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Statistical dynamics and kinetics of unimolecular processes
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8.(b) R. S. Dumont and P. Brumer (unpublished);
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12.Relaxation is possible in nonmixing systems, but only for phase‐space distributions spanning a range of indecomposable manifolds. See C. Jaffe and P. Brumer, J. Phys. Chem. 88, 4829 (1984);
12.and R. S. Dumont and P. Brumer, J. Chem. Phys. 87, 6437 (1987).
13.This condition is the generalization of an analogous condition on simple unimolecular decomposition dynamics which provides a basis for the delayed lifetime gap model [see Ref. 8(a)].
14. is only strictly a “survival probability” when Nevertheless, we term the entire matrix of “number‐number correlations” the survival probability matrix.
15.Time‐reversal invariance of the phase‐space partition means time‐reversal invariance of each phase‐space reactant cell. Such symmetry exists when the Hamiltonian is time‐reversal invariant (i.e., in the absence of external magnetic fields and overall rotation) and transition states are defined in terms of configuration‐space dividing surfaces. In cases without this symmetry, the argument leading to Eq. (26) must be modified: Equation (26) follows from time reversal of the version of Eq. (23b) associated with the time‐reversed phase‐space partition.
16.Equation (34) utilizes [see Eq. (9)] and as from above [see Eq. (16)].
17.The random gap assumption of N. B. Slater [Theory of Unimoleculár Reactions (Cornell Univ. Press, Ithaca, 1959)] is the assumption of simple exponential decay of gap distributions.
18.Time‐reversal invariance of the phase‐space partition is required in order that under time reversal. Only then does and detailed balance follow. This condition is analogous to conditions (i) and (ii) in van Kampen’s proof of detailed balance (see Sec. 6 of Chap. V in Ref. 10).
19.In this paper, we do not consider practical means of extracting strong collision components with short‐time trajectories. We simply assume that it can be done. For applications of the “divergence method” of identifying strong collision components, see J. W. Duff and P. Brumer, J. Chem. Phys. 71, 3895 (1979);
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19.and Refs. 8(b), 8(c), and 8(d).
20.For example, direct components are responsible for the plateau behavior observed in models of liquid‐phase isomerizations [see D. Chandler, J. Chem. Phys. 68, 2959 (1978);
20.and J. A. Montgomery, D. Chandler, and B. J. Berne, J. Chem. Phys. 70, 4056 (1979)]. Important effects due to direct components have been observed in unimolecular reaction models based on stadium billiard dynamics [see Refs. 8(b), 8(c), and 8(d)]., J. Chem. Phys.
21.The lack of a connection between strict statistical temporal behavior and statistical product distributions has previously been recognized. See W. L. Hase, Chem. Phys. Lett. 67, 263 (1979);
21.and Refs. 8(a), 8(b), and 8(c).
22.R. S. Dumont and P. Brumer, J. Chem. Phys. 90, 96 (1989).
23.This type of so‐called “straight‐line‐path” behavior is well known in kinetics. See, for example, C. Lim and D. G. Truhlar, J. Chem. Phys. 79, 3296 (1983), and references therein.
24.See B. Davies, Integral Transforms and their Applications, 2nd ed. (Springer, New York, 1985), Sec. 6.5.
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