Addition Taft equation

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 both of the above equations, the symbol e denotes the effective sum of and must be used when a solute contains more than one hydrogen bonding moiety in close proximity so that their effect is not additive (Taft 1996). 

Thiazoles readily undergo AT-alkylation by alkyl halides or tosylates (Menshutkin reaction). The sensitivity of this SN2 quaternization reaction to the molecular environment of the nitrogen atom has been used to evaluate, in a quantitative way, steric and electronic effects of ring substituents. The electronic effect of alkyl substituents (unperturbed by any steric effect) may be evaluated from the rate constants for the reaction of 5-alkylthiazoles with methyl iodide (in nitrobenzene at 30 °C) Table 19 shows that introducing a methyl group at the 5-position corresponds to an acceleration of the rate by a factor of 2 but that each addition of a methyl ramification to the 5-alkyl group enhances the rate only by a factor of 1.1. The data in Table 19 fit well with a Hammett-Taft equation (3) ... 

The correlations outlined above are empirical, that is, their applicability is proved by their success. The finding that the carrier alone or the concentration of platinum on the carrier did not change the parameters of the Taft equation to any essential degree makes possible some generalization of the results. All alkyl-substituted ethylenes are hydrogenated under the same mechanism, most likely through a simultaneous addition of both hydrogen particles to the Ti-adsorbed olefin (48, 78). 

Values for many more substituents are available along with Hammett equations for many additional acids along with Taft equations and substituent constants for aliphatic compounds." " So this approach is quite versatile and it is possible to predict pAa values for molecules with rather complex structures. This procedure provides a system for evaluating how substituents influence the distribution of charge in a molecule. 

The dependence has the form log( x/ o)" p o. Later this equation was modified. Taft introduced the principle of additivity of the influence of different ctors on the reactivity of a compound each factor, being it inductive, conjugation or steric, affects AG independently, so that for each reaction series log( / o) or logfX/ATp) can be presented as the sum 2p,aliphatic compounds the Taft equation has the form... 

In this respect, the solvatochromic approach developed by Kamlet, Taft and coworkers38 which defines four parameters n. a, ji and <5 (with the addition of others when the need arose), to evaluate the different solvent effects, was highly successful in describing the solvent effects on the rates of reactions, as well as in NMR chemical shifts, IR, UV and fluorescence spectra, sol vent-water partition coefficients etc.38. In addition to the polarity/polarizability of the solvent, measured by the solvatochromic parameter ir, the aptitude to donate a hydrogen atom to form a hydrogen bond, measured by a, or its tendency to provide a pair of electrons to such a bond, /, and the cavity effect (or Hildebrand solubility parameter), S, are integrated in a multi-parametric equation to rationalize the solvent effects. 

For example, Figure 2.3 shows plots of the a constants of X vs. log p/T of aliphatic carboxylic acids (XCOaH) and vs. log k for the dehydration of acetaldehyde hydrate by XC02H. Deviations from Equations 2.18 and 2.19 occurwhen the rate of reaction or position of equilibrium becomes dependent on steric factors. For example, Taft studied the enthalpies of dissociation, A Hd, of the addition compounds formed between boron trimethyl and amines (X1X2X3N) and found that when the amine is ammonia or a straight-chain primary amine the dissociation conforms to Equation 2.20, in which 2 ° is the sum of the a values for the... 

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... 

Now, there is no satisfactory theory of steric effects, although attempts to rationalize the barrier of ethane by quantum-mechanical calculations are appearing more frequently (dementi and Davis, 1966). Furthermore, simple group-additivity schemes of various kinds have had limited success, at best, e.g. for estimating rotational barriers in ethanes (Tang and Chen, 1962), correlating relative reactivities with Taft EB values (Wells, 1963), or evaluating asymmetric induction (Ugi, 1965 Ruch and Ugi, 1966). Semi-empirical calculations by equation (197) have... 

Px is the partition coefficient of a derivative and PH is that for the parent compound.) Also used were Hammett s o- constant, Taft s polar constant, steric parameter, Es. In a few examples (Equations 17, 21, 24, and 30), P values from oleyl alcohol/water have been used. In one instance (Equation 69) the chemical shift of a phenolic proton has been used for comparison with the a constant. Where possible, the experimentally measured partition coefficients for all members of the series have been used. In other instances only one member of a set has been measured. Values for the other members were obtained by taking advantage of the additivity principles of log P and tr. Details are given elsewhere (4, 7, and 8). For the new work of Table II, log P values for the parent compounds are given in the footnotes. 

The rate equation for the alkaline hydrolysis of amides such as urea (Lynn, 1965), anilides (Biechler and Taft, 1957 Bender and Thomas, 1961a Mader, 1965 Schowen and Zuorick, 1966), chloroacetamide (Bruylants and K zdy, 1960) andN,N-diacylamines (Behme and Cordes, 1964), is known to contain both first- and second-order terms in hydroxide. It is highly improbable that the term which is second-order in hydroxide is due to base-catalysis of the addition of hydroxide ion to the carbonyl carbon, because of the low acidity of hydroxide. 

Several two-parameter equations have been suggested based on the additivity of I and R effects, each being the combination of various components as described earlier. Taft originally introduced this approach for the electronic effects of benzene and defined Or values employing values of Oj (from the aliphatic series - see Chapter 2) and Hammett s a for para substituents (Equation 18). 

The Dewar-Grisdale Equation An approach to field and resonance transmission of the polar effect essentially the same as that of Taft s group was suggested by Dewar and Grisdale. The localised and delocalised polar effects are represented by F and M which are taken to be additive in any given a value. The value a,y is related to the sum of... 

An even more complicated situation is encountered in the alkaline hydrolysis ofp-substitutcd acetanilides (30) (Bender and Thomas, 1961a). The rate equation for the isotopic exchange of these compounds involves terms in [OH-] and [OH-]2. The original mechanism of hydrolysis proposed by Biechler and Taft (1957) in which there is a rapid pre-equilibrium addition and loss of hydroxide in the first step, is disproved by the fact that, although oxygen exchange is accompanied by hydrolysis, exchange is not as complete as it would be expected to be from that scheme. Bender considers the initial attack of hydroxide to be a rate process not an equilibrium. By use of low hydroxide ion concentrations... 

BR is the relative biologic activity under investigation, for example the molar EDr>o or the percent response at a given dose. Log P is the logarithm of the octanol-water partition coefficient, a is the approprite Hammett signa constant (electronic in nature), and Es is the Taft steric parameter. With the important demonstration by Hansch that the partition coefficient is often an additive constitutive property, all of the physical parameers may be obtained from the literature. A second important contribution by Hansch is the recognition that the use of statistical techniques is essential to the analysis of quantitative structure-activity relationships. To develop an equation such as that above, one feeds the... 

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