Hammett equations defined

The numerical values of the terms a and p are defined by specifying the ionization of benzoic acids as the standard reaction to which the reaction constant p = 1 is assigned. The substituent constant, a, can then be determined for a series of substituent groups by measurement of the acid dissociation constant of the substituted benzoic acids. The a values so defined are used in the correlation of other reaction series, and the p values of the reactions are thus determined. The relationship between Eqs. (4.12) and (4.14) is evident when the Hammett equation is expressed in terms of fiee energy. For the standard reaction, o%K/Kq = ap. Thus,... 

Reactions that occur with the development of an electron deficiency, such as aromatic electrophilic substitutions, are best correlated by substituent constants based on a more appropriate defining reaction than the ionization of benzoic acids. Brown and Okamoto adopted the rates of solvolysis of substituted phenyldimeth-ylcarbinyl chlorides (r-cumyl chlorides) in 90% aqueous acetone at 25°C to define electrophilic substituent constants symbolized o-. Their procedure was to establish a conventional Hammett plot of log (.k/k°) against (t for 16 /wcra-substituted r-cumyl chlorides, because meta substituents cannot undergo significant direct resonance interaction with the reaction site. The resulting p value of —4.54 was then used in a modified Hammett equation. 

A completely different approach has been taken by Hine, who has considered that the substituent and reaction center are not really distinct, both being substituents in a benzene nucleus, and has then related substituent and reaction constants. Although of considerable theoretical interest, Hine s work has little bearing on practical applications of the Hammett equation since he starts from the premise of unique, single-valued substituent constants. This premise is invalid whether we are utilizing the naive approach with three separate, well-defined sets or the more refined methods with a continuous range of para values. 

Over the years, the Hammett equation has been modified many times, usually by defining an alternative scale of a constants, the better to allow for special features found in some mechanisms, such as resonance stabilization and mesomeric effects. Thus, there are substituent scales known at cr+, er , crj, etc. The reader is referred to specialized treatises for further details.5-811... 

The Hammett equation is not successful for reactions of aliphatic compounds if the normal cr constants are used. A new scale of substituent constants, labeled cr, was invented to allow the extension of the method to such systems. The difference in the rates of hydrolysis of esters in basic versus acidic solutions is used to define the scale. The transition states are... 

The only physical property which has been studied for substituted vinylidene sets is the nmr chemical shift of the vinylidene proton in substituted ethylenes and in tra s-l,2-disubstituted ethylenes. The first attempt at correlating chemical shift data for substituted ethylenes with the Hammett equation appears to be the work of Banwell and Sheppard (53), who reported a correlation of A2 values with the or constants, the A2 values being defined by the equation... 

Ritchie and Sager (124) distinguish three types of reaction series according to whether the Hammett equation or the isokinetic relationship is obeyed, or both. The result that the former can be commonly valid without the latter seems to be based on previous incorrect statistical methods and contradicts the theoretical conclusions. Probably both equations are much more frequently valid together than was anticipated. The last case, when the isokinetic relationship holds and the Hammett equation does not, may be quite common, of course, and has a clear meaning. Such a series meets the condition for an extrathermo-dynamic treatment when enough experimental material accumulates, it is only necessary to define a new kind of substituent constant. 

On the analogy of the physicochemical relation, one was led to define a biological Hammett equation which related the equilibrium constant of the drug-receptor complex to the electronic a parameters of the substituents (e.g. chlorine, bromine, methyl, ethyl, hydroxyl, carboxyl, acetyl, etc.) of the drug molecule. Since the equilibrium constant of a drug-receptor complex is reflected by the biological activity, this led to the first extrathermodynamic relationship in QS AR ... 

The structure-reactivity relationship is a concept familiar to every organic chemist. As commonly used it refers to a linear free energy relationship, such as the Bronsted or Hammett equations, or some more general measure of the effect of changing substituent on the rate or equilibrium of a reaction. A substituent constant is conveniently defined as the effect of the substituent on the free-energy change for a control reaction. So the so-called structure-reactivity relationship is in fact usually a reactivity-reactivity relationship. 

The symbols were defined in Section IV.B.) A full discussion of the ortfio-effect as revealed in this work would be inappropriate here. We must restrict ourselves to the more limited task of indicating the role of o-N02. We discuss first the work involving alcohols as solvents. To apply the extended Hammett equation, i.e. to determine the regression coefficients a, fi and

intercept term h, it is first necessary to select a set of substituents which can be expected to be well-behaved . Particular problems for or and v may be caused by conformational effects, and internal hydrogen-bonding may occur... 

The Hammett equation has been further extended to include substituents of aliphatic systems too. In this case the constants that quantify the inductive effects, which are represented as o, have different values compared to those concerned with aromatic systems and are defined as Taft constants. Some values of these latter are also reported in Table 1. 

Extensive collections of pK values are available in the literature, e.g., [98-101]. It is also possible to predict pK values for a broad range of organic acids and bases using linear free energy relationships based on a systematic treatment of electronic (inductive, electrostatic, etc.) effects of substituents which modify the charge on the acidic and basic center. Quantitative treatment of these effects involves the use of the Hammett Equation which has been a real landmark in mechanistic organic chemistry. A Hammett parameter (a), defined as follows ... 

The Hammett equation traditionally combines 3-substituted and 4-substituted benzene derivatives into a single data set using the composite constants for the former and constants for the latter. This is justifiable only if p3 is equal to P4 (Ap 0). We have shown that this is generally not the case except when the geometry of XGY is comparable to that of the benzoic acids from which the and Op constants were defined. The Yukawa-Tsuno and related equations are based on the assumption that P3 is equal to p4 and are limited to applications in which this is at least approximately correct. They are briefly reviewed elsewhere. ... 

By the use of a model reaction (ionization of benzoic acids), die ability of a substituent to modify die electron-donating or electron-withdrawing ability of die phenyl group and tiius influence tiiat reaction can be defined quantitatively by the Hammett equation,... 

The first adequate examination of the applicability of the Hammett equation to aromatic substitution was made by Roberts and his associates (1954). New data on the nitration of the halobenzenes together with the results for other substituted benzenes (Ingold, 1953) revealed that the rates for nitration in the meta position were, indeed, correlated satisfactorily by the Hammett rr-constants. Para substituents, in particular groups directing to the ortho and para positions, exhibit important deviations from the line defined by the meta reactivities (Fig. 3). It was suggested that these deviations were the consequence of significant resonance interactions in the transition state. At the same time, de la Mare (1954) examined the application of the Hammett parameters for the correlation of the relative rate data for non-catalytic chlorination. The poor agreement achieved (Fig. 4) prompted his conclusion that variable resonance interactions in the... 

Hammett, after illustrating the existence of linear relationships among the data for a variety of side-chain reactions, defined the (7-constants to characterize the behavior of substituent groups. In the application of the Hammett equation the cr-parameters are assumed to be constant. The assessment of the validity of this same assumption for substituents in aromatic substitution reactions is the major problem which must be considered prior to the adoption of a simple two-parameter linear free-energy relationship for these reactions. Preliminary evaluations of linear relationships were undertaken through somewhat modified procedures as discussed in Section IV. Now, however, with many quantitative data available it is no longer necessary to rely on the less direct Selectivity Relationship. Rather, the more straightforward conventional Hammett approach is applicable. This procedure requires the adoption of the a1 -constants derived from the study of substituted phenyldimethylcarbinyl chlorides and the assumption of constancy of the values. This assumption is shown to be fully justified in subsequent tests of the relationship. 

Proposed by Hammett in 1937 [Hammett, 1937 Hammett, 1938], the Hammett equation is defined for the rate constants k and equilibrium constants K of reactions of meta- and para-substituted benzoic acid derivatives ... 

From the Hammett equation, several o - electronic substituent constants are derived from different reactions and different experimental conditions a modification of the Hammett equation was defined as the - Yukawa-Tsuno equation. 

In principle, extrathermodynamic relationships that deviate from the simple Hammett equation (equation 8) can be treated by equation 14. The major problem is the determination of the different sets of o s, (e.g., set and 0 set) in a way that will indeed reflect their relation to independent properties. An example of such a procedure is the separation of polar and steric effects (10). The need for such a separation arose when a nearly complete lack of correlation was observed between substituent effects represented by the Hammet a constants and the rates for alkaline hydrolysis of aliphatic systems (12). Inspection of the structures indicated that the proximity of the substituents to the reaction site was a common feature. The steric interaction between R and X had to be considered separately from the electronic effects. Polar substituent constants were thus defined as the difference between the rate constants of base and acid catalyzed hydrolysis of esters. From the structural similarity of the transition states for these reactions (equation 15) it was assumed that the difference in their charge reflects only the polar effect of the substituent... 

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