Taft equation discussion

In order to gain an insight into the mechanism on the basis of the slope of a Type A correlation requires a more complicated procedure. Consider the Hammett equation. The usual statement that electrophilic reactions exhibit negative slopes and nucleophilic ones positive slopes may not be true, especially when the values of the slopes are low. The correct interpretation has to take the reference process into account, for example, the dissociation equilibrium of substituted benzoic acids at 25°C in water for which the slope was taken, by definition, as unity (p = 1). The precise characterization of the process under study is therefore that it is more or less nucleophilic than the reference process. However, one also must consider the possible influence of temperature on the value of the slope when the catalytic reaction has been studied under elevated temperatures there is disagreement in the literature over the extent of this influence (cf. 20,39). The sign and value of the slope also depend on the solvent. The situation is similar or a little more complex with the Taft equation, in which the separation of the molecule into the substituent, link, and reaction center may be arbitrary and may strongly influence the values of the slopes obtained. This problem has been discussed by Criado (33) with respect to catalytic reactions. 

The decrease in hydrogenation rate with increasing size of the alkyl group (Table VI) (93-96) can be correlated by the Taft equation. However, the correlation of the data by Smith and Pennekamp (93) (series 70) using the polar parameter Taft equation is applied that also includes steric constants. Similarly, Kieboom (34) has discussed Yoshida s correlation of series 73 based on main conclusion has been that the data do not allow a clear distinction between steric and polar effects. It seems that both operate in the same direction. Series 72 and 73, in which the rate data have been separated into the rate constants and adsorption coefficients, show opposite trends with the latter parameter. A similar problem has been encountered by Volter, Hermann, and Heise (100) and by Najemnik and Zdrazil (103) in the series of methylbenzenes (Table VII) and is discussed in this connection. 

Taft equation (eq 16 in reference (36)) and reverse osmosis data on solute transport parameter Dam/K6 (defined by eq 12 later in this discussion) for different solutes and membranes (44,45,46), and (iv) the functional similarity of the thermodynamic quantity AAF+ representing the transition state free energy change (36) and the quantity AAG defined as... 

Abstract—A review of the literature is presented for the hydrolysis of alkoxysilane esters and for the condensation of silanols in solution or with surfaces. Studies using mono-, di-, and trifunctional silane esters and silanols with different alkyl substituents are used to discuss the steric and electronic effects of alkyl substitution on the reaction rates and kinetics. The influences of acids, bases, pH, solvent, and temperature on the reaction kinetics are examined. Using these rate data. Taft equations and Brensied plots are constructed and then used to discuss the mechanisms for acid and base-catalyzed hydrolysis of silane esters and condensation of silanols. Practical implications for using organofunctional silane esters and silanols in industrial applications are presented. 

Diparametric equation A relationship in which the effect of structure on a property is represented by two parameters, one of which is generally composite. Examples discussed in this work include the LD, CR and MYT equations. Other examples are the Taft, Ehrenson and Brownlee DSP (dual substituent parameter), Yukawa-Tsuno YT and the Swain, Unger, Rosenquist and Swain SURS equations. The DSP equation is a special case of the LDR equation with the intercept set equal to zero. It is inconvenient to use and has no advantages. The SURS equation uses composite parameters which are of poorer quality than... 

The PSP equation is written by Taft and Topsom151 in various forms. Equation 19 is a convenient form with which to begin this discussion ... 

Taft and Topsom s article151 and also Topsom s171 should be consulted for details of the setting up of the scales of substituent parameters. The equation has been applied to a wide range of gas-phase reactivities. (In the multiple regressions an intercept term is often permitted, but usually this turns out to be indistinguishable from zero, as it should be if equation 20 is valid.) For aliphatic and alicyclic saturated systems the resonance term is duly negligible. The roles of field, resonance and polarizability effects are discussed and the interpretat of the various p values is attempted. 

Taft originally suggested that the mechanism for hydration involves an additional step, namely the rapid, reversible formation of a 7r complex from a proton and the olefin, and that this complex then rearranges, in the rate-determining step, to the carbocation as shown in Equation 7.3. This is consistent with all the data discussed so far, but it has recently been shown to be incorrect. The... 

The rate constants of the reaction of 2,6-dimethyloct-7-en-2-ol separately with ozone and hydroxyl radical, in the gas phase, have been determined. The OH radical can either abstract hydrogen or add to the double bond. Ozone adds to the double bond. The formation of acetone, 2-methylpropanal, 2-methylbutanal, ethanedial, and 2-oxopropanal was discussed.191 The rate laws and activation parameters for the ozone oxidation of alcohols in aqueous solution have been determined and explained on the basis of formation of an ozone-alcohol complex.192 The reactivity of alkenes towards ozone, in aqueous solution, correlates well with Taft s equation.193... 

The alternative approach is the attempt to quantify substituent effects, and this has been most successfully done by the Hammett equation and its various extensions (Hammett, 1970). Here one set of free energy data is compared with another set. One set is taken as standard (originally the dissociation constants of benzoic acids) and other rate or equilibrium data are compared (by logarithmic plots). So much has been written about this treatment that discussion here is unnecessary. Absolute values of a (the substituent constant) are not to be expected, in fact one would expect a different a for every reaction (i.e. for every p). In the present context it is important to note that both the Hammett equation and the closely related Taft treatment are based on systems where solvation is known to be important and therefore the application of these treatments using parameters derived from solution phase studies to reactions in the gas phase may be of uncertain value. 

This approach to separating the different types of interactions contributing to a net solvent effect has elicited much interest. Tests of the ir, a, and p scales on other solvatochromic or related processes have been made, an alternative ir scale based on chemically different solvatochromic dyes has been proposed, and the contribution of solvent polarizability to it has been studied. Opinion is not unanimous, however, that the Kamlet-Taft system constitutes the best or ultimate extrathermodynamic approach to the study of solvent effects. There are two objections One of these is to the averaging process by which many model phenomena are combined to yield a single best-fit value. We encountered this problem in Section 7.2 when we considered alternative definitions of the Hammett substituent constant, and similar comments apply here Reichardt has discussed this in the context of the Kamlet-Taft parameters. The second objection is to the claim of generality for the parameters and the correlation equation we will return to this controversy later. 

As Table III indicates, the nature of the substituents in distannanes can influence both the chemical shift (S referenced relative to tetramethyltin) and the direct one-bond coupling constant, J(" Sn-" Sn). The influence of substituents on chemical shifts has been discussed in detail elsewhere (42 a) therefore, an in-depth analysis of the nature of this influence will not be repeated here. However, the influence of substituents on the J(" Sn-" Sn) values deserves some comment 43-44 a-c). In the case of peralkyidistannanes (Table III), it has been proposed that from an apparent linear correlation between J( " Sn-" Sn) and 2cr (the sum of the Taft cr constants of the six alkyl groups bound to the tin atoms), the main factor involved in determining the value of J(" Sn-" Sn) in these compounds is eff) the effective nuclear charge at the tin nucleus 43 a,b). However, an alternative proposal to explain the trend observed in Table III is based on the equation derived by Pople and Santry 45) for the coupling mechanism in a two-body spin system [Eq. (7)]. Here, s(0)... 

In the discussed series (77) of hydrogenated compounds the reaction rate and relative adsorptivity of substrates in most solvents were affected to a comparable degree by steric and polar influences. Negative values of the parameter p and positive values of the parameter 8, were obtained in most cases in the correlation of the reaction rates by the Taft-Pavelich equation, while correlation of the relative adsorption coefficients gave opposite results. This can be seen as an example of an interesting compensation of the kinetic and adsorption terms. 

The Taft adaptation of equation 1.9 to aliphatic systems (with substituent parameters cj) does not distinguish between through-space and through-bond effects. Very recently it has been convincingly shown that this can mislead effects of substituents in carbohydrate frameworks depend on their orientation. Many supposed inductive effects in aliphatic systems are in fact the simple effects of electrostatic dipoles, as discussed in detail in the carbohydrate context in Chapters 3 and 6. 

It follows that one may discuss the effect of various types of substituents on photoacidity using arguments and terminology that have been traditionally used for ground state acids. In particular, Hammett [127,128] and Taft [129,131] have contributed much to the discussion of the substituent effect on equilibrium and reactivity of aromatic acids in the ground electronic state. Their arguments seem to be valid also for the excited state of aromatic acids but with different scaling factors (i.e., different values in the Hammett Equation) [24]. 

Some of the general principles governing the reactivity of tetraco-ordinate phosphorus compounds have been discussed. While rates of reaction of compounds ABP(0)X depend on A, B, and X, they can be described, with some degree of success, by the use of the Hammett equation, and Taft and Kabachnik constants, but a correlation is not always achieved. If substances react by the same mechanism, the effects of the substituents A and B are additive. When reaction conditions change then—... 

Zollinger examined the empirical correlation equation for Wcxy ( q- 4) in the context of dual substituent parameter equations for a number of other, unrelated reactions (e.g., the loss of nitrogen from ArN2 ). [78] Eq. 4 was thus shown to be one of a family of equations that can be derived to separate the influences of substituent resonance and field (inductive) effects on chemical reactivity. These equations trace back to Taft s formulation, Eq. 7, in which separate p and a terms are used to represent the field and resonance electronic properties of substituents. [79] Zollinger points out that our Wcxy version of this expression is one of few dual substituent parameter equations in which the signs of the resonance and field terms are opposed (cf, Eq. 4, where the coefficients are -1.10 and +0.53, respectively). We have discussed the meaning of this opposition in Section 1.2, above. 

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