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A threshold study of the classical dynamics of collision‐induced dissociation in collinear H+H2
1.For leading references to earlier work see the chapters by P. J. Kuntz and D. J. Diestler in Atom‐Molecule Collision Theory, edited by R. B. Bernstein (Plenum, New York, 1979).
2.(a) A. J. Kaye and A. Kuppermann, J. Chem. Phys. 84, 1463 (1986);
2.(b) A. J. Kaye and A. Kuppermann, Chem. Phys. Lett. 115, 158 (1985).
3.(a) C. Leforestier, Chem. Phys. Lett. 125, 373 (1986);
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3.(c) C. Leforestier, Chem. Phys. Lett. 87, 241 (1984); , Chem. Phys. Lett.
3.(d) C. Leforestier, B. Bergeron, and P. C. Hiberty, Chem. Phys. Lett. 84, 385 (1981).
4.J. A. Kaye and A. Kuppermann, Chem. Phys. Lett. 78, 546 (1981);
4.(b) J. Manz and J. Romelt, Chem. Phys. Lett. 77, 172 (1981); , Chem. Phys. Lett.
4.(c) G. Hauke, J. Manz, and J. Romelt, J. Chem. Phys. 73, 5040 (1980).
5.J. E. Dove, M. E. Mandy, N. Sathyamurthy, and T. Joseph, Chem. Phys. Lett. 127, 1 (1986).
6.J. C. Gray, G. A. Fraser, and D. G. Truhlar, Chem. Phys. Lett. 68, 359 (1979).
7.P. M. Hunt and M. S. Child, J. Phys. Chem. 86, 1116 (1982).
8.B. K. Andrews and W. J. Chesnavich, Chem. Phys. Lett. 104, 24 (1984).
9.K. G. Tan, K. J. Laidler, and J. S. Wright, J. Chem. Phys. 67, 5883 (1977), and references therein.
10.E. Pollak, M. S. Child, and P. Pechukas, J. Chem. Phys. 72, 1669 (1980), and references therein.
11.P. Pechukas, Annu. Rev. Phys. Chem. 32, 159 (1981), and references therein.
12.D. G. Truhlar and B. C. Garrett, Annu. Rev. Phys. Chem. 35, 159 (1984), and references therein.
13.E. Pollak in Molecular Structure and Dynamics, edited by M. Balaban (International Sciences, Glenside, PA, 1979), and references therein.
14.W. J. Chesnavich and M. T. Bowers, Prog. React. Kinetics 11, 137 (1982), and references therein.
15.D. G. Truhlar, W. L. Hase, and J. T. Hynes, J. Phys. Chem. 87, 2664 (1983), and references therein.
16.E. Pollak, J. Phys. Chem. 90, 3619 (1986), and references therein.
17.W. J. Chesnavich, J. Chem. Phys. 77, 2988 (1982).
18.R. N. Porter and M. Karplus, J. Chem. Phys. 40, 1105 (1964).
19.M. E. Grice and W. J. Chesnavich (unpublished results).
20.(a) See, e.g., M. S. Child in Semiclassical Methods in Molecular Scattering and Spectroscopy, edited by M. S. Child (Reidel, Boston, 1980), pp. 155–177. Note that we have used the pure classical rather than the quasiclassi‐cal definition of the action except that we have divided the phase integral by Planck’s constant;.
20.(b) E. Pollak in Theory of Recaction Dynamics, edited by M. Baer (Chemical Rubber, Cleveland, 1985). In compressing the bands Pollak changed only the sign Nevertheless, the interpretation is identical to that given here. Also, note that the bands studied by Pollak spiral counterclockwise, whereas those reported here spiral clockwise. However, by applying Eqs. (3)–(6) to a Morse oscillator, one finds that for a trajectory of vibrational energy the distance it must travel along x to undergo one vibrational period is directly proportional to Clearly, as increases, for whereas for Therefore, even though the trajectories spiral in opposite directions, the surfaces must be moved in the same direction in order to compress the bands.
21.In Fig. 11 of Ref. 2(a) Kaye and Kuppermann illustrate what appears to be three sets of bands. Since the two very narrow sets correspond to the long and narrow lower tip of the set which originates in the upper right hand corner of Fig. 5 of Ref. 2(a), it is not clear to us whether the narrow sets in Fig. 11 are actually distinct sets or are two cuts through the same single set.
22.It should be noted that the left‐hand side of the dissociative main band actually gets narrower as n increases. However, for any given n the left‐hand side is two or more orders of magnitude narrower than the right‐hand side. Hence, the behavior of the right‐hand side dominates.
23.We use the word snarled for trajectories that oscillate many times in the interaction region before exiting. This should not be confused with the use of the word “chattering” by Kaye and Kuppermann to describe trajectories for which very small changes in initial conditions lead to very large changes in final state. Indeed, as is discussed in the text, Kaye and Kuppermann note that although chattering regions typically imply snarled trajectories at energies below the dissociation threshold, this correlation does not necessarily hold above the dissociation threshold.
24.Since only one equipotential exists on the PK2 surface for there are no periodic trajectories of the first kind for
25.See also the trajectories plotted in Ref. 8.
26.Kaye and Kuppermann also found that for their model system trajectories cross the symmetric stretch line no more than three times.
27.If square well attractive potentials are added to the model system, all of the features of the trajectory in Fig. 13(a) can be approximated quite nicely.
28.W. J. Chesnavich (unpublished results).
29.S. K. Gray, S. A. Rice, and M. J. Davis, J. Phys. Chem. 90, 3470 (1986), and references therein.
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