cpc.2022.108338https://doi.org/10.1103/PhysRevLett.122.225701https://doi.org/10.1103/PhysRevLett.122.225701https://doi.org/10.1038/s41467-020-20427-2https://doi.org/10.1038/s41467-020-20427-2https://doi.org/10.1088/2516-1075/ac59cahttps://doi.org/10.1088/2516-1075/ac59cahttps://members.cecam.org/storage/presentation/Martti_Louhivuori-1622790941.pdfhttps://members.cecam.org/storage/presentation/Martti_Louhivuori-1622790941.pdfhttps://doi.org/10.1103/PhysRevB.77.245417https://doi.org/10.1103/PhysRevB.77.245417https://doi.org/10.1021/jp9059888https://doi.org/10.1021/jp9059888https://doi.org/10.1103/PhysRevLett.110.086104https://doi.org/10.1103/PhysRevLett.110.086104https://doi.org/10.1063/1.4922615https://doi.org/10.1063/1.4922615https://doi.org/10.1103/PhysRevB.84.115452https://doi.org/10.1103/PhysRevB.84.115452https://doi.org/10.1039/B700099Ehttps://doi.org/10.1039/B700099Ehttps://doi.org/10.1039/b803541ehttps://doi.org/10.1039/b803541ehttps://doi.org/10.1143/JPSJ.77.024802https://doi.org/10.1143/JPSJ.77.024802https://doi.org/10.1063/1.1379327https://doi.org/10.1063/1.1379327J. Phys. Energy 5 (2023) 041501 C Zhang et al[270] Bonnet N, Morishita T, Sugino O and Otani M 2012 First-principles molecular dynamics at a constant electrode potential Phys.Rev. Lett. 109 266101[271] Cheng J and Sprik M 2012 alignment of electronic energy levels at electrochemical interfaces Phys. Chem. Chem. Phys.14 11245–67[272] Hansen M H, Jin C, Thygesen K S and Rossmeisl J 2016 Finite bias calculations to model interface dipoles in electrochemical cellsat the atomic scale J. Phys. Chem. C 120 13485–91[273] Rossmeisl J, Chan K, Ahmed R, Tripkovíc V and Björketun M E 2013 pH in atomic scale simulations of electrochemical interfacesPhys. Chem. Chem. Phys. 15 10321–5[274] Bouzid A and Pasquarello A 2018 Atomic-scale simulation of electrochemical processes at electrode/water interfaces underreferenced bias potential J. Phys. Chem. Lett. 9 1880[275] Bouzid A and Pasquarello A 2021 Atomic—scale modelling of electrochemical interfaces through constant fermi level moleculardynamics Atomic—Scale Modelling of Electrochemical Systems (Wiley) pp 221–40[276] Bouzid A, Gono P and Pasquarello A 2019 Reaction pathway of oxygen evolution on Pt(111) revealed through constant Fermilevel molecular dynamics J. Catal. 375 135–9[277] Bouzid A and Pasquarello A 2017 Redox levels through constant Fermi-level ab initiomolecular dynamics J. Chem. TheoryComput. 13 1769–77[278] Yang J, Falletta S and Pasquarello A J 2022 Phys. Chem. Lett. 13 3066–71[279] Barducci A, Bonomi M and Parrinello M 2011 MetadynamicsWiley Interdiscip. Rev. Comput. Mol. Sci. 1 826–43[280] Kirkwood J G 1935 Statistical mechanics of fluid mixtures J. Chem. Phys. 3 300–13[281] Schmickler W 2020 Double layer theory J. Solid State Electrochem. 24 2175–6[282] Climent V, Coles B A and Compton R G 2002 Laser-induced potential transients on a Au(111) single-crystal electrode.Determination of the potential of maximum entropy of double-layer formation J. Phys. Chem. B 106 5258–65[283] Jang T, Paik D, Shin S-J and Kim H 2022 Density functional theory in classical explicit solvents: mean-field QM/MMmethod forsimulating solid–liquid interfaces Bull. Korean Chem. Soc. 43 476–83[284] Lim H-K et al 2018 Insight into the microenvironments of the metal–ionic liquid interface during electrochemical CO2 reductionACS Catal. 8 2420–7[285] Gim S, Cho K J, Lim H-K and Kim H 2019 Structure, dynamics, and wettability of water at metal interfaces Sci. Rep. 9 14805[286] Gim S, Lim H-K and Kim H 2018 Multiscale simulation method for quantitative prediction of surface wettability at the atomisticlevel J. Phys. Chem. Lett. 9 1750–8[287] Shin S-J et al 2022 On the importance of the electric double layer structure in aqueous electrocatalysis Nat. Commun. 13 174[288] Bard A J and Faulkner L R 2001 Double-layer structure and adsorption Electrochemical Methods: Fundamentals and Applications2nd edn (Wiley)[289] Clabaut P, Beisert M, Michel C and Steinmann S N 2022 Beyond single-crystal surfaces: the GAL21 water/metal force field J.Chem. Phys. 157 194705[290] Shin S-J et al 2022 A unifying mechanism for cation effect modulating C1 and C2 productions from CO2 electroreduction Nat.Commun. 13 5482[291] Guo J, Haji-Akbari A and Palmer J C 2018 Hybrid Monte Carlo with LAMMPS Comput. Theor. Chem. 17 1840002[292] Finney A R, McPherson I J, Unwin P R and Salvalaglio M 2021 Electrochemistry, ion adsorption and dynamics in the doublelayer: a study of NaCl(aq) on graphite’ Chem. Sci. 12 11166–80[293] Naserifar S and Goddard W A 2018 The quantum mechanics-based polarizable force field for water simulations J. Chem. Phys.149 174502[294] Lamoureux G, Harder E, Vorobyov I V, Roux B and MacKerell A D 2006 A polarizable model of water for molecular dynamicssimulations of biomolecules Chem. Phys. Lett. 418 245–9[295] Ponder J W et al 2010 Current status of the AMOEBA polarizable force field J. Phys. Chem. B 114 2549–64[296] Fedkin M V et al 2019 Development of the ReaxFF methodology for electrolyte–water systems J. Phys. Chem. A 123 2125–41[297] Zhang W and van Duin A C T 2017 Second-generation ReaxFF water force field: improvements in the description of waterdensity and OH-anion diffusion J. Phys. Chem. B 121 6021–32[298] Tully J C 1990 Molecular dynamics with electronic transitions J. Chem. Phys. 93 1061–71[299] Akimov A V and Prezhdo O V 2013 The PYXAID program for non-adiabatic molecular dynamics in condensed matter systems J.Chem. Theory Comput. 9 4959–72[300] Zhang L Y, Friesner R A and Murphy R B 1997 Ab initio quantum chemical calculation of electron transfer matrix elements forlarge molecules J. Chem. Phys. 107 450–9[301] Goodwin Z A H and Kornyshev A A 2017 Underscreening, overscreening and double-layer capacitance Electrochem. Commun.82 129–33[302] Bhattacharyya D et al 2022 Sub-nanometer mapping of the interfacial electric field profile using a vibrational stark shift ruler J.Am. Chem. Soc. 144 14330–8[303] Yang S et al 2022 Nature of the electrical double layer on suspended graphene electrodes J. Am. Chem. Soc. 144 13327–33[304] Delley M F, Nichols E M and Mayer J M 2021 Interfacial acid–base equilibria and electric fields concurrently probed by in situsurface-enhanced infrared spectroscopy J. Am. Chem. Soc. 143 10778–92[305] Tomasi J, Mennucci B and Cammi R 2005 Quantum mechanical continuum solvation models Chem. Rev. 105 2999–3093[306] Hille C, Ringe S, Deimel M, Kunkel C, Acree W E, Reuter K and Oberhofer H 2019 Generalized molecular solvation innon-aqueous solutions by a single parameter implicit solvation scheme J. Chem. Phys. 150 041710[307] Fattebert J-L and Gygi F 2002 Density functional theory for efficient ab initiomolecular dynamics simulations in solution J.Comput. Chem. 23 662–6[308] Dupont C, Andreussi O and Marzari N 2013 Self-consistent continuum solvation (SCCS): the case of charged systems J. Chem.Phys. 139 214110[309] Gunceler D, Letchworth-Weaver K, Sundararaman R, Schwarz K A and Arias T A 2013 The importance of nonlinear fluidresponse in joint density-functional theory studies of battery systemsModelling Simul. Mater. Sci. Eng. 21 074005[310] Sundararaman R, Letchworth-Weaver K and Schwarz K A 2018 Improving accuracy of electrochemical capacitance and solvationenergetics in first-principles calculations J. Chem. Phys. 148 144105[311] Sundararaman R and Goddard W A 3rd 2015 The charge-asymmetric nonlocally determined local-electric (CANDLE) solvationmodel J. Chem. Phys. 142 064107[312] Truscott M and Andreussi O 2019 Field-aware interfaces in continuum solvation J. Phys. Chem. B 123 3513–2455https://doi.org/10.1103/PhysRevLett.109.266101https://doi.org/10.1103/PhysRevLett.109.266101https://doi.org/10.1039/c2cp41652bhttps://doi.org/10.1039/c2cp41652bhttps://doi.org/10.1021/acs.jpcc.6b00721https://doi.org/10.1021/acs.jpcc.6b00721https://doi.org/10.1039/c3cp51083bhttps://doi.org/10.1039/c3cp51083bhttps://doi.org/10.1021/acs.jpclett.8b00573https://doi.org/10.1021/acs.jpclett.8b00573https://doi.org/10.1016/j.jcat.2019.05.025https://doi.org/10.1016/j.jcat.2019.05.025https://doi.org/10.1021/acs.jctc.6b01232https://doi.org/10.1021/acs.jctc.6b01232https://doi.org/10.1021/acs.jpclett.2c00414https://doi.org/10.1021/acs.jpclett.2c00414https://doi.org/10.1063/1.1749657https://doi.org/10.1063/1.1749657https://doi.org/10.1007/s10008-020-04597-zhttps://doi.org/10.1007/s10008-020-04597-zhttps://doi.org/10.1021/jp020054qhttps://doi.org/10.1021/jp020054qhttps://doi.org/10.1002/bkcs.12485https://doi.org/10.1002/bkcs.12485https://doi.org/10.1021/acscatal.7b03777https://doi.org/10.1021/acscatal.7b03777https://doi.org/10.1038/s41598-019-51323-5https://doi.org/10.1038/s41598-019-51323-5https://doi.org/10.1021/acs.jpclett.8b00466https://doi.org/10.1021/acs.jpclett.8b00466https://doi.org/10.1038/s41467-021-27909-xhttps://doi.org/10.1038/s41467-021-27909-xhttps://doi.org/10.1063/5.0130368https://doi.org/10.1063/5.0130368https://doi.org/10.1038/s41467-022-33199-8https://doi.org/10.1038/s41467-022-33199-8https://doi.org/10.1142/S0219633618400023https://doi.org/10.1142/S0219633618400023https://doi.org/10.1039/D1SC02289Jhttps://doi.org/10.1039/D1SC02289Jhttps://doi.org/10.1063/1.5042658https://doi.org/10.1063/1.5042658https://doi.org/10.1016/j.cplett.2005.10.135https://doi.org/10.1016/j.cplett.2005.10.135https://doi.org/10.1021/jp910674dhttps://doi.org/10.1021/jp910674dhttps://doi.org/10.1021/acs.jpca.8b10453https://doi.org/10.1021/acs.jpca.8b10453https://doi.org/10.1021/acs.jpcb.7b02548https://doi.org/10.1021/acs.jpcb.7b02548https://doi.org/10.1063/1.459170https://doi.org/10.1063/1.459170https://doi.org/10.1021/ct400641nhttps://doi.org/10.1021/ct400641nhttps://doi.org/10.1063/1.474406https://doi.org/10.1063/1.474406https://doi.org/10.1016/j.elecom.2017.07.008https://doi.org/10.1016/j.elecom.2017.07.008https://doi.org/10.1021/jacs.2c05563https://doi.org/10.1021/jacs.2c05563https://doi.org/10.1021/jacs.2c03344https://doi.org/10.1021/jacs.2c03344https://doi.org/10.1021/jacs.1c05419https://doi.org/10.1021/jacs.1c05419https://doi.org/10.1021/cr9904009https://doi.org/10.1021/cr9904009https://doi.org/10.1063/1.5050938https://doi.org/10.1063/1.5050938https://doi.org/10.1002/jcc.10069https://doi.org/10.1002/jcc.10069https://doi.org/10.1063/1.4832475https://doi.org/10.1063/1.4832475https://doi.org/10.1088/0965-0393/21/7/074005https://doi.org/10.1088/0965-0393/21/7/074005https://doi.org/10.1063/1.5024219https://doi.org/10.1063/1.5024219https://doi.org/10.1063/1.4907731https://doi.org/10.1063/1.4907731https://doi.org/10.1021/acs.jpcb.9b01363https://doi.org/10.1021/acs.jpcb.9b01363J. Phys. Energy 5 (2023) 041501 C Zhang et al[313] Sundararaman R, Vigil-Fowler D and Schwarz K 2022 Improving the accuracy of atomistic simulations of the electrochemicalinterface Chem. Rev. 122 10651–74[314] Heenen H H, Gauthier J A, Kristoffersen H H, Ludwig T and Chan K 2020 Solvation at metal/water interfaces: an ab initiomolecular dynamics benchmark of common computational approaches J. Chem. Phys. 152 144703[315] Petrosyan S A, Briere J-F, Roundy D and Arias T A 2007 Joint density-functional theory for electronic structure of solvatedsystems Phys. Rev. B 75 205105[316] Weitzner S E et al 2020 Toward engineering of solution microenvironments for the CO reduction reaction: unraveling pH andvoltage effects from a combined density-functional-continuum theory J. Phys. Chem. Lett. 11 4113–8[317] Le J-B, Fan Q-Y, Li J-Q and Cheng J 2020 Molecular origin of negative component of Helmholtz capacitance at electrifiedPt(111)/water interface Sci. Adv. 6 eabb1219[318] Schmidt P S and Thygesen K S 2018 Benchmark database of transition metal surface and adsorption energies from many-bodyperturbation theory J. Phys. Chem. C 122 4381–90[319] Maldonado AM et al 2021 Quantifying uncertainties in solvation procedures for modeling aqueous phase reaction mechanisms J.Phys. Chem. A 125 154–64[320] Clary J, Del Ben M, Sundararaman R and Vigil-Fowler D 2023 Impact of solvation on the GW quasiparticle spectra of moleculesJ. Appl. Phys. 134 085001[321] Wei Z, Göltl F, Steinmann S N and Sautet P 2022 Modeling electrochemical processes with grand canonical treatment ofmany-body perturbation theory J. Phys. Chem. Lett. 13 6079–84[322] Chehaibou B, Badawi M, Bučko T, Bazhirov T and Rocca D 2019 Computing RPA adsorption enthalpies by machine learningthermodynamic perturbation theory J. Chem. Theory Comput. 15 6333–42[323] Campbell Q 2023 Voltage-dependent first-principles simulation of insertion of chloride ions into Al/Al2O3 interfaces using thequantum continuum approximation J. Electrochem. Soc. 170 03150656https://doi.org/10.1021/acs.chemrev.1c00800https://doi.org/10.1021/acs.chemrev.1c00800https://doi.org/10.1063/1.5144912https://doi.org/10.1063/1.5144912https://doi.org/10.1103/PhysRevB.75.205105https://doi.org/10.1103/PhysRevB.75.205105https://doi.org/10.1021/acs.jpclett.0c00957https://doi.org/10.1021/acs.jpclett.0c00957https://doi.org/10.1126/sciadv.abb1219https://doi.org/10.1126/sciadv.abb1219https://doi.org/10.1021/acs.jpcc.7b12258https://doi.org/10.1021/acs.jpcc.7b12258https://doi.org/10.1021/acs.jpca.0c08961https://doi.org/10.1021/acs.jpca.0c08961https://doi.org/10.1063/5.0160173https://doi.org/10.1063/5.0160173https://doi.org/10.1021/acs.jpclett.2c01376https://doi.org/10.1021/acs.jpclett.2c01376https://doi.org/10.1021/acs.jctc.9b00782https://doi.org/10.1021/acs.jctc.9b00782https://doi.org/10.1149/1945-7111/acc48bhttps://doi.org/10.1149/1945-7111/acc48b 2023 Roadmap on molecular modelling of electrochemical energy materials 1. Introduction—where are we heading in computational electrochemistry? 2. Modelling and characterization of transition metal oxide electrodes 3. Metal anodes for rechargeable next-generation batteries 4. Organic electrode materials 5. MOF-based supercapacitors 6. Ionic liquids and carbon-based supercapacitors 7. Liquid electrolytes for multivalent batteries 8. Theoretical understanding of single-atom electrocatalysis 9. Theory and computation of the local reaction environment in electrocatalytic media 10. Modelling and machine learning of fuel cell 11. Modelling electrochemical interfaces and reactions with GPAW: grand canonical ensemble DFT approaches 12. Constant Fermi-level molecular dynamics: recent achievements and future challenges 13. Density functional theory in classical explicit solvents (DFT-CES): efforts towards understanding the unseen, buried electric double layer 14. Implicit solvation models for electrochemical interfaces References