Atomic-Scale Modelling of Electrochemical Systems

Description

Atomic-Scale Modelling of Electrochemical Systems A comprehensive overview of atomistic computational electrochemistry, discussing methods, implementation, and state-of-the-art applications in the field The first book to review state-of-the-art computational and theoretical methods for modelling, understanding, and predicting the properties of electrochemical interfaces. This book presents a detailed description of the current methods, their background, limitations, and use for addressing the electrochemical interface and reactions. It also highlights several applications in electrocatalysis and electrochemistry. Atomic-Scale Modelling of Electrochemical Systems discusses different ways of including the electrode potential in the computational setup and fixed potential calculations within the framework of grand canonical density functional theory. It examines classical and quantum mechanical models for the solid-liquid interface and formation of an electrochemical double-layer using molecular dynamics and/or continuum descriptions. A thermodynamic description of the interface and reactions taking place at the interface as a function of the electrode potential is provided, as are novel ways to describe rates of heterogeneous electron transfer, proton-coupled electron transfer, and other electrocatalytic reactions. The book also covers multiscale modelling, where atomic level information is used for predicting experimental observables to enable direct comparison with experiments, to rationalize experimental results, and to predict the following electrochemical performance. Uniquely explains how to understand, predict, and optimize the properties and reactivity of electrochemical interfaces starting from the atomic scale Uses an engaging “tutorial style” presentation, highlighting a solid physicochemical background, computational implementation, and applications for different methods, including merits and limitations Bridges the gap between experimental electrochemistry and computational atomistic modelling Written by a team of experts within the field of computational electrochemistry and the wider computational condensed matter community, this book serves as an introduction to the subject for readers entering the field of atom-level electrochemical modeling, while also serving as an invaluable reference for advanced practitioners already working in the field. Cover Title Page Copyright Contents List of Contributors Part I Chapter 1 Introduction to Atomic Scale Electrochemistry 1.1 Background 1.2 The thermodynamics of electrified interface 1.2.1 Electrode 1.2.2 Electrical double layer 1.2.3 Solvation sheets 1.2.4 Electrode potential 1.3 Chemical interactions between the electrode and redox species 1.4 Reaction kinetics at electrochemical interfaces 1.4.1 Outer and inner sphere reactions 1.4.2 Computational aspects 1.4.3 Challenges 1.5 Charge transport 1.6 Mass transport to the electrode 1.7 Summary References Part II Chapter 2 Retrospective and Prospective Views of Electrochemical Electron Transfer Processes: Theory and Computations 2.1 Introduction – interfacial molecular electrochemistry in recent retrospective 2.1.1 An electrochemical renaissance 2.1.2 A bioelectrochemical renaissance 2.2 Analytical theory of molecular electrochemical ET processes 2.2.1 A Reference to molecular ET processes in homogeneous solution 2.2.2 Brief discussion of contemporary computational approaches 2.2.3 Molecular electrochemical ET processes and general chemical rate theory 2.2.4 Some electrochemical ET systems at metal electrodes 2.2.4.1 Some outer sphere electrochemical ET processes 2.2.4.2 Dissociative ET: the electrochemical peroxodisulfate reduction 2.2.5 d‐band, cation, and spin catalysis 2.2.6 New solvent environments in simple electrochemical ET processes – ionic liquids 2.2.7 Proton transfer, proton conductivity, and proton coupled electron transfer (PCET) 2.2.7.1 Some further notes on the nature of PT/PCET processes 2.2.7.2 The electrochemical hydrogen evolution reaction, and the Tafel plot on mercury 2.3 Ballistic and stochastic (Kramers‐Zusman) chemical rate theory 2.4 Early and recent views on chemical and electrochemical long‐range ET 2.5 Molecular‐scale electrochemical science 2.5.1 Electrochemical in situ STM and AFM 2.5.2 Nanoscale mapping of novel electrochemical surfaces 2.5.2.1 Self‐assembled molecular monolayers (SAMs) of functionalized thiol 2.5.3 Electrochemical single‐molecule ET and conductivity of complex molecules 2.5.4 Selected cases of in situ STM and STS of organic and inorganic redox molecules 2.5.4.1 The viologens 2.5.4.2 Transition metal complexes as single‐molecule in operando STM targets 2.5.5 Other single‐entity nanoscale electrochemistry 2.5.5.1 Electrochemistry in low‐dimensional carbon confinement 2.5.5.2 Electrochemistry of nano‐ and molecular‐scale metallic nanoparticles 2.5.6 Elements of nanoscale and single‐molecule bioelectrochemistry 2.5.6.1 A single‐molecule electrochemical metalloprotein target – P. aeruginosa azurin 2.5.6.2 Electrochemical SPMs of metalloenzymes, and some other “puzzles” 2.6 Computational approaches to electrochemical surfaces and processes revisited 2.6.1 Theoretical methodologies and microscopic structure of electrochemical interfaces 2.6.2 The electrochemical process revisited 2.7 Quantum and computational electrochemistry in retrospect and prospect 2.7.1 Prospective conceptual challenges in quantum and computational electrochemistry 2.7.2 Prospective interfacial electrochemical target phenomena 2.7.2.1 Some conceptual, theoretical, and experimental notions and challenges 2.7.2.2 Non‐traditional electrode surfaces and single‐entity structure and function 2.7.2.3 Semiconductor and semimetal electrodes 2.7.2.4 Metal deposition and dissolution processes 2.7.2.5 Chiral surfaces and ET processes of chiral molecules 2.7.2.6 ET reactions involving hot electrons (femto‐electrochemistry) 2.8 A few concluding remarks Acknowledgement References Part III Chapter 3 Continuum Embedding Models for Electrolyte Solutions in First‐Principles Simulations of Electrochemistry 3.1 Introduction to continuum models for electrochemistry 3.2 Continuum models of liquid solutions 3.2.1 Continuum interfaces 3.2.2 Beyond local interfaces 3.2.3 Electrostatic interaction: polarizable dielectric embedding 3.2.4 Beyond electrostatic interactions 3.3 Continuum diffuse‐layer models 3.3.1 Continuum models of electrolytes 3.3.2 Helmholtz double‐layer model 3.3.3 Poisson–Boltzmann model 3.3.4 Size‐modified Poisson–Boltzmann model 3.3.5 Stern layer and additional interactions 3.3.6 Performance of the diffuse‐layer models 3.4 Grand canonical simulations of electrochemical systems 3.4.1 Thermodynamics of interfaces 3.4.2 Ab‐initio based thermodynamics of electrochemical interfaces 3.4.3 Grand canonical simulations and the CHE approximation 3.5 Selected applications Acknowledgments References Chapter 4 Joint and grand‐canonical density‐functional theory 4.1 Introduction 4.2 JDFT variational theorem and framework 4.2.1 Variational principle and underlying theorem 4.2.2 Separation of effects and regrouping of terms 4.2.3 Practical functionals and universal form for coupling 4.3 Classical DFT with atomic‐scale structure 4.3.1 Ideal gas functionals with molecular geometry 4.3.1.1 Effective ideal gas potentials 4.3.1.2 Integration over molecular orientations 4.3.1.3 Auxiliary fields 4.3.2 Minimal excess functionals for molecular fluids 4.4 Continuum solvation models from JDFT 4.4.1 JDFT linear response: nonlocal ‘SaLSA’ solvation 4.4.2 JDFT local limit: nonlinear continuum solvation 4.4.3 Hybrid semi‐empirical approaches: ‘CANDLE’ solvation 4.5 Grand‐canonical DFT 4.6 Conclusions References Chapter 5 Ab initio modeling of electrochemical interfaces and determination of electrode potentials 5.1 Introduction 5.2 Theoretical background of electrochemistry 5.2.1 Definition of electrode potential 5.2.2 Absolute potential energy of SHE 5.3 Short survey of computational methods for modeling electrochemical interfaces 5.4 Ab initio determination of electrode potentials of electrochemical interfaces 5.4.1 Work function based methods 5.4.1.1 Vacuum reference 5.4.1.2 Vacuum reference in two steps 5.4.2 Reference electrode based methods 5.4.2.1 Computational standard hydrogen electrode 5.4.2.2 Computational standard hydrogen electrode in two steps 5.4.2.3 Computational Ag/AgCl reference electrode 5.5 Computation of potentials of zero charge 5.6 Summary Acknowledgement References Chapter 6 Molecular Dynamics of the Electrochemical Interface and the Double Layer 6.1 Introduction 6.2 Continuum description of the electric double layer 6.3 Equilibrium coverage of metal electrodes 6.4 First‐principles simulations of electrochemical interfaces and electric double layers 6.5 Electric double layers at battery electrodes 6.6 Conclusions Acknowledgement References Chapter 7 Atomic‐Scale Modelling of Electrochemical Interfaces through Constant Fermi Level Molecular Dynamics 7.1 Introduction 7.2 Method 7.3 CFL‐MD in aqueous solution: Determination of redox levels 7.4 CFL‐MD at metal‐water interface: The case of the Volmer reaction 7.5 Referencing the bias potential to the SHE 7.6 Macroscopic properties at the metal‐water interface 7.7 Atomic‐scale processes at the metal‐water interface 7.8 Conclusion Acknowledgements References Part IV Chapter 8 From electrons to electrode kinetics: A tutorial review 8.1 Global electro‐neutrality 8.2 The electrochemical reference state 8.3 The chemical potential 8.4 The electrostatic potential 8.5 The electrochemical potential 8.5.1 The molar electrochemical potential 8.5.2 The electrochemical potential of a single electron 8.5.3 The Nernst equation 8.5.4 Fermi–Dirac distribution function 8.5.5 The molar electrochemical potential of an electron 8.5.6 Parsing the electrochemical potential. (I) Metal in a vacuum 8.5.7 The Volta potential difference 8.5.8 Scanning Kelvin Probe Microscopy 8.5.9 The membrane potential 8.5.10 The electrochemical potential of a single proton 8.5.11 The proton motive force 8.5.12 The standard hydrogen half‐cell 8.5.13 The hydrated electron 8.5.14 The hydrogen atom H* 8.5.15 Parsing the electrochemical potential. (II) The co‐sphere 8.5.16 Electron transfer (general introduction) 8.5.17 Johnson–Nyquist noise 8.5.18 The Molar Gibbs reorganization energy 8.5.19 The reaction co‐ordinate 8.5.20 The vertical energy gap 8.5.21 Permittivity of solutions 8.6 Electrolytes and non‐electrolytes 8.6.1 Equivalent circuit of a non‐electrolyte solution 8.6.2 Equivalent circuit of an electrolyte solution 8.6.3 Probability of an electron jump 8.6.4 The Klopman–Salem equation 8.6.5 Electrode kinetics 8.6.6 Homogeneous kinetics, first order 8.6.7 Homogeneous kinetics, second order 8.6.8 Homogeneous versus heterogeneous kinetics 8.6.9 Tunneling layer approximation 8.6.10 The back of the envelope 8.6.11 The total rate constant of an electron transfer process 8.7 Heterogeneous electron transfer 8.7.1 Tafel slopes for multi‐step reactions 8.8 The future: supercatalysis by superexchange References Chapter 9 Constant potential rate theory – general formulation and electrocatalysis 9.1 Kinetics at electrochemical interfaces 9.2 Rate theory in the grand canonical ensemble 9.3 Adiabatic reactions 9.3.1 Classical nuclei 9.3.2 Fixed potential empirical valence bond theory 9.3.3 Nuclear tunneling 9.4 Non‐adiabatic reactions 9.4.1 Non‐adiabatic reactions in electrochemistry 9.4.2 Rate of ET and CPET reactions 9.5 Computational aspects 9.6 Conclusions References Part V Chapter 10 Thermodynamically consistent free energy diagrams with the solvated jellium method 10.1 Computational studies of electrochemical systems – Recent advances and modern challenges 10.2 Thermodynamic consistency with a decoupled computational electrode model 10.3 Solvated jellium method (SJM) 10.3.1 Introduction 10.3.2 Electrostatic potential profiles and charge localization 10.3.3 Workflow of potential equilibration 10.3.3.0 Comparison of the implemented potential equilibration schemes 10.3.4 Shape of the jellium background charge 10.4 Example: Mechanistic studies of the hydrogen evolution reaction (HER) 10.4.1 Potential dependence of the elementary steps of HER 10.4.2 Charge transfer along reaction trajectories 10.4.3 Thermodynamically consistent free energy diagrams from first principles References Chapter 11 Generation of Computational Data Sets for Machine Learning Applied to Battery Materials 11.1 Introduction 11.2 Computational workflows for production of moderate‐fidelity data sets 11.2.1 Ionic diffusion: NEB calculations 11.2.1.1 Symmetric NEB 11.2.1.2 Choice of functionals for NEB 11.2.2 Disordered materials: Cluster Expansion 11.3 High‐Fidelity data sets: Ab initio molecular dynamics simulations 11.4 Machine Learning Acknowledgements References Index EULA