Parameters linear free energy

Valko et al. [37] developed a fast-gradient RP-HPLC method for the determination of a chromatographic hydrophobicity index (CHI). An octadecylsilane (ODS) column and 50 mM aqueous ammonium acetate (pH 7.4) mobile phase with acetonitrile as an organic modifier (0-100%) were used. The system calibration and quality control were performed periodically by measuring retention for 10 standards unionized at pH 7.4. The CHI could then be used as an independent measure of hydrophobicity. In addition, its correlation with linear free-energy parameters explained some molecular descriptors, including H-bond basicity/ acidity and dipolarity/polarizability. It is noted [27] that there are significant differences between CHI values and octanol-water log D values. 

A. Verloop, Drug. Des., 3,133 (1972). The Use of Linear Free Energy Parameters and Other Experimental Constants in Structure-Activity Studies. 

Verloop, A., The use of linear free energy parameters and other experimental constants in structure-activity studies, [n Drug Design (E. J. Afiens, ed.) Academic Press, New York, 1972. 

Although racemization appeared to obey first-order kinetics during the early stages of the reaction, the apparent rate changed with time. The rate constants we used for calculation of thermo- namic and linear free-energy parameters were derived from the initial, linear rates. 

Solvents exert their influence on organic reactions through a complicated mixture of all possible types of noncovalent interactions. Chemists have tried to unravel this entanglement and, ideally, want to assess the relative importance of all interactions separately. In a typical approach, a property of a reaction (e.g. its rate or selectivity) is measured in a laige number of different solvents. All these solvents have unique characteristics, quantified by their physical properties (i.e. refractive index, dielectric constant) or empirical parameters (e.g. ET(30)-value, AN). Linear correlations between a reaction property and one or more of these solvent properties (Linear Free Energy Relationships - LFER) reveal which noncovalent interactions are of major importance. The major drawback of this approach lies in the fact that the solvent parameters are often not independent. Alternatively, theoretical models and computer simulations can provide valuable information. Both methods have been applied successfully in studies of the solvent effects on Diels-Alder reactions. 

The applicability of the two-parameter equation and the constants devised by Brown to electrophilic aromatic substitutions was tested by plotting values of the partial rate factors for a reaction against the appropriate substituent constants. It was maintained that such comparisons yielded satisfactory linear correlations for the results of many electrophilic substitutions, the slopes of the correlations giving the values of the reaction constants. If the existence of linear free energy relationships in electrophilic aromatic substitutions were not in dispute, the above procedure would suffice, and the precision of the correlation would measure the usefulness of the p+cr+ equation. However, a point at issue was whether the effect of a substituent could be represented by a constant, or whether its nature depended on the specific reaction. To investigate the effect of a particular substituent in different reactions, the values for the various reactions of the logarithms of the partial rate factors for the substituent were plotted against the p+ values of the reactions. This procedure should show more readily whether the effect of a substituent depends on the reaction, in which case deviations from a hnear relationship would occur. It was concluded that any variation in substituent effects was random, and not a function of electron demand by the electrophile. ... 

Linear free energy relationships, see Bronsted equation, Dual substituent parameter (equations), Hammett equation(s), Quantitative structure-activity relationships, Ritchie nucleophilicity equation... 

Recently, more detailed parameters for hydrogen bonding bases have been introduced and applied to many reactions demonstrating the existence of a linear free energy relationship between the hydrogen bonding donor and acceptor abilities and many kinetic or thermodynamic parameters91. 

If equation 5 is valid, if a linear relationship exists between AH and the calculated AE(t) parameters, and if a linear free energy relationship exists between AH and EA , we might expect that the following linear relationship might hold for the decomposition of reactant Y to produce free radicals R(Y) ... 

Nucleophilic reactivity toward Pt(II) complexes may be conveniently systematized via linear free energy relationships established between reactions of trans Ptpy2Cl2 (py = pyridine) with various nucleophiles and reactions of other Pt(II) complexes with the same nucleophiles. First, each nucleophile is characterized by a nucleophilicity parameter, derived from its reactivity toward the common substrate, trans Ptpy2Cl2. Reactivity toward other Pt(II) substrates is then quite satisfactorily represented by an equation of the form (21), wherein ky is the value of in the reaction with nucleophile Y... 

Equation (12) is a linear free-energy relationship, since activity coefficients/can be represented as AG° values. The reason for defining the slope parameter as in equation (12) (subscript e for equilibrium) is that a little rearranging of equations (11) and (12) leads to the easy-to-use Bunnett-Olsen equation for equilibria, equation (13) 30... 

The data for influence of solvents on oxidation propanthiole by chlorine dioxide are satisfactorily generalized by means of five parameters equation according to principles of Linear Free Energies Relationships (LFER). An essential role plays the density of media cohesion energy, that bears out radical process nature. 

Xrx is a parameter characterizing the homologous series RX. The values of /j,r are direct measures of the polar inductive effects of alkyl groups relative to that of methyl and correlate well with Taft s a values. Substituent-induced IP shifts can thus be handled by linear free energy relationships (LFER) of the Hammett pcr-type. 

Extensive collections of pK values are available in the literature, e.g., [98-101]. It is also possible to predict pK values for a broad range of organic acids and bases using linear free energy relationships based on a systematic treatment of electronic (inductive, electrostatic, etc.) effects of substituents which modify the charge on the acidic and basic center. Quantitative treatment of these effects involves the use of the Hammett Equation which has been a real landmark in mechanistic organic chemistry. A Hammett parameter (a), defined as follows ... 

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. 

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