Transition state scaling relations

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. 

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. ... 

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

Of related interest are results for water response to an instantaneous change in the dipole of a solute [44a], for the time scale of the solvent response for several charge-transfer reactions in water, including the SN2 reaction [49], and for a similar response for Fc21 - Fe3+ in water [44b]. The time scales found in those studies for the water solvent relaxation - and that originally found in [5] for time-dependent friction on the Sn2 transition state - are similar to those observed for the prior reorganization of the solvent H20. 

By changing the reactivity of the alkylating agent, it is possible to vary the magnitude of an ortho steric effect. Thus, the reactivity of 2-substituted pyridines toward Mel in acetone is linearly related on a logarithmic scale to the reactivity of the same substrates toward methyl fluorosulfonate in benzene. The fluorosulfonate is about 104 times more reactive than the iodide, and so the transition state for quaternization occurs earlier. The earlier transition state gives rise to a smaller steric effect the slope of the plot demonstrating the dependence of the steric effect on reactivity is 0.69.76... 

Fig. 2.51 Effect of reciprocating shear (strain amplitude, k = 200%) on the ODT of an /pep = 0.55 PEP-PEE diblock (Koppi etal. 1993). Here y denotes the shear rate.The equilibrium order-disorder transition (, A) and disordered state stability limit (A.O) are shown. The upper curve is a fit to the scaling relation Tom y2- The lower curve represents the. scaling rs(A) A-i,3Todt> where A = y/y, with y an adjustable, parameter. Points given by and O were obtained at fixed temperature by varying y, while those represented by A and A were determined by varying the temperature at fixed y.

The existence of polarizability thus renders impossible any unique scale of electrophilic reactivity. The two most common theoretical measures, namely ir-electron densities and localization energies, correspond to transition states approximating the ground state and the Wheland intermediate, respectively, whereas the transition state (the precise structure of which is unknown), lies somewhere in between, it Densities, which relate to a situation where inductive effects are dominant, will tend to predict a relatively low 2- 3-rate ratio since all of the heteroatoms are inductive acceptors (-/). By contrast, since it electrons are delocalized from the heteroatoms more to the 2- than to the 3-position, localization energies will predict a high 2- 3-rate ratio. The importance of these factors becomes particularly evident in consideration of the substitution of benzo derivatives of these molecules (Chapter 8). 

Scheme 14 is related to the potential energy profile in the vicinity of the transition state in the dissociation/recombination equilibria of [3C (X = Y = Z)] given by the Br0nsted-type analysis, the rate-equilibrium relationship in terms of a fixed Y-T a scale for the equilibrium. The potential energy surface should be essentially non-crossing, and consistently, the assumption that the Hammond shift in the transition-state coordinate is reflected exclusively in the p value but not in the r value can be applied to systems involving an appreciable shift in the structure of the solvolytic transition states. 

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