Energy localization in molecules, bifurcation phenomena, and their spectroscopic signatures: the global view

Chemical Reviews

Volumn 109, Issue 9, 2009, Pages 4248-4271

  Farantos, Stavros C ^a   Schinke, Reinhard ^b   Guo, Hua ^c   Joyeux, Marc ^d  

^a INSTITUTE OF ELECTRONIC STRUCTURE AND LASER   (Greece)

^b MAX PLANCK INSTITUTE FOR DYNAMICS AND SELF ORGANIZATION   (Germany)

^c UNIVERSITY OF NEW MEXICO   (United States)

^d UNIV GRENOBLE ALPES   (France)

Author keywords

[No Author keywords available]

Indexed keywords

AMINO ACIDS; BIFURCATION (MATHEMATICS); DEGREES OF FREEDOM (MECHANICS); MOLECULAR DYNAMICS; SPECTROSCOPIC ANALYSIS;

BIFURCATION PHENOMENA; CARTESIAN COORDINATE; CONFIGURATION SPACE; ENERGY LOCALIZATION; POLYATOMIC MOLECULES; SPECTRAL DISTRIBUTION; SPECTROSCOPIC SIGNATURES; SPECTROSCOPIC STUDIES;

MOLECULES;

EID: 70349160754     PISSN: 00092665     EISSN: 15206890     Source Type: Journal    
DOI: 10.1021/cr900069m     Document Type: Article

References (242)

1. Levine, R. D.; Berstein, R. B. Molecular Reaction Dynamics and Chemical Reactivity, 3rd ed.; Oxford University Press: New York, 1987.
2. Crim, F. F. Proc. Natl Acad. Sci. USA. 2008, 105, 12654-12661.
3. Liu, Z.; Feldman, L. C.; Tolk, N. H.; Zhang, Z.; Cohen, P. I. Science 2006, 312, 1024-1026.
4. Tully, J. C. Science 2006, 312, 1004-1005.
5. Dai, H.-L.; Field, R. Molecular Dynamics and Spectroscopy by Stimulated Emission Pumping; Advanced Series in Physical Chemistry; World Scientific Publishing Company: Singapore, 1995.
6. Guckenheimer, J.; Holmes, P. Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, 2nd ed.; Springer-Verlag: New York, 1990; Vol.42.
7. Wiggins, S. Introduction to Applied Nonlinear Dynamical Systems and Chaos; Springer-Verlag: New York, 1990.
8. Poincaré, H. New Methods of Celestial Mechanics; Springer-Verlag: New York, 1992; Vol.13.
9. Ishikawa, H.; Field, R. W.; Farantos, S. C.; Joyeux, M.; Koput, J.; Beck, C.; Schinke, R. Annual Review of Physical Chemistry; Annual Reviews: Palo Alto, CA, 1999; Vol.50, pp 443-484.
10. Joyeux, M.; Farantos, S. C.; Schinke, R. J. Phys. Chem. 2002, 106, 5407-5421.
11. Joyeux, M.; Grebenshchikov, S. Y.; Bredenbeck, J.; Schinke, R.; Farantos, S. C. Adv. Chem. Phys. 2005, 130, 267-303.
12. Brown, R. C.; Wyatt, R. E. Phys. Rev. Lett. 1986, 57, 1-4.
13. Brown, R. C.; Wyatt, R. E. J. Phys. Chem. 1986, 90, 3590-3594.
14. Wiggins, S. Normally Hyperbolic Invariant Manifolds in Dynamical Systems; Springer-Verlag: New York, 1994.
15. Wiggins, S.; Wiesenfeld, L.; Jaffé, C.; Uzer, T. Phys. Rev. Lett. 2001, 86, 5478-5481.
16. Uzer, T.; Jaffé, C.; Palacián, J.; Yanguas, P.; Wiggins, S. Nonlinearity 2002, 15, 957-992.
17. Waalkens, H.; Schubert, R.; Wiggins, S. Nonlinearity 2008, 21, R1-R118.
18. Child, M. S. Semiclassical Mechanics with Molecular Applications; Oxford University Press: Cary, NC, 1991.
19. Gutzwiller, M. C. Chaos in classical and quantum mechanics; Springer-Verlag: New York, 1990; Vol.1.
20. Miller, W. H. J. Phys. Chem. A 2001, 105, 2942-2955.
21. Jacobson, M. P.; O'Brien, J. P.; Silbey, R. J.; Field, R. W. J. Chem. Phys. 1998, 109, 121-123.
22. Jacobson, M. P.; O'Brien, J. P.; Field, R. W. J. Chem. Phys. 1998, 109, 3831-3840.
23. Jacobson, M. P.; Silbey, R. J.; Field, R. W. J. Chem. Phys. 1999, 110, 845-859.
24. Jung, C.; Taylor, H. S.; Jacobson, M. P. J. Phys. Chem. A 2001, 105, 681-693.
25. Temsamani, M. A.; Herman, M.; Solina, S. A. B.; O'Brien, J. P.; Field, R. W. J. Chem. Phys. 1996, 105, 11357-11359.
26. El Idrini, M.; Lievin, J.; Campargue, A.; Herman, M. J. Chem. Phys. 1999, 110, 2074-2086.
27. Jonas, D. M.; Solina, S. A. B.; Rajaram, B.; Cohen, S. J.; Field, R. W.; Yamanouchi, K.; Tsuchiya, S. J. Chem Phys. 1993, 99, 7350-7370.
28. Ishikawa, H.; Nagao, C.; Mikami, N.; Field, R. J. Chem. Phys. 1998, 109, 492-503.
29. Yamanouchi, K.; Takeuchi, S.; Tsuchiya, S. J. Chem. Phys. 1990, 92, 4044-4054.
30. Yamanouchi, K.; Yamada, H.; Tsuchiya, S. J. Chem. Phys. 1988, 88, 4664-4670.
31. Sako, T.; Yamanouchi, K. Chem. Phys. Lett. 1996, 264, 403-410.
32. Choi, Y. S.; Moore, C. B. J. Chem. Phys. 1991, 94, 5414-5425.
33. Yamamoto, T.; Kato, S. J. Chem. Phys. 1998, 109, 9783-9794.
34. Tobiason, J. D.; Dunlop, J. R.; Rohlfing, E. A. J. Chem. Phys. 1995, 103, 1448-1469.
35. Keller, H.-M.; Flöthmann, H.-M.; Dobbyn, A. J.; Schinke, R.; Werner, H.-J.; Bauer, C.; Rosmus, P. J. Chem. Phys. 1996, 105, 4983-5004.
36. Keller, H.-M.; Stumpf, M.; Schröder, T.; Stock, C.; Temps, F.; Schinke, R.; Werner, H.-J.; Bauer, C.; Rosmus, P. J. Chem. Phys. 1997, 106, 5359-5378.
37. Northrup, F. J.; Bethardy, G. A.; Macdonald, R. G. J. Mol. Spectrosc. 1997, 186, 349-362.
38. Delon, A.; Reiche, F.; Abel, B.; Grebenshchikov, S. Y.; Schinke, R. J. Phys. Chem. 2000, 104, 10374-10382.
39. Chowdary, P. D.; Gruebele, M. J. Chem. Phys. 2009, 130, 024305.
40. Henry, B. R. Vibrational Spectra and Structure; Elsevier: New York, 1993; Vol.10.
41. Crim, F. F. Acc. Chem. Res. 1999, 32, 877-884.
42. Leitner, D. M. Adv. Chem. Phys. 2005, 130, 205-256.
43. Leitner, D. M. Annual Review Physical Chemistry; Annual Reviews: Palo Alto, CA, 2008; Vol.59, pp 233-259.
44. Backus, E. H.; Nguyen, P. H.; Botan, V.; Pfister, R.; Moretto, A.; Crisma, M.; Toniolo, C.; Stock, G.; Hamm, P. J. Phys. Chem. B 2008, 112, 9091-9099.
45. Kolano, C.; Helbing, J.; Sander, W.; Hamm, P. J. Phys. Chem. B 2008, 111, 11297-11302.
46. Hamm, P.; Helbing, J.; Bredenbeck, J. Annu. Rev. Phys. Chem. 2008, 59, 291-317.
47. Treuffet, J.; Kubarych, K. J.; Lambry, J.-C.; Pilet, E.; Masson, J.B.; Martin, J.-L.; Vos, M. H.; Joffre, M.; Alexandrou, A. Proc. Natl. Acad. Sci. USA. 2007, 104, 15705-15710.
48. Koutsoupakis, C.; Pinakoulaki, W.; Stavrakakis, S.; Daskalakis, V.; Varotsis, C. Biochim. Biophys. Acta 2004, 1655, 347-352.
49. Koutsoupakis, C.; Soulimane, T.; Varotsis, C. Biophys. J. 2004, 86, 2438-2444.
50. Varotsis, C.; Babcock, G. T. Biochemistry 1990, 29, 7357-7362.
51. Aubry, S. Physica D 1997, 103, 201-250.
52. Campbell, D. K.; Flach, S.; Kivshar, Y. S. Phys. Today 2004, 43, 43-49.
53. Sievers, A. J.; Takeno, S. Phys. Rev. Lett. 1988, 61, 970-973.
54. Goldfield, E. M.; Gray, S. K. Adv. Chem. Phys. 2007, 136, 1-37.
55. Zou, S.; Bowman, J. M. J. Chem. Phys. 2002, 117, 5507-5510.
56. Kellman, M. E. Annu. Rev. Phys. Chem. 1995, 46, 395-422.
57. Kellman, M. E.; Tyng, V. Acc. Chem. Res. 2007, 40, 243-250.
58. Joyeux, M.; Sugny, D. Can. J. Phys. 2002, 80, 1459-1480.
59. Joyeux, M.; Sugny, D.; Tyng, V.; Kellman, M.; Ishikawa, H.; Field, R. W.; Beck, C.; Schinke, R. J. Chem. Phys. 2000, 112, 4162-4172.
60. Jung, C.; Taylor, H. S. J. Phys. Chem. A 2007, 111, 3047-3068.
61. Manikandan, P.; Semparithi, A.; Keshavamurthy, S. J. Phys. Chem. A 2009, 113, 1717-1730.
62. Landau, L. D.; Lifshitz, E. M. Mechanics, 3rd ed.; Pergamon Press: Oxford, England, 1976.
63. Vleck, J. H. V. Rev. Mod. Phys. 1951, 23, 213-227.
64. Birkhoff, G. D. Colloq. Pub. No.9 1979, 14-22.
65. Gustavson, F. G. Astron. J. 1966, 71, 670-686.
66. Farantos, S. C. Int. Rev. Phys. Chem. 1996, 15, 345-374.
67. Montaldi, J.; Roberts, M.; Stewart, I. Nonlinearity 1990, 3, 695-730.
68. Hanssmann, H. Local and Semi-Local Bifurcations in Hamiltonian Dynamical Systems: Results and Examples; Springer-Verlag: Berlin, Heidelberg, 2007.
69. Main, J.; Mandelshtam, V. A.; Wunner, G.; Taylor, H. S. Nonlinearity 1998, 11, 1015-1035.
70. Martens, C. C.; Davis, M. J.; Ezra, G. S. Chem. Phys. Lett. 1987, 142, 519-528.
71. Engel, Y. M.; Levine, R. D. Chem. Phys. Lett. 1989, 164, 270-278.
72. Heller, E. J. Phys. Rev. Lett. 1984, 53, 1515-1518.
73. Polavieja, G.; Borondo, F.; Benito, R. M. Phys. Rev. Lett. 1994, 73, 1613-1616.
74. Schweizer, W.; Jans, W.; Uzer, T. Phys. Rev. A 1998, 58, 1382-1388.
75. Wales, D. J. Energy Landscapes: Applications to Clusters, Biomolecules and Glasses; Cambridge University Press: 2004.
76. 68 instead of the term saddle-node (SN) used for generic dynamical systems and employed in our previous publications.
77. Lawton, R. T.; Child, M. S. Mol. Phys. 1981, 44, 709-723.
78. Prosmiti, R.; Farantos, S. C.; Guo, H. Chem. Phys. Lett. 1999, 311, 241-247.
79. Herzberg, G. Infrared and Raman Spectra; Van Nostrand: New York, 1945.
80. Halonen, L. Adv. Chem. Phys. 1998, 104, 41-179.
81. Jensen, P. Mol. Phys. 2000, 98, 1253-1285.
82. Keshavamurthy, S.; Ezra, G. S. J. Chem. Phys. 1997, 107, 156-179.
83. Paskauskas, R.; Chandre, C.; Uzer, T. Phys. Rev. Lett. 2008, 100, 083001-83004
84. Prosmiti, R.; Farantos, S. C. J. Chem. Phys. 1995, 103, 3299-3314.
85. Prosmiti, R.; Farantos, S. C. J. Chem. Phys. 2003, 118, 8275-8280.
86. Murrell, J. N.; Carter, S.; Farantos, S. C.; Huxley, P.; Varandas, A. J. C. Molecular Potential Energy Functions; John Wiley and Sons Ltd: 1984.
87. Mezey, P. G. Potential Energy Hypersurfaces; Elsevier Science Publishers B.V.: Amsterdam, The Netherlands, 1987; Vol.53.
88. Collins, M. A. Adv. Chem. Phys. 1996, 93, 389-453.
89. Werner, H.-J.; Knowles, P. J.; Lindh, R.; Manby, F. R.; Schütz, M.; et al. MOLPRO, version 2008.1, a package of ab initio programs; 2008.
90. Ahlrichs, R.; Bär, M.; Häser, M.; Horn, H.; Kölmel, C. Chem. Phys. Lett. 1989, 162, 165-169.
91. Ahlrichs, R.; et al. TURBOMOLE v5-8-0; 2005.
92. Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery, J. A., Jr.; Vreven, T.; Kudin, K. N.; Burant, J. C.; et al. Gaussian03; Gaussian Inc.: Wallingford, CT, 2003.
93. Wang, S.; Hu, P.; Zhang, Y. J. Phys. Chem. B 2007, 111, 3758-3764.
94. Lagana, A.; Riganelli, A. Reaction and Molecular Dynamics; Lecture Notes in Chemistry; Springer: 1999; Vol.75.
95. Ch. Beck, H.-M. K.; Grebenshchikov, S. Y.; Schinke, R.; Farantos, S. C.; Yamashita, K.; Morokuma, K. J. Chem. Phys. 1997, 107, 9818-9834.
96. Stamatiadis, S.; Farantos, S. C.; Keller, H.-M.; Schinke, R. Chem. Phys. Lett. 2001, 344, 565-572.
97. Qu, Z.; Zhu, H.; Tashiro, M.; Schinke, R.; Farantos, S. C J. Chem. Phys. 2004, 120, 6811-6814.
98. Qu, Z.; Zhu, H.; Schinke, R.; Farantos, S. C. J. Chem. Phys. 2004, 121, 11731-11745.
99. Siebert, R.; Fleurat-Lessard, P.; Schinke, R.; Bittererová, M.; Farantos, S. C. J. Chem. Phys. 2002, 116, 9749-9767.
100. Wang, J.; Cieplak, P.; Kollman, P. A. J. Comput. Chem. 2000, 21, 1049-1074.
101. Foloppe, N.; MacKerell, A. D. J. Comput. Chem. 2000, 21, 86-104.
102. Rapaport, D. C. The Art of Molecular Dynamics Simulation; Cambridge University Press: 1995.
103. Farantos, S. C J. Chem. Phys. 2007, 1726, 175101-175107.
104. Daskalakis, V.; Farantos, S. C.; Varotsis, C J. Am. Chem. Soc. 2008, 130, 12385-12393.
105. Iachello, F.; Perez-Bemal, F. Mol. Phys. 2008, 106, 223-231.
106. Tabor, M. Chaos and Integrability in Nonlinear Mechanics, 1st ed.; John Wiley & Sons Inc.: New York, 1989.
107. Kellman, M. E. J. Chem. Phys. 1990, 93, 6630-6635.
108. Fried, L. E.; Ezra, G. S. J. Chem. Phys. 1987, 86, 6270-6282.
109. Bacic, Z.; Light, J. C. Annu. Rev. Phys. Chem. 1989, 40, 469-498.
110. Fornberg, B. A Practical Guide to Pseudospectral Methods; Cambridge University Press: Cambridge in Applied and Computational Mathematics, 1998.
111. Kosloff, R. Dynamics of Molecules and Chemical Reactions; Wyatt, R. E., Zhang, J. Z. H., Eds.; New York, 1996.
112. Guantes, R.; Farantos, S. C. J. Chem. Phys. 1999, 111, 10827-10835.
113. Guantes, R.; Farantos, S. C. J. Chem. Phys. 2000, 113, 10429-10437.
114. Gray, S. K.; Goldfield, E. M. J. Chem. Phys. 2001, 115, 8331-8344.
115. Goldfield, E. M. Comput. Phys. Commun. 2000, 128, 178-189.
116. Goldfield, E. M.; Gray, A. K. Comput. Phys. Commun. 1996, 98, 1-14.
117. Medvedev, D. M.; Goldfield, E. M.; Gray, A. K. Comput. Phys. Commun. 2005, 166, 94-108.
118. Suarez, J.; Farantos, S. C.; Stamatiadis, S.; Lathouwers, L. Comput. Phys. Commun., in press.
119. Kosloff, R. Annu. Rev. Phys. Chem. 1994, 45, 145-178.
120. Wall, M. R.; Neuhauser, D. J. Chem. Phys. 1995, 102, 8011-8022.
121. Mandelshtam, V. A.; Taylor, H. S. J. Chem. Phys. 1995, 102, 7390-7399.
122. Chen, R.; Guo, H. J. Chem. Phys. 1996, 105, 1311-1317.
123. Mandelshtam, V. A.; Grozdanov, T. P.; Taylor, H. S. J. Chem. Phys. 1995, 103, 10074-10084.
124. Mandelshtam, V. A.; Taylor, H. S. J. Chem. Soc., Faraday Trans. 1997, 93, 847-860.
125. Carrington, T., Jr. Can. J. Chem. 2004, 82, 900-914.
126. Guo, H. Rev. Comput. Chem. 2007, 25, 285-347.
127. Golub, G. H.; Loan, V. Matrix Computations, 3rd ed.; The Johns Hopkins University Press: Baltimore, MD, 1996.
128. Lanczos, C. J. Res. Natl. Bur. Stand. 1950, 45, 255.
129. Guo, H.; Chen, R.; Xie, D. J. Theor. Comput. Chem. 2002, 1, 173-185.
130. Parlett, B. N. The Symmetric Eigenvalue Problem; Prentice Hall: Englewood Cliffs, NJ, 1980.
131. Wyatt, R. E. Adv. Chem. Phys. 1989, 73, 231-278.
132. Chen, R.; Guo, H. J. Chem. Phys. 1999, 111, 9944-9951.
133. Azzam, T.; Schinke, R.; Farantos, S. C.; Joyeux, M.; Peterson, K. A. J. Chem. Phys. 2003, 118, 9643-9652.
134. Jung, C.; Taylor, H. S.; Atilgan, E. J. Phys. Chem. A 2002, 106, 3092-3101.
135. Jung, C.; Taylor, H. S.; Sibert, E. L. J. Phys. Chem. A 2006, 110, 5317-5325.
136. Keshavamurthy, S. J. Phys. Chem. A 2001, 105, 2668-2676.
137. Semparithi, A.; Charaulatha, V.; Keshavamurthy, S. J. Chem. Phys. 2003, 118, 1146-1157.
138. Semparithi, A.; Keshavamurthy, S. Phys. Chem. Chem. Phys. 2003, 5, 5051-5062.
139. Semparithi, A.; Keshavamurthy, S. Chem Phys. Lett. 2004, 395, 327-334.
140. Laskar, J. Physica D 1993, 67, 257-281.
141. von Milczewski, J.; Uzer, T. Modern Methods for Multidimensional Dynamics Computations in Chemistry; Singapore, 1998; pp 190-200.
142. Safi, S. Z.; Losada, J. C.; Benito, R. M.; Borondo, F. J. Chem. Phys. 2008, 129, 164316.
143. Losada, J. C.; Benito, R. M.; Borondo, F. Eur. Phys. J. - Spec. Top. 2008, 165, 183-193.
144. Vela-Arevalo, L. V.; Wiggins, S. Int. J. Bifurcation Chaos 2001, 11 1359-1380.
145. Chandre, C. Wiggins, S.; Uzer, T. Physica D 2003, 181, 171-196.
146. Crawford, J. D. Rev. Mod. Phys. 1991, 63, 991-1037.
147. Farantos, S. C. Qu, Z.; Zhu, H.; Schinke, R. Int. J. Bifurcation Chaos Appl. Sci. Eng. 2006, 16, 1913-1928.
148. Founargiotakis, M.; Farantos, S. C.; Contopoulos, G.; Polymilis, C. J. Chem. Phys. 1989, 91, 1389-1402.
149. Contopoulos, G.; Farantos, S. C.; Papadaki, H.; Polymilis, C. Phys. Rev. E 1994, 50, 4399-4403.
150. Arnold, V. I. Mathematical Methods of Classical Mechanics, 2nd ed.; Springer-Verlag: New York, 1980.
151. Scheck, F. Mechanics, 1st ed.; Springer-Verlag: Berlin, Heidelberg, 1990.
152. Lichtenberg, A. J.; Liberman, M. A. Regular and Chaotic Dynamics, 2nd ed.; Springer: Berlin, 1992.
153. Birkhoff, G. D. Trans. Am. Math. Soc. 1913, 14, 14-22.
154. Gaspard, P.; Burghardt, I. Adv. Chem. Phys. 1997, 101, 491-621.
155. Yakubovich, V. A.; Starzhinskii, V. M. Linear Differential Equations With Periodic Coefficients; Krieger: Malabar, FL, 1975.
156. Farantos, S. C. Chemical Dynamics: A Periodic Orbits Approach. In Time Dependent Quantum Mechanics: Experiments and Theory; Broeckhove, J., Lathouwers, L., Eds.; 1992; pp 7-43.
157. Allgower, E. L.; Georg, K. Numerical Continuation Methods; Springer series in computational mathematics; Springer-Verlag: Berlin, 1993; Vol.13.
158. van der Meer, J.-C. The Hamiltonian Hopf Bifurcation; Springer-Verlag: New York, 1985.
159. Seydel, R. From Equilibrium to Chaos: Practical bifurcation and stability analysis; Elsevier: 1988.
160. Reithmeier, E. Periodic Solutions of Nonlinear Dynamical Systems; Lecture Notes in Mathematics; Springer-Verlag: 1991.
161. Stoer, J.; Bulirsch, R. Introduction to Numerical Analysis; Springer: New York, 1980.
162. Farantos, S. C. Comput. Phys. Commun. 1998, 108, 240-258.
163. Stamatiadis, S.; Prosmiti, R.; Farantos, S. C. Comput. Phys. Commun. 2000 127 343-355.
164. Vrahatis, M. N. J. Comput. Phys. 1995, 119, 105-119.
165. Vrahatis, M. N.; Perdiou, A. E.; Kalantonis, V. S.; Perdios, E. A.; Papadakis, K.; Prosmiti, R.; Farantos, S. C. Comput. Phys. Commun. 2001, 138, 53-68.
166. Davis, M. J. Int. Rev. Phys. Chem. 1995, 14, 15-66.
167. Guantes, R.; Nezis, A.; Farantos, S. C. J. Chem. Phys. 1999, 111, 10836-10842.
168. Bhatia, P.; Maiti, B.; Sathyamurthy, N.; Stamatiadis, S.; Farantos, S. C. Phys. Chem. Chem. Phys. 1999, 1, 1105-1113.
169. Maiti, B.; Sathyamurthy, N.; Stamatiadis, S.; Farantos, S. C. Indian J. Chem. A 2000, 39A, 338-344.
170. Founargiotakis, M.; Farantos, S. C.; Skokos, H.; Contopoulos, G. Chem. Phys. Lett. 1997, 277, 456-464.
171. Farantos, S. C. Laser Chem. 1993, 13, 87-99.
172. Farantos, S. C.; Lin, S. Y.; Guo, H. Chem. Phys. Lett. 2004, 399, 260-265.
173. Lin, S. Y.; Guo, H.; Farantos, S. C. J. Chem. Phys. 2005, 122, 124308-124311
174. Banares, L.; Aoiz, F. J.; Vázquez, S. A.; Ho, T.-S.; Rabitz, H. Chem. Phys. Lett. 2003, 374, 243-251.
175. Bussery-Honvault, B.; Honvault, P.; Launay, J.-M. J. Chem. Phys. 2001, 115, 10701-10708.
176. Weinstein, A. Inv. Math. 1973, 20, 47-57.
177. Moser, J. Commun. Pure Appl. Math. 1976, 29, 727-747.
178. Kopidakis, G.; Aubry, S. Physica D 1999, 130, 155-309.
179. 2v minima of methylene are distinct only on the plane, and they are rotated into one another when rotations are allowed.
180. Haller, E.; Koppel, H.; Cederbaum, L. S. Chem. Phys. Lett. 1983, 101, 215-220.
181. Wigner, E. P. SIAM Rev. 1967, 9, 1-23.
182. Dyson, F. J.; Mehta, M. L. J. Math. Phys. 1963, 4, 701-712.
183. Green, W. H.; Handy, N. C.; Knowles, P. J.; Carter, S. J. Chem. Phys. 1991, 94, 118-132.
184. Jacobson, M. P.; Child, M. S. J. Chem. Phys. 2001, 114, 250-261.
185. Jacobson, M. P.; Child, M. S. J. Chem. Phys. 2001, 114, 262-275.
186. Newhouse, S. E. Publ. Math. IHES 1979, 50, 101-151.
187. Borondo, F.; Zembekov, A. A.; Benito, R. M. J. Chem. Phys. 1996, 105, 5068-5081.
188. Yang, S.; Tyng, V.; Kellman, M. E. J. Phys. Chem. A 2003, 107, 8345-8354.
189. Porter, C. E.; Thomas, R. G. Phys. Rev. 1956, 104, 483-491.
190. Baer, T.; Hase, W. L. Unimolecular Reaction Dynamics, Theory and Experiments; Oxford University Press: New York, 1996.
191. Quack, M.; Troe, J. Ber. Bunsen-Ges. Phys. Chem. 1974, 78, 240-252.
192. Xu, C.; Jiang, B.; Xie, D.; Farantos, S. C.; Lin, S. Y.; Guo, H. J. Phys. Chem. A 2007, 111 (41), 10353-10361.
193. Lin, S. Y.; Xie, D.; Guo, H. J. Chem. Phys. 2006, 125, 091103.
194. Ivanov, M. V.; Grebenshchikov, S. Y.; Schinke, R. J. Chem. Phys. 2004, 120, 10015-10024.
195. Mauersberger, K.; Erbacher, B.; Krankowsky, D.; Günther, J.; Nickel, R. Science 1999, 283, 370-372.
196. Thiemens, M. H. Science 2001, 293, 226.
197. Gao, Y. Q.; Marcus, R. A. Science 2001, 293, 259-263.
198. Janssen, C.; Marcus, R. A. Science 2001, 294, 951.
199. Mauersberger, K.; Krankowsky, D.; Janssen, C.; Schinke, R. Adv. At. Mol. Opt. Phys. 2005, 50, 1-54.
200. Janssen, C.; Guenther, J.; Mauersberger, K.; Krankowsky, D. Phys. Chem. Chem. Phys. 2001, 3, 4718-4721.
201. Schinke, R.; Fleurat-Lessard, P. J. Chem. Phys. 2005, 122, 094317.
202. Schinke, R.; Grebenshchikov, S. Y.; Ivanov, M. V.; Fleurat-Lessard, P. Annu. Rev. Phys. Chem. 2006, 57, 625-661.
203. Hathorn, B. C.; Marcus, R. A. J. Chem. Phys. 1999, 111, 4087-4100.
204. Hathorn, B. C.; Marcus, R. A. J. Chem. Phys. 2000, 113, 9497-9509.
205. Miklovc, A.; Peyrimhoff, S. D. Chem. Phys. Lett. 2001, 359, 55-62.
206. Fleurat-Lessard, P.; Grebenshchikov, S. Y.; Siebert, R.; Schinke, R.; Halberstadt, N. J. Chem. Phys. 2003, 118, 610-621.
207. Houston, P. L. In Modern Trends in Chemical Dynamics; Advanced Series in Physical Chemistry; Liu, K., Yang, X., Ed.; World Scientific: Singapore, 2004; Vol.14 (part II), p 281.
208. Grebenshchikov, S. Y.; Qu, Z.; Zhu, H.; Schinke, R. Phys. Chem. Chem. Phys. 2007, 9, 2044-2060.
209. Grozdanov, T. P.; Mandelshtam, V. A.; Taylor, H. S. J. Chem. Phys. 1995, 103, 7990-7995.
210. Mandelshtam, V. A.; Taylor, H. S. J. Chem. Phys. 1997, 106, 5085-5090.
211. Ervin, K. M.; Ho, J.; Lineberger, W. C. J. Chem. Phys. 1989, 91, 5974-5992.
212. Bramley, M. J.; Handy, N. C. J. Chem. Phys. 1993, 98, 1378-1397.
213. Xu, D.; Li, G.; Xie, D.; Guo, H. Chem. Phys. Lett. 2002, 365, 480-486.
214. Xu, D.; Chen, R.; Guo, H. J. Chem. Phys. 2003, 118, 7273-7282.
215. Zou, S.; Bowman, J. M. J. Chem. Phys. 2002, 116, 6667-6673.
216. Stanton, J. F.; Gauss, J. J. Chem. Phys. 1999, 110, 1831-1832.
217. Stanton, J. F.; Gauss, J. J. Chem. Phys. 1999, 110, 6079-6080.
218. Carter, S.; Mills, I. M.; Murrell, J. N. Mol. Phys. 1980, 41, 191-203.
219. Tremblay, J. C.; Carrington, T., Jr. J. Chem. Phys. 2006, 125, 094311.
220. Lin, B.; Bian, W. J. Chem. Phys. 2008, 129, 024111.
221. Jacobson, M. P.; Jung, C.; Taylor, H. S.; Field, R. W. J. Chem. Phys. 1999, 111, 600-618.
222. Yu, J.; Wu, G. J. Chem. Phys. 2000, 113, 647-652.
223. Xu, D.; Guo, H.; Zou, S.; Bowman, J. M. Chem. Phys. Lett. 2003, 377, 582-588.
224. Tyng, V.; Kellman, M. E. J. Phys. Chem. B 2006, 110, 18859-18871.
225. Bigqood, R.; Millan, B.; Gruebele, M. Chem. Phys. Lett. 1998, 287, 333-341.
226. Chowdary, P. D.; Gruebele, M. J. Chem. Phys. 2009, 130, 1343108.
227. Bolhuis, P. G.; Dellago, C.; Chandler, D. Proc. Natl. Acad. Sci. U.S.A. 2000, 97, 5877-5882.
228. Ren, W.; Vanden-Eijnden, E.; Maragakis, P.; Weinani, E. J. Chem. Phys. 2005, 123, 134109-134112
229. Han, W.-G.; Jalkanen, K. J.; Elstner, M.; Suhai, S. J. Phys. Chem. B 1998, 102, 2587-2602.
230. Drozdov, A. N.; Grossfield, A.; Pappu, R. V. J. Am. Chem. Soc. 2004, 126, 2574-2581.
231. Farantos, S. C. CPS-IEEE Comput. Soc. 2007, 444-450.
232. Xie, A.; van der Meer, L.; Hoff, W.; Austin, R. H. Phys. Rev. Lett. 2000, 84, 5435-5438.
233. Gruebele, M. Annu. Rev. Phys. Chem. 1999, 50, 485-516.
234. Gruebele, M. Adv. Chem. Phys. 2000, 5F1, 193.
235. Woutersen, S.; Mu, Y. G. S.; Hamm, P. Proc. Natl. Acad. Sci. U.S.A. 2001, 98, 11254-11258.
236. Herman, M.; Lievin, J.; Auwera, J. V.; Campargue, A. Adv. Chem. Phys. 1999, 108, 1-431.
237. Fermi, E.; Pasta, J.; Ulam, S. Document LA-1940, May 1955, 978-988.
238. Ford, J. Phys. Rep. 1992, 213, 271-310.
239. Campbell, D. K.; Rosenau, P.; Zaslavsky, G. M. Chaos 2005, 15, 015101-015121.
240. Huang, S.; Chandre, C.; Uzer, T. J. Chem. Phys. 2008, 128, 174105.
241. Li, C.; Toda, M.; Komatsuzaki, T. J. Chem. Phys. 2009, 130, 1241167.
242. Keshavamurthy, S. Int. Rev. Phys. Chem. 2007, 26, 521-584.