Non-RRKM

Figure A3.12.2. Relation of state oeeupation (sehematieally shown at eonstant energy) to lifetime distribution for the RRKM theory and for various aetiial situations. Dashed eiirves in lifetime distributions for (d) and (e) indieate RRKM behaviour, (a) RRKM model, (b) Physieal eounterpart of RRKM model, (e) Collisional state seleetion. (d) Chemieal aetivation. (e) Intrinsieally non-RRKM. (Adapted from [9].)...

A situation that arises from the intramolecular dynamics of A and completely distinct from apparent non-RRKM behaviour is intrinsic non-RRKM behaviour [9], By this, it is meant that A has a non-random P(t) even if the internal vibrational states of A are prepared randomly. This situation arises when transitions between individual molecular vibrational/rotational states are slower than transitions leading to products. As a result, the vibrational states do not have equal dissociation probabilities. In tenns of classical phase space dynamics, slow transitions between the states occur when the reactant phase space is metrically decomposable [13,14] on the timescale of the imimolecular reaction and there is at least one bottleneck [9] in the molecular phase space other than the one defining the transition state. An intrinsic non-RRKM molecule decays non-exponentially with a time-dependent unimolecular rate constant or exponentially with a rate constant different from that of RRKM theory. 

In the above discussion it was assumed that the barriers are low for transitions between the different confonnations of the fluxional molecule, as depicted in figure A3.12.5 and therefore the transitions occur on a timescale much shorter than the RRKM lifetime. This is the rapid IVR assumption of RRKM theory discussed in section A3.12.2. Accordingly, an initial microcanonical ensemble over all the confonnations decays exponentially. However, for some fluxional molecules, transitions between the different confonnations may be slower than the RRKM rate, giving rise to bottlenecks in the unimolecular dissociation [4, ]. The ensuing lifetime distribution, equation (A3.12.7), will be non-exponential, as is the case for intrinsic non-RRKM dynamics, for an mitial microcanonical ensemble of molecular states. 

The first classical trajectory study of iinimoleciilar decomposition and intramolecular motion for realistic anhannonic molecular Hamiltonians was perfonned by Bunker [12,13], Both intrinsic RRKM and non-RRKM dynamics was observed in these studies. Since this pioneering work, there have been numerous additional studies [9,k7,30,M,M, ai d from which two distinct types of intramolecular motion, chaotic and quasiperiodic [14], have been identified. Both are depicted in figure A3,12,7. Chaotic vibrational motion is not regular as predicted by tire nonnal-mode model and, instead, there is energy transfer between the modes. If all the modes of the molecule participate in the chaotic motion and energy flow is sufficiently rapid, an initial microcanonical ensemble is maintained as the molecule dissociates and RRKM behaviour is observed [9], For non-random excitation initial apparent non-RRKM behaviour is observed, but at longer times a microcanonical ensemble of states is fonned and the probability of decomposition becomes that of RRKM theory. 

For some systems qiiasiperiodic (or nearly qiiasiperiodic) motion exists above the unimoleciilar tlireshold, and intrinsic non-RRKM lifetime distributions result. This type of behaviour has been found for Hamiltonians with low uninioleciilar tliresholds, widely separated frequencies and/or disparate masses [12,, ]. Thus, classical trajectory simulations perfomied for realistic Hamiltonians predict that, for some molecules, the uninioleciilar rate constant may be strongly sensitive to the modes excited in the molecule, in agreement with the Slater theory. This property is called mode specificity and is discussed in the next section. 

Apparent non-RRKM behaviour occurs when the molecule is excited non-randomly and there is an initial non-RRKM decomposition before IVR fomis a microcanonical ensemble (see section A3.12.2). Reaction patliways, which have non-competitive RRKM rates, may be promoted in this way. Classical trajectory simulations were used in early studies of apparent non-RRKM dynamics [113.114]. 

To detect tlie initial apparent non-RRKM decay, one has to monitor the reaction at short times. This can be perfomied by studying the unimolecular decomposition at high pressures, where collisional stabilization competes with the rate of IVR. The first successful detection of apparent non-RRKM behaviour was accomplished by Rabinovitch and co-workers [115], who used chemical activation to prepare vibrationally excited hexafluorobicyclopropyl-d2 ... 

The chemically activated molecules are fonned by reaction of with the appropriate fliiorinated alkene. In all these cases apparent non-RRKM behaviour was observed. As displayed in figure A3.12.11 the measured imimolecular rate constants are strongly dependent on pressure. The large rate constant at high pressure reflects an mitial excitation of only a fraction of the total number of vibrational modes, i.e. initially the molecule behaves smaller than its total size. However, as the pressure is decreased, there is time for IVR to compete with dissociation and energy is distributed between a larger fraction of the vibrational modes and the rate constant decreases. At low pressures each rate constant approaches the RRKM value. 

Apparent non-RRKM dynamics has also been observed in time-resolved femtosecond (fs) experiments in a collision-free enviromnent [117], An experimental study of acetone illustrates this work. Acetone is dissociated to the CH and CH CO (acetyl) radicals by a fs laser pulse. The latter which dissociates by the channel... 

As discussed in section A3.12.2. intrinsic non-RRKM behaviour occurs when there is at least one bottleneck for transitions between the reactant molecule s vibrational states, so drat IVR is slow and a microcanonical ensemble over the reactant s phase space is not maintained during the unimolecular reaction. The above discussion of mode-specific decomposition illustrates that there are unimolecular reactions which are intrinsically non-RRKM. Many van der Waals molecules behave in this maimer [4,82]. For example, in an initial microcanonical ensemble for the ( 211 )2 van der Waals molecule both the C2H4—C2H4 intennolecular modes and C2H4 intramolecular modes are excited with equal probabilities. However, this microcanonical ensemble is not maintained as the dimer dissociates. States with energy in the intermolecular modes react more rapidly than do those with the C2H4 intramolecular modes excited [85]. 

Definitive examples of intrinsic non-RRKM dynamics for molecules excited near their unimolecular tluesholds are rather limited. Calculations have shown that intrinsic non-RRKM dynamics becomes more pronounced at very high energies, where the RRKM lifetime becomes very short and dissociation begins to compete with IVR [119]. There is a need for establishing quantitative theories (i.e. not calculations) for identifying which molecules and energies lead to intrinsic non-RRKM dynamics. For example, at thenual... 

Bunker D L and Hase W L 1973 On non-RRKM unimolecular kinetics molecules in general and CH3NC in particulars Chem. Rhys. 59 4621-32... 

F. Gabern, W. S. Koon, J. E. Marsden, and S. D. Ross, Theory and computation of non-RRKM lifetime distributions and rates in chemical systems with three or more degrees of freedom, Physica D 211, 391 (2005). 

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]. 

At this point it is worthwhile to review the possible failures of RRKM theory [9, 14] within a classical framework. First, the dynamics in some regions of phase space may not be ergodic. In this instance, which has been termed intrinsic non-RRKM behaviour [38], the use of the statistical distribution in Eq. (2.2) is inappropriate. In the extreme case of two disconnected regions of space, with one region nonreactive, the lifetime distribution is still random with an exponential decay of population to a non-zero value. However, the averaging of the flux must then be restricted to the reactive part of the phase space, and the rate coefficient is then increased by a factor equal to the reciprocal of the proportion of the phase space that is reactive. 

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... 

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