Linear free energy correlations

The development of linear free energy correlations of the rate of aromatic substitutions has been discussed ( 7.3). We record here the results of such correlations for nitration. 

Calculate AS° for ionization of each compound. Comment on the contribution of AH° and AS° to the free energy of ionization. Test the data for linear fiee-energy correlations. Are the linear free-energy correlations dominated by entropy or enthalpy terms ... 

The borohydride reduction rate data are paralleled by the rate data for many other carbonyl addition reactions. In fact, for a series of ketones, most of which are cyclic, a linear free-energy correlation of the form... 

In all cases where a sufficiently large number of substituents has been tested, a linear free-energy correlation is found with Hammett s reaction constants are fairly high, the values rang-... 

The fact that in this work a satisfactory linear free energy correlation was obtained for reaction at an ortho position again shows that hydrogen exchange is a reaction of very small steric requirement, as noted elsewhere504. 

Willi, A. V., Paper presented at the 2nd Symposium on Linear Free Energy Correlations, Irvine, 1968. 

Hammett, L. P., Symposium on Linear Free Energy Correlations, U.S. Army Research Office, Durham, North Carolina, 1964, p. 77. 

Figure 7.11 Linear free energy correlation plots for inhibition of subtilisin BPN mutants by wild type (open circles) and mutant (close circles) chymotrypsin inhibitor 2. Left panel Correlation between AGbinding for the inhibitor and AGm. Right panel Correlation between AGbinding for the inhibitor and AGES.

It is instructive to consider the rationale underlying the various linear free energy correlations and to indicate in qualitative fashion how substituents may influence reaction rates. The relation between an equilibrium constant and the standard free energy change accompanying a reaction is given by... 

Gaffney, J.S., Levine, S.Z. (1979) Predicting gas phase organic molecule reaction rates using linear free-energy correlations. I. 0(3P) and OH addition and abstraction reactions. Int. J. Chem. Kinet. 11, 1197-1209. 

Vesala, A. (1974) Thermodynamics of transfer nonelectrolytes from light and heavy water. I. Linear free energy correlations of free energy of transfer with solubility and heat of melting of nonelectrolyte. Acta Chem. Scand. 28A(8), 839-845. 

If one takes out of this list the polyhalomethanes and tries to understand what the chemistry is about, certainly a simple-minded view is that this is simply a halogen atom abstraction reaction such as one finds in a gas phase reaction, like sodium atom with organic halides. There is a linear free energy correlation in that the logarithms of the rate constants bear a linear relation to one another. 

LAPLACE TRANSFORM LINEAR FREE-ENERGY CORRELATIONS RHO VALUE... 

Gaffney, J. S., and S. Z. Levine, Predicting Gas-Phase Organic Molecule Reaction Rates Using Linear Free Energy Correlations. I. OC P) and OH Addition and Abstraction Reactions, Int. J. Chem. Kinet., 11, 1197-1209 (1979). 

Wurster in 1879 had already prepared crystalline salts containing radical cation 23 (equation 12). Subsequently, radical cations of many different structural types have been found, especially by E. Weitz and S. Hunig, and recently these include a cyclophane structure 24 containing two radical cations (Figure 3). Leonor Michaelis made extensive studies of oxidations in biological systems, " and reported in 1931 the formation of the radical cation species 25, which he designated as a semiquinone. Michaelis also studied the oxidation of quinones, and demonstrated the formation of semiquinone radical anions such as 26 (equation 13). Dimroth established quantitative linear free energy correlations of the effects of oxidants on the rates of formation of these species. ... 

The lifetimes of 75n and 75o are calculated to be ca. 0.6 ps and 0.2 ps, respectively, if 5 x 10 s K These are remarkably long lifetimes in comparison with the 4-phenylcumyl cation and the l-(4-biphenylyl)ethyl cation, which have estimated lifetimes of ca. 0.5 ns and 0.1 ns, respectively, in 1/1 TFE-H2O based on linear free energy correlations found in the... 

Fig. 4. Linear free energy correlation between the rates of reduction of iron(III) and osmiumGII) complexes [cf. Eq. (2) J. The line is drawn with a slope of 1.00. The data are from Table II.

The existence of linear free energy correlations is well known for numerous series of organic reactions. Such correlations are particularly useful for systematic studies of substituent effects. A necessary consequence for the linearity of such plots for two reaction series is that for any two members (i, j) in either reaction series... 

Despite its usefulness, the Y parameter system is not without flaw. Like most linear free-energy correlations, it fails if rigorously applied to compounds of diverse structural types. Thus when a given substrate is studied in different solvent systems (for example acetone-water, ethanol-water, acetic acid-formic acid), slightly different slopes m are obtained.66... 

The nature of the transition state for the E2 reaction of some 3-thiophenoxypro-panones in aprotic solvents has been investigated.5 The linear free energy correlation and the calculated activation parameters Aand Aof the reactions suggested an unequal and synchronous E2cB mechanism via base-catalysed amine-elimination reaction. 

There are certain rules, according to which n values can be estimated for solvents for which they have not been measured (Kamlet et al. 1983). As a generalization, n values of solutes can be obtained from multivariate linear free energy correlations involving these solutes... 

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