Classical dynamical analysis of the vibrational spectra for small polyatomic molecules
S. C. Farantos
Department of Chemistry, University of Southern California, Los Angeles, California 90089-0482
Department of Chemistry, University of Crete, and Institute of Electronic Structure and Laser, FORTH, Iraklion, Crete 711 10, Greece.
Search for more papers by this authorJ. M. Gomez Llorente
Department of Chemistry, University of Southern California, Los Angeles, California 90089-0482
Search for more papers by this authorO. Hahn
Department of Chemistry, University of Southern California, Los Angeles, California 90089-0482
Search for more papers by this authorH. S. Taylor
Department of Chemistry, University of Southern California, Los Angeles, California 90089-0482
Search for more papers by this authorS. C. Farantos
Department of Chemistry, University of Southern California, Los Angeles, California 90089-0482
Department of Chemistry, University of Crete, and Institute of Electronic Structure and Laser, FORTH, Iraklion, Crete 711 10, Greece.
Search for more papers by this authorJ. M. Gomez Llorente
Department of Chemistry, University of Southern California, Los Angeles, California 90089-0482
Search for more papers by this authorO. Hahn
Department of Chemistry, University of Southern California, Los Angeles, California 90089-0482
Search for more papers by this authorH. S. Taylor
Department of Chemistry, University of Southern California, Los Angeles, California 90089-0482
Search for more papers by this authorAbstract
With the study of three specific molecules, Na3(C2E″), HCN(X1Σ+), and O3(D1B2), each showing a distinctly different dynamical behavior at the energies studied, we show how techniques of nonlinear classical mechanics can be applied to simulate low resolution vibrational spectra and to extract the underlying dynamics from them. Particularly the importance of the single unstable periodic orbits in the chaotic regions of phase space is demonstrated.
Bibliography
- 1 I. C. Percival, Adv. Chem. Phys. 36, 1 (1977).
- 2
S. C. Farantos, and
J. Tennyson, in
Stochasticity and Intramolecular Redistribution of Energy
R. Lefevbre and
S. Mukamel, Eds.
(Reidel, Dordrecht,
1987),
pp. 15–30.
10.1007/978-94-009-3837-3_2 Google Scholar
- 3 O. Bohigas, M.-J. Giannoni, and C. Schmidt, in Quantum Chaos and Nuclear Statistical Physics, Lecture Notes in Physics T. H. Seligman and H. Nishioka, Eds. (Springer-Verlag, Berlin, 1986), Vol. 263.
- 4 A. Holle, G. Wiebusch, J. Main, B. Hager, H. Rottke, and K. H. Welge, Phys. Rev. Lett. 56, 2594 (1986).
- 5 E. Abramson, R. W. Field, D. Imre, K. K. Innes, and J. L. Kinsey, J. Chem. Phys. 83, 453 (1985).
- 6 A. Carrington and R. A. Kennedy, J. Chem. Phys. 81, 91 (1984).
- 7 M. Broyer, G. Delacretaz, G.-Q. Ni, R. L. Whetten, J.-P. Wolf, and L. Wöste, Phys. Rev. Lett. 62, 2100 (1989).
- 8 D. Wintgen and H. Friedrich, Phys. Rev. A 36, 131 (1987).
- 9 J. M. Gomez Llorente and E. Pollak, J. Chem. Phys. 90, 5406 (1989).
- 10 J. M. Gomez Llorente, H. S. Taylor, and E. Pollak, Phys. Rev. Lett. 62, 2096 (1989).
- 11 J. M. Gomez Llorente and H. S. Taylor, J. Chem. Phys. 91, 953 (1989).
- 12 S. C. Farantos and J. Tennyson, J. Chem. Phys. 84, 6210 (1986).
- 13 E. J. Heller, Acc. Chem. Res. 14, 368 (1981).
- 14 M. Baranger, Phys. Rev. 111, 481 (1958).
- 15 S. C. Farantos, J. M. Gomez Llorente, O. Hahn, and H. S. Taylor, Chem. Phys. Lett. 166, 71 (1990).
- 16 R. S. MacKay, J. D. Meiss, and I. C. Percival, Physica D 13, 155 (1984).
- 17 D. Bensimon and L. P. Kadanoff, Physica D 13, 821 (1984).
- 18 R. S. MacKay, J. D. Meiss, and I. C. Percival, Physica D 27, 1 (1987).
- 19 E. J. Heller and M. J. Davis, J. Phys. Chem. 84, 1999 (1980).
- 20 M. Founargiotakis, S. C. Farantos, G. Contopoulos, and C. Polymilis, J. Chem. Phys. 91, 1389 (1989).
- 21 S. C. Farantos, M. Founargiotakis, and C. Polymilis, Chem. Phys. 135, 347 (1989).
- 22 S. C. Farantos and M. Founargiotakis, Chem. Phys. 142, 345 (1990).
- 23 V. I. Arnold, Graduate Text in Mathematics (Springer-Verlag, Berlin, 1980), Vol. 60.
- 24 T. C. Thompson, G. Izmirlian, Jr., S. J. Lemon, D. G. Truhlar, and C. A. Mead, J. Chem. Phys. 82, 5597 (1985).
- 25 R. S. Dumont and P. Brumer, J. Chem. Phys. 88, 1481 (1988).
- 26 J. M. Gomez Llorente and E. Pollak, J. Chem. Phys. 90, 5406 (1989).
- 27 A. P. Baronavski, Chem. Phys. Lett. 61, 532 (1979).
- 28 X. Yang, C. A. Rogaski, and A. M. Wodtke, J. Chem. Phys. 92, 2111 (1990).
- 29 X. Yang, C. A. Ragashi, and A. M. Wodtke, J. Opt. Soc. Am. B, to appear.
- 30 S. L. Coy, W. Klemperer, A. M. Smith, and K. K. Lehmann, J. Mol. Spectrosc. 134, 134 (1989).
- 31 M. Founargiotakis, S. C. Farantos, and J. Tennyson, J. Chem. Phys. 88, 1598 (1988).
- 32 Z. Bacic and J. C. Light, J. Chem. Phys. 86, 3065 (1987).
- 33 J. C. Light and Z. Bacic, J. CHem. Phys. 87, 4008 (1987).
- 34 T. A. Holme and Hutchinson, J. Chem. Phys. 83, 2860 (1985).
- 35 Z. Bacic, R. B. Gerber, and M. A. Ratner, J. Phys. Chem. 90, 3605 (1986).
- 36 M. Peric, M. Mladenovic, S. D. Peyrimhoff, and R. J. Buenker, Chem. Phys. 82, 317 (1983).
- 37 M. Peric, M. Mladenovic, S. D. Peyrimhoff, and R. J. Buenker, Chem. Phys. 86, 85 (1984).
- 38 R. S. Smith, R. B. Shirts, and C. W. Patterson, J. Chem. Phys. 86, 4452 (1987).
- 39 J. A. Bentley, J.-P. Brunet, R. E. Wyatt, R. A. Friesner, and C. Leforestier, Chem. Phys. Lett. 161, 393 (1989).
- 40 R. E. Wyatt, in J. O. Hirschfelder, R. E. Wyatt, and R. D. Coallson, Eds., Laser, Molecules, and Methods (Wiley, New York, 1989), p. 231.
- 41 J. N. Murrell, S. Carter, and L. O. Halonen, J. Mol. Spectrosc. 93, 307 (1982).
- 42 S. C. Farantos, J. M. Gomez Llorente, O. Hahn, and H. S. Taylor, J. Chem. Phys., to appear.
- 43 P. J. Hay, R. T. Pack, R. B. Walker, and E. J. Heller, J. Phys. Chem. 86, 862 (1982).
- 44 M. G. Sheppard and R. B. Walker, J. Chem. Phys. 78, 7191 (1983).
- 45 D. E. Freeman, K. Yoshino, J. R. Esmond, and W. H. Parkinson, Planet. Space Sci. 32, 239 (1984).
- 46 O. Atabek, M. T. Bourgeois, and M. Jacon, J. Chem. Phys. 84, 6699 (1986).
- 47 B. R. Johnson and J. L. Kinsey, J. Chem. Phys. 87, 1525 (1987).
- 48 D. Chasman, D. J. Tannor, and D. G. Imre, J. Chem. Phys. 89, 6667 (1988).
- 49 B. R. Johnson and J. L. Kinsey, J. Chem. Phys. 91, 7638 (1989).
- 50 F. Le Quéré and C. Leforestier, J. Chem. Phys. 92, 247 (1990).
- 51 D. Kosloff and R. Kosloff, J. Comput. Phys. 52, 35 (1983).
- 52 M. D. Feit, J. A. Fleck, and A. Steiger, J. Comput. Phys. 47, 412 (1982).
- 53 C. Lanczos, J. Res. Natl. Bur. Stand. 45, 255 (1950).