Structure-based free energy relationships

More recent measurements related to carbocation stabilities in strongly acidic media have involved rates of reaction rather than equilibria.52,54,72 75 Application of the X0 function to the correlation of reaction rates as well as equilibria mirrors the use of structure-based free energy relationships. Of interest is the access this gives to rate constants for (a) protonation of weakly basic alkenes and (b) acid-catalyzed ionization of alcohols to relatively unstable... 

Because of the large number of chemicals of actual and potential concern, the difficulties and cost of experimental determinations, and scientific interest in elucidating the fundamental molecular determinants of physical-chemical properties, considerable effort has been devoted to generating quantitative structure-property relationships (QSPRs). This concept of structure-property relationships or structure-activity relationships (QSARs) is based on observations of linear free-energy relationships, and usually takes the form of a plot or regression of the property of interest as a function of an appropriate molecular descriptor which can be calculated using only a knowledge of molecular structure or a readily accessible molecular property. 

The usual experimental approach3 is based on the Hammond postulate (Hammond, 1955). A transition state, which lies by definition between the starting materials and products for a particular step of a reaction, is supposed to be closer in structure, because closer in energy, to the higher energy species of the two. Various techniques, particularly linear free energy relationships, are available to compare the effects of various probes... 

The hydrolysis of alkoxysilane esters has been extensively studied. The influences of the silane ester structure and acids, bases, solvent, and temperature on the reaction rates and kinetics have been investigated. Linear free energy relationships, such as Taft equations and Brensted plots, were used to gain... 

What is required is a value of pA extrapolated to water (pAH2°). Fortunately, the dependences of the relevant equilibrium constants on the composition of the acidic medium are well described by free energy relationships. This means that an unknown pAa (or pAR) can be obtained from measurements in concentrated acidic solutions by plotting values against known pAas for the protonation of a reference base.52,53 In practice, medium acidity parameters, XQ = pKa — pAaH2°, are conveniently defined for a family of structurally... 

Quantitative structure/activity relationships (QSARs) for hydrolysis are based on the application of linear free energy relationships (LFERs) (Well, 1968). An LFER is an empirical correlation between the standard free energy of reaction (AG0), or activation energy (Ea) for a series of compounds undergoing the same type of reaction by the same mechanism, and the reaction rate constant. The rate constants vary in a way that molecular descriptors can correlate. 

Hilal (1994) calculated the pKa values of 214 dye molecules using the SPARC (SPARC Performs Automated Reasoning in Chemistry) computer program. SPARC computational methods use the knowledge base of organic chemistry and conventional Linear Free Energy Relationships (LFER), Structure/Activity Relationships (SAR), and Perturbed Molecular Orbital (PMO) methods. 

It was evident that a Mannich base that would allow the study of the elimination process free from consecutive reactions must have piiiiB <8- Since no such p.K values were foimd in the literature, the principle of linear free energy relationships was adopted for selection of the suitable model, starting from the available pA u-values of various amines. It was assumed that structural changes would similarly affect the pA if alues for amines and the pA wR-values for Mannich bases, as expressed in equation (6). 

The pJ a values of phosphine oxides have been measured. Their deviation from Hammett base behaviour, their Ho dependencies, and their sites of protonation have been studied. The acidifying effects of phosphoryl, phosphinyl, and thiophosphinyl groups have been studied. Ionization constants have been used to examine substituent effects in alkanephosphonic acids and phosphinyl-carboxylic acids, structural correlations in various phosphorus acids, and solvent effects on the properties of thiophosphorus acids. The linear free-energy relationships, which are based mainly on p a data, have been analysed and reviewed. ... 

This study is a comprehensive review of data reported on the effect of the composition of the reaction mixture on the hydrogenation of olefinic reactants in the liquid phase. It is mainly based on papers published by the authors, which deal with the effect of the structure of the reacting compounds on their reactivity and adsorptivity on hydrogenation catalysts, and with the effect of solvents on hydrogenation in the liquid phase. The majority of these studies were carried out with a view to quantify the particular effects, with the utilization of the LFER (linear free energy relationship) method. On the one hand, new possibilities for the application of these relationships appeared, but on the other, a number of limiting factors were found, connected predominantly with the considerably complex character of the systems involved in catalytic hydrogenation in the liquid phase. 

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 best known of the extrathermodynamic equation based on linear free energy relationship on the reaction rate or eqnilibrinm of the aromatic system to the structure of the reagent, is the Hammett eqnation ... 

The strength of this interaction is shown to depend on the basicity of the hydrogen bond acceptor site in the inhibitor. This correlation is based on a linear free energy relationship in a series of benzophenones with different substituents. Also, the dissolution inhibition efficiencies of a series of sulfonyl esters are shown to be better than structurally similar carbonyl esters. These experiments reveal a set of criteria for the rational design of dissolution inhibitors. 

However equally important is the availability of physically grounded models that can provide understanding of chemical reactivity. In the past, theories of reactivity have been based on empirical structure-reactivity relationships (viz. linear free energy relationships) or qualitative theoretical concepts (viz. Woodward-Hoffmann approach or the frontier orbital method)[4-ll]. However, there is a different approach, which is potentially more fruitful. In this approach one uses physically grounded models that can be obtained from the best state of the art methodology of quantum chemistry. These physically grounded models must be both quantitative and qualitative. On the one hand, any model used should reproduce the numerically computed quantities exactly, on the... 

Rustad JR, Dixon DA, Kubicki JD, Felmy AR (2000a). The gas phase acidities of tetrahedral oxyacids from ab initio electronic structure theory. J Phys Chem A 104 4051-4057 Rustad JR, Dixon DA, Rosso KM, Felmy AR (1999a) Trivalent ion hydrolysis reactions A linear free energy relationship based on density functional electronic structure calculations. J Am Chem Soc... 

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