Taft correlation equation

Another approach to the quantitative correlation between the structure and the reactivity of hydrocarbons may be the use of the Taft correlation equation. A consideration of the dependence of the exchange rate on the constant a for a number of functionally substituted methane and ethane derivatives has shown [10] that the two-parameter equation is obeyed ... 

The study of solute-solvent and solvent-solvent interactions in mixed solvents has been gaining significance in recent years61-64, because of the increasing application of these solvents. Casassas and collaborators67 have used the Kamlet-Taft multiparametric equation for the correlation of dissociation constants of acids in 1, 4-dioxane-water mixtures. They found that when the main solvent is retained the property does not involve significant changes in the cavity volumes and, in those cases, the pK in binary solvents can be described by equation 8 ... 

A common probe of reaction mechanisms used to infer charge distribution in the transition state involves variation of substituent groups near the reaction center. From the variation in reaction rate produced by electron-donating and electron-withdrawing groups or by the steric hindrance of various sized groups, transition state characteristics can be inferred. Two empirical correlations have been proposed and refined which provide a common framework for this process. The Hammett equation is applied to aromatic systems [45]. The Taft correlation is applied to aliphatic systems [45], Definitions of terms, collections of substituent constants (steric and electronic effects for various substituents), and listings of observed reaction response parameters (for typical reaction types) have been collected [45]. 

In a similar fashion, Shirai et al. constructed a modified Taft correlation for the hydrolysis of a series of triaikylalkoxysilanes of R,SiOR structures (in which R was varied to include different alkyl groups) in 55% aqueous acetone using a similar extraction/quenching technique [35]. The resulting modified Taft equation was log(fcHO//cHO ) = 1.50 silane esters and the reaction conditions were very different for the Pohl and Shirai studies, the values of p and s were quite similar, (p and a are empirically derived coefficients for the polar parameter and the steric parameter, respectively.)... 

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... 

Various methods are available for predicting the acid dissociation constant (pKa) within homologous series. Most are based on the Hammett equation (benzene derivatives) and the Taft correlation (aliphatics and alicyclics). A comprehensive review of methods was published by Perrin et al. (1981). 

Theoretical Linear Solvation Energy Relationship (TLSER) With the LSER descriptors of Kamlet and Taft in mind, Famini and Wilson developed QM-derived parameters to model terms in Eq. [18] and dubbed these the TLSER descriptors. Descriptor calculations are done with the MNDO Hamiltonian in MOPAC and AMP AC. MNDO has greater systematic errors than do AMI and PM3, but the errors tend to cancel out better in MNDO-derived correlation equations. A program called MADCAP was developed to facilitate descriptor calculation from MOPAC output files. 

The general SPP scale of solvent dipolarity/polarizability and the specific SB and SA scales of solvent HBA basicity and HBD acidity, respectively, are orthogonal to one another and they can be used in the correlation analysis of solvent effects in single- or, in combination with the others, in two- or three-parameter correlation equations, depending on the solvent-influenced process under consideration see also Section 7.7. Examples of the correlation analysis of a variety of other solvent-dependent processes by means of SPP, SB, and SA values, including those used for the introduction of other solvent polarity parameters, can be found in references [335-337, 340-342]. In particular, comparisons with Kamlet and Taft s n scale [340] and Winstein and Grunwald s Y scale [341] have been made. 

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. 

Distinguishing the contributions of carbon and hydrogen atoms, the Bowden-Wooldridge steric constant Ef" is defined by a correlation equation with the Taft steric constant ... 

These speculations concerning the reaction mechanism resulted in four forms of the Taft equation differing in the procedure used in the calculation of polar and steric constants. Correlation analysis has revealed (78, 79) that kinetic data may be correlated in a single manner, namely, by employing the Taft-Pavelich equation in the form... 

Fig. 1. Correlation of the rate data by means of the reduced Taft-Pavelich equation 1, 1-hexene 2, l-hcptene 3, 1-octene 4, 3,3-dimethyl-l-butene 5, 4-methyl-1-pentene 6, 4,4-dimethyl-1-pentene 7, 2,3-dimethyl-1-butene 8, tran.v-3-heptene 9, zrani -4-nonene 10, (rani-4-methyl-2-pentene 11, 2-methyl-1-hexene 12, trflni-2-hexene 13, 2-methyl-2-hexene 14, 2,4-dimethyl-2-pentene 15, 2,3-dimethyl-2-butene.

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 measured data also were used (700) in a quantitative representation of the effect of structure on the reactivity and adsorptivity of substrates by means of the Taft-Pavelich equation (22). The adsorption data suffered from a larger scatter than the rate data. No substrate or substituent could be detected that would fail to satisfy completely the correlation equations. In the correlation of the initial reaction rates and relative adsorption coefficients the parameter p was negative, while the parameter S was positive. In correlations of the reaction rates obtained by the hydrogenation of a similar series of substrates on the same catalyst in a number of solvents, the parameters p and had the same sign as in the hydrogenation in solvent-free systems, while in the correlation of the adsorption coefficients the signs of the parameters p and in systems with solvents were opposite to those in solvent-free systems. This clearly indicates that solvents considerably affect the influence of the structure of substrates on their reactivity. 

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. 

The Kamlet-Taft solvatochromic parameters )t a, and p for a micellar medium are usually determined by measuring the spectroscopic parameters of certain probes using known correlation equations. The correlation equations are, however, obtained from studies in pure solvents. It is assumed that the correlation equation obtained for pure solvents is also valid for micellar media. Both absorption [14-17] and fluorescence [18,90] probes have been used for estimating values of a, p, and it for the micellar media. 

Gas-phase elimination kinetics of alkyl A,iV-diethylcarbamates (Et2NCOOR) are affected markedly by branching of R and fall in the rate order t-Bu > i-Pr > Et the effects of heteroatom substituents Z on pyrolysis of ZCOOEt have been correlated using the Taft-Topsom equation, log(i /i H) = —(0.68 0.12)cTa -l- (2.57 0.12)ctf — (1.18 0.27)ctr, which reveals that the field effect outweighs steric and resonance factors. ... 

The occurrence of steric as well as polar substituent effects in aliphatic systems and orf/io-substituted aromatic systems complicates the devising of correlation equations. A typical situation is shown in Figure 2. There is clearly no simple relationship between the rates of alkaline hydrolysis of the ethyl esters of the alkanoic acids and the strengths of the acids themselves. Little progress was made until the early 1950s, when Taft made an excellent start in developing linear free energy relationships in this area. This topic is sometimes referred to as the separation of polar, steric, and resonance effects and is the subject of Section 3. 

Rates of esterification of 2-substituted nicotinic acids by diazodiphenylmethane in nine aprotic solvents at 303 K were correlated using the Kamlet-Taft solvatochromic equation. ... 

Equation (7-51), the Taft equation, provides good correlations for many aliphatic reactions. The scope of this relationship is illustrated by Table 7-10. The reaction constant p has been interpreted along the lines described for the Hammett p values. 

The conclusions about the influence of azole ring substituents on the tautomeric equilibria are summarized in Table VIII. Although sufficient data are available for pyrazoles and imidazoles, it is difficult to correlate them within any well-defined scheme. The energy differences between pairs of tautomers are generally quite small and attempts to analyze these using, for example, the Taft-Topson model failed [95JCR(S)172]. In the case of mono-substituted compounds, Hammet-type equations... 

The approach Taft has presented gives rise to an equation that is obviously more powerful than the Hammett relation. It correlates more reactions and can be extended to include steric parameters. It takes the form... 

Then the AH values of sulphoxides and amides were correlated with Taft s a affording the following equation ... 

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