Evans-Polanyi correlation

Strengths of the substrate C-H bond which is broken and that of the O-H bond which is being formed. The successful application of Evans-Polanyi correlations of the type shown in Fig. 17.6 for transition metal oxidants has led to the generalization that these reactions proceed by a synchronous PCET process that is mechanistically identical to hydrogen abstraction by an organic radical oxidant [52, 54]. 

Reactions involving simple reactants and products often offer simple descriptions of activity or selectivity. The Bronsted-Evans-Polanyi (BEP) relation, for instance, states that the activation barrier, Ea, and the heat of reaction, AE, of elementary dissociation reactions are often linearly correlated (Fig. 1). Extensive DFT calculations have supported this empirical relation for a large number of elementary dissociation reactions and suggest that it is due to the structural similarities between the transition state and the product states. When such a dissociation step is rate-limiting, knowing AE is sufficient to capture the activity of the overall reaction, which exhibits volcano-shaped... 

In the present chapter, we have attempted to illustrate how surface bonding and catalytic activity are closely related. One of the main conclusions is that adsorption energies of the main intermediates in a surface catalyzed reaction is often a very good descriptor of the catalytic activity. The underlying reason is that we find correlations, Brpnsted-Evans-Polanyi relations, between activation barriers and reaction energies for a number of surface reactions. When combined with simple kinetic models such correlations lead to volcano-shaped relationships between catalytic activity and adsorption energies. 

The most widely used correlation of this type is the Evans-Polanyi relationship... 

Table 4 presents a fairly consistent correlation of reactivity and selectivity. The value of a in the Evans-Polanyi equation increases as the strength of the new bond (HX in... 

A closely related statement of the correlation of energy barriers with heats of reaction is known as the Bell-Evans-Polanyi (BEP) principle (equation 6.69). ° Note that the BEP principle is concerned with the activation energies, while the Hammond and Leffler postulates are concerned with the structures of transition states. Of course, bonding and energy are inherently related, so the Hammond-Leffler postulate and the Bell-Evans-Polanyi principle are complementary. 

The objective of the study presented in this paper is to inspect the nature of the relation between the acidity and the activity of a given site towards the transformation of hydrocarbons over zeolites and to compare the relation derived from first-principles modelling of the catalytic mechanism with the type of correlations that are experimentally obtained and which can be viewed as an application of the Bell-Evans-Polanyi principle. 

The addition reactions shown in Table 2 have small barriers that correlate roughly with the stability of the produced alkyl radical. Such correlations are more obvious for other types of reactions, e.g., abstraction reactions. They are known as linear free-energy relationships (LFER), and the most prominent correlation is the Evans-Polanyi relationship... 

This simple model shows how linear free energy relationships can arise from reactant and product energy surfaces with a transition state between them that is defined by the curve-crossings. Figure 19.19 shows how shifting the equilibrium to stabilize the products can speed up the reaction. It also illustrates that such stabilization can shift the transition state to the left along the reaction coordinate, to earlier in the reaction. If mil Im l, the transition state will be closer to the reactants than to the products, and if I mi Evans-Polanyi model rationalizes why stabilities should correlate linearly with rates. 

An Evans-Polanyi type of correlation is used to parameterize activation energies i a based on known thermod5mamic properties of gas phase hydrocarbons and carbocations. That is, i a = + ocAff where A// is the... 

Our initial interest in applying the cross relation to HAT grew out of the limitations of the Bell Evans Polanyi (BEP) equation diseussed above. This equation holds within a set of similar reactions, but with the expansion of HAT reactions to include transition metal reactions it was not clear what made reagents similar. It was not evident why different classes of reactions fall on different correlation lines (defined by the parameters a and p, see above). For example, it has long been known that, at the same driving force, H abstraction from O-H bonds is substantially faster than from C-H bonds. Transition metal... 

Figure 5.5 Potential energy profile along the reaction coordinate for an early, midway, and late barrier. We show the two asymmetric cases as corresponding to an exoergic and endoergic reaction. The correlation between location of the barrier, shown by an arrow, and relative stability of reactants and products can be understood on the basis of the Evans-Polanyi mode/that we will discuss. The correlation shown is a useful rule of thumb, known in organic chemistry as Hammond s postulate. In structural terms this is sometimes stated as the more exoergic the reaction, the more the configuration at the barrier will be reactant-like.

Let us bring together several key ideas that we have discussed. We seek a imified approach where both the role of the solvent and the rearrangement of the reactants to form products are taken into consideration. We further want the approach to center attention on the correlation of reactivity with slmcture, a theme that we started in Chapter In essence, we generalize the one-coordinate discussion of solvation in Section 11.1 to a two-dimensional world that consists of a solvation coordinate and a reaction coordinate. Starting from the gas phase, what we do is generalize the one-coordinate Evans-Polanyi model to include the role of the solvent. 

BEP = Bell-Evans-Polanyi BOVB = breathing orbital VB FMVB = fragments in molecules based VB HL structure = Heitler-London structure PRS = perfectly resonating state VBCM = VB configuration mixing VBSCD = VB state correlation diagram VBSCF = self-consistent field VB. 

In the mid-1930s of the twentieth century, Bell, Evans and Polanyi correlated energies of activation, E, for several reactions in the vapour phase with heats of reaction, A/I°, according to the following expression ... 

Transition state properties cannot be directly estimated from this method. To do this, as mentioned in Chapter 3, Br0nsted—Evans—Polanyi relationships are appHed relating kinetics with thermochemical properties. Such relationships use correlations developed from similar reactions belonging to the same homologous series. 

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