Reaction Rate Theory and Rare Events bridges the historical gap between these subjects because the increasingly multidisciplinary nature of scientific research often requires an understanding of both reaction rate theory and the theory of other rare events. The book discusses collision theory, transition state theory, RRKM theory, catalysis, diffusion limited kinetics, mean first passage times, Kramers theory, Grote-Hynes theory, transition path theory, non-adiabatic reactions, electron transfer, and topics from reaction network analysis. It is an essential reference for students, professors and scientists who use reaction rate theory or the theory of rare events.
In addition, the book discusses transition state search algorithms, tunneling corrections, transmission coefficients, microkinetic models, kinetic Monte Carlo, transition path sampling, and importance sampling methods. The unified treatment in this book explains why chemical reactions and other rare events, while having many common theoretical foundations, often require very different computational modeling strategies.
Key Features
- Offers an integrated approach to all simulation theories and reaction network analysis, a unique approach not found elsewhere
- Gives algorithms in pseudocode for using molecular simulation and computational chemistry methods in studies of rare events
- Uses graphics and explicit examples to explain concepts
- Includes problem sets developed and tested in a course range from pen-and-paper theoretical problems, to computational exercises
Chapter 1: Introduction
- Abstract
- 1.1. Motivation for this book
- 1.2. Why are rare events important?
- 1.3. The role of computation and simulation
- 1.4. Polemics
- References
Chapter 2: Chemical equilibrium
- Abstract
- 2.1. Chemical potential and activity
- 2.2. Equilibrium constants and compositions
- Exercises
- References
Chapter 3: Rate laws
- Abstract
- 3.1. Rates, mass balances, and reactors
- 3.2. Reaction order and elementary reactions
- 3.3. Initial rates and integrated rate laws
- 3.4. Reversible reactions
- 3.5. Multistep reactions
- 3.6. The pseudo-steady-state approximation
- 3.7. Rate determining steps and quasi-equilibrated steps
- Exercises
- References
Chapter 4: Catalysis
- Abstract
- 4.1. Acid-base catalysis
- 4.2. Enzymes
- 4.3. Heterogeneous catalysis
- 4.4. Microkinetic models
- 4.5. Degree-of-rate-control
- 4.6. Catalysts with non-uniform sites
- Exercises
- References
Chapter 5: Diffusion control
- Abstract
- 5.1. Complete diffusion control
- 5.2. Partial diffusion control
- 5.3. Diffusion control with long range interactions
- 5.4. Diffusion control for irregularly shaped reactants
- Exercises
- References
Chapter 6: Collision theory
- Abstract
- 6.1. Hard spheres: Trautz and Lewis
- 6.2. Cross sections and rate constants
- Exercises
- References
Chapter 7: Potential energy surfaces and dynamics
- Abstract
- 7.1. Molecular potential energy surfaces
- 7.2. Atom-exchange reactions
- 7.3. Mass weighted coordinates and normal modes
- 7.4. Features of molecular potential energy surfaces
- 7.5. Reaction path Hamiltonian
- 7.6. Empirical valence bond models
- 7.7. Disconnectivity graphs
- Exercises
- References
Chapter 8: Saddles on the energy landscape
- Abstract
- 8.1. Newton-Raphson
- 8.2. Cerjan-Miller algorithm
- 8.3. Partitioned-Rational Function Optimization
- 8.4. The dimer method
- 8.5. Reduced landscape algorithms
- 8.6. Coordinate driving
- 8.7. Nudged elastic band
- Exercises
- References
Chapter 9: Unimolecular reactions
- Abstract
- 9.1. Lindemann-Christiansen mechanism
- 9.2. Hinshelwood and RRK theories
- 9.3. RRKM theory
- 9.4. Transition state theory from RRKM theory
- Exercises
- References
Chapter 10: Transition state theory
- Abstract
- 10.1. Foundations
- 10.2. Statistical mechanics for chemical equilibria
- 10.3. Harmonic transition state theory
- 10.4. Thermodynamic formulation
- 10.5. Flux across a dividing surface
- 10.6. Variational transition state theory
- 10.7. Harmonic TST with internal coordinates
- 10.8. Non-idealities
- Exercises
- References
Chapter 11: Landau free energies and restricted averages
- Abstract
- 11.1. Monte Carlo, molecular dynamics, and hybrid sampling
- 11.2. Thermodynamic perturbation theory
- 11.3. Projections
- 11.4. Non-Boltzmann sampling
- 11.5. Thermodynamic integration
- 11.6. Other methods for computing free energies
- 11.7. Cautionary notes
- Exercises
- References
Chapter 12: Tunneling
- Abstract
- 12.1. One-dimensional tunneling models
- 12.2. Kinetic isotope effects
- 12.3. Tunneling or tunnel splitting
- 12.4. Multidimensional tunneling models
- Exercises
- References
Chapter 13: Reactive flux
- Abstract
- 13.1. Phenomenological rate laws and time correlations
- 13.2. Reactive flux formalism
- 13.3. Effective positive flux
- 13.4. Quantum dynamical correlation functions
- Exercises
- References
Chapter 14: Discrete stochastic variables
- Abstract
- 14.1. Basic definitions
- 14.2. The master equation
- 14.3. Classical nucleation theory
- 14.4. Kinetic Monte Carlo
- 14.5. Markov state models
- 14.6. Spectral theory
- Exercises
- References
Chapter 15: Continuous stochastic variables
- Abstract
- 15.1. Inertial Langevin dynamics
- 15.2. Overdamped Langevin dynamics
- 15.3. Fokker-Planck equations
- 15.4. From discrete models to Fokker-Planck equations
- 15.5. Stationary solutions of Fokker-Planck equations
- 15.6. Spectral theory revisited
- Exercises
- References
Chapter 16: Kramers theory
- Abstract
- 16.1. Intermediate and high friction
- 16.2. Low friction: the energy diffusion limit
- 16.3. Insights and limitations
- Exercises
- References
Chapter 17: Grote-Hynes theory
- Abstract
- 17.1. The Grote-Hynes equations
- 17.2. Multidimensional models and interpretations
- Exercises
- References
Chapter 18: Diffusion over barriers
- Abstract
- 18.1. The forward and backward equations
- 18.2. Mean first passage times
- 18.3. Langer's multidimensional theory
- 18.4. Committors (splitting probabilities)
- 18.5. Berezhkovskii and Szabo: back to one dimension
- 18.6. Classical nucleation theory revisited
- 18.7. Rates from the committor
- 18.8. Discrete committors and rates
- Exercises
- References
Chapter 19: Transition path sampling
- Abstract
- 19.1. The transition path ensemble
- 19.2. Transition path sampling
- 19.3. Basin definitions and foliations
- 19.4. Rate constants from transition path sampling
- 19.5. Transition interface sampling
- 19.6. Forward flux sampling
- Exercises
- References
Chapter 20: Reaction coordinates and mechanisms
- Abstract
- 20.1. Properties of an ideal reaction coordinate
- 20.2. Variational theories and eigenfunctions
- 20.3. Committor analysis
- 20.4. Square error minimization
- 20.5. Likelihood maximization
- 20.6. Inertial likelihood maximization
- Exercises
- References
Chapter 21: Nonadiabatic reactions
- Abstract
- 21.1. Diabatic and adiabatic representations
- 21.2. Spin-forbidden reactions
- 21.3. Electron transfer
- 21.4. Classical MD methods for electron transfer
- 21.5. Nonadiabatic models of enzyme catalysis
- Exercises
- References
Chapter 22: Free energy relationships
- Abstract
- 22.1. BEP relations and the Bronsted catalysis law
- 22.2. The Marcus equation
- 22.3. Externally controlled driving forces
- Exercises
- References
- Frenkel and Smit, Understanding Molecular Simulation: From Algorithms to Applications, 2nd Edition, 9780122673511, AP, 664 pages, 2002, $91.95
- Parmon, Thermodynamics of Non-Equilibrium Processes for Chemists with a Particular Application to Catalysis, 9780444530288, Elsevier, 340 pages, 2010, $255.00
- Demirel, Nonequilibrium Thermodynamics: Transport and Rate Processes in Physical, Chemical and Biological Systems, 2nd Edition, 9780444530790, Elsevier, 754 pp, 2007, $245.00
Chemists, physicists, and engineers worldwide who use computational methods to study activated processes will be interested in this book. Academics, Graduate students, and Researchers in National Labs and corporate Research centers. The book could be used for teaching graduate courses
