The Bell-Evans-Polanyi Principle

In Section 1.2.1 we discussed the stabilities of reactive radicals. It is interesting that they make an evaluation of the relative rates of formation of these radicals possible. This follows from the Bell-Evans-Polanyi principle (Section 1.3.1) or the Hammond postulate (Section 1.3.2). 

Equation 1.1 becomes Equation 1.2 after (a) dividing by T, (b) taking the logarithm, and (c) differentiating with respect to T. 

With Equation 1.2 it was possible to calculate the activation enthalpy ARP for each individual reaction. 

The thermolyses presented in this chapter are one example of a series of analogous reactions. The Bell-Evans-Polanyi relationship of Equation 1.3 also holds for many other series of analogous reactions. The general principle that can be extracted from Equation 1.3 is that, at least for a reaction series, the more exothermic the enthalpy of reaction, the faster it will be. But this doesn t mean that all reactions that are exothermic are fast, so be careful. 

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The Bell-Evans-Polanyi Principle/Hammond Postulate/... 

For a reaction adequately described by just two configurations, reactant and product, the analysis of substituents effects is straightforward and was first treated by Horiuti and Polanyi (1935) almost 50 years ago. Subsequent contributions by Bell (1936) and Evans and Polanyi (1938) have led to these general ideas being jointly termed the Bell-Evans-Polanyi principle (Dewar, 1969). The treatment of multiconfiguration reactions is analogous and is illustrated in Fig. 12. Let us discuss this in detail. 

Fig. 1.10. Enthalpy change along the reaction coordinate in a series of thermolyses of aliphatic azo compounds. All thermolyses in this series except the one highlighted in color follow the Bell-Evans-Polanyi principle.

For five out of the six reactions investigated, Figure 1.10 shows a decrease in the activation enthalpy AH with increasingly negative reaction enthalpy AH. Only for the sixth reaction— drawn in red in Figure 1.10—is this not true. Accordingly, except for this one reaction AH and AHr are proportional for this series of radical-producing thermolyses. This proportionality is known as the Bell-Evans-Polanyi principle and is described by Equation 1.3. 

This stabilization of the radical intermediates, arising from a better mesomeric stabilization of radicals in the phthalimide moiety, consequently increase the exoenergicity of reactions and, according to the Bell-Evans-Polanyi principle, lowers the activation barrier and thus enables processes that are unknown from ketones. The unique photochemical reactivity of phthalimides will be demonstrated with some examples. 

This follows from the Bell-Evans-Polanyi principle (Section 1.3.1) or the Hammond postulate (Section 1.3.2). 

The Bell-Evans-Polanyi Principle/Hammond Postulate/ Marcus Theory---------------------------------------------... 

The Bell-Evans-Polanyi principle rationalizes the increase in rates of many reactions with increase in exothermicity (the release of heat by a system as a reaction occurs) by describing the transition states as a blend of reactant and product configurations.As shown in Figure 6.12, the... 

Figure 19.1 Intersecting curves to illustrate the Bell-Evans-Polanyi Principle for a general group-transfer reaction (19.1a). Three members of a reaction series involving different acceptor groups B (/ = 1,2, 3) give separate energy curves for step (19.1c) each intersecting the energy curve for step (19.1 b).

Many reactions exhibit effects of thermodynamics on reaction rates. Embodied in the Bell-Evans-Polanyi principle and extended and modified by many critical chemists in a variety of interesting ways, the idea can be expressed quantitatively in its simplest form as the Marcus theory (15-18). Murdoch (19) showed some time ago how the Marcus equation can be derived from simple concepts based on the Hammond-Leffler postulate (20-22). Further, in this context, the equation is expected to be applicable to a wide range of reactions rather than only the electron-transfer processes for which it was originally developed and is generally used. Other more elaborate theories may be more correct (for instance, in terms of the physical aspects of the assumptions involving continuity). For the present, our discussion is in terms of Marcus theory, in part because of its simplicity and clear presentation of concepts and in part because our data are not sufficiently reliable to choose anything else. We do have sufficient data to show that Marcus theory cannot explain all of the results, but we view these deviations as fairly minor. 

THE BELL-EVANS-POLANYI PRINCIPLE/HAMMOND POSTULATE/MARCUS THEORY... 

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. 

More complete lists of calculated energies of the gas-phase Sn2 reactions of Y -h CH3X general type are available in Refs. [30,37] (the >i-INDO method) and [26,34] (4-3IG). The data obtained make it possible to check how the well-known relationships among the structural, kinetic and thermodynamic characteristics, such as the Bell-Evans-Polanyi principle, the Hammond postulate, etc., are obeyed in the case of the reactions which proceed without a solvent. 

The Bell-Evans-Polanyi principle relates the reaction barrier to the thermodynamic driving force of the reaction. 

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