havior in PCET 3400 5.3. Adiabatic and Nonadiabatic PCET Interpreted in the Context of the Schrodinger Equation and the Born−Oppenheimer (Adiabatic) Approximation 3404 5.3.1. Quantum-State Dynamics of PCET Systems and the Underlying Potential (Free) Energy Surfaces 3404 5.3.2. Investigating Coupled Electronic−Nuclear Dynamics and Deviations from the Adiabatic Approximation in PCET Systems via a Simple Model 3408 5.3.3. Formulation and Representations of Electron−Proton States 6. Extension of Marcus Theory to Proton and Atom Transfer Reactions 6.1. Extended Marcus Theory for Electron, Proton, and Atom Transfer Reactions 6.2. Implications of the Extended Marcus Theory: Brønsted Slope, Kinetic Isotope Effect, and Cross-Relation 7. Beyond Marcus Theory: Nuclear Tunneling and Structural Constraints on PCET 8. Proton-Activated Electron Transfer: A Special Case of Separable and Coupled PT and ET 9. Dogonadze−Kuznetsov−Levich (DKL) Model of PT/HAT and Connections with ET and PCET Theories 10. Borgis−Hynes (BH) Theory for PT and HAT 10.1. Dynamical Regimes of the BH Theory 10.2. Splitting and Coupling Fluctuations 10.3. Reaction Rate Constant 10.4. Analytical Rate Constant Expressions in Limiting Regimes 11. Cukier Theory of PCET 11.1. Double-Adiabatic and Two-Dimensional Approaches 11.2. Reorganization and Solvation Free Energy in ET, PT, and EPT 11.3. Generalization of the Theory and Connections between PT, PCET, and HAT 12. Soudackov−Hammes-Schiffer (SHS) Theory of PCET 12.1. Regarding System Coordinates and Interactions: Hamiltonians and Free Energies 12.2. Electron−Proton States, Rate Constants, and Dynamical Effects 12.3. Note on the Kinetic Isotope Effect in PCET 12.4. Distinguishing between HAT and Concerted PCET Reactions 12.5. Electrochemical PCET 13. Conclusions and Prospects Appendix A Appendix B Associated Content Supporting Information