Theory of Unimolecular Reactions

Theory of Unimolecular Reactions provides a comprehensive analysis of the theory of unimolecular reactions, also known to kineticists as the Rice-Marcus or the Rice-Ramsperger-Kassel-Marcus theory, and to those working in mass spectrometry and related fields as the quasi-equilibrium theory or the theory of mass spectra. This book demonstrates how theoretical parameters are related to experimental observables and describes the methods that are used to obtain useful numerical answers.
This monograph consists of 11 chapters and begins by explaining the derivation of the expression for the basic rate k(E), with emphasis on the unimolecular rate constant, intramolecular energy transfer, and potential energy surfaces in unimolecular reactions. The statistical calculation of unimolecular rate under vibrational potential is also given, along with pertinent degrees of freedom. The remaining chapters explore the energy distribution functions appropriate to each system, the averaging of k(E), and the relations between theoretical and experimental parameters. Thermal reactions, chemical activation systems, and the theory of mass spectra are examined. The last chapter is devoted to the transition state and its ambiguities.
This text will be of interest to gas kineticists, mass spectrometrists, and students and researchers working in the field of physical chemistry.

Contenu

Foreword
Preface
Acknowledgments
Part I Introduction
Chapter 1. The Unimolecular Rate Constant

1. The Unimolecular Process
2. Decay of a Pure Bound State into a Single Channel
3. Average Rate
4. Average Lifetime
5. Basic Assumption
   Exercises
   References
   Chapter 2. Intramolecular Energy Transfer
6. Theory of Slater
7. Theory of Rice, Ramsperger, and Kassel
8. Intramolecular Energy Transfer
9. Randomization of Energy and Experimental Evidence
10. Theoretical Treatment of Energy Randomization
11. The Rice-Marcus (RRKM) Theory
    References
    Chapter 3. Potential Energy Surfaces in Unimolecular Reactions
12. Triatomic Potential Energy Surface for a Vibrational Potential
13. Triatomic Potential Energy Surfaces for an Effective Potential
14. Triatomic Potential Energy Surfaces for Nonadiabatic Reactions
15. Extrapolation to Polyatomic Potential Energy Surfaces
    References
    Chapter 4. Statistical Calculation of Unimolecular Rate under Vibrational Potential
16. Unimolecular Process in Classical Phase Space
17. The Quantum-Mechanical Unimolecular Rate Constant
18. An Alternative Derivation
19. Nonclassical Effects Near Potential Barrier Maximum
20. Reaction Path Degeneracy
    Exercises
    References
    Chapter 5. Pertinent Degrees of Freedom
21. Degrees of Freedom Excluded by Conservation Requirements
22. Internal Degrees of Freedom
23. External Degrees of Freedom
24. Model for Particle
    References
    Chapter 6. Calculation of Energy-Level Densities
25. Terminology and Basic Concepts
26. Direct Evaluation of W(E) and G{E) in Simple Systems
27. Approximation to N(E) and G(E): General Considerations
28. Inversion of the Partition Function
29. Approximation to N(E) and G(E) for Rotational States
30. Direct Evaluation of Nvr(E) and Gvr(E) in Simple Systems
31. Approximations Based on Inversion of Classical Partition Function
32. Approximations Based on the Inversion of the Quantum-Mechanical Partition Function
33. Approximation to Nvr(E) and Gyr(E) for more Realistic Systems
34. Conclusions
    Exercises
    References
    Chapter 7. Unimolecular Rate with an Effective Potential
35. The Rotational Potential
36. Type 1 Vibrational Potential
37. Effective Potential for Type 1 Reaction
38. Effective Potential for Type 2 and Type 3 Reactions
    Exercise
    References
    Part II Introduction
    Chapter 8 Thermal Reactions
39. Collisional Activation: General Features of Lindemann's Simple Mechanism
40. Averaging over Equilibrium Distribution
41. Averaging over Steady-State Distribution
42. Evaluation of Centrifugal Correction Factors
43. Pressure Dependence
44. Temperature Dependence
45. Theoretical Parameters and Experimental Observables
46. Generalized Lindemann's Mechanism and the Nonequilibrium Distribution
    Exercises
    References
    Chapter 9 Chemical Activation Systems
47. Nature of Chemical Activation
48. Determination of the Energy Distribution Function
49. Pressure Dependence of Rate
50. Temperature Dependence of Rate
51. Collisional Deactivation in a Multilevel System
52. Photo-activation
53. Theoretical Parameters and Experimental Observables
54. Centrifugal Effects
    Exercises
    References
    Chapter 10 Fragmentation of Highly Excited Species: Theory of Mass Spectra
55. Unimolecular Reactions of Positive Ions
56. Consecutive-Parallel Reactions: Energy Partitioning
57. Production of Ionized Species
58. Potential Energy Surfaces of Polyatomic Ions
59. Randomization of Electronic Energy
60. Determination of Energy Distribution Function
61. Primary Yield in Radiolysis
62. Theoretical Parameters and Experimental Observables
63. Kinetic Energy of Fragments and Rotational Effects
    Exercises
    References
    Chapter 11 Transition States in Unimolecular Reactions
64. General Remarks; Isotope Effect
65. Transition States for Type 1 Reactions
66. Transition States for Type 2 Reactions
67. Transition States for Type 3 Reactions
    Exercises
    References
    Appendix
    List of Symbols
    Author Index
    Subject Index