Theory of activated complexes

Following collision theory, a model of the bimolecular reaction, called the theory of activated complexs or the theory of absolute speeds, was estabhshed in 1938 by Eyring and Polanyi respectively. 

This theory is based on the following reflection. Collision theory describes a physical impact using classical mechanics. At the scale of the impact between two molecules, classical mechanics fails aird so this is replaced by quantum mechaitics. In the latter, the molecrrles are no longer rigid, which leads to the replacement of the mechairical impact by an energetic inrpact , which is an interaction between the atoms of two molecules. 

To introduce the elements of this theory, we will reason on the reaction between an atomX and a diatomic molecule YZ, such as  

We observe that these surfaces clearly show two valleys separated by pass, called the saddle point, and assume that the potential energy will always be minimal We deduce that during the reaction, the system follows these two valleys. Thus, starting from point P (far X) we follow the first valley, then we pass through the saddle point - which is characterized by its two distances - and we follow the second valley to reach point Q, where atom Z is separated from molecule XY. 

The top of the saddle point is called the activated complex, which will be denoted QCYZf (hence one of the names of the theory). 

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The theory of activated complex formation can be applied to mineral... 

Despite difficulties of interpretation, the application of theoretical concepts permits conclusions, or at least hints at conclusions, concerning the mechanism. As a result of the application of the theory of activated complexes, Equ. 5.3a can be recast as... 

A more complete analysis based on the theory of activated complexes and on statistical mechanics has been given by Zener (1951,1952). He considered the system or an atom in its initial equilibrium condition and in the activated state at the top of the potential barrier which separates the initial position from its neighbouring equilibrium position. The rate of transition from one equilibrium site to another is given by... 

For direct reactions, the reaction path profile has one potential barrier. In the frameworic of the theory of activated complex, the deviations of the temperature dependence of the rate constant from the Arrhenius equation for direct reactions can be explained by the temperature dependence of statistical sums of the reactants and activated complex. After inserting rotation, vibration, and translational statistical sums into expression (4.76), the temperature dependence of the rate constant is presented by the expression... 

Figure 10.11. Eyring and Polanyi developed the theory of activated complexes...

The most widely accepted treatment of reaction rates is transition state theory (TST), devised by Henry Eyring.17 It has also been known as absolute rate theory and activated complex theory, but these terms are now less widely used. 

The theory of equilibrium is treated on the basis of thermodynamics considering only the initial and final states. Time or intermediate states have no concern. However, there is a close relationship between the theory of rates and the theory of equilibria, in spite of there being no general relation between equilibrium and rate of reaction. A good approximation of equilibrium can be regarded between the reactants and activated state and the concentration of activated complex can, therefore, be calculated by ordinary equilibrium theory and probability of decomposition of activated complex and hence the rate of reaction can be known. 

The localization method was originally described by Wheland (1942) with reference to resonance theory, the activated complex being considered as a resonance hybrid consisting of a variable mixture of structures including (I) and (II). 

In transition state theory, an activated complex occurs at an intermediary point prior to the formation of products ... 

In theory, one can use statistical thermod3mamics to calculate the partition functions of all the species from first principles, AS, AH, and hence k. For simple systems, the calculation results are in good agreement with experimental data (e.g.. Chapter 3 in Laidler, 1987). For complicated geological systems, however, it is not possible to calculate k from first principles, but the concept of activated complexes is very useful for a microscopic understanding of the reaction... 

It should be stated at the beginning that despite quite numerous partial successes the present state of the quantum-chemical theory of reactivity is far from satisfactory. First of all, it is not clear whether the present shortcomings are due to the non-adequacy of models of activated complexes or to the drastic approximations made in the calculation of the energy of the activated complex and the reactants. On the other hand, some other deficiencies of most of the reported attempts to interpret reactivity in terms of the theory are obvious the very nature of the HMO method is thought148 to make it necessary to treat as large sets of theoretical and experimental data as possible and, in addition, to respect the distinction in properties of the three classes of positions mentioned (in this connection we do not refer to the difference in the stereochemistry of these positions). 

Fig. 10.4 Creation of activated complex in transition-state theory.

In contrast to spatial distribution, the equilibrium energy distribution of adsorbed particles cannot be violated to any substantial degree by reaction since energy is rapidly transferred between adsorbed particles and solids. Therefore, the activated complex method may be applied to rates of surface reactions. For this we consider the activated complex (transition state) of a surface reaction as a likeness of adsorbed particle (21). But, assuming that each adsorbed particle occupies only one site, it is necessary, even in the simplest kinetic model, to consider that activated complexes are able to occupy not only one, but also several surface sites (21). For example, the usual picture of a reaction between two particles adsorbed on neighboring sites involves, in fact, the notion that the activated complex occupies both sites. When the activated complex occupies several sites, this does not create any difficulty for the theory since the surface concentration of activated complexes is an infinitesimal quantity, and so the possibility of overlapping the required sites is excluded. 

Show how collision theory and activated complex theory account for the temperature dependence of reactions, Sections 13.8 and 13.9. 

The first assumption, that phase space is populated statistically prior to reaction, implies that the ratio of activated complexes to reactants is obtained by the evaluation of the ratio between the respective volumes in phase space. If this assumption is not fulfilled, then the rate constant k(E, t) may depend on time and it will be different from rrkm(E). If, for example, the initial excitation is localized in the reaction coordinate, k(E,t) will be larger than A rrkm(A). However, when the initially prepared state has relaxed via IVR, the rate constant will coincide with the predictions of RRKM theory (provided the other assumptions of the theory are fulfilled). 

According to transition state theory, the rate of a reaction is the number of activated complexes passing per second over the top of potential energy barrier. This rate is equal to the concentration of activated complex times the average velocity with which a complex moves across to the product side. The activated complex is not in a state of stable equilibrium, since it lies at a maximum potential energy. 

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