Linear free energy relations reactions

These techniques are known as linear free energy relations, LFER. Imagine that one has determined the rate constants, or the Gibbs free energies of activation, for a series of reactions. The reactions are all the same, save for (for example) a different substituent on each reactant. The substituent is not a direct participant in the reaction. In an LFER, the values of log k or AG are correlated with some characteristic of the substituent as manifested in another reaction series. If the correlation is successful, then the two series of reactions have a common denominator. This technique has proved to be a powerful one for systematizing reactivity. We shall see a number of such correlations. 

Transition state theory is presented with an emphasis on solution reactions and the Marcus approach. Indeed, to allow for this, I have largely eliminated the small amount of material on gas-phase reactions that appeared in the First Edition. Several treatments have been expanded, including linear free-energy relations, NMR line broadening, and pulse radiolytic and flash photolytic methods for picosecond and femtosecond transients. 

Despite many papers over many years, there is still a serious shortage of information that allows linear free energy relation treatment of these reactions. The available linear free energy relations, some of them calculated for this chapter, are collected in Tables 1.4 and 1.5. There are definite indications that p is... 

By linear free energy relation arguments, Williams et al. concluded that in the case of a five-membered ring sultone the reaction with a phenoxide was either stepwise or, if concerted, had a transition state close to the pentacoordinated intermediate. ... 

The Hammett equation is the best-known and most widely studied of the various linear free energy relations for correlating reaction rate and equilibrium constant data. It was first proposed to correlate the rate constants and equilibrium constants for the side chain reactions of para and meta substituted benzene derivatives. Hammett (37-39) noted that for a large number of reactions of these compounds plots of log k (or log K) for one reaction versus log k (or log K) for a second reaction of the corresponding member of a series of such derivatives was reasonably linear. Figure 7.5 is a plot of this type involving the ionization constants for phenylacetic acid derivatives and for benzoic acid derivatives. The point labeled p-Cl has for its ordinate log Ka for p-chlorophenylacetic acid and for its abscissa log Ka for p-chloroben-zoic acid. The points approximate a straight line, which can be expressed as... 

We are concerned in this chapter with the mechanism of a reaction, that is, the detailed manner in which it proceeds, with emphasis on the number and nature of the steps involved. There are several means available for elucidation of the mechanism, including using the rate law, and determining the effect on the rate constant of varying the structure of reactants (linear free energy relations) and of outside parameters such as temperature and pressure. Finally chemical intuition and experiments are often of great value. These means will be analyzed. 

The Tafel relationship as expressed in eqns. (82b) and (83b) is a linear free energy relation of the rate coefficient of a net electrode reaction (neglecting the back reaction). From eqn. (78)... 

As will be discussed in Sect. 5, linear free energy relations allow comparisons between the kinetics of heterogeneous (electrode) and homogeneous homomolecular charge transfer reactions. 

The simplest linear free energy relation that has been used to describe the attack of a series of nucleophiles in an SN2 reaction is the Swain-Scott relation (Swain and Scott, 1953). In our notation the relation becomes (45), where the nucleophilicity parameter for X, x, is defined by (46) or its equivalent (47)... 

Finally, we would like to emphasize that, besides obtaining values of ccfrom the Marcus analysis, another great advantage is that one can separate kinetic and thermodynamic contributions to the parameters in linear free-energy relations. In this article we have done this for the Swain-Scott nucleophilicity parameter n, for m describing the change of reaction rate with solvent, and for the Hammett p-values. 

Warshel, A., Hwang, J-K and Aqvist (1992) Computer simulations of enzymatic reactions examination of linear free-energy relation ship and quantum-mechanical corrections in the initial proton-transfer step of carbonic anhydryse, Farad. Dissc. 93, 225-238. 

The bacteriostatic activity of a series of substituted trans-3-benzoylacrylic acids has been successfully correlated by Hansch linear free energy relations involving polar and partition substituent constants. The activity-lipophilicity relations for this series closely parallel those found previously for other antibacterial agents, with an ideal lipophilic character for gram-positive cells of 6.1 and, for linear dependence, a slope of 0.7. A polar reaction constant, p, of about —0.6 to —0.7 is given. A possible mode of action for these acids and their related substituted cis- and trans-3-benzoyl acrylic acids and esters is discussed as an enzyme-inhibitor interaction. 

The interest in proton transfer to and from carbon arises partly because this process occurs as an elementary step in the mechanisms of a number of important reactions. Acid and base catalysed reactions often occur through intermediate carbonium ions or carbanions which are produced by reactions (1) and (2). A knowledge of the acid—base properties of carbonium ions or carbanions may also help in understanding reactions in which these species are present as reactive intermediates, even when they are generated by processes other than proton transfer. Kinetic studies of simple reactions such as proton transfer are also important in the development of theories of kinetics. Since both rates and equilibrium constants can often be measured for (1) and (2) these reactions have been useful in the investigation of correlations between rate coefficients and equilibrium constants (linear free energy relations). 

Surface complexation is a typical multi-component reaction, similar to cation exchange. The database for surface complexation includes complexation constants for major elements in groundwater such as and S04 , but not for and HCOs". In the first instance, constants for these ions can be estimated with linear free energy relations (LFER s) in which the properties of similar chemical systems are compared and interpolated (Dzombak and Morel, 1990). Thus, the surface complexation constant for is expected to lie in between the ones for and for Zn, in line with the known differences of the association constants of these heavy metals with OH in water. For the weak sites, the LFER gives ... 

R. Parsons, Croat. Chem. Acta, 42, 281 (1970) is simply the slope of a linear free-energy relation for the elementary electrochemical reaction. 

At the time that the basic formulation and testing of the mathematical models of quantitative structure-activity correlations were being made, another type of approach, the linear free-energy related model, was introduced (2). Using the basic Hammett equation (22, 36) for the chemical reactions of benzoic acid derivatives (Equation 12), several investigators attempted quantitative correlations between physicochemical properties... 

This relation has been used to predict and interpret both self-exchange and crossreaction rates (or even "12), depending on which of the quantities have been measured experimentally. Alternatively, one could study a series of closely related electron-transfer reactions (to maintain a nearly constant X12) as a function of AG 2 a plot of In ki2 vs. In A 12 is predicted to be linear, with slope 0.5 and intercept 0.5 In ( 11 22)- The Marcus prediction (for the normal free-energy region) amounts to a linear free-energy relation (LFER) for outer-sphere electron transfer. 

By about 1980, a reasonable empirical understanding of carbenic philicity seemed to be at hand electrophiles, ambiphiles, and nucleophiles had been identified and could be assigned m xy or p xv values that reflected the magnitude and character of their selectivity during their additions to alkenes. And yet, our rationalization of these reactions only in terms of relative reactivities and linear free energy relations was surely incomplete. 

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