Potential Energy Surfaces and Reaction Dynamics

40 lessons, pages 4161–4200.

  1. Potential Energy Surfaces: The Research Picture — How nuclear arrangements map to electronic energies and possible reaction pathways
  2. Choosing Molecular Coordinates — Cartesian, internal and collective coordinates for a high-dimensional surface
  3. Born–Oppenheimer Surfaces and Their Limits — Electronic states as functions of nuclear geometry and cases requiring state coupling
  4. Stationary Points on a Surface — Zero gradients, Hessian curvature and classification by negative eigenvalues
  5. Local Minima and Molecular Conformers — Stable structures, conformer families and barriers between minima
  6. First-Order Saddle Points — Transition-state geometries and the one downhill direction on each side
  7. Imaginary Frequencies as Diagnostics — Using vibrational Hessians to test a claimed transition structure
  8. The Intrinsic Reaction Coordinate — Steepest-descent paths from a saddle point and their interpretation
  9. Verifying Reactant and Product Connectivity — Following both directions from a transition state instead of assuming its endpoints
  10. Electronic, Enthalpic and Free-Energy Barriers — Zero-point, thermal and entropy corrections and their different meanings
  11. Multiple Conformers in a Reaction Profile — Population weighting and conformer-specific pathways
  12. Competing Reaction Channels — Parallel saddle points, product branching and kinetic versus thermodynamic outcomes
  13. Constrained Coordinate Scans — Mapping a candidate pathway while recognizing artifacts of fixed coordinates
  14. Nudged Elastic Band and String Methods — Finding paths between endpoints without presupposing a single bond coordinate
  15. Why a Single Reaction Coordinate Can Fail — Orthogonal modes, hidden intermediates and multidimensional bottlenecks
  16. Two-Dimensional Energy Landscapes — Contours, ridges, valleys and coupled bond changes
  17. Valley–Ridge Inflection and Product Bifurcation — When trajectories leaving one saddle region can reach different products
  18. Hammond Reasoning and Transition-State Structure — Using relative energetics cautiously to discuss early and late transition states
  19. Transition-State Theory from Flux — Dividing surfaces, equilibrium population and the no-recrossing assumption
  20. The Eyring Equation — Rate constants from activation free energy, temperature and transmission coefficient
  21. Recrossing and Variational Transition-State Theory — Moving the dividing surface to reduce overcounted reactive flux
  22. Quantum Tunneling in Chemical Reactions — Barrier penetration, temperature trends and isotope-sensitive corrections
  23. Kinetic Isotope Effects on a Surface — Mass-dependent zero-point energies, tunneling and mechanistic interpretation
  24. Unimolecular RRKM Theory — Microcanonical rates from transition-state and reactant state counts
  25. Energy Transfer and Master Equations — Pressure dependence and collisional redistribution in gas-phase kinetics
  26. Collision Energy and Scattering — Impact parameter, orientation and state-resolved reaction probabilities
  27. Molecular Beam Reaction Experiments — Controlling collision conditions and interpreting angular product distributions
  28. Classical Trajectory Simulations — Integrating nuclear motion and sampling initial conditions on a fitted surface
  29. Direct Dynamics and On-the-Fly Forces — Computing electronic forces during trajectories and assessing method cost
  30. Nonadiabatic Transitions — Breakdown of single-surface motion when electronic states interact
  31. Conical Intersections — Electronic-state degeneracy and ultrafast radiationless pathways
  32. Surface Hopping Models — Approximate mixed quantum–classical trajectories and their interpretation limits
  33. Solvent Friction and Barrier Crossing — How fluctuating environments change reaction dynamics beyond gas-phase profiles
  34. Free-Energy Surfaces in Solution — Potential of mean force, solvent coordinates and ensemble averaging
  35. Rare-Event Sampling — Umbrella sampling and enhanced-sampling approaches to infrequent transitions
  36. Committor Analysis — Testing whether a proposed coordinate identifies a true dynamical bottleneck
  37. Dynamics at Catalytic Interfaces — Adsorption, diffusion and reaction pathways on a heterogeneous surface
  38. Uncertainty in Computed Reaction Paths — Electronic method, conformational search, sampling and model-domain errors
  39. Validating a Reaction Mechanism — Connecting predicted barriers and products to kinetic, isotope and spectroscopic observations
  40. Potential Energy Surfaces and Dynamics: Unit Review — Integrating stationary points, reaction coordinates, rate theory and trajectories