Quantum Electrochemistry, Softcover reprint of the original 1st ed. 1979

The origin of this book lies in a time before one of the authors (J. O'M. B.) left the University of Pennsylvania bound for the Flinders University. His collaboration with Dennis Matthews at the University of Pennsylvania had contributed a singular experimental datum to the quantum theory of elec­ trode processes: the variation of the separation factor with potential, which could only be interpreted in terms of a quantum theory of electrode kinetics. The authors came together as a result of grad~ate work of one of them (S. U. M. K.) on the quantum mechanics and photo aspects of elec­ trode processes, and this book was written during a postdoctoral fellowship held by him at the Flinders University. Having stated the book's origin, it is worthwhile stating the rational­ izations the authors had for writing it. Historically, quantization in elec­ trochemistry began very early (1931) in the applications of the quantum theory to chemistry. (See the historical table on pages xviii-xix.) There was thereafter a cessation of work on the quantum theory in electrochemistry until a continuum dielectric viewpoint, based on Born's equation for solvation energy, began to be developed in the 1950s and snowballed during the 1960s.

1. Electric Double Layers at Metals.- 1.1. Structure of the Double Layer.- 1.1.1. The Diffuse Layer.- 1.1.2. Stern-Grahame-Devanathan Model.- 1.1.3. Water Structure in the Double Layer.- 1.2. Methods of Investigation.- 1.2.1. Objectives of a Double-Layer Study.- 1.2.2. Classical Electrocapillary Curve.- 1.2.3. Capacitance Method.- 1.2.4. Ellipsometry.- 1.2.5. Radiotracer Measurements.- 1.2.6. Heat of Adsorption.- 1.2.7. Time Dependence.- 1.3. The Potential of Zero Charge.- 1.3.1. Nature of the Potential of Zero Charge.- 1.3.2. Importance of the Potential of Zero Charge.- 1.3.3. Methods of Determination of the Potential of Zero Charge.- 1.3.4. For Liquid Metals.- 1.3.5. For Solids.- 1.3.6. Numerical Values of the Absolute Potential Differences at an Interface.- 1.4. Forces in Contact Adsorption.- 1.5. Isotherms.- 1.6. Dielectric Constants in the Double Layer.- 1.7. Relaxation of Solvent Origin in the Double Layer.- 1.8. Double-Layer Properties as a Function of a Potential-Dependent Dipole Term.- 1.9. Adsorption of Undissociated Organic Molecules.- 1.10. Radicals on Electrodes.- 1.11. Double Layer on Solids.- 1.12. Oxygen on Electrodes.- 1.13. The Near Future in the Development of the Model of the Interface.- References.- 2. Electrode Kinetics.- 2.1. Nature of Electrochemical Reactions.- 2.2. Overpotential.- 2.3. Rate as a Function of Overpotential.- 2.4. Exchange Current Density.- 2.5. Rate Constants.- 2.6. The Symmetry Factor.- 2.7. The Transfer Coefficient.- 2.8. Stoichiometric Number.- 2.9. Stoichiometric Factors.- 2.10. Rate as a Function of Temperature.- 2.11. Comparative Reaction Rates of Isotopic Reactions.- 2.12. Chemical Surface Reactions.- 2.13. Consecutive Reaction Rates.- 2.14. Chemical Homogeneous Reactions.- 2.15. Effect of Mass Transport on Electrochemical Reactions.- 2.16. Electrode Kinetics as a Function of the Double-Layer Structure.- 2.17. Reaction Rates and Isotherms.- 2.18. Transients (Sweeps).- 2.19. Electric Equivalent Circuits.- 2.20. Electrocatalysis.- 2.21. Mechanisms.- 2.22. Electrocrystallization.- 2.23. Steps before Crystal Growth.- 2.24. Crystal Growth.- 2.25. Interphasial Charge Transfer in Engineering, Metallurgy, and Biology.- 2.26. Techniques of Study.- References.- 3. Quanta and Surfaces.- 3.1. Introduction.- 3.2. Quantum Particles.- 3.2.1. The Phonon.- 3.2.2. The Plasmon.- 3.2.3. The Polaron.- 3.2.4. The Exciton.- 3.3. Electron Distribution in the Metal Electrode.- 3.3.1. Fermi Distribution Law.- 3.3.2. Density of States.- 3.3.3. Fermi Surface.- 3.3.4. Cyclotron Resonance.- 3.4. Quantal Discussion of Surfaces.- 3.5. Theory of Surface States.- 3.6. Surface Energy.- 3.7. Quantum Mechanical Calculations of Adsorption Energy.- 3.8. Spectra of Adsorbed Atoms.- 3.9. Further Work on the Quantum Mechanics of Adsorbed Species.- 3.9.1. Ionic Adsorption.- 3.9.2. Other Treatments of Adsorption.- 3.10. Concluding Remarks.- References.- 4. Time-Dependent Perturbation Theory.- 4.1. Introduction.- 4.1.1. Time-Dependent Perturbation Theory in Kinetics.- 4.1.2. Radiationless Transition.- 4.2. General Background.- 4.3. An Interim Comment.- 4.4. Probability of Transition.- 4.5. Golden Rule for Transition Rates.- 4.5.1. A More Realistic Approach to the Calculation of the Probability of Transition.- 4.5.2. Calculation of Rate.- 4.6. Applicability of Time-Dependent Perturbation Theory (TDPT).- 4.7. Example of the Applicabilities of TDPT.- 4.8. Magnitude of the Perturbation.- 4.9. Relation of Time-Dependent Perturbation Theory to Reaction Kinetics.- 4.10. Perturbations by Electromagnetic Radiation: Bohr’s Resonance (Coherence) Condition.- 4.11. Constant Perturbation for Electron Transition at Interfaces: Gurney Condition of Radiationless Transfer of Electrons.- 4.12. Types of Perturbation: Adiabatic and Nonadiabatic.- References.- 5. Long-Range Radiationless Energy Transfer in Condensed Media.- 5.1. Introduction.- 5.2. Experimental Evidence for Radiationless Energy Transfer over Long Distances.- 5.3. Mechanisms of Radiationless Long-Range Energy Transfer.- 5.3.1. Resonance Transfer Mechanisms.- 5.3.2. The Exciton Theory.- 5.3.3. Energy Transfer by Polaron Motion.- References.- 6. Mechanisms of Activation.- 6.1. Mechanism of Activation in the Gas Phase.- 6.2. Conversion of Translational Energy during Collision.- 6.2.1. Translational Energy to Vibrational Energy.- 6.2.2. Translational Energy to Rotational Energy.- 6.3. Collisional Activation Model in Liquids.- 6.3.1. Expressions for the Free Energy of Activation in Liquid.- 6.3.2. Mechanism of Activation.- 6.4. Need for Alternate Activation Mechanisms in Condensed Media.- 6.5. Activation Due to Continuum Solvent Polarization Fluctuation.- 6.5.1. The Polaron Model.- 6.5.2. Frequency of a Fluctuation in the Energy of a Central Ion.- 6.6. An Expression for the Free Energy of Activation from the Continuum Solvent Polarization Fluctuation Model.- 6.7. Expression for Es.- 6.8. Formulation of Activation Energy.- 6.9. Comparison between Free Energy of Activation from Continuum Expressions and Experiment.- 6.10. Activation Due to Phonon-Vibron Coupling (PVC).- 6.11. Formulation of the Probability of Activation from the PVC Model.- References.- 7. The Continuum Theory.- 7.1. Introduction.- 7.2. Model of a Polar Solvent.- 7.2.1. Polarization of the Liquid and Its Fluctuations.- 7.2.2. Energy Associated with a Local Fluctuation of Polarization in a Solvent System.- 7.2.3. Hamiltonian for the Pure Solvent.- 7.2.4. Hamiltonian for the Total Reacting System in a Polar Solution (Ions, Electrons, and a Quasi-Continuum Solvent).- 7.3. Transition Probability of a Quantum Particle from Ion to Ion in the Original Levich-Dogonadze Treatment.- 7.4. Transition Probability in the Bond-Breaking Reactions.- 7.5. Recent Treatments of the Continuum Model.- 7.5.1. Schmickler-Vielstich Treatment.- 7.5.2. Kestner, Logan, and Jortner (KLJ) Treatment.- 7.5.3. Schmidt’s Treatment.- 7.6. Difficultes of the Continuum Theory.- 7.6.1. Fluctuation in Continuum Theory.- 7.6.2. Comparison of the Continuum Theory with Experiment.- 7.7. Summary.- Appendix 7.1. Derivation of Pekar Hamiltonian.- References.- 8. Interfacial Electron Tunneling.- 8.1. Introduction.- 8.2. Solution of Schrödinger Equation: Particle at a Rectangular Potential Barrier.- 8.3. WKB Approximation and Tunneling through Barriers.- 8.3.1. Derivation of the WKB Wave Functions.- 8.3.2. Nature of the WKB Approximation.- 8.3.3. Transmission through a Barrier: WKB Tunneling Expression.- 8.4. Tunneling through an Eckart Potential Barrier.- 8.5. Gurney’s Application of Gamow’s Tunneling Theory to Electron Transfer at Interfaces.- 8.5.1. Neutralization of a Gaseous Ion at an Electrode.- 8.5.2. Neutralization of an Ion in Solution at the Electrode.- 8.5.3. Distribution of Acceptor Levels.- 8.5.4. Velocity of Interfacial Electron Transfer in the Original Gurney Quantum Mechanical Model.- 8.6. Tunneling through the Adsorbed Layer in Free Space.- 8.7. Electron Transfer through Adsorbed Layers in Solution.- Appendix 8.I. Derivation of Eq. (8.52) for the WKB Transmission Coefficient from WKB Wave Functions.- Appendix 8.II Solution of Eq. (8.68) and Derivation of Transmission Coefficient PT for Eckart Barrier.- References.- 9. Proton Transfer in Solution.- 9.1. Introduction.- 9.2. First Theory of Quantum Mechanical Transfer of Protons.- 9.3. Conway, Bockris, and Linton (CBL) Model of 1956.- 9.4. Eigen and De Maeyer’s Model.- 9.5. Polarization of the Hydrogen Bond and the Proton Transfer Mechanism.- 9.6. Lifetime of H3O+.- 9.7. Recent Quantum Mechanical Work on Proton Transfer in Solution.- 9.8. Application of Continuum Theories to Proton Transfer Reactions.- References.- 10. Proton Transfer at Interfaces.- 10.1. Introduction.- 10.2. Historical Perspective.- 10.3. The Proton-Associated Aspects of the Gurney Quantum Mechanical Model.- 10.4. Butler’s Modification of Gurney’s Model: Electrocatalysis.- 10.5. Rate-Determining Step and Path in Hydrogen Evolution.- 10.6 The Basic Role of the Calculation of Separation Factors.- 10.6.1. Calculation of the Separation Factor.- 10.6.2. Results of Separation-Factor Calculations.- 10.7. Quantum Character of Proton Transfer: Contributions of Christov.- 10.8. Quantum Character of Proton Transfer: Bockris and Matthews.- 10.8.1. Variation of the Separation Factor with Potential.- 10.9. Quantum Mechanical Interpretation of the Evolution of the Separation Factor with Potential.- 10.9.1. Quantum Mechanical Correction to Separation Factor.- 10.9.2. Results of Tunneling.- 10.9.3. Conclusion.- 10.10. Variation of the Symmetry Factor with Potential.- 10.11. A BEBO Approach to Proton Transfer Calculations.- 10.12. Double-Layer Model and Proton Transfer.- 10.13. Validity of the WKB Tunneling Expression.- 10.14. The Continuum Theory to Proton Transfer.- 10.14.1. Qualitative Discussion of the Continuum Model for Proton Transfer.- 10.14.2. Transition Probability of Proton from Continuum Treatments.- 10.15. Work of Kharkats and Ulstrup.- 10.16. Christov’s Work on an Oscillator Model for Proton Transfer.- 10.17. Solvent Reorganizational Viewpoint in Proton Transfer Kinetics.- 10.17.1. Historical Aspects.- 10.17.2. Role Played by the Solvent.- 10.17.3. Isotopic Effects.- 10.17.4. Tafel Equation.- References.- 11. The Hydrated Electron.- 11.1. Introduction.- 11.2. Continuum Approach to the Hydrated Electron.- 11.3. Semicontinuum Model of the Hydrated Electron.- 11.3.1. Short-Range Energies of the Hydrated Electron.- 11.3.2. Long-Range Energies of the Hydrated Electron.- 11.3.3. Total Ground-State Energy of the Hydrated Electron.- 11.3.4. Excited-State Energy of the Hydrated Electron.- 11.3.5. Numerical Results of the Semicontinuum Treatment (from the SCF Approach).- 11.4. Structural Models for the Hydrated Electron.- 11.5. Theory of Electron Transfer Reaction from a Hydrated Electron to an Acceptor in Solution.- 11.5.1. Calculation of the Rate Constant kr.- 11.5.2. Calculation of the Free Energy of Activation ?F*.- 11.5.3. Numerical Results of ?F* and kr.- 11.6. Hydrated Electron in Photoelectrochemical Processes.- 11.6.1. Energetic Condition for the Production of Hydrated Electrons at an Electrode.- 11.6.2. Can There Be an Electrochemical Production of the Hydrated Electron?.- 11.6.3. Photoelectrochemical Production of the Hydrated Electron.- Appendix 11.I. Calculation of Orientational Polarization Energy of an Electron in a Solvent.- Appendix 11.II. Solution of Poisson Equation (11.2).- Appendix 11.III. Proof of Equation for Average Polarization Energy [Eq. (11.66b)].- References.- 12. Photoelectrochemical Kinetics.- 12.1. Introduction.- 12.2. Rate of Photoemission into a Vacuum.- 12.3. Rate of Photoemission into a Vacuum under an Electric Field.- 12.4. Quantum Mechanical Theory of the Photoemission Rate into an Electrolytic Solution.- 12.4.1. Models.- 12.4.2. Limitations of Brodskii’s Quantum Mechanical Treatment of Photoemission.- 12.5. Theory of Photoelectrochemical Kinetics.- 12.5.1. Introduction.- 12.5.2. The BKU Theory.- 12.5.3. Photocurrent from the BKU Theory.- 12.5.4. Computation of the Photocurrent from the BKU Expression.- 12.5.5. Non-Tafel Behavior of the Photocurrent.- 12.5.6. Limitations of the BKU Theory.- 12.6. Photoeffects on Semiconductor Electrodes.- 12.6.1. Photoeffect on a Cathodic Current at a p-Type Semiconductor-Solution Interface.- 12.6.2. Photoeffect on the Anodic Current at an n-Type Semiconductor.- 12.6.3. Results of the Calculation of Photocurrent for p-and n-Type Semiconductors.- 12.7. The Whole-Cell System.- 12.7.1. Relation between the Potential of an Electrode and a Cell.- 12.7.2. Calculated Hydrogen Production Rate from Solar Energy Using TiO2 Photodriven Cells.- 12.8. Gurevich’s Model for the Semiconductor-Electrolyte Interface.- References.- 13. Quantum Electrode Kinetics.- 13.1. Introduction.- 13.2. Quantum Theory of the Electrochemical Current Density and Tafel behavior.- 13.3. Relations between Spectroscopic and Electrochemical Transitions.- 13.4. Adiabaticity and Nonadiabaticity in Electron Transfer Processes.- 13.5. Time-Dependent Perturbation Theory of Electron Transfer at Electrodes.- 13.5.1. Transition Probability of Electrons from Electrodes.- 13.5.2. KWB Model for the Calculation of the Transition Probability.- 13.5.3. Unperturbed 3d State Wave Function of the Fe2+ Ion.- 13.5.4. Perturbed 3d State Wave Function of the Fe2+(H2O)6 Ion.- 13.5.5. Transition Probability Using the Perturbed Wave Function $$\psi _d^{(1)}$$ of the Fe2+(H2O)6 Ion.- 13.5.6. Transition Probability: Quantitative.- 13.5.7. Results: Transition Probability.- 13.5.8. Transition Probability from Gamow’s Equation.- 13.5.9. Potential Dependence of the Transition Probability.- 13.6. Quantum Theory of Electrochemical Processes at Semiconductor Electrodes.- References.