Trends in Activation Energies

A more accurate interpolation scheme can be obtained from calculations of oxygen adsorption on systems with overlayers of metal A and metal B on the same host material B. This is calculated as 

While the interpolation model is far from perfect, it gives a fast and easy way of estimating the adsorption energies for alloys based on calculations or experiments for simpler systems. Given how simple the two models are, it is surprising how well it woiks. In fact, the d-band model can be used to elucidate why this is the case. 

Under the assumption that in Equation (8.1) is independent of the metal considered, all effects due to having several metal components are to be found in the A d hyb term. For a systan where an adsorbate couples to an ensemble of different surface metal atoms, the natural approach is to assume that the adsorption strength is a linear combination of contributions from each metal. We have seen earlier that AEd.hyb is a function of the 7-band center, and in a case where the adsorbate couples to several different metal atoms, then according to the arguments earlier, the d-band center of relevance should be an average of the d-band centers for each of the transition metal atoms to which the adsorbate couples  

is the coupling matrix element between the adsorbate state and the d-states on surface atom j. To the extent that AE. yb is a linear function of e, variations in the adsorption energy with varying types of surface transition metal atoms will be an average of the contribntions from each type. 

So far, we have only focused on electronic structure effects on the chemisorption of intermediates on metal and metal alloy surfaces. To be able to describe the behavior of complete catalytic reaction, we also need information about the activation energies, the energy needed to jump between two intermediate steps on a potential energy surface. The importance of this has been described in some detail in Chapters 6 and 7. 

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Table XV lists the isokinetic temperatures of several reactions representing a wide variety of mechanisms, these examples having been chosen because the isokinetic temperature happened to fall in the popular experimental range between 0 and 100°. There are many other polar reactions that have isokinetic temperatures well outside of the accessible temperature range there are many whose variations in activation energy and entropy are not parallel and these, of course, do not have an isokinetic temperature even approximately. When one of a series of reactions deviates markedly from a parallel trend in activation energy and entropy established by the others, it is probable that it differs in mechanism from the others. This is a better indication of a change in mechanism than either marked differences in rate or in activation energy.

The trend in activation energies (Table I) shows the electrophilic nature of attack by the sulfur atom increasing number of alkyl substituents on the doubly bonded carbons decreases the value of E, while increasing number of halogen substituents on the doubly bonded carbons increases the value of . These variations are correlated with molecular properties such as ionization potentials, excitation energies, and bond... 

The results were in agreement with the trend in activation energy observed experimentally for a series of dioxetans with an increasing number of alkyl groups. The unsubstituted parent dioxetan is not sufficiently stable (as predicted) to allow its isolation, but the others gave good experimental values. This analysis does not constitute a proof of the diradical formation, but is compatible with it. 

Trends in dissociative energies and activation energies for dissociation as a function of the number of d-electrons. The results are calculated in the Newns-Anderson model including the coupling between an adsorbate level epsilon a and the metal d-band. 

In the following, we first consider trends in chemisorption energies. Similar trends in activation barriers will be dealt with in the next section. 

The trend in reactivity is almost entirely determined by differences in activation energies. 

The rate of elementary reactions of certain transition-metal complexes, such as insertions or substitutions, can be controlled by the substituents at the metal center. In favorable cases, usually in families of closely related systems, these substituents can affect the reactivities and the chemical shifts of the transition metal nuclei in a similar, parallel fashion, resulting in an apparent correlation of both properties. Modem DFT methods can reproduce these findings, provided that changes in rate constants are reflected in corresponding trends in activation barriers or BDEs on the potential energy surface. 

The Arrhenius parameters for the gas-phase unimolecular structural isomerizations of 1,1,2-trimethylcyclopropane28 to three isomeric methylpentenes and two dimethyl-butenes, and of 1,1,2,2-tetramethylcyclopropane29 to 2,4-dimethylpent-2-ene have been determined over a wide range of temperatures. Despite previous reports on substantial decreases in activation energies for structural isomerizations of methyl-substituted cyclopropanes, this study has revealed that the trend does not continue beyond dimethylcyclopropane isomerization. 

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