Linear free energy relationships, and

Linear Free-Energy Relationships and Substituent Effects... 

Equation (9.72) is known as a linear free energy relationship, and it shows that there should be a linear relationship between the logarithm of the rate constant for a reaction and the free energy for the dissociation of the acid. 

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. 

M. H. Abraham, New solute descriptors for linear free energy relationships and quantitative structure-activity relationships, in Quantitative Treatments of Solute/Solvent Interactions, P. Politzer and J. S. Murray, eds., Elsevier, Amsterdam (1994) pp. 83-134. 

Wolfe NL, Bums LA, Steen WC. 1980. Use of linear free energy relationships and an evaluate model to assess the fate and transport of phthalate esters in the aquatic environment. Chemosphere 9 393-402. 

The success of equations such as (7), (10) and (11) depends on the validity of linear free energy relationships and of the applicability to these of the variation of the solvent as a perturbation. 

Non-linear free energy relationships and transient intermediates... 

Experimental studies of the reactivity of other aniline derivatives in substitution reactions are far more limited, de la Mare and Hassan (1958) and Bradfield and Jones (1928) examined the influence of acyl substituents on the amino function on the rate of halogenation at the para position. These interesting data are too limited to be useful for the evaluation of a linear free-energy relationship and are not included in Table 4. 

The partial rate factors for many substituents in many substitution reactions have been explored in the previous sections. Analyses of these data by the Selectivity and Extended Selectivity Treatments indicate the adherence of the data to the predictions of a linear free-energy relationship, and only two groups, p-phenyl andp-fluoro, deviate significantly. Several comparisons of the applicability of a linear relationship for substitution and for Hammett side-chain reactions reveal the... 

Schneider, H. J. (1994) Linear Free-Energy Relationships and Pairwise Interactions in Supramolecular Chemistry, Chem. Soc. Rev. 23, 227-234. 

Evaluation of steric effects can also be made by separating electronic from steric effects with the help of linear free energy relationship and appropriate parameters. Applications of the Hammett equation to heterocycles have been reviewed (64AHC(3)209 76AHC(20)1) and the influence of substituent effects on the basicity and N-alkylation of pyridines, which have been by far the most widely studied, shows the difficulties in this approach. Jaffe and Jones (64AHC(3)209) reported a good correlation between pKA of 3- and 4-substituted pyridines and Hammett a parameters ([Pg.179]

LINEAR FREE ENERGY RELATIONSHIPS AND BIOLOGICAL ACTION-... 

Another approach employing linear free energy relationships and correlation analysis depends upon a theoretical set of substituent parameters developed by Topsom and coworkers". The correlation involves three substituent parameters (Tro, a resonance parameter tTp, a field effect parameter which is virtually identical to (Tj and (7x, an electronegativity parameter. The correlations (equation 10) are displayed in Table 4. 

The Kamlet-Taft n scale Is based on a linear free energy relationship and measures the strength of the polarity and polarizability of the solvent, n values In SC fluids have been measured by Yonker and coworkers (19,21) with values for COj ranging from -0.5 to -0.1. This would predict I1/I3 values of 0.4 to 0.5, which are much lower than those observed. Therefore, we observe I1/I3 values Indicative of much stronger solute/ solvent Interactions than those predicted, suggesting a serious difference between the Interactions In SCF s and those observed In normal liquid organics. 

Warshel, A., Hwang, J.K. and Aqvist, J. (1992). Computer simulations of enzymatic reactions examination of linear free-energy relationships and quantum-mechanical corrections in the initial proton-transfer step of carbonic anhydrase. Faraday Discuss 93, 225... 

Table 5. Examples of Linear Free-Energy Relationships and Their Fit to Eq. (1)...

Kang, S.-l., Spears, C. P Linear free energy relationships and cytotoxicities of para-substituted 2-haloethyl aryl selenides and bis (-chloroethyl) selenides. J. Med. Chem. 1987, 30, 597-602. 

Hansch incorporated several chemical/physical chemical characteristics into this approach (4). He found Log P values (log octanol/water portion coefficient) were usually applicable with other parameters, such as Hammet linear free-energy relationships and Van der Waals radii selectively applicable. Continued work in this area by Hansch and other workers (5) has expanded the number of relevant characteristics to include molecular orbital calculations and diffusion parameters. Still, this quantitative approach embodies continuous parameters as an endpoint, a parametric philosophy. 

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