Classical, Semiclassical, and Quantum Mechanical Unimolecular Reaction Rate Theory

Geometric Structures of Phase Space in Multidimensional Chaos: Applications to Chemical Reaction Dynamics in Complex Systems

Volumn 130, Issue , 2005, Pages 1-142

  Zhao, Meishan ^a,b   Gong, Jiangbin ^a,b   Rice, Stuart A ^a,b  

^a UNIVERSITY OF CHICAGO   (United States)

^b UNIVERSITY OF CHICAGO   (United States)

Author keywords

Cantorus; Deterministic chaos; Dynamical bottleneck; Predissociation; Quantum chaos; Quantum scars; Unimolecular reaction; Van der Waals molecules; Wave packet

Indexed keywords

QUANTUM THEORY; REACTION RATES; VAN DER WAALS FORCES; WAVE PACKETS;

CANTORUS; DETERMINISTIC CHAOS; DYNAMICAL BOTTLENECK; PRE-DISSOCIATION; QUANTUM CHAOS; QUANTUM SCARS; UNIMOLECULAR REACTIONS; VAN DER WAALS MOLECULES;

CHAOS THEORY;

EID: 20844435991     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1002/0471712531.ch1     Document Type: Chapter

References (103)

1. O. K. Rice, H. C. Ramsperger, J. Am. Chem. Soc. 49, 1616 (1927); 50, 617 (1928).
2. L. S. Kassel, J. Phys. Chem. 32, 225 (1928).
3. R. A. Markus, O. K. Rice, J. Phys. Colloid. Chem. 55, 894 (1951).
4. R. A. Markus, J. Chem. Phys. 20, 359 (1952); 43, 2658 (1965).
5. W. Frost, Theory of Unimolecular Reactions, Wiley-Interscience, London, 1972.
6. T. Baer and W. L. Hase, Unimolecular Reaction Dynamics: Theory and Experiments, Oxford University Press, New York, 1996.
7. A. J. Lichtenberg and M. A. Lieberman, Regular and Chaotic Dynamics, 2nd ed., Springer-Verlag, New York, 1992.
8. R. MacKay, J. D. Meiss, and I. C. Percival, Physica D 13, 55 (1984).
9. R. MacKay, J. D. Meiss, and I. C. Percival, Physica D 27, 1 (1987).
10. D. Bensimon and L. P. Kadanoff, Physica D 13, 82 (1984).
11. M. J. Davis and S. K. Gray, J. Chem. Phys. 84, 5389 (1986).
12. S. K. Gray, S. A. Rice, and M. J. Davis, J. Phys. Chem. 90, 3470 (1986).
13. M. S. Zhao and S. A. Rice, J. Chem. Phys. 96, 3542 (1992).
14. M. S. Zhao and S. A. Rice, J. Chem. Phys. 96, 6654 (1992).
15. M. S. Zhao and S. A. Rice, J. Chem. Phys. 97, 943 (1992).
16. M. S. Zhao and S. A. Rice, J. Chem. Phys. 96, 7483 (1992).
17. M. Toda, Adv. Chem. Phys. 123, 153 (2002).
18. R. E. Gillilan and G. S. Ezra, J. Chem. Phys. 94, 2648 (1991).
19. H. Tang, S. Jang, M. Zhao, and S. A. Rice, J. Chem. Phys. 101, 8737 (1994).
20. S.Wiggins, Normally Hyperbolic Invariant Manifolds in Dynamcial Systems, Springer-Verlag, New York, 1994.
21. S. Wiggins, Chaotic Transport in Dynamcial Systems, Springer-Verlag, New York, 1992.
22. S. Wiggins, L. Wiesenfeld, C. Jaffe, and T. Uzer, Phys. Rev. Lett. 86, 5478 (2001).
23. N. De Leon and C. C. Marston, J. Chem. Phys. 91, 3405 (1989).
24. N. De Leon, M. A. Mehta, and R. Q. Topper, J. Chem. Phys. 94, 8310 (1991).
25. A. M. O. De Almeida, N. De Leon, M. A. Mehta, and C. C. Marston, Physica D 46, 265 (1990).
26. T. Komatsuzaki and R. S. Berry, Adv. Chem. Phys. 123, 79 (2002).
27. M. C. Gutzwiller, Chaos in Classical and Quantum Mechanics, Springer-Verlag, New York, 1990.
28. G. Casati and B. Chirikov, Quantum Chaos: Between Order and Disorder, Cambridge University Press, New York, 1995.
29. F. Haake, Quantum Signatures of Chaos, Springer-Verlag, New York, 1991.
30. S. A. Rice and M. S. Zhao, Optical Control of Molecular Dynamics, John Wiley & Sons, New York, 2000.
31. M. Shapiro and P. Brumer, Principles of the Quantum Control of Molecular Processes, John Wiley & Sons, New York, 2003.
32. S. H. Tersigni and S. A. Rice, Ber. Bunseges. Phys. Chem. 92, 227 (1988).
33. C. C. Martens, M. J. Davis, and G. S. Ezra, Chem. Phys. Lett. 142, 519 (1987).
34. D. Carter and P. Brumer, J. Chem. Phys. 77, 4208 (1982); 78, 2104E (1983).
35. P. Gaspard and S. A. Rice, J. Phys. Chem. 93, 6947 (1989).
36. D. J. Davis, J. Chem. Phys. 83, 1016 (1985).
37. W. H. Miller, N. C. Handy, and J. E. Adams, J. Chem. Phys. 72, 99 (1980).
38. W. H. Miller, Potential Energy Surfaces and Dynamics Calculations, D. G. Truhlar, ed., Plenum, New York, 1981, p. 265.
39. K. E. Johnson, L. Wharton, and D. H. Levy, J. Chem. Phys. 69, 2719 (1978).
40. J. E. Kenny, K. E. Johnson, W. Shafin, and D. H. Levy, J. Chem. Phys. 72, 1109 (1980).
41. D. M. Willberg, M. Gutmann, J. J. Breen, and A. H. Zewail, J. Chem. Phys. 96, 198 (1992).
42. J. J. Breen, D. M.Willberg,M. Gutmann, and A. H. Zewail, Chem. Phys. Lett. 93, 9180 (1990).
43. J. A. Beswick and J. Jortner, Mol. Phys. 39, 1137 (1980).
44. J. I. Cline, D. D. Evard, F. Thommen, and K. C. Janda, J. Chem. Phys. 84, 1165 (1986).
45. D. D. Evard, F. Thommen, J. I. Cline, and K. C. Janda, J. Phys. Chem. 91, 2508 (1987).
46. J. I. Cline, N. Sivakumer, D. D. Evard, and K. C. Janda, J. Chem. Phys. 86, 1636 (1987).
47. C. E. Wozny and S. K. Gray, Ber. Bunsenges. Phys. Chem. 92, 236 (1988).
48. J. I. Cline, B. P. Reid, D. D. Evard, N. Sivakumer, N. Halberstadt, and K. C. Janda, J. Chem. Phys. 89, 3535 (1988).
49. S. K. Gray and C. E. Wozny, J. Chem. Phys. 94, 2816 (1991).
50. D. H. Zhang and J. Z. H. Zhang, J. Chem. Phys. 95, 6449 (1991).
51. S. K. Gray, S. A. Rice, and D. W. Noid, J. Chem. Phys. 84, 3745 (1986).
52. J. M. Skene, J. C. Drobits, and M. I. Lester, J. Chem. Phys. 85, 2329 (1986).
53. R. L. Waterland, J. M. Skene, and M. I. Lester, J. Chem. Phys. 89, 7277 (1988).
54. J. M. Skene and M. I. Lester, Chem. Phys. Lett. 116, 93 (1985).
55. S. K. Gray and S. A. Rice, J. Chem. Phys. 86, 2020 (1987).
56. N. De Leon and S. Ling, J. Chem. Phys. 101, 4790 (1994).
57. N. De Leon, J. Chem. Phys. 96, 285 (1992).
58. S. M. Jang and S. A. Rice, J. Chem. Phys. 99, 9585 (1993).
59. N. De Leon, M. A. Mehta, and R. Q. Topper, J. Chem. Phys. 94, 8329 (1991).
60. S. M. Jang, M. S. Zhao, and S. A. Rice, J. Chem. Phys. 97, 8188 (1992).
61. M. A. Harthcock and J. Lanne, J. Mol. Spectrosc. 91, 300 (1982).
62. M. A. Harthcock and J. Lanne, J. Chem. Phys. 79, 2103 (1983).
63. C. C. Marston and N. De Leon, J. Chem. Phys. 91, 3392 (1989).
64. M. S. Zhao and S. A. Rice, J. Chem. Phys. 98, 2837 (1993).
65. J. N. Murrell, S. Carter, and L. O. Halonen, J. Mol. Spectrosc. 93, 307 (1982).
66. J. Zhang, W. Chiang, and J. Laane, J. Chem. Phys. 100, 3455 (1994).
67. H. Tang, S. M. Jang, M. S. Zhao, and S. A. Rice, Chem. Phys. Lett. 285, 143 (1998).
68. H. W. Lee, Phys. Rep. 259, 147 (1995).
69. H. Weyl, Z. Phys. 46, 1 (1927).
70. J. E. Moyal, Proc. Cambridge Philos. Soc. 45, 99 (1949).
71. M. V. Berry, in Chaotic Behavior of Deterministic Systems, G. Iooss, R. H. G. Helleman, and R. Stora, eds., North-Holland, Amsterdam, pp. 171-271.
72. E. J. Heller, Phys. Rev. Lett. 53, 1515 (1984).
73. M. V. Berry, Proc. R. Soc. Lond. A 423, 219 (1989).
74. E. B. Bogomolny, Physica D 31, 169 (1988).
75. S. M. Jang, M. S. Zhao, and S. A. Rice, Chem. Phys. 230, 237 (1998).
76. W. H. Miller, J. Chem. Phys. 61, 1823 (1970).
77. K. G. Kay, J. Chem. Phys. 65, 3813 (1976).
78. W. H. Miller, S. D. Schwartz, and J. W. Tromp, J. Chem. Phys. 79, 4889 (1983).
79. T. Yamamoto, J. Chem. Phys. 33, 281 (1960).
80. W. H. Miller, Faraday Discuss. 110, 1 (1998).
81. W. H. Miller, J. Chem. Phys. 53, 3578 (1970).
82. K. G. Kay, J. Chem. Phys. 100, 4377 (1994); 100, 4432 (1994).
83. G. Campolieti and P. Brumer, J. Chem. Phys. 96, 5969 (1992).
84. X. Sun and W. H. Miller, J. Chem. Phys. 106, 916 (1997).
85. H. Wang, X. Sun, and W. H. Miller, J. Chem. Phys. 108, 9726 (1998).
86. X. Sun, H. Wang, and W. H. Miller, J. Chem. Phys. 109, 4190 (1998).
87. F. Remacle and R. D. Levine, J. Phys. Chem. 100, 7962 (1996).
88. M. S. Zhao, S. M. Jang, and S. A. Rice, Int. J. Chem. 2, art. no. 1 (1999).
89. J. C. Light and T. Carrington, Adv. Chem. Phys. 114, 263 (2000).
90. F. Le Quéré and S. K. Gray, J. Chem. Phys. 98, 5396 (1993).
91. R. C. Brown and R. E. Wyatt, Phys. Rev. Lett. 57, 1 (1986).
92. G. Radons, T. Geisel, and J. Rubner, Phys. Rev. Lett. 57, 2883 (1986); 58, 2506 (1987).
93. N. T. Maitra and E. J. Heller, Phys. Rev. E 61, 3620 (2000).
94. D. M. Leitner and P. G. Wolynes, Phys. Rev. Lett. 79, 55 (1997).
95. V. Ya. Demikhovskii, F. M. Izrailev, and A. I. Malyshev, Phys. Rev. Lett. 88, 154101 (2002).
96. V. Ya. Demikhovskii, F. M. Izrailev, and A. I. Malyshev, Phys. Rev. E. 66, 036211 (2002).
97. J. B. Gong, H. J. Wörner, and P. Brumer, Phys. Rev. E. 68, 026209 (2003).
98. L. Hufnagel, R. Ketzmerick, M. F. Otto, and H. Schanz, Phys. Rev. Lett. 89, 154101 (2002).
99. M. Gruebele and R. Bigwood, Int. Rev. Phys. Chem. 17, 91 (1998).
100. M. Gruebele, Theor. Chem. Acc. 109, 53 (2003).
101. D. Giulini, E. Joos, C. Kiefer, J. Kupsch, I. O. Stamatescu, and H. D. Zeh, Decoherence and the Appearance of a Classical World in Quantum Theory, Springer-Verlag, New York, 1996.
102. S. Habib, K. Shizume, and W. H. Zurek, Phys. Rev. Lett. 80, 4361 (1998).
103. J. B. Gong and P. Brumer, Phys. Rev. E 60, 1643 (1999).