Non-RRKM behavior

Statistical theories would require decreases in reaction rates that are orders of magnitude larger than the modest differences noted. The key vibrational energy redistribution leading to the second ot-cleavage is restricted to modes near the acyl function and involved importantly in the reaction coordinate. These acylalkyl diradical intermediates do not achieve complete statistical redistributions of vibrational energy throughout all vibrational modes, and only then lose CO. The experimental results indicate non-RRKM behavior. 

The accurate determination of rate constants for the reactions of 19F atoms is often hampered by the presence of reactive F2 and by the occurrence of side reactions. The measurement of the absolute concentration of F atoms is sometimes a further problem. The use of thermal-ized 18F atoms is not subject to these handicaps, and reliable and accurate results for abstraction and addition reactions are obtained. The studies of the reactions of 18F atoms with organometallic compounds are unique, inasmuch as such experiments have not been performed with 19F atoms. In the case of addition reactions, the fate of the excited intermediate radical can be studied by pressure-dependent measurements. The non-RRKM behavior of tetraallyltin and -germanium compounds is very interesting inasmuch as not many other examples are known. The next phase in the 18F experiment should be the determination of Arrhenius parameters for selected reactions, i.e., those occurring in the earth s atmosphere, since it is expected that the results will be more precise than those obtained with 19F atoms. 

It should be pointed out that while most of the reactions can be solved using traditional RRKM approach, experimental and theoretical studies have shown that non-RRKM dynamics is important for moderate to large-sized molecules with various barriers for unimolecular dissociation [57,58]. In these cases, non-RRKM behavior needs to be taken into account and direct chemical dynamic simulation is suggested to serve this purpose [58]. 

Classical dynamics of a micro-canonical ensemble intrinsic RRKM and non-RRKM behavior... 

Initiated by the work of Bunker [323,324], extensive trajectory simulations have been performed to determine whether molecular Hamiltonians exhibit intrinsic RRKM or non-RRKM behavior. Both types have been observed and in Fig. 43 we depict two examples, i.e., classical lifetime distributions for NO2 [271] and O3. While Pd t) for NO2 is well described by a single-exponential function — in contrast to the experimental and quantum mechanical decay curves in Fig. 31 —, the distribution for ozone shows clear deviations from an exponential decay. The classical dynamics of NO2 is chaotic, whereas for O3 the phase space is not completely mixed. This is in accord with the observation that the quantum mechanical wave... 

It is not immediately obvious, by simply looking at a molecule s Hamiltonian and/or its PES, whether the unimolecular dynamics will be intrinsic RRKM or not and computer simulations as outlined here are required. Intrinsic non-RRKM dynamics is indicative of mode-specific decomposition, since different regions of phase space are not strongly coupled and a micro-canonical ensemble is not maintained during the fragmentation. The phase space structures, which give rise to intrinsic RRKM or non-RRKM behavior, are discussed in the next section. 

The Uniformity in an Exponential Decay Expression Appendix A A Short Detour to Non-RRKM Behaviors... 

Trajectory calculations have been used to study the intrinsic RRKM and apparent non-RRKM dynamics of ethyl radical dissociation, i.e. C2H5 — H - - C2H4 [61,62]. When C2H5 is excited randomly, with a microcanonical distribution of states, it dissociates with the exponential P t) of RRKM theory [61], i.e. it is an intrinsic RRKM molecule. However, apparent non-RRKM behavior is present in a trajectory simulation of C2H5... 

Direct dynamics has made it possible to investigate the unimolecular decomposition of a broad group of molecules for different excitation processes, to compare with experiment and determine fundamental information concerning intramolecular and unimolecular dynamics. Summarized in Table 15.1 are the unimolecular direct dynamics simulations performed by the Hase research group [117-129]. Some degree of non-RRKM behavior is present in each of the reactions. It would not have been possible to determine this level of understanding of the unimolecular dynamics of these reactions without access to direct dynamics. 

To detect the initial apparent non-RRKM decay in a photoactivation or chemical activation experiment, one has to monitor the reaction at short times. This can be performed by studying the unimolecular decomposition at high pressures, where colli-sional stabilization competes with the rate of IVR. The first successful detection of apparent non-RRKM behavior was accomplished by Rynbrandt and Rabinovitch (1971) who used chemical activation to prepare vibrationally excited hexafluoro-bicyclopropyl-dj as described in chapter 1 (Eq. 1.21). Similar studies were also performed (Meagher et al., 1974) on the series of chemically activated fluoroalkyl cyclopropanes ... 

The chemically activated molecules are formed by reaction of CDj with the appropriate fluorinated alkene. In all these cases apparent non-RRKM behavior was observed. As displayed in figure 8.7, the measured unimoleeular rate constants are strongly dependent on pressure. However, at low pressures each rate constant approaches the RRKM value. 

Classical trajectory studies of unimolecular decomposition have helped define what is meant by RRKM and non-RRKM behavior (Bunker, 1962, 1964 Bunker and Hase, 1973 Hase, 1976, 1981). RRKM theory assumes that the phase space density of a decomposing molecule is uniform. A microcanonical ensemble exists at t = 0 and rapid intramolecular processes maintain its existence during the decomposition [fig. 8.9(a), (b)]. The lifetime distribution, Eq. (8.35a), is then... 

Intrinsic non-RRKM behavior occurs when an initial microcanonical ensemble decays nonexponentially or exponentially with a rate constant different from that of RRKM theory. The former occurs when there is a bottleneck (or bottlenecks) in the classical phase space so that transitions between different regions of phase space are less probable than that for crossing the transition state [fig. 8.9(e)]. Thus, a micro-canonical ensemble is not maintained during the unimolecular decomposition. A limiting case for intrinsic non-RRKM behavior occurs when the reactant molecule s phase space is metrically decomposable into two parts, for example, one part consisting of chaotic trajectories which can decompose and the other of quasiperiodic trajectories which are trapped in the reactant phase space (Hase et al., 1983). If the chaotic motion gives rise to a uniform distribution in the chaotic part of phase space, the unimolecular decay will be exponential with a rate constant k given by... 

Figure 8.15 illustrates the presence of an intramolecular bottleneck in the interaction region of phase space. The transition rate through the turnstile in this bottleneck can be calculated using concepts described in section 4.3.1. An intramolecular bottleneck, such as the one depicted in figure 8.15, is expected to give rise to intrinsic non-RRKM behavior. 

N. De Leon, Chem. Phys. Lett., 189, 371 (1992). Dynamical Correaions for Non-RRKM Behavior. 

The invocation of non-RRKM behavior in thermal reactions is ordinarily frowned upon by the chemical kinetic community. Here, however, we are dealing with rapid non-adiabatic isomerization of two constitutionally and structurally identical, but energetically different, triplets. It may well be a case in which strong and sometimes peculiar effects (e.g. isotope effects) can be brought about by. .. the non-constancy of the transmission coefficient as a function of kinetic energy [47, 48]. 

Non-RRKM behavior is discussed by W. L. Hase, in Modern Theoretical Chemistry, W. H. Miller, ed. (New York Plenum Press, 1976), Vol. 2, Part B, Chapter 3 and D. L. Bunker, Theory of Elementary Gas Reaction Rates (Oxford Pergamon Press, 1966), Chapter 3. 

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