Equilibrium, chemical linear free-energy relationships

Linear free energy relationship (LFER) — For various series of similar chemical reactions it has been empirically found that linear relationships hold between the series of free energies (-> Gibbs energy) of activation AG and the series of the standard free energies of reactions AGf, i.e., between the series of log fc (k -rate constants) and log K (Kt - equilibrium constants) (z labels the compounds of a series). Such relations correlate the - kinetics and -> thermodynamics of these reactions, and thus they are of fundamental importance. The LFER s can be formulated with the so-called Leffler-Grunwald operator dR ... 

Numerous relationships exist among the structural characteristics, physicochemical properties, and/or biological qualities of classes of related compounds. Simple examples include bivariate correlations between physicochemical properties such as aqueous solubility and octanol-water partition coefficients (Jtow) and correlations between equilibrium constants of related sets of compounds. Perhaps the best-known attribute relationships to chemists are the correlations between reaction rate constants and equilibrium constants for related reactions commonly known as linear free-energy relationships or LFERs. The LFER concept also leads to the broader concepts of property-activity and structure-activity relationships (PARs and SARs), which seek to predict the environmental fate of related compounds or their bioactivity (bioaccumulation, biodegradation, toxicity) based on correlations with physicochemical properties or structural features of the compounds. Table 1 summarizes the types of attribute relationships that have been used in chemical fate studies and defines some important terms used in these relationships. 

The phenomenon of compensation is not unique to heterogeneous catalysis it is also seen in homogeneous catalysts, in organic reactions where the solvent is varied and in numerous physical processes such as solid-state diffusion, semiconduction (where it is known as the Meyer-Neldel Rule), and thermionic emission (governed by Richardson s equation ). Indeed it appears that kinetic parameters of any activated process, physical or chemical, are quite liable to exhibit compensation it even applies to the mortality rates of bacteria, as these also obey the Arrhenius equation. It connects with parallel effects in thermodynamics, where entropy and enthalpy terms describing the temperature dependence of equilibrium constants also show compensation. This brings us the area of linear free-energy relationships (LFER), discussion of which is fully covered in the literature, but which need not detain us now. 

The history of quantitative structure-activity relationships dates back to the last century, when Crum-Brown and Fraser in 1865 postulated that there ought to be a relationship between physiological activities <1> and chemical structures C. Later, Richet correlated toxicities with aqueous solubility. Around 1900, Meyer and Overton found linear relationships between the narcotic potencies of organic compounds and their partitioning behavior. In the mid-1930s, Hammett defined a reaction constant p to describe the reactivity of aromatic systems R, expressed by rate constants k (or equilibrium constants K) and a parameter o to describe the electronic properties of aromatic substituents X (1 equation 1) (see Linear Free Energy Relationships (LFER)) ... 

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