RRKM theory application

Of course, in a thermal reaction, molecules of the reactant do not all have the same energy, and so application of RRKM theory to the evaluation of the overall unimolecular rate constant, k m, requires that one specify the distribution of energies. This distribution is usually derived from the Lindemann-Hinshelwood model, in which molecules A become activated to vibrationally and rotationally excited states A by collision with some other molecules in the system, M. In this picture, collisions between M and A are assumed to transfer energy in the other direction, that is, returning A to A ... 

E. Poliak The RRKM theory and Kramers theory and its later generalizations by Grote, Hynes, and other are two sides of the same coin. In the spatial diffusion limit, one can show that Kramers s rate expression is identical in form to the RRKM expression, that is, a ratio of equilibrium unidirectional flux and density of reactants. The difficult problem in the application of RRKM theory to the stilbene molecule with a few attached benzenes is whether the equilibration of energy occurs fully on the time scale of the isomerization. One should also... 

Simplified Rate Ratio for Non-Equilibrium Activation. Deuterium labeling is widely used and isotope effects may be sufficiently large to alter significantly the kinetic behavior of these systems. The secondary isotope effect, especially, serves to illustrate some recent developments in the formulation and application of the RRKM theory. 

A comprehensive quantum mechanical model for the effect has been developed by Marcus and his colleagues at the California Institute of Technology. The Gao and Marcus (2001, 2002) model accounts for many of the experimental observations and utilizes classical quantum mechanical RRKM theory in its development. Statistical RRKM theory quantitatively describes the energetics of gas phase atom-molecule encounters and the relevant parameters which lead to either stabilization and product formation or re-dissociation to atomic and molecular species. This is a well-developed theory and will not be described in detail here. An important application of this theory is that it determines... 

These problems arise because of the use of the classical density of states rather than the proper vibrational energy levels, and, of course an alternative would be to use the more difficult QRRK theory. If this is done, acceptable fits may be obtained to experimental data using the full number of oscillators. However, QRRK theory is not easily applicable with a realistic spectrum of vibrational frequencies, and it is preferable to use an alternative theory such as the RRKM theory instead. 

The density of states is a central concept in the development and application of RRKM theory. The density of states of a classical system is the number of states of that system per unit energy, expressed as a function of energy. This quantity may be formulated as a phase space integral in several ways. 

With this replacement of the strong collider assumption now commonplace, the term RRKM theory has become largely synonymous with quantum TST for unimolecular reactions, and we use this terminology here. The foundations of RRKM theory have been tested in depth with a wide variety of inventive theoretical and experimental studies [9]. While these tests have occasionally indicated certain limitations in its applicability, for example to timescales of a picosecond or longer, the primary conclusion remains that RRKM theory is quantitatively valid for the vast majority of conditions of importance to chemical kinetics. The H + O2 HO2 OH + O reaction is an example of an important reaction where deviations from RRKM predictions are significant [10, 11]. The foundations of RRKM theory and TST have been aptly reviewed in various places [7, 9, 12-15]. Thus, the present chapter begins with only a brief... 

The focus of this chapter is a review of the methodologies employed in a priori implementations of RRKM theory for the collisionless dissociation/ isomerization steps in gas-phase unimolecular reactions. Special attention will be paid to recent developments, particularly those that have proven their utility through substantive applications. With microscopic reversibility, RRKM treatments of the dissociation process are directly applicable to the reverse bimolecular associations. Furthermore, some of the more interesting illustrations are for bimolecular reactions and so we do not limit our discussion of RRKM theory to unimolecular reactions. However, one should bear in mind that TST was originally derived for bimolecular reactions and the specific term RRKM theory is really only applicable to the unimolecular direction. 

Applications of RRKM theory often focus on the high pressure limit of the dissociation rate coefficient. The presence of multiple collisions prior to reaction generally maintains a Boltzmann population distribution. Correspondingly, the thermal rate coefficient is then expressed as a Boltzmann average over the energy and angular momentum resolved rate coefficient, which reduces to... 

There is a fall-off of k at low pressures. Application of the rrk treatment led to an s value of 21-23. The rrkm theory was applied to the results, and agreement was obtained provided that a collision efficiency of 0.04-0.09 was assumed. This seems too low, and it is possible that this anomaly would disappear if the back reaction were taken into account . 

A method developed to predict the rates of ion-molecule association reactions (Olmstead et al, 1976) was based on a quick randomization of energy in the collision complex and on treating the baekward decomposition of the collision complex by an application of the RRKM theory. The method was successfully applied to predict both the pressure dependence and the temperature dependence of the association rates of proton-bound dimers of ammonia, methylamine, and dimethylamine. 

Aubanel et al. (1991) have discussed the application of variational RRKM theory to product energy distributions. What follows is a summary of this review. 

Application of the RRKM theory (used for to reactions in the gas phase) to surface reactions required detailed analysis of contributions from vibrations that belong to the matrix to the statistical sums of the prereaction state and transition state [29,68]. Inclusion of the low-frequency phonons of the solid (<200 cm ) leads to appreciable dependence of the preexponential of the rate constant (feo) on the temperature. It should be noted that the ko values calculated on the basis of the experimental therma-grams (TPD-MS) at various temperature sections on the assumption of the nondependence of on T can differ by three orders of magnitude (Table 37.7). 

During the application of the RRKM theory to the destruction of the surface groups [29,42,68,73] we assumed that ... 

In recent years the semiclassical "statistical theory of RICE, RAMSPERGER, KASSEL, and MARCUS /136/ has made great progress in its development. The computational techniques of this theory provide the possibility of calculating the velocities of unimolecular reactions using suitable, models for the activated complex. This approach is certainly very useful for a correlation of the experimental facts and a description of various aspects of the observed phenomena. The success of such applications of the RRKM-theory does not at all preclude an alternative treatment based on the collision theory of... 

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