Transition state scaling

The transition state scaling relations imply scaling relations for the activation energy of a surface chemical reaction (see Fig. 6.7). Let X and Y define two minima on a potential energy surface if both E and AE scale with a set of adsorption energies, then E will as well. 

Similarly, reaction energies are differences between energies of two intermediates. If a BEP relation exists, then there will also be a transition state scaling relation. There can, however, be many transition state scaling relations that are not covered by a BEP relation. By restricting the independent variable to the reaction energy in a BEP relation, one does not derive the full potential of the scaling relations. 

FIGURE 6.9 Linear transition state scaling relations for the dissociation of a number of simple diatomic molecules. It is clear from the plots that for a given surface geometry, aU the data cluster around the same universal line. Adapted from Nprskov et al. (2002). (See insert for color representation of the figure.)... 

We note that there are two parameters describing the catalyst, AE and E, and because of the transition state scaling relation, there is only one independent variable, which we choose to be AEj. The scaling relation means that there is a single descriptor of reactivity, AE. We will show later in this chapter how the scaling relations allow the identification of a few descriptors of reactivity even for more complicated reactions. 

Dissociation of A follows a transition state scaling line with the slope of 0.87 and the intercept of 1.34 eV, which is what is found for the dissociation of diatomic molecules on the 211 steps of transition metal snrfaces (see Chapter 6). 

Figure 9.5 suggests a classification of structure dependence of catalytic reactions. In the figure, we show transition state scaling lines for activation energies and the... 

Transition states are often considered special because they have a very short lifetime. In terms of their adsorption properties, however, they are not different from any other surface species and obey the same physical principles. It is therefore not surprising that scaling laws for transition states exist in the same way as they do for other surface intermediates. The truly remarkable aspect is that transition state scaling for a large number of reactions is universal and can be described by a single linear relationship " However, before we continue to discuss the beauty of transition state scaling it is important to clarify several technical terms used in the following discussion. 

Figure 1.7 Transition state scaling (a) and BEP relation (b) for (de-)hydrogenation reactions.

Using transition state scaling we can find xs as a function of ps. 

Reaction steps (3) and (4) in the mechanism for CO oxidation are both surface reactions, i.e. all reactants and the transition state are adsorbed species, and for this type of reactions the pre-exponential factors are typically on the order of v=10 s . The underlying assumption is that the entropy of the transition state is similar to the entropy of the initial state (A5 = 0) and eqn (1.33) reduces to z/= 10 5 at room temperature. The activation barriers for steps (3) and (4) can be found from the (transition state) scaling relations identified by Falsig et al. for fcc(lll) surfaces. ... 

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