Reaction Rate Theory and Rare Events - 1st Edition - ISBN: 9780444563491, 9780444594709

Reaction Rate Theory and Rare Events

1st Edition

Authors: Baron Peters
eBook ISBN: 9780444594709
Hardcover ISBN: 9780444563491
Imprint: Elsevier
Published Date: 22nd March 2017
Page Count: 634
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Description

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

Readership

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

Table of Contents

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

Details

No. of pages:
634
Language:
English
Copyright:
© Elsevier 2017
Published:
Imprint:
Elsevier
eBook ISBN:
9780444594709
Hardcover ISBN:
9780444563491

About the Author

Baron Peters

Baron Peters (1976 - ) is from Moberly, Missouri. He completed a B.S. in Chemical Engineering and a B.S. in Mathematics at the University of Missouri - Columbia. He studied catalysis and reaction rate theory to obtain a PhD with Alex Bell and Arup Chakraborty at the University of California - Berkeley in 2004. He then worked as a post-doc with Bernhardt Trout at the Massachusetts Institute of Technology, and with Berend Smit at the Centre Europeen de Calcul Atomique et Moleculaire (CECAM). Baron is currently a professor in the Department of Chemical Engineering and in the Department of Chemistry and Biochemistry at the University of California - Santa Barbara. Baron has contributed several leading computational methods and theoretical advances for understanding chemical reaction rates, heterogeneous catalysis, enzyme catalysis, and also rare events like crystal nucleation kinetics. He is among the few investigators whose research bridges the historical gap between the theory of chemical reaction rates and the theory of other types of rare events.

Affiliations and Expertise

Professor, Chemical Engineering Department, University of California at Santa Barbara, Santa Barbara, CA, USA