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Nonstatistical inversion dynamics of T‐shaped Ar3
1.(a) R. S. Dumont and P. Brumer, J. Phys. Chem. 90, 3509 (1986);
1.(b) R. S. Dumont and P. Brumer, Chem. Phys. Lett. 188, 565 (1992);
1.(c) R. S. Dumont, J. Chem. Phys. 91, 4679 (1989);
1.(d) R. S. Dumont, 91, 6839 (1989)., J. Chem. Phys.
2.See W. L. Hase, in Dynamics of Molecular Collisions, Part B, edited by W. H. Miller, (Plenum, New York, 1976) for an introduction to statistical theories of unimolecular reactions.
3.Zero angular momentum in three dimensions, has been shown to possess dynamical characteristics typical of chaos. See T. L. Beck, D. M. Leitner, and R. S. Berry, J. Chem. Phys. 89, 1681 (1988).
4.The nonstatisticality of chaotic T-shaped contrasts recent claims of a strict connection between chaos and statistical unimolecular decay. See W. Bauer and G. F. Bertsch, Phys. Rev. Lett. 65, 2213 (1990).
5.J. E. Straub and B. J. Berne, J. Chem. Phys. 83, 1138 (1985);
5.J. E. Straub, D. A. Hsu, and B. J. Berne, J. Phys. Chem. 89, 5188 (1985).
6.M. J. Davis, J. Chem. Phys. 83, 1016 (1985);
6.M. J. Davis and S. K. Gray, J. Chem. Phys. 84, 5389 (1986); , J. Chem. Phys.
6.S. K. Gray, S. A. Rice, and M. J. Davis, J. Phys. Chem. 90, 3470 (1986).
6.The role of phase space bottlenecks, in the context of isomerization, is described in S. K. Gray and S. A. Rice, J. Chem. Phys. 86, 2020 (1987).
7.In variational transition state theory, one treats recrossing by systematically varying a configuration space dividing surface to achieve minimum flux. See, e.g., D. G. Truhlar, W. L. Hase, and J. T. Hynes, J. Phys. Chem. 87, 2644 (1983).
8.Recrossing is also understood in terms of separatrix and cantori bottlenecks which restrict phase space flow and redirect it back across the primitive transition state. See M. J. Davis, J. Chem. Phys. 86, 3978 (1987);
8.R. T. Skodje and M. J. Davis, J. Chem. Phys. 88, 2429 (1988); , J. Chem. Phys.
8.Y. J. Cho, S. R. Vande Linde, and W. L. Hase (preprint)
8.[see also S. R. Vande Linde and W. L. Hase, J. Phys. Chem. 94, 2778 (1990)].
9.N. De Leon and B. J. Berne, J. Chem. Phys. 75, 3495 (1981).
10.R. A. Aziz and M. J. Slaman, Mol. Phys. 58, 679 (1986).
11.(a) Energy is measured in units of K via scaling by Boltzmann’s constant;
11.(b) The atomic unit of time consistent with energy units of K is However, times reported in this paper are given in picoseconds;
11.(c) distance is measured in bohr;
11.(d) the usual atomic unit of mass, the “electron,” is modified by the energy conversion factor of hartrees to Kelvin;
12.Very long trajectories exhibiting 10 000 successive visits to A and B were computed. The mean visitation time provides a mean gap time associated with the minimal invariant manifold containing the trajectory. Agreement of this quantity with associated microcanonical values obtained from Monte Carlo computations constitutes support for our contention that T-shaped is ergodic (or very nearly so) at the energies considered. Specifically, the numerical results suggest that the chaotic minimal invariant manifolds occupy the bulk of their energy hypersurfaces ( of microcanonical invariant measure).
13.I. C. Percival, Proc. R. Soc. London Ser. A 413, 131 (1987).
14.R. S. Dumont, J. Comp. Chem. 12, 391 (1991).
15.D. Chandler, J. Chem. Phys. 68, 2959 (1978);
15.see also Ref. 1(b).
16.See Ref. 1(d) and N. G. van Kampen, Stochastic Processes in Physics and Chemistry (North-Holland, Amsterdam, 1981).
17.R. S. Dumont, Ph.D. dissertation, University of Toronto, 1987.
18.This is just the DLGM gap distribution Fourier transform [see Eq. (13a)], except for the additional factor and the shift of by δ. The latter two modifications constitute the Fourier representation of the shift by δ transformation.
19.The amplitude of a damped harmonic oscillator satisfies the following differential equation: Its solution has the Fourier representation where are interpretable as decay rates. When the decay rates are real and the oscillator is overdamped. If the decay rates have imaginary parts which correspond to oscillation frequenices. In the case, the oscillator is said to be underdamped. Comparison with the model survival provability of Eq. (21) yields the identification of model parameters and with damped harmonic oscillator parameters γ and respectively.
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