Transition state theory statistical kinetic models

A simplified approach is statistical rate theory (transition state theory) with the help of which the overall rate constant k(T) may be obtained from potential energy surface (PES) in a single jump averaging out all of the intermediate details. It is generally not possible to extract microscopic details such as energy-dependent cross sections from conventional kinetics experiments. The preferable approach is to calculate microscopic quantities from some model and then perform the downward averaging for comparison with measured quantities. 

The RRKM theory is the most widely used of the microcanonical, statistical kinetic models It seeks to predict the rate constant with which a microcanonical ensemble of molecules, of energy E (which is greater than Eq, the energy of the barrier to reaction) will be converted to products. The theory explicitly invokes both the transition state hypothesis and the statistical approximation described above. Its result is summarized in Eq. 2... 

An alternative approach to MD for modeling kinetics of molecular systems is based on (a) statistical theories of the rate and (b) the concept of a reaction coordinate [2]. The latter is usually identified as the steepest descent path (SDP). The SDP is a curve with a low-energy barrier connecting two minima, a reactant and a product. It provides a qualitative view of the progress of the reaction, along with useful input to theories of rate such as the transition state theory [3]. 

Table 10.4 lists the rate parameters for the elementary steps of the CO + NO reaction in the limit of zero coverage. Parameters such as those listed in Tab. 10.4 form the highly desirable input for modeling overall reaction mechanisms. In addition, elementary rate parameters can be compared to calculations on the basis of the theories outlined in Chapters 3 and 6. In this way the kinetic parameters of elementary reaction steps provide, through spectroscopy and computational chemistry, a link between the intramolecular properties of adsorbed reactants and their reactivity Statistical thermodynamics furnishes the theoretical framework to describe how equilibrium constants and reaction rate constants depend on the partition functions of vibration and rotation. Thus, spectroscopy studies of adsorbed reactants and intermediates provide the input for computing equilibrium constants, while calculations on the transition states of reaction pathways, starting from structurally, electronically and vibrationally well-characterized ground states, enable the prediction of kinetic parameters. 

Abstract The statistical thermodynamic theory of isotope effects on chemical equilibrium constants is developed in detail. The extension of the method to treat kinetic isotope effects using the transition state model is briefly described. 

On a modest level of detail, kinetic studies aim at determining overall phenomenological rate laws. These may serve to discriminate between different mechanistic models. However, to it prove a compound reaction mechanism, it is necessary to determine the rate constant of each elementary step individually. Many kinetic experiments are devoted to the investigations of the temperature dependence of reaction rates. In addition to the obvious practical aspects, the temperature dependence of rate constants is also of great theoretical importance. Many statistical theories of chemical reactions are based on thermal equilibrium assumptions. Non-equilibrium effects are not only important for theories going beyond the classical transition-state picture. Eventually they might even be exploited to control chemical reactions [24]. This has led to the increased importance of energy or even quantum-state-resolved kinetic studies, which can be directly compared with detailed quantum-mechanical models of chemical reaction dynamics [25,26]. 

TST calculations apply in the high-pressure hmit pressure-dependent reactions can be analyzed via more complex kinetic analyses such as Pace—Ramsperger—Kassel—Marcus (PJkKM) theory. The RRKM theory is used to model the energy transfer in the transition state (or activated complex) of a molecule, using statistical mechanical methods that describe the density of energy states, which depend upon the vibrational and rotational partition functions for the molecule. 

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