No data available.
Please log in to see this content.
You have no subscription access to this content.
No metrics data to plot.
The attempt to load metrics for this article has failed.
The attempt to plot a graph for these metrics has failed.
Statistical dynamical theory of isomerization
1.(a) R. A. Marcus and O. K. Rice, J. Phys. Coll. Chem. 55, 894 (1951);
1.S. Gladstone, K. J. Laidler, and H. Eyring, The Theory of Rate Processes (McGraw‐Hill, New York, 1941);
1.P. Pechukas, in Dynamics of Molecular Collisions, Part B, edited by W. H. Miller (Plenum, New York, 1976);
1.(b) for a recent review, see B. J. Berne, M. Borkevec, and J. E. Straub, J. Phys. Chem. 92, 3711 (1988).
2.See, for example, W. L. Hase, in Dynamics of Molecular Collisions, Part B, edited by W. H. Miller (Plenum, New York, 1976);
2.D. M. Wardlaw and R. A. Marcus, Chem. Phys. Lett. 110, 230 (1984);
2.D. G. Trulhar, W. L. Hase, and J. T. Hynes, J. Phys. Chem. 87, 2664 (1983).
3.See, for example, N. DeLeon and B. J. Berne, J. Chem. Phys. 75, 3495 (1981);
3.R. J. Wolf and W. L. Hase, J. Chem. Phys. 72, 316 (1980)., J. Chem. Phys.
4.M. J. Davis, J. Chem. Phys. 83, 1016 (1985);
4.M. J. Davis and S. K. Gray, J. Chem. Phys. 84, 5389 (1986); , J. Chem. Phys.
4.S. K. Gray, S. A. Rice, and M. J. Davis, J. Phys. Chem. 90, 3470 (1986);
4.S. K. Gray and S. A. Rice, J. Chem. Phys. 86, 2020 (1987).
5.(a) R. S. Dumont and P. Brumer, J. Phys. Chem. 90, 3509 (1986);
5.(b) see also Ref. 2.
6.I. Hamilton and P. Brumer, J. Chem. Phys. 82, 1937 (1985).
6.For applications to bimolecular reactions, see J. W. Duff and P. Brumer, J. Chem. Phys. 71, 3895 (1979), and references therein.
7.For example, bottleneck analyses are currently based on surface of section techniques. The quantitative components of this methodology are so far restricted to two degree‐of‐freedom systems. Divergence, on the other hand, can be calculated for any conservative, deterministic dynamical system.
8.(a) R. S. Dumont and P. Brumer (to be published); and Ref. 5(a);
8.(b) R. S. Dumont, Ph.D. dissertation, University of Toronto, 1987.
9.J. E. Straub and B. J. Berne, J. Chem. Phys. 83, 1138 (1985);
9.J. E. Straub, D. A. Hsu, and B. J. Berne, J. Phys. Chem. 89, 5188 (1985). See also Ref. 1(b) and J. E. Straub, Ph.D. dissertation, Columbia University, 1987.
10.V. I. Arnold and A. Avez, Ergodic Problems of Classical Mechanics (Benjamin, New York, 1968).
11.E. Thiele, J. Chem. Phys. 36, 1466 (1962).
11.See also R. S. Dumont and P. Brumer, J. Chem. Phys. 90, 96 (1989) for the decomposition of unimolecular decay dynamics.
12.Many dynamics studies of unimolecular reactions utilize more general nonequilibrium initial ensembles. See, for example, W. L. Hase, R. J. Duchovic, K. N. Swamy, and R. J. Wolf, J. Chem. Phys. 80, 714 (1984);
12.R. W. Numrich and K. G. Kay, J. Chem. Phys. 70, 4343 (1979); and Ref. 4. We choose to study the pseudoequilibrium initial ensemble, described in Sec. II A, because it is the natural prototype. Also, note that the application of statistical theories to describe results obtained from other nonequilibrium initial ensembles assumes the existence of strong relaxation mechanisms which make the nonequilibrium ensembles behave just like the pseudo‐equilibrium ensemble of the current study. Thus, statistical theories primarily treat the behavior of pseudoequilibrium initial ensembles., J. Chem. Phys.
13.(a) T. Yamamoto, J. Chem. Phys. 33, 281 (1960);
13.J. C. Keck, Adv. Chem. Phys. 13, 85 (1967);
13.J. B. Anderson, J. Chem. Phys. 58, 4684 (1973);
13.H. Bennett, in Algorithms for Chemical Computation, edited by R. E. Christofferson (American Chemical Society, Washington, 1977);
13.(b) D. Chandler, J. Chem. Phys. 68, 2959 (1978);
13.J. Montgomery, D. Chandler, and B. J. Berne, J. Chem. Phys. 70, 4056 (1979)., J. Chem. Phys.
14.This terminology originates in statistical unimolecular decay theory. See Ref. 8.
15.A form of the ABM/DLGM has already been applied to the decay of an open stadium billiard [see Ref. 8(b)]. There, the model was used in conjunction with a decay mechanism involving competition with an isomerization process.
16.The “divergence” method of partitioning A into direct and strong collision components is described in the Appendix.
17.Each of these subgap distributions is a bona fide gap time probability distribution: is the distribution of gap times associated with trajectories initiated on that part of which crosses the gap to before a divergence threshold is exceeded (see the Appendix); is associated with the remainder of
18.The Siamese stadium billiard isomerization dynamics was previously studied by N. De Leon and B. J. Berne, Chem. Phys. Lett. 93, 162 (1982).
19.D. R. Cox, Renewal Theory (Methuen, London, 1962).
20.The application of the FRM to more chemically interesting isomerization problems is currently underway. This follow‐up study will focus more closely on accurate and efficient means of estimating rate constants. A generalization of the FRM to unimolecular reactions with competing isomerizations and decompositions has recently been developed [see R. S. Dumont, J. Chem. Phys. (in press)]. This new theory can provide a simple rate constant estimate, but it deals with a modified form of the rate constant.
21.In fact, the Siamese stadium billiard is a K system; i.e., it has an infinitely degenerate Lebesgue spectrum and a nonzero K entropy. For the definition of the K property, see Ref. 10. The K property of the Siamese stadium is essentially proven in Ref. 22.
22.L. A. Bunimovich, Funkt. Analiz. Jeg. Prilog. 8, 73 (1974)
22.[L. A. Bunimovich, Funct. Anal. Appl. 8, 254 (1974)].
23.G. Bennettin and J.‐M. Strelcyn, Phys. Rev. A 17, 773 (1978).
24.V. I. Oseledets, Trans. Moscow Math. Soc. 19, 197 (1968).
24.See also, P. Walters, An Introduction to Ergodic Theory (Springer‐Verlag, New York, 1982), p. 233.
25.This mean growth rate is just the Lyapunov exponent.
26.R. S. Dumont and P. Brumer, J. Chem. Phys. 87, 6437 (1987).
Article metrics loading...
Full text loading...
Most read this month
Most cited this month