Part I 1 -- 1 Introduction to Atomic Scale Electrochemistry 3
Marko M. Melander, Tomi Laurila, and Kari Laasonen -- 1.1 Background 3 -- 1.2 The thermodynamics of electrified interface 4 -- 1.2.1 Electrode 6 -- 1.2.2 Electrical double layer 7 -- 1.2.3 Solvation sheets 8 -- 1.2.4 Electrode potential 8 -- 1.3 Chemical interactions between the electrode and redox species 12 -- 1.4 Reaction kinetics at electrochemical interfaces 13 -- 1.4.1 Outer and inner sphere reactions 13 -- 1.4.2 Computational aspects 16 -- 1.4.3 Challenges 17 -- 1.5 Charge transport 18 -- 1.6 Mass transport to the electrode 18 -- 1.7 Summary 19 -- References 20 -- Part II 25 -- 2 Retrospective and Prospective Views of Electrochemical Electron Transfer Processes: Theory and Computations 27
Renat R. Nazmutdinov and Jens Ulstrup -- 2.1 Introduction -- interfacial molecular electrochemistry in recent retrospective 27 -- 2.1.1 An electrochemical renaissance 27 -- 2.1.2 A bioelectrochemical renaissance 27 -- 2.2 Analytical theory of molecular electrochemical ET processes 28 -- 2.2.1 A Reference to molecular ET processes in homogeneous solution 28 -- 2.2.2 Brief discussion of contemporary computational approaches 30 -- 2.2.3 Molecular electrochemical ET processes and general chemical rate theory 31 -- 2.2.4 Some electrochemical ET systems at metal electrodes 35 -- 2.2.4.1 Some outer sphere electrochemical ET processes 35 -- 2.2.4.2 Dissociative ET: the electrochemical peroxodisulfate reduction 38 -- 2.2.5 d-band, cation, and spin catalysis 39 -- 2.2.6 New solvent environments in simple electrochemical ET processes -- ionic liquids 40 -- 2.2.7 Proton transfer, proton conductivity, and proton coupled electron transfer (PCET) 40 -- 2.2.7.1 Some further notes on the nature of PT/PCET processes 44 -- 2.2.7.2 The electrochemical hydrogen evolution reaction, and the Tafel plot on mercury 44 -- 2.3 Ballistic and stochastic (Kramers-Zusman) chemical rate theory 45 -- 2.4 Early and recent views on chemical and electrochemical long-range ET 50 -- 2.5 Molecular-scale electrochemical science 53 -- 2.5.1 Electrochemical in situ STM and AFM 53 -- 2.5.2 Nanoscale mapping of novel electrochemical surfaces 54 -- 2.5.2.1 Self-assembled molecular monolayers (SAMs) of functionalized thiol [192-194] 54 -- 2.5.3 Electrochemical single-molecule ET and conductivity of complex molecules 56 -- 2.5.4 Selected cases of in situ STM and STS of organic and inorganic redox molecules 58 -- 2.5.4.1 The viologens 58 -- 2.5.4.2 Transition metal complexes as single-molecule in operando STM targets 59 -- 2.5.5 Other single-entity nanoscale electrochemistry 61 -- 2.5.5.1 Electrochemistry in low-dimensional carbon confinement 61 -- 2.5.5.2 Electrochemistry of nano- and molecular-scale metallic nanoparticles 62 -- 2.5.6 Elements of nanoscale and single-molecule bioelectrochemistry 63 -- 2.5.6.1 A single-molecule electrochemical metalloprotein target -- P. aeruginosa azurin 63 -- 2.5.6.2 Electrochemical SPMs of metalloenzymes, and some other "puzzles" 65 -- 2.6 Computational approaches to electrochemical surfaces and processes revisited 67 -- 2.6.1 Theoretical methodologies and microscopic structure of electrochemical interfaces 67 -- 2.6.2 The electrochemical process revisited 68 -- 2.7 Quantum and computational electrochemistry in retrospect and prospect 69 -- 2.7.1 Prospective conceptual challenges in quantum and computational electrochemistry 70 -- 2.7.2 Prospective interfacial electrochemical target phenomena 71 -- 2.7.2.1 Some conceptual, theoretical, and experimental notions and challenges 71 -- 2.7.2.2 Non-traditional electrode surfaces and single-entity structure and function 71 -- 2.7.2.3 Semiconductor and semimetal electrodes 72 -- 2.7.2.4 Metal deposition and dissolution processes 72 -- 2.7.2.5 Chiral surfaces and ET processes of chiral molecules 72 -- 2.7.2.6 ET reactions involving hot electrons (femto-electrochemistry) 73 -- 2.8 A few concluding remarks 73 -- Acknowledgement 74 -- References 74 -- Part III 93 -- 3 Continuum Embedding Models for Electrolyte Solutions in First-Principles Simulations of Electrochemistry 95
Oliviero Andreussi, Francesco Nattino, and Nicolas Georg Hörmann -- 3.1 Introduction to continuum models for electrochemistry 95 -- 3.2 Continuum models of liquid solutions 97 -- 3.2.1 Continuum interfaces 98 -- 3.2.2 Beyond local interfaces 103 -- 3.2.3 Electrostatic interaction: polarizable dielectric embedding 105 -- 3.2.4 Beyond electrostatic interactions 107 -- 3.3 Continuum diffuse-layer models 109 -- 3.3.1 Continuum models of electrolytes 109 -- 3.3.2 Helmholtz double-layer model 110 -- 3.3.3 Poisson-Boltzmann model 111 -- 3.3.4 Size-modified Poisson-Boltzmann model 113 -- 3.3.5 Stern layer and additional interactions 114 -- 3.3.6 Performance of the diffuse-layer models 114 -- 3.4 Grand canonical simulations of electrochemical systems 118 -- 3.4.1 Thermodynamics of interfaces 119 -- 3.4.2 Ab-initio based thermodynamics of electrochemical interfaces 121 -- 3.4.3 Grand canonical simulations and the CHE approximation 123 -- 3.5 Selected applications 126 -- Acknowledgments 129 -- References 129 -- 4 Joint and grand-canonical density-functional theory 139
Ravishankar Sundararaman and Tomás A. Arias -- 4.1 Introduction 139 -- 4.2 JDFT variational theorem and framework 142 -- 4.2.1 Variational principle and underlying theorem 142 -- 4.2.2 Separation of effects and regrouping of terms 146 -- 4.2.3 Practical functionals and universal form for coupling 147 -- 4.3 Classical DFT with atomic-scale structure 148 -- 4.3.1 Ideal gas functionals with molecular geometry 149 -- 4.3.1.1 Effective ideal gas potentials 149 -- 4.3.1.2 Integration over molecular orientations 150 -- 4.3.1.3 Auxiliary fields 151 -- 4.3.2 Minimal excess functionals for molecular fluids 152 -- 4.4 Continuum solvation models from JDFT 157 -- 4.4.1 JDFT linear response: nonlocal 'SaLSA' solvation 158 -- 4.4.2 JDFT local limit: nonlinear continuum solvation 160 -- 4.4.3 Hybrid semi-empirical approaches: 'CANDLE' solvation 163 -- 4.5 Grand-canonical DFT 164 -- 4.6 Conclusions 168 -- References 169 -- 5 Ab initio modeling of electrochemical interfaces and determination of electrode potentials 173
Jia-Bo Le, Xiao-Hui Yang, Yong-Bing Zhuang, Feng Wang, and Jun Cheng -- 5.1 Introduction 173 -- 5.2 Theoretical background of electrochemistry 175 -- 5.2.1 Definition of electrode potential 175 -- 5.2.2 Absolute potential energy of SHE 178 -- 5.3 Short survey of computational methods for modeling electrochemical interfaces 179 -- 5.4 Ab initio determination of electrode potentials of electrochemical interfaces 180 -- 5.4.1 Work function based methods 180 -- 5.4.1.1 Vacuum reference 180 -- 5.4.1.2 Vacuum reference in two steps 181 -- 5.4.2 Reference electrode based methods 183 -- 5.4.2.1 Computational standard hydrogen electrode 183 -- 5.4.2.2 Computational standard hydrogen electrode in two steps 185 -- 5.4.2.3 Computational Ag/AgCl reference electrode 187 -- 5.5 Computation of potentials of zero charge 187 -- 5.6 Summary 190 -- Acknowledgement 191 -- References 191 -- 6 Molecular Dynamics of the Electrochemical Interface and the Double Layer 201
Axel Groß -- 6.1 Introduction 201 -- 6.2 Continuum description of the electric double layer 202 -- 6.3 Equilibrium coverage of metal electrodes 204 -- 6.4 Firs