Dissociation unimolecular reaction rates

G.M. Wieder and R.A. Marcus. Dissociation and Isomerization of Vibrationally Excited Species. II. Unimolecular Reaction Rate Theory and Its Application. J. Chem. Phys., 37 1835-1852,1962. 

We have seen that the radiation hypothesis is not supported by experiment and that it can not be used to explain the fact that unimolecular reaction rates are uninfluenced by collisions. When investigators found this avenue of explanation closed they resumed consideration of the collision hypothesis. As early as 1922 Lindemann suggested that since a time interval exists between activation, of a molecule and its dissociation the apparent connection between the two phenomena would ordinarily be lost. This view was received with increasing favor as the radiation hypothesis became more and more discredited. Rodebush7 in 1923 howed that the known facts could be explained on the basis of collisions... 

Initiated by the chemical dynamics simulations of Bunker [37,38] for the unimolecular decomposition of model triatomic molecules, computational chemistry has had an enormous impact on the development of unimolecular rate theory. Some of the calculations have been exploratory, in that potential energy functions have been used which do not represent a specific molecule or molecules, but instead describe general properties of a broad class of molecules. Such calculations have provided fundamental information concerning the unimolecular dissociation dynamics of molecules. The goal of other chemical dynamics simulations has been to accurately describe the unimolecular decomposition of specific molecules and make direct comparisons with experiment. The microscopic chemical dynamics obtained from these simulations is the detailed information required to formulate an accurate theory of unimolecular reaction rates. The role of computational chemistry in unimolecular kinetics was aptly described by Bunker [37] when he wrote The usual approach to chemical kinetic theory has been to base one s decisions on the relevance of various features of molecular motion upon the outcome of laboratory experiments. There is, however, no reason (other than the arduous calculations involved) why the bridge between experimental and theoretical reality might not equally well start on the opposite side of the gap. In this paper... results are reported of the simulation of the motion of large numbers of triatomic molecules by... 

The reaction coordinate for dissociation must be some linear combination of stretch modes. If the energy remains localized in the stretch modes then the actual rate of dissociation will be much faster than that expected from statistical considerations. The latter assume that energy is fully shared over all modes prior to dissociation. Specifically, the RRK (115) unimolecular reaction rate at the energy E is given by... 

See, for example, D. L. Bunker, /. Chem. Phys., 40,1946 (1963). Monte Carlo Calculations. IV. Further Studies of Unimolecular Dissociation. D. L. Bunker and M. Pattengill,/. Chem. Phys., 48, 772 (1968). Monte Carlo Calculations. VI. A Re-evaluation erf Ae RRKM Theory of Unimolecular Reaction Rates. W. J. Hase and R. J. Wolf, /. Chem. Phys., 75,3809 (1981). Trajectory Studies of Model HCCH H -P HCC Dissociation. 11. Angular Momenta and Energy Partitioning and the Relation to Non-RRKM Dynamics. D. W. Chandler, W. E. Farneth, and R. N. Zare, J. Chem. Phys., 77, 4447 (1982). A Search for Mode-Selective Chemistry The Unimolecular Dissociation of t-Butyl Hydroperoxide Induced by Vibrational Overtone Excitation. J. A. Syage, P. M. Felker, and A. H. Zewail, /. Chem. Phys., 81, 2233 (1984). Picosecond Dynamics and Photoisomerization of Stilbene in Supersonic Beams. II. Reaction Rates and Potential Energy Surface. D. B. Borchardt and S. H. Bauer, /. Chem. Phys., 85, 4980 (1986). Intramolecular Conversions Over Low Barriers. VII. The Aziridine Inversion—Intrinsically Non-RRKM. A. H. Zewail and R. B. Bernstein,... 

Unimolecular reactions with thermal, optical, or chemical activation are governed by a competition between intramolecular isomerization, dissociation, or the reverse association (or recombination) processes, and intermolecular energy transfer in collisions. In addition to these traditional unimolecular reactions, many other reaction systems may be considered from a unimolecular point of view when a particular intramolecular event can be separated from preceding or other subsequent processes. Following this more general use of the term, unimolecular reaction rate theory has found a quite general application, and has been harmonized with other theories of reaction dynamics. 

Wieder GM, Marcus RA. Dissociation and isomerization of vibrationally excited species. II. Unimolecular reaction rate theory and its application. J Chem Phys. 1962 37 1835-52. 

Klippenstein SJ, Marcus RA. (1989) Application of unimolecular reaction rate theory for highly flexible transition states to the dissociation of CH2CO into CH2 and CO. J. Chem. Phys. 91 2280-2292. 

Fast transient studies are largely focused on elementary kinetic processes in atoms and molecules, i.e., on unimolecular and bimolecular reactions with first and second order kinetics, respectively (although confonnational heterogeneity in macromolecules may lead to the observation of more complicated unimolecular kinetics). Examples of fast thennally activated unimolecular processes include dissociation reactions in molecules as simple as diatomics, and isomerization and tautomerization reactions in polyatomic molecules. A very rough estimate of the minimum time scale required for an elementary unimolecular reaction may be obtained from the Arrhenius expression for the reaction rate constant, k = A. The quantity /cg T//i from transition state theory provides... 

So the tertiary halide reacts by a different mechanism, which we call SnI- It s still a nucleophilic substitution reaction (hence the S and the N ) but this time it is a unimolecular reaction, hence the 1 . The rate-determining step during reaction is the slow unimolecular dissociation of the alkyl halide to form a bromide ion and a carbocation that is planar around the reacting carbon. 

These, and similar data for other systems, demonstrate the tremendous potential that the MICR technique has for the qualitative elucidation of potential energy surfaces of relatively complex organic reactions. Once implementation of the quadrupolar excitation technique has been effected to relax ions to the cell center, the technique will become even more powerful, in that the determination of highly accurate unimolecular decomposition lifetimes of chemically activated intermediates will also become possible. No other technique offers such a powerful array of capabilities for the study of unimolecular dissociation mechanisms and rates. 

The relative reaction rates and the stability of the aquo complex make it possible to identify the aquo complex as an intermediate and study the individual acts separately. However, if the solvento complex were less stable and the anation rate much faster than the solvolysis, it would not be possible to observe this intermediate, and the process would be kinetically indistinguishable from a unimolecular dissociative process. Both processes would exhibit overall first-order kinetics and the usual mass-law retardation and other competitive phenomena characteristic of an extremely reactive intermediate. 

At the present time a number of gaseous unimolecular reactions are known. The view that none exist, although it appeared plausible for a time, has now been definitely abandoned. Nevertheless, unimolecular reactions are rather exceptional and appear to be confined to molecules of rather complex structure. It is possible that the decomposition of diatomic molecules into atoms at high temperatures is unimolecular but more probable that it is bimolecular, the reverse reaction of recombination being termolecular. Thus the rate of dissociation of chlorine would be k1 [Cl2]2 while the rate of recombination of the atoms would be 2 [Cl]2 [Clg], according to the Herzfeld theory (p. 111). 

After in the foregoing chapter thermodynamic properties at high pressure were considered, in this chapter other fundamental problems, namely the influence of pressure on the kinetic of chemical reactions and on transport properties, is discussed. For this purpose first the molecular theory of the reaction rate constant is considered. The key parameter is the activation volume Av which describes the influence of the pressure on the rate constant. The evaluation of Av from measurement of reaction rates is therefor outlined in detail together with theoretical prediction. Typical value of the activation volume of different single reactions, like unimolecular dissociation, Diels-Alder-, rearrangement-, polymerization- and Menshutkin-reactions but also on complex homogeneous and heterogeneous catalytic reactions are presented and discussed. 

The RRKM theory of unimolecular reactions predicts that the rate constant for dissociation will be given by eq. (5-3). The probability of populating a state with energy Ev restricted into the chromophore vibrations is proportional to the ratio of the density of van der Waals states at E — Ev to that at ... 

The development of a theory of unimolecular reactions proceeded rapidly in the mid-1920s, initiated by Hinshelwood with an A whose collision-free lifetime for reaction was approximated by an energy-independent one. The analysis was much elaborated by Rice and Ramsperger [60] and Kassel [61], known later as the RRK theory, where now the lifetime was, as it is in modern times, energy-dependent [62]. These theoretical works of the 1920s stimulated many measurements of the unimolecular rates of dissociation of organic compounds as a function of the gas pressure. Within a few years, however, this entire field collapsed or, more precisely, evolved into a new field It was shown experimentally that the unimolecular reactions , assumed originally to consist of only one chemical step, in-... 

The dynamics near the TS have been the subject of many theoretical [52-66] and experimental [24,25] investigations. The experiments of Lovejoy and co-workers [24,25] see the TS via the photofragment excitation spectra for unimolecular dissociation of excited ketene. They have shown that, in the vicinity of the barrier, the reaction rate is controlled by the flux through quantized thresholds. The observability of quantized thresholds in the TS was first discussed by Chatfield et al. [23]. Marcus pointed out that this indicates that the transverse vibrational quantum numbers might indeed be approximate constants of the motion in the saddle region [60]. 

The dissociation of N2O4 has a frequency factor in excess of 10 sec and this seems reasonable if in the transition complex the originally stiff vibrations of the two NO2 groups change over to only slightly hindered rotations. This dissociation is of further interest in that it is one of the few unimolecular reactions for which the experimental first-order rate... 

This effect of CO2 is at first somewhat surprising because it implies that the rate of dissociation of N2OB is being accelerated by CO2, which we would expect only if this dissociation were a unimolecular reaction below its high-pressure limit. N2O6 has 7 atoms and 15 internal vibrations (or their equivalent) and probably 2 active rotations. For a completely classical molecule (which N2O6 is not), the RRK theory (Table XI.2) would predict deviations from the high-pressure limit near 0.1 mm Hg, which is... 

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