Transition state theory of surface reactions

We obtain the temperature dependence of the pre-exponential factor by inserting the values of Tab. 3.5 in Eq. (139) for the prefactor  

The reader may now wish to verify that the activation energy calculated by logarithmic differentiation contains a contribution Sk T/l in addition to A , whereas the pre-exponential needs to be multiplied by the factor e in order to properly compare Eq. (139) with the Arrhenius equation. Although the prefactor turns out to have a rather strong temperature dependence, the deviation of a In k versus 1/T Arrhenius plot from a straight line will be small if the activation energy is not too small. 

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Transition state theory of surface reactions was developed independently by Temldn and Laidler, Glasstone and Eyring shortly after the more general treatment of Eyring and Polanyi appeared. It was supposed that each molecule occupies one elementary space and there is a random distribution of molecules. Activated complexes occupy several adjacent elementary sites (s) and there are several possible positions of activated complexes (g). For a reaction of A and B there is a possibility to have several equivalent positions of the activated complexes (here g=4)... 

The second point is that the new phase-space representation permits the definition of a true dividing surface in phase space which truly separates the reactant and product sides of a reaction. Traditional transition state theory of chemical reactions, based simply on coordinate-space definitions of the degrees of freedom, required an empirical correction factor, the transmission... 

In the case of one independent variable, a local maximum could be distinguished from a local minimum or an inflection point by determining the sign of the second derivative. With more than one variable, the situation is more complicated. In addition to inflection points, we can have points corresponding to a maximum with respect to one variable and a minimum with respect to another. Such a point is called a saddle point, and at such a point, the surface representing the function resembles a mountain pass or the surface of a saddle. Such points are important in the transition-state theory of chemical reaction rates. 

The transition state theory of reaction rates [21] provides the link between macroscopic reaction rates and molecular properties of the reactants, such as translational, vibrational, and rotational degrees of freedom. For an extensive discussion of transition state theory applied to surface reactions we refer to books by Zhdanov [25] and by Van Santen and Niemantsverdriet [27]. The desorption of a molecule M proceeds as follows ... 

An example of the application of transition state theory to atmospheric reactions is the reaction of OH with CO. As discussed earlier, this reaction is now believed to proceed by the formation of a radical adduct HOCO, which can decompose back to reactants or go on to form the products H + COz. For complex reactions such as this, transition state theory can be applied to the individual reaction steps, that is, to the steps shown in reaction (15). Figure 5.3 shows schematically the potential energy surface proposed for this reaction (Mozurkewich et al., 1984). The adduct HOCO, corresponding to a well on the potential energy surface, can either decompose back to reactants via the transition state shown as HOCO./ or form products via transition state HOCO,/. ... 

We would, therefore, agree with Bond s conclusion (3) that application of the transition state theory to heterogeneous reactions has not so far provided insight into the mechanisms of surface reactions and that the failures of the theory are generally more significant than the successes. We do not accept that the use of the theory of absolute reaction rates in the interpretation of kinetic data provides a general and reliable method for the estimation of the concentration of surface active sites but conclude that results should always be considered with reference to appropriate quantitative supporting evidence (133). 

Picosecond absorption spectroscopy studies of the contact ion pairs formed in the photo-initiated, S N 1 reaction of three substituted benzhydryl acetates (18) provided the rate constants for the k and k2 steps of the reaction (Scheme 10), in acetonitrile and DMSO.83 The activation parameters for the k and k2 steps were obtained from the temperature dependence of these steps and the transition state energies were calculated from the rate constants. This allowed the energy surfaces for three substituted substrates to be calculated in each solvent. The effect of solvent reorganization on the reactions of the unsubstituted and methyl-substituted benzhydryl contact ion pairs (CIP) was significant, causing a breakdown of transition state theory for these reactions. The results indicated that it will be very difficult to develop a simple theory of nucleophilicity in, S N1 reactions and that Marcus theory cannot be applied to SnI processes. 

In this chapter, we discuss TPR and reduction theory in some detail, and show how TPR provides insight into the mechanism of reduction processes. Next, we present examples of TPO, TP sulfidation (TPS) and TPRS applied on supported catalysts. In the final section we describe how thermal desorption spectroscopy reveals adsorption energies of adsorbates from well-defined surfaces in vacuum. A short treatment of the transition state theory of reaction rates is included to provide the reader with a feeling for what a pre-exponential factor of desorption tells about a desorption mechanism. The chapter is completed with an example of TPRS applied in ultra-high vacuum (UHV), in order to illustrate how this method assists in unraveling complex reaction mechanisms. 

Various quantum-mechanical theories have been proposed which allow one to calculate isotopic Arrhenius curves from first principles, where tunneling is included. These theories generally start with an ab initio calculation of the reaction surface and use either quantum or statistical rate theories in order to calculate rate constants and kinetic isotope effects. Among these are the variational transition state theory of Truhlar [15], the instanton approach of Smedarchina et al. 

Transition state theory or absolute reaction rate theory is built upon these ideas of a potential energy surface and reaction coordinate to account for reactivity. The theory seeks to understand and appreciate reactivity in terms of the structure and behaviour of reaction transition states. A transition state is dehned as a transient, unstable species that is found... 

For the explanation of hydrolytic dissolution processes currently is widely used activated-complex theory, which is also called transition state theory or absolute reaction rate theory. According to this theory, at hydration and protonation on the surface of the mineral form functional groups X-OH, X-OH and X-0 , which have acid-alkali properties dependent on pH of the solution. However, not the entire specific surface of the mineral participates in dissolution reactions but only its effective portion, which is taken by the... 

Variational transition state theory (VTST) is formulated around a variational theorem, which allows the optimization of a hypersurface (points on the potential energy surface) that is the elfective point of no return for reactions. This hypersurface is not necessarily through the saddle point. Assuming that molecules react without a reverse reaction once they have passed this surface... 

Rather than using transition state theory or trajectory calculations, it is possible to use a statistical description of reactions to compute the rate constant. There are a number of techniques that can be considered variants of the statistical adiabatic channel model (SACM). This is, in essence, the examination of many possible reaction paths, none of which would necessarily be seen in a trajectory calculation. By examining paths that are easier to determine than the trajectory path and giving them statistical weights, the whole potential energy surface is accounted for and the rate constant can be computed. 

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