Index k saddles and dividing surfaces in phase space with applications to isomerization dynamics

Journal of Chemical Physics

Volumn 134, Issue 24, 2011, Pages

  Collins, Peter ^a   Ezra, Gregory S ^b   Wiggins, Stephen ^a  

^a UNIVERSITY OF BRISTOL   (United Kingdom)

^b Cornell University ^*  (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BATH MODES; CODIMENSION; DIVIDING SURFACES; ENERGY INDEXES; ENERGY SHELLS; EXPLICIT FORMULA; IN-PHASE; INITIAL CONDITIONS; INTEGRALS OF MOTION; LOW ENERGIES; NON-RESONANCES; NORMAL FORM; PARAMETRIZATIONS; PHASE SPACE GEOMETRY; POINCARE; SADDLE DYNAMICS; SYMBOLIC DESCRIPTION;

ISOMERIZATION; ISOMERS; NUMERICAL METHODS; PHASE SPACE METHODS; POTENTIAL ENERGY; POTENTIAL ENERGY SURFACES; QUANTUM CHEMISTRY; TRAJECTORIES;

DYNAMICS;

EID: 79960157573     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.3602465     Document Type: Article

References (83)

1. E. P. Wigner, Trans. Faraday Soc. 34, 29 (1938). 10.1039/tf9383400029
2. J. C. Keck, Adv. Chem. Phys. XIII, 85 (1967). 10.1002/SERIES2007
3. P. Pechukas, Ann. Rev. Phys. Chem. 32, 159 (1981). 10.1146/annurev.pc.32. 100181.001111
4. D. G. Truhlar, W. L. Hase, and J. T. Hynes, J. Phys. Chem. 87, 2664 (1983). 10.1021/j100238a003
5. J. B. Anderson, Adv. Chem. Phys. XCI, 381 (1995). 10.1002/SERIES2007
6. D. G. Truhlar, B. C. Garrett, and S. J. Klippenstein, J. Phys. Chem. 100, 12771 (1996). 10.1021/jp953748q
7. j has n nonzero eigenvalues. The index of the critical point is the number of negative eigenvalues.
8. P. G. Mezey, Potential Energy Hypersurfaces (Elsevier, Amsterdam, 1987).
9. D. J. Wales, Energy Landscapes (Cambridge University Press, Cambridge, 2003).
10. S. Wiggins, Physica D 44, 471 (1990). 10.1016/0167-2789(90)90159-M
11. S. Wiggins, L. Wiesenfeld, C. Jaffe, and T. Uzer, Phys. Rev. Lett. 86 (24), 5478 (2001). 10.1103/PhysRevLett.86.5478 (Pubitemid 32548945)
12. T. Uzer, C. Jaffe, J. Palacian, P. Yanguas, and S. Wiggins, Nonlinearity 15, 957 (2002). 10.1088/0951-7715/15/4/301 (Pubitemid 37026639)
13. H. Waalkens, A. Burbanks, and S. Wiggins, J. Phys. A 37, L257 (2004). 10.1088/0305-4470/37/24/L04 (Pubitemid 38846243)
14. H. Waalkens and S. Wiggins, J. Phys. A 37, L435 (2004). 10.1088/0305-4470/37/35/L02 (Pubitemid 39234020)
15. H. Waalkens, A. Burbanks, and S. Wiggins, J. Chem. Phys. 121 (13), 6207 (2004). 10.1063/1.1789891
16. H. Waalkens, A. Burbanks, and S. Wiggins, Phys. Rev. Lett. 95, 084301 (2005). 10.1103/PhysRevLett.95.084301 (Pubitemid 41505931)
17. H. Waalkens, A. Burbanks, and S. Wiggins, J. Phys. A 38, L759 (2005). 10.1088/0305-4470/38/45/L03 (Pubitemid 41551374)
18. R. Schubert, H. Waalkens, and S. Wiggins, Phys. Rev. Lett. 96, 218302 (2006). 10.1103/PhysRevLett.96.218302 (Pubitemid 43838407)
19. H. Waalkens, R. Schubert, and S. Wiggins, Nonlinearity 21 (1), R1 (2008). 10.1088/0951-7715/21/1/R01
20. R. S. MacKay, Phys. Lett. A 145, 425 (1990). 10.1016/0375-9601(90)90306-9
21. T. Komatsuzaki and R. S. Berry, J. Mol. Struct.: THEOCHEM 506, 55 (2000). 10.1016/S0166-1280(00)00402-4
22. T. Komatsuzaki and R. S. Berry, Adv. Chem. Phys. 123, 79 (2002). 10.1002/0471231509
23. L. Wiesenfeld, A. Faure, and T. Johann, J. Phys. B 36, 1319 (2003). 10.1088/0953-4075/36/7/304
24. L. Wiesenfeld, J. Phys. A 37, L143 (2004). 10.1088/0305-4470/37/12/L04 (Pubitemid 38483033)
25. L. Wiesenfeld, Few-Body Syst. 34, 163 (2004). 10.1007/s00601-004-0050-6
26. T. Komatsuzaki, K. Hoshino, and Y. Matsunaga, Adv. Chem. Phys. B 130, 257 (2005). 10.1002/0471712531
27. C. Jaffé, S. Kawai, J. Palacian, P. Yanguas, and T. Uzer, Adv. Chem. Phys. A 130, 171 (2005). 10.1002/0471712531.ch3
28. L. Wiesenfeld, Adv. Chem. Phys. A 130, 217 (2005). 10.1002/0471712531
29. F. Gabern, W. S. Koon, J. E. Marsden, and S. D. Ross, Physica D 211, 391 (2005). 10.1016/j.physd.2005.09.008 (Pubitemid 41550122)
30. F. Gabern, W. S. Koon, J. E. Marsden, and S. D. Ross, Few-Body Syst. 38, 167 (2006). 10.1007/s00601-005-0136-9 (Pubitemid 43952686)
31. A. Shojiguchi, C. B. Li, T. Komatsuzaki, and M. Toda, Commun. Nonlinear Sci. Numer. Simul. 13, 857 (2008). 10.1016/j.cnsns.2006.08.002 (Pubitemid 350131502)
32. G. S. Ezra and S. Wiggins, J. Phys. A 42, 205101 (2009). 10.1088/1751-8113/42/20/205101
33. G. Haller, J. Palacian, P. Yanguas, T. Uzer, and C. Jaffé, Commun. Nonlinear Sci. Numer. Simul. 15, 48 (2010). 10.1016/j.cnsns.2009.04.034
34. G. Haller, T. Uzer, J. Palacian, P. Yanguas, and C. Jaffé, Nonlinearity 24, 527 (2011). 10.1088/0951-7715/24/2/007
35. M. Toda, Adv. Chem. Phys. A 130, 337 (2005). 10.1002/0471712531
36. M. Toda, AIP Conf. Proc. 1076, 245 (2008). 10.1063/1.3046261
37. H. Teramoto, M. Toda, and T. Komatsuzaki, Phys. Rev. Lett. 106, 054101 (2011). 10.1103/PhysRevLett.106.054101
38. Without loss of generality, throughout this paper the equilibrium point considered will be located at the origin with zero energy.
39. D. Heidrich and W. Quapp, Theor. Chim. Acta 70, 89 (1986). 10.1007/BF00532206
40. J. N. Murrell and K. J. Laidler, Trans. Faraday Soc. 64, 371 (1968). 10.1039/tf9686400371
41. R. M. Minyaev, J. Struct. Chem. 32, 559 (1991). 10.1007/BF00753040
42. R. M. Minyaev and E. A. Lepin, Russ. J. Phys. Chem. 71, 1449 (1997). 10.1070/MC1997v007n02ABEH000717
43. V. S. Bryantsev, T. K. Firman, and B. P. Hay, J. Phys. Chem. A 109, 832 (2005). 10.1021/jp0457287 (Pubitemid 40213224)
44. S. Fau and G. Frenking, Theochem J. Mol. Struct. 338, 117 (1995). 10.1016/0166-1280(94)04053-U
45. B. K. Carpenter, in Reactive Intermediate Chemistry, edited by, R. A. Moss, M. S. Platz, and, M. Jones Jr., (Wiley, New York, 2004), pp. 925-960.
46. D. M. Bachrach, Computational Organic Chemistry (Wiley Interscience, New York, 2007).
47. S. O. Meroueh, Y. F. Wang, and W. L. Hase, J. Phys. Chem. A 106, 9983 (2002). 10.1021/jp020664q (Pubitemid 35410172)
48. A. Cavagna, I. Giardini, and G. Parisi, J. Phys. A 34, 5317 (2001). 10.1088/0305-4470/34/26/302
49. A. Cavagna, Europhys. Lett. 53, 490 (2001). 10.1209/epl/i2001-00179-4
50. J. P.K. Doye and D. J. Wales, J. Chem. Phys. 116, 3777 (2002). 10.1063/1.1436470
51. D. J. Wales and J. P.K. Doye, J. Chem. Phys. 119, 12409 (2003). 10.1063/1.1625644
52. L. Angelini, G. Ruocco, and F. Zamponi, J. Chem. Phys. 118, 8301 (2003). 10.1063/1.1565996
53. M. S. Shell, P. G. Debenedetti, and A. Z. Panagiotopoulos, Phys. Rev. Lett. 92, 035506 (2004). 10.1103/PhysRevLett.92.035506
54. T. S. Grigera, J. Chem. Phys. 124, 064502 (2006). 10.1063/1.2151899 (Pubitemid 43248028)
55. D. Coslovich and G. Pastore, J. Chem. Phys. 127, 124505 (2007). 10.1063/1.2773720 (Pubitemid 47505204)
56. L. Angelini, G. Ruocco, and F. Zamponi, Phys. Rev. E 77, 052101 (2008). 10.1103/PhysRevE.77.052101 (Pubitemid 351705635)
57. M. Kastner, Rev. Mod. Phys. 80, 167 (2008). 10.1103/RevModPhys.80.167
58. D. J. Mann and W. L. Hase, J. Am. Chem. Soc. 124, 3208 (2002). 10.1021/ja017343x (Pubitemid 34272283)
59. L. P. Sun, K. Y. Song, and W. L. Hase, Science 296, 875 (2002). 10.1126/science.1068053 (Pubitemid 34464886)
60. S. L. Debbert, B. K. Carpenter, D. A. Hrovat, and W. T. Borden, J. Am. Chem. Soc. 124, 7896 (2002). 10.1021/ja026232a (Pubitemid 34755499)
61. S. C. Ammal, H. Yamataka, M. Aida, and M. Dupuis, Science 299, 1555 (2003). 10.1126/science.1079491 (Pubitemid 36297700)
62. J. G. Lopez, G. Vayner, U. Lourderaj, S. V. Addepalli, S. Kato, W. A. Dejong, T. L. Windus, and W. L. Hase, J. Am. Chem. Soc. 129, 9976 (2007). 10.1021/ja0717360 (Pubitemid 47257783)
63. U. Lourderaj, K. Park, and W. L. Hase, Int. Rev. Phys. Chem. 27, 361 (2008). 10.1080/01442350802045446
64. D. Townsend, S. A. Lahankar, S. K. Lee, S. D. Chambreau, A. G. Suits, X. Zhang, J. Rheinecker, L. B. Harding, and J. M. Bowman, Science 306, 1158 (2004). 10.1126/science.1104386 (Pubitemid 39488989)
65. J. M. Bowman, Proc. Natl. Acad. Sci. U.S.A. 103, 16061 (2006). 10.1073/pnas.0607810103 (Pubitemid 44715150)
66. B. C. Shepler, B. J. Braams, and J. M. Bowman, J. Phys. Chem. A 111, 8282 (2007). 10.1021/jp074646q (Pubitemid 47387978)
67. B. C. Shepler, B. J. Braams, and J. M. Bowman, J. Phys. Chem. A 112, 9344 (2008). 10.1021/jp802331t
68. A. G. Suits, Acc. Chem. Res. 41, 873 (2008). 10.1021/ar8000734
69. B. R. Heazlewood, M. J. T. Jordan, S. H. Kable, T. M. Selby, D. L. Osborn, B. C. Shepler, B. J. Braams, and J. M. Bowman, Proc. Natl. Acad. Sci. U.S.A. 105, 12719 (2008). 10.1073/pnas.0802769105
70. K. D. Ball, R. S. Berry, R. E. Kunz, F. Y. Li, A. Proykova, and D. J. Wales, Science 271, 963 (1996). 10.1126/science.271.5251.963
71. R. S. Berry, Int. J. Quantum Chem. 58, 657 (1996). 10.1002/(SICI)1097- 461X(1996)58:6657::AID-QUA83.0.CO;2-X
72. N. Shida, Adv. Chem. Phys. B 130, 129 (2005). 10.1002/0471712531
73. B. Eckhardt and K. Sacha, Europhys. Lett. 56, 651 (2001). 10.1209/epl/i2001-00570-7
74. K. Sacha and B. Eckhardt, Phys. Rev. A 63, 043414 (2001). 10.1103/PhysRevA.63.043414 (Pubitemid 33722210)
75. B. Eckhardt and K. Sacha, J. Phys. B 39, 3865 (2006). 10.1088/0953-4075/39/18/016 (Pubitemid 44403624)
76. C. N. Nguyen and R. M. Stratt, J. Chem. Phys. 133, 124503 (2010). 10.1063/1.3481655
77. S. Wiggins, Normally Hyperbolic Invariant Manifolds in Dynamical Systems (Springer-Verlag, New York, 1994).
78. H. Waalkens, A. Burbanks, and S. Wiggins, Mon. Not. R. Astron. Soc. 361, 763 (2005). 10.1111/j.1365-2966.2005.09237.x (Pubitemid 41180129)
79. H. Waalkens and S. Wiggins, Regular Chaotic Dyn. 15 (1), 1 (2010). 10.1134/S1560354710010016
80. S. K. Gray and S. A. Rice, J. Chem. Phys. 86, 2020 (1987). 10.1063/1.452152
81. S. A. Rice and M. S. Zhao, Int. J. Quantum Chem. 58, 593 (1996). 10.1002/(SICI)1097-461X(1996)58:6593::AID-QUA53.0.CO;2-T
82. H. Teramoto and T. Komatsuzaki, J. Chem. Phys. 129, 094302 (2008). 10.1063/1.2973639
83. H. Teramoto and T. Komatsuzaki, Phys. Rev. E 78, 017202 (2008). 10.1103/PhysRevE.78.017202