Leffler principle

The hypothesis that Bronsted exponents measure transition state structure in this way may be traced back to the Leffler principle [2]. This principle assumes that some perturbation on a reacting system, say a substituent change in one of the reactants, will change the free energy of its transition state by an amount intermediate between the changes produced in the free energy of the reactants and the free energy... 

In other words, under these restrictive conditions, outer sphere electron-transfer reactions obeying the Marcus-Hush model are typical examples where the Hammond-Leffler postulate and the reactivity-selectivity principle (see, for example, Pross, 1977, and references cited therein, for the definition of these notions) are expected to apply. 

ACIDITY FUNCTION BUNNETT-OLSEN EQUATIONS DECREE OF DISSOCIATION HAMMETT EQUATION HAMMOND PRINCIPLE/POSTULATE LEFFLER S ASSUMPTION REACTING BOND RULES HANES PLOT... 

An extensive review with many examples125 shows that the reactivity-selectivity principle cannot be used to predict the selectivity of a reaction except in unique systems where one reaction is close to or diffusion controlled. The relative importance of the Hammond effect and the frontier-orbital effects determines the reactivity-selectivity relationship that will be found in a particular system. The review also concludes that the Hammond-Leffler a-value cannot be used as an indicator of transition-state structure. 

On the basis of the Leffler-Hammond postulate the theoretical justification for the reactivity-selectivity principle may be observed. First, let us define the selectivity 5, of a species A, in its reaction with two competing reagents X and Y, as indicated by (4), where k ... 

It is important to note that the above presentation, justifying the reactivity-selectivity principle, is based on a number of fundamental assumptions. First, it is assumed that the Leffler-Hammond postulate is valid, which in turn implies that the reaction under consideration obeys a rate-equilibrium relationship [eqn (2)]. This assumption often cannot be verified since for reactions of highly active species such as carbenes, free radicals, carbonium ions, etc., equilibrium constants are generally not measurable. However it follows that for reactions which do not conform to a rate-equilibrium relationship, no reactivity-selectivity relationship is expected. Also, in Fig. 4, the difference in the free energy of the... 

In line with the Leffler-Hammond postulate, which is a differential analogue of the Hammond postulate, the rationale for a differential reactivity-selectivity principle has been demonstrated, i.e., the marginal stabilization of a particular species will result in a corresponding increase in its selectivity. Recently, the view has been expressed that there is no substantive evidence for such behaviour... 

Equation (112) was originally proposed for electron transfer reactions and modified for proton transfer. It has been derived in other ways [192, 201, 202], for example from [192] Leffler s Principle (Sect. 3.2.2) and by assuming a model for reaction of AH with B in which the energies of AH and BH+ are represented by two intersecting parabolae [202]. ... 

The curve acts as a reference line, but it also shows that the slope, a, in Equation (1.30) has a value near one for AG° near zero, and approaches zero as AG ° becomes a large negative number. Such behavior is an expected consequence of the Bell-Evans-Polanyi-Leffler-Hammond principle.It corresponds to a late transition state for the more difficult reactions and a progressively earlier transition state for more exergonic reactions. However, the curve appears to level off at an n value near 8, which corresponds to a second-order rate constant of about 1 s at 25 °C, far from the diffusion-controlled limit. 

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. 

In principle, similar types of relationships are also applicable to other reaction types, such as electron-transfer and substitution reactions. Hammett, for example, has had considerable success in correlating the rate of benzene substitution reactions [29]. For an interesting treatise on this general subject, see Leffler and Grunwald [32]. 

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. 

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