Unimolecular reaction rate

The effective rate law correctly describes the pressure dependence of unimolecular reaction rates at least qualitatively. This is illustrated in figure A3,4,9. In the lunit of high pressures, i.e. large [M], becomes independent of [M] yielding the high-pressure rate constant of an effective first-order rate law. At very low pressures, product fonnation becomes much faster than deactivation. A j now depends linearly on [M]. This corresponds to an effective second-order rate law with the pseudo first-order rate constant Aq ... 

Bunker D L and Pattengill M 1968 Monte Carlo calculations. VI. A re-evaluation of the RRKM theory of unimolecular reaction rates J. Chem. Phys. 48 772-6... 

Miller W H 1988 Effect of fluctuations in state-specific unimolecular rate constants on the pressure dependence of the average unimolecular reaction rated. Phys. Chem. 92 4261-3... 

Table 3. Unimolecular Reaction Rate Constants for Isotopically Analogous Reactions [Ac (CHaljCO, B CeHe, E (CHjIjO, W HjO]...

The theory of Lindemann explains most of the trends observed in the kinetics of uni-molecular reactions. It has been very useful in understanding the qualitative behavior of this class of reactions. It provides the starting point for all modem theories of unimolecu-lar reactions. The theoretical basis for unimolecular reaction rates is treated in much more detail in Chapter 10. 

Summary of QRRK Unimolecular Rate Constant In summary, the QRRK result for the observed unimolecular reaction rate constant fcun was given by Eq. 10.154 as... 

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. 

Experimental rate constants, kinetic isotope effects and chemical branching ratios for the CF2CFCICH3-do, -d, -d2, and -d2 molecules have been experimentally measured and interpreted using statistical unimolecular reaction rate theory.52 The structural properties of the transition states needed for the theory have been calculated by DFT at the B3PW91 /6-31 G(d,p/) level. 

Shalashilin and Thompson [46-48] developed a method based on classical diffusion theory for calculating unimolecular reaction rates in the IVR-limited regime. This method, which they referred to as intramolecular dynamics diffusion theory (IDDT) requires the calculation of short-time ( fs) classical trajectories to determine the rate of energy transfer from the bath modes of the molecule to the reaction coordinate modes. This method, in conjunction with MCVTST, spans the full energy range from the statistical to the dynamical limits. It in essence provides a means of accurately... 

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... 

Unimolecular reaction rates and products quantum states distribution... 

The field of unimolecular reaction rates had an interesting history beginning around 1920, when chemists attempted to understand how a unimolecular decomposition N2Os could occur thermally and still be first-order, A — products, even though the collisions which cause the reaction are second-order (A + A— products). The explanation, one may recall, was given by Lindemann [59], i.e., that collisions can produce a vibrationally excited molecule A, which has a finite lifetime and can form either products (A — products), or be deactivated by a collision (A + A— A + A). At sufficiently high pressures of A, such a scheme involving a finite lifetime produces a thermal equilibrium population of this A. The reaction rate is proportional to A, which would then be proportional to A and so the reaction would be first-order. At low pressures, the collisions of A to form A are inadequate to maintain an equilibrium population of A, because of the losses due to reaction. Ultimately, the reaction rate at low pressures was predicted to become the bimolecular collisional rate for formation of A and, hence, second-order. 

Fig. 1.9. Developments in unimolecular reaction rates and related areas [1].

CLASSICAL, SEMICLASSICAL, AND QUANTUM MECHANICAL UNIMOLECULAR REACTION RATE THEORY... 

With this brief overview of classical theories of unimolecular reaction rate, one might wonder why classical mechanics is so useful in treating molecular systems that are microscopic, and one might question when a classical statistical theory should be replaced by a corresponding quantum theory. These general questions bring up the important issue of quantum-classical correspondence in general and the field of quantum chaos [27-29] (i.e., the quantum dynamics of classically chaotic systems) in particular. For example, is it possible to translate the above classical concepts (e.g., phase space separatrix, NHIM, reactive islands) into quantum mechanics, and if yes, how What is the consequence of... 

Recent years have also witnessed exciting developments in the active control of unimolecular reactions [30,31]. Reactants can be prepared and their evolution interfered with on very short time scales, and coherent hght sources can be used to imprint information on molecular systems so as to produce more or less of specified products. Because a well-controlled unimolecular reaction is highly nonstatistical and presents an excellent example in which any statistical theory of the reaction dynamics would terribly fail, it is instmctive to comment on how to view the vast control possibihties, on the one hand, and various statistical theories of reaction rate, on the other hand. Note first that a controlled unimolecular reaction, most often subject to one or more external fields and manipulated within a very short time scale, undergoes nonequilibrium processes and is therefore not expected to be describable by any unimolecular reaction rate theory that assumes the existence of an equilibrium distribution of the internal energy of the molecule. Second, strong deviations Ifom statistical behavior in an uncontrolled unimolecular reaction can imply the existence of order in chaos and thus more possibilities for inexpensive active control of product formation. Third, most control scenarios rely on quantum interference effects that are neglected in classical reaction rate theory. Clearly, then, studies of controlled reaction dynamics and studies of statistical reaction rate theory complement each other. 

The most important element of the Davis-Gray theory of unimolecular reaction rate is the identification of bottlenecks to intramolecular energy flow and the intermolecular separatrix to molecular fragmentation. Davis and Gray s work was motivated by the discovery of bottlenecks in chaotic transport by MacKay, Meiss, and Percival [8,9] and by Bensimon and Kadanoff [10]. 

The Davis-Gray theory teaches us that by retaining the most important elements of the nonhnear reaction dynamics it is possible to accurately locate the intramolecular bottlenecks and to have an exact phase space separatrix as the transition state. Unfortunately, even for systems with only two DOFs, there may be considerable technical difficulties associated with locating the exact bottlenecks and the separatrix. Exact calculations of the fluxes across these phase space structures present more problems. For these reasons, further development of unimolecular reaction rate theory requires useful approximations. 

As shown above, classical unimolecular reaction rate theory is based upon our knowledge of the qualitative nature of the classical dynamics. For example, it is essential to examine the rate of energy transport between different DOFs compared with the rate of crossing the intermolecular separatrix. This is also the case if one attempts to develop a quantum statistical theory of unimolecular reaction rate to replace exact quantum dynamics calculations that are usually too demanding, such as the quantum wave packet dynamics approach, the flux-flux autocorrelation formalism, and others. As such, understanding quantum dynamics in classically chaotic systems in general and quantization effects on chaotic transport in particular is extremely important. 

In this chapter we have reviewed the development of unimolecular reaction rate theory for systems that exhibit deterministic chaos. Our attention is focused on a number of classical statistical theories developed in our group. These theories, applicable to two- or three-dimensional systems, have predicted reaction rate constants that are in good agreement with experimental data. We have also introduced some quantum and semiclassical approaches to unimolecular reaction rate theory and presented some interesting results on the quantum-classical difference in energy transport in classically chaotic systems. There exist numerous other studies that are not considered in this chapter but are of general interest to unimolecular reaction rate theory. 

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