Taft equation derivation

The application of the Taft equation, derived from the Hammett equation (262)... 

A large number of modifications and refinements have been made on this equation, the most relevant being those which attempt to separate inductive < j and mesomeric Taft equation. In addition to substituent constants based on reactivity, acidity and the like, a variety of spectroscopically derived constants such as those from... 

When a second nitrogen atom is introduced into the pyridine ring the basicity is reduced (pjRTa 5.23 for pyridine and 2.33 for pyridazine). The effect of the additional substituents on pKK depends on the position of the substituents (Table 3). An extensive set of pK values of pyridazine derivatives has been submitted to correlation analysis using the Hammett and the two Taft equations, which shows that the pKa values are most sensitive to the effect of a 2-substituent followed by the effects of 3- and 4-substituents. The interactions between nitrogen atom and 2-substituents represent over 70% of the inductive character. The composition of the effects of +M 4-substituents is significantly enriched in the resonance interactions, whereas -M 4-substituents interact with the nitrogen atom mainly by induction (77MI21201). 

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.)... 

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)... 

Following the original work of Hammett [47] several other linear Gibbs energy relationships have been derived. The most important of these is the Taft relationship [50] which allows consideration of aliphatic as well as aromatic systems and also of steric effects. The Taft equation has the same form as equation (7.11.4) but the substituent constants are defined in another way. More information about this relationship and other linear Gibbs energy relationships can be found in the monograph by Hammett [48]. 

The reference compounds are an unsubstituted benzene derivative in the case of the Hammett equation (i.e., crjj=0) and a methylated derivative in the case of the Taft equation (i.e., crcH = ) ... 

However, a number of points remain open. The Taft equation has been tested here only by a narrow set of alkyl substituents with the cr values covering at most the range of 0.7-0.8 units whereas the complete list (cf. Wells, 2 Leifler and Grunwald, 3) spreads over three units. The explanation of deviations of the butyl derivatives by steric effects needs further support. 

My student, Dr. William J. Colucci, with the help of Dr. Steven Jungk, has developed an equation (Eq. 3) for determining conformations about C—C bonds. His equation [17] like those of Pachler [18] and of Altona [19] is a modified Karplus expression [20]. Rather than using electronegativities to account for substituent effects, Colucci s equation employs empirically derived substituent constants. The ASi term is a group substituent effect. The equation is a classical free-energy relationship such as the Taft equation. 

XPS spectra of adsorbed PdCl2 contain no lines that could be attributed to PddD complexes with Pd-0 bonds. Although it points out that PdCl2 does not interact directly with the surface oxides, the adsorption eqtiilibria constants still increase after e carbon surface has been covered by oxygen groups [7]. Ki and K2 were found to depend on the type and number of the surface oxides in accordance with an equation derived with some assumptions from the equation of Hammet and Taft (fig. 4). 

Sections 2 and 3 contain accounts of the Yukawa-Tsuno equation, the dual substituent-parameter (DSP) equation, the extended Hammett (EH) equation, and multiparameter equations derived from Taft s separation of polar, steric, and resonance effects . These equations are not now the only possibilities for multiparameter treatment. In this section we shall give brief accounts of some of the other approaches, with key references for further information. 

The kinetics of the ethylene hydration reaction have been investigated for a tungstic oxide—siHca gel catalyst, and the energy of activation for the reaction deterrnined to be 125 kJ/mol (- 30 kcal/mol) (106,120). The kinetics over a phosphoric acid-siHca gel catalyst have been examined (121). By making some simplifying assumptions to Taft s mechanism, a rate equation was derived ... 

Before we close this section we make reference to an extended form of the Hammett equation in which the substituent constant and the reaction constant are separated into contributions from the field effect (F) and the mesomeric effect (R). This procedure was suggested by Taft in 1957 for 4-substituted benzene derivatives. It is called a dual substituent parameter (DSP) equation (Scheme 7-2). 

Taft emphasized that this equation can also be applied to 3-substituted derivatives, but with some reservations (see Ehrenson et al., 1973). 

Finally, in this account of multiparameter extensions of the Hammett equation, we comment briefly on the origins of the a, scale. This had its beginning around 1956 in the a scale of Roberts and Moreland for substituents X in the reactions of 4-X-bicyclo[2.2.2]octane-l derivatives. However, at that time few values of o were available. A more practical basis for a scale of inductive substituent constants lay in the o values for XCHj groups derived from Taft s analysis of the reactivities of aliphatic esters into polar, steric and resonance effects . For the few o values available it was shown that o for X was related to o for XCHj by the equation o = 0.45 <7. Thereafter the factor 0.45 was used to calculate c, values of X from o values of XCH2 . ... 

Vai der Waals Radii And Related Sterlc Parameters Van der Waals radii have long been considered a valid meas ure of atomic size Taft proposed the first valid set of sterlc parameters for correlation analysis defined from acid hydrolysis of esters caiarton derived equations for the calculation of Van der Waals radii, ry of symmetric top MZs groups( ) These values of the Van der Waals radii were used, together with that for H, to show that Es Is a linear function of i>y ... 

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