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WIREs Comput Mol Sci
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Recent progress on multiscale modeling of electrochemistry

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Abstract Computational electrochemistry, an important branch of electrochemistry, has shown its advantages in studying electrode/electrolyte interfaces, such as the structures of electric double layers. However, modeling electrochemical systems is still a challenge, especially in interface electrochemistry, because not only solvation effects and ion distribution in electrolyte solutions should be considered, but also the treatment of the electrode potential and the response of electrolytes to applied potentials. Here, we review the latest development in the field of computational electrochemistry. We first introduce various energy models used in simulating electrolytes and electrodes at multiple scales. Then, to better explain and compare between different methods, we discuss the calculation methods of solution electrochemistry and interface electrochemistry in separate. At last, we introduce the methods to electrify the interfaces in various multiscale models. This review aims to help understand various levels of methods in simulations of different scenarios in electrochemistry, and summarizes a set of schemes covering multiple scales. This article is categorized under: Electronic Structure Theory > Combined QM/MM Methods Molecular and Statistical Mechanics > Molecular Dynamics and Monte‐Carlo Methods Electronic Structure Theory > Density Functional Theory
Energy models used in simulations of electrochemical systems. (a) Schematic diagram of the structural information and model scales for these energy models. (b) Comparison of time and spatial scale among various energy models. (Reprinted with permission from Ref. 21)
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(a) Schematic illustration of imposing an finite field in a periodic cell, as demonstrated by a parallel plate capacitor at constant electric field, E, and at constant electric displacement, D. is the surface charge density on the metal electrode, and is the polarization surface charge density of the dielectric material. (Reprinted with permission from Ref. 142). (b) Interface models of classical polarizable electrodes under applied potentials. Top: Electrolyte‐centered supercell under 2D PBC, with fixed applied potential between two electrodes. Bottom: Conductor‐centered supercell under 3D PBC, with a finite field and a single electrode in which all atoms are set to have the same electric potential. (Reprinted with permission from Ref. 135)
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(a) Schematic illustration of alignment of electrostatic potentials between metal/water interface model (left) and pure water model (right) in the computational standard hydrogen electrode scheme. (Reprinted with permission from Ref. 125). (b) Schematic representation of the AIMD full‐cell model used to realize an electrolytic cell. The figure on the left shows the alignment between two metal electrodes before (superscript “ini”) and after (superscript “fin”) charge transfer. The figure on the right shows a doped semiconductor electrode allows for controlling the position of the Fermi level. (Reprinted with permission from Ref. 134)
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(a) Side view of the QM/MM interface model including the water/EMIM‐BF4 mixture as the electrolyte on Ag(111) surface. (Reprinted with permission from Ref. 4). (b) Model of nitrobenzene on Au(111). Isosurface of the electrostatic potential obtained with full DFT (left) and QM/MM model (right). The transparent isosurface is from the conventional QM/MM model, and the solid isosurface is from the IC‐QM/MM model. (Reprinted with permission from Ref. 126). (c) Schematic illustration of the electrostatic QM/MM cluster embedding model used for the TiO2/water interface. (Reprinted with permission from Ref. 101)
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(a) Snapshot of the Pt(111)/water interface model (top), and the projected density of states (PDOS) plots (bottom) of Pt and water molecules at the interface computed by the PBE functional. In this figure, water molecules adjacent to the Pt surface with the dipole pointing away from the surface is called watA. The PDOS of watA is lower than the Fermi level of the Pt electrode, which proves that there are a few water molecules close to the surface (i.e., watA) chemisorb on Pt. (Reprinted with permission from Ref. 125). (b) Potential‐dependent evolution of the hydrogen‐bond network of interface water. Insets are structure models of interface water in the corresponding potential regions. (Reprinted with permission from Ref. 1). (c) Capacitance model of the Helmholtz layer. Decomposition of differential Helmholtz capacitance CH (blue) as a function of electrode potential U into two constituent components, i.e. the normal capacitance Csol (green) of interface water and the capacitance CA (red) due to chemisorbed water. The inset indicates that Csol and CA are connected in series. (Reprinted with permission from Ref. 5)
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(a) Schematic illustration of QM/continuum interface model. The electrode is represented by QM model, and the large blue region is the implicit electrolyte region. The red curve represents the variation of the dielectric constant from the QM electrode (i.e., 1) to the bulk of solution continuum (i.e., 78). (b) Comparison between computed and experimental capacitances of Ag(100) in aqueous solution. Toy models consist of non‐linear solvent and electrolyte ions response with vacuum gap thickness x1 and extended distance x2 (i.e., distance between ionic radius r and vacuum thickness x1, and ) to the surface. (Reprinted with permission from Ref. 59). (c) Comparison between potentials of zero charge computed by the JDTF surface model at the DFT‐GGA level and experimental data122
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(a) Schematic view of grid‐based treatment of electrostatic potentials. Only electrostatic potentials on the grid points are employed in the QM/MM electrostatic embedding calculations, where blue and orange represent the QM and MM regions, respectively. (Reprinted with permission from Ref. 99). (b) Schematic view of the QM/MM model with restraining potentials (dashed circle). Molecules inside and outside the circle are QM molecules and MM molecules, respectively. The Rinner is the radius of the dashed circle. (Reprinted with permission from Ref. 103). (c) Schematic representations of QM/(AA+CG) (left) and QM/AA/CG (right) models under PBC without the Ewald summation technique. (Reprinted with permission from Ref. 20)
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Schematic representation of the ab initio molecular dynamics based method for computing redox potentials and acidity constants. (Reprinted with permission from Ref. 91)
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Electronic Structure Theory > Density Functional Theory
Molecular and Statistical Mechanics > Molecular Dynamics and Monte-Carlo Methods
Electronic Structure Theory > Combined QM/MM Methods

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