Bell-Evans-Polanyi

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

BASE PAIRING BECQUEREL BEER-LAMBERT LAW ABSORPTION SPECTROSCOPY Bell-Evans-Polanyi principle,... 

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. 

Fukuzumi and Kochi, 1981a). On the basis of a Bell-Evans-Polanyi diagram, an -value closer to 0.5 would have been expected. However we do not feel that the -value of 1 necessarily constitutes evidence for the ion-pair-like character of the transition state. On the basis of the CM model the transition state is described by (74). This would imply only c. 50% ion-pair character in... 

Equation (82) predicts that for reactions with zero free energy change a = 0.5, while for exothermic reactions, a < 0.5 and for endothermic reactions, a > 0.5. Since according to both Marcus theory and the Bell— Evans-Polanyi model early transition states are related to exothermic reactions and late transition states to endothermic reactions, a may be interpreted as a relative measure of transition state geometry. However, in our view even this interpretation should be treated with a measure of healthy scepticism. Even if one accepts Marcus theory without reservation, the a... 

The predictions of the CM model are exactly the same. In line with a simple Bell-Evans-Polanyi diagram (e.g. Fig. 18), stabilization of the product configuration leads to an earlier transition state, while stabilization of an intermediate configuration leads it increasingly to mix into the transition-state wave-function. For example, stabilization of the carbocationic configuration [36] results in the transition state acquiring more of that character so that an E2 process becomes more El-like (Fig. 266). 

Apparently, these results implied an inverse relationship between reactivity and selectivity, with the reactivity of the carbocation measured by the inverse of the rate constant for solvolysis. This indeed was not unexpected in the context of a general perception that highly reactive reagents, especially reactive intermediates such as carbocations, carbanions, or carbenes are unselective in their reactions.257 259 Such a relationship is consistent with a natural inference from the Hammond postulate258 and Bell-Evans-Polanyi relationship,260 and is illustrated experimentally by the dependence of the Bronsted exponent for base catalysis of the enolization of ketones upon the reactivity of the ketone,261,262 and other examples21,263 including Richard s careful study of the hydration of a-methoxystyrenes.229... 

For reactions that satisfactorily can be represented in terms of independent bondbreaking and bond-forming processes the Bell-Evans-Polanyi (BEP) Principle [16, 17] holds ... 

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). 

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. 

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. 

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 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. 

Figure 2. The Bell-Evans-Polanyi treatment for the reaction A + BC - AB + C indicating the reaction profile. (Taken from Dewar, 1969.)...

This final point signifies that the value of a in the rate-equilibrium relationship (2) is not constant but decreases as the reaction becomes increasingly exothermic. It should be noted however that since the Bell- Evans-Polanyi model and the Hammond postulate are couched in energy terms the assumption that free energy changes (AG°) are proportional to energy changes (A °) is inherent in eqns (1) and (2). 

Chemical intuition, which is very useful in the location of minima, usually fails in the search for saddle points. The symmetry of the transition-state structure was discussed and it was shown that many transition states exhibit low symmetry (130-132). Some empirical rules have been developed for approximate localization of the transition state. The rule referred to in the literature as the Bell-Evans- Polanyi-Leffler-Hammond rule is well known the more exoergic the process, the more the transition-state geometry resembles that structure which belongs to a higher energy minimum on the given potential energy surface. This idea has been supported by calculations on SN2-activated complexes (133). 

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

THE BELL-EVANS-POLANYI PRINCIPLEIHAMMOND POSTULATE/MARCUS Tl lEORY... 

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