Hammett equation substituent constants

A linear correlation (equation 19) has been found between the logarithm of the yield Q (%) of the stabilization product and the value of the Hammett para-substituent constants dp by taking... 

The influence of substituents on equilibrium ratios of arenium ions differing in the site of proton attachment can be described with a modified Hammett equation using constants. The experimental data on the basicities of methylated benzenes (see Table 2) has shown (cf. the reaction constant q (0°) of protonation in HF at 0 °C is —11.3. As the protonation of ifromatic hydrocarbons is, for a first approximation, and isentropic reaction it requires the fulfilment of... 

In an early paper on this subject, the action of nuclear substituted phenoxy-acetic acid auxins on plants was investigated [79]. There is evidence that one of the points of attachment of these molecules to the active site is the position ortho to the carboxyl group. The attachment was therefore considered to be influenced by the electron density of this position, as predicted by Hammett s substituent constants (p. 210). kj was therefore expressed as op, the choice of o depending on whether the substituent was meta or para to the position of attachment. Substitution for f(a) and k in Equation (59), and taking logarithms gives Equation (60). 

The fundamental assumption of SAR and QSAR (Structure-Activity Relationships and Quantitative Structure-Activity Relationships) is that the activity of a compound is related to its structural and/or physicochemical properties. In a classic article Corwin Hansch formulated Eq. (15) as a linear frcc-cncrgy related model for the biological activity (e.g.. toxicity) of a group of congeneric chemicals [37, in which the inverse of C, the concentration effect of the toxicant, is related to a hy-drophobidty term, FI, an electronic term, a (the Hammett substituent constant). Stcric terms can be added to this equation (typically Taft s steric parameter, E,). 

Many equilibrium and rate processes can be systematized when the influence of each substituent on the reactivity of substrates is assigned a characteristic constant cr and the reaction parameter p is known or can be calculated. The Hammett equation... 

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,... 

The Hammett equation in the form of Eq. (4.14) or Eq. (4.15) is free of complications due to steric effects, since it is applied only to meta and para substituents. The geometry of the benzene ring ensures that groups in these positions cannot interact stoically with the site of reaction. Tables of a values for many substituents have been collected some values are given in Table 4.5, but substituent constants are available for a much wider range of... 

Given in Table 4.5 in addition to the Hammett equation are ct and substituent constant sets which reflect a recognition that the extent of resonance participation can vary for different reactions. The values are used for reactions in which there is direct resonance interaction between an electron-donor substituent and a cationic reaction center, hereas the a set pertains to reactions in which there is a direct resonance interaction between the substitutent and an electron-rich reaction site. These are cases in which the resonance conqionent of the... 

Because the substituent groups have a direct resonance interaction with the charge that develops in the a-complex, quantitative substituent effects exhibit a high resonance component. Hammett equations usually correlate best with the substituent constants (see Section 4.3). ... 

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. 

The Hammett equation and LFER in general added no new concepts to the qualitative picture that had been built up of electronic effects in organic reactions, but they did provide a quantitative measure that had been lacking and that has been found very useful. Here we will describe the further development of ideas concerning the substituent constant. 

Following the early work by one of the authors and by Sixma on the evaluation of substituent and reaction constants by molecular orbital theory, little more has been done along these hnes. Reaction constants have further been treated theoretically with at least moderate success, and a complete theoretical treatment of the Hammett equation awaits detailed testing. 

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. 

In the manner outlined, a few attempts have been made to apply the Hammett equation to the transmission of substituent effects in the pyridine series. In the alkaline hydrolysis of 5-substituted ethyl picolinates (5-R-2-COOEt) in 85% ethanol at 25, 35, and 45°, the reaction constants are about 60% as large as those in the corresponding benzene series the overall fit to the Hammett equation, however, is at best fair, since out of four points (R = Et, H, I, Ac) one (Ac) deviates widely. 

These constants, K toK/, may be estimated by use of the Hammett equation. Estimation of 1 and K 4 involves application of the methods outlined in Section II, A, i.e., application of substituent constants for and N+H to the Hammett equation for the acid-base equilibria of benzoic acids. Estimation of A2 and involves application of the method used in Section III,A, i.e., the p-value for the basicity of substituted pyridines, with cr-values for COOH and COO . Provided the necessary a- and p-values are known, this procedure permits the calculation of four independent, or virtually independent, estimates of Krp. A check on the method is available from the relationships shown in Eq. (16) which is readily obtained by multiplication of Eq. (12) and (14) and of Eq. (13) and (15). 

The fundamental understanding of the diazonio group in arenediazonium salts, and of its reactivity, electronic structure, and influence on the reactivity of other substituents attached to the arenediazonium system depends mainly on the application of quantitative structure-reactivity relationships to kinetic and equilibrium measurements. These were made with a series of 3- and 4-substituted benzenediazonium salts on the basis of the Hammett equation (Scheme 7-1). We need to discuss the mechanism of addition of a nucleophile to the P-nitrogen atom of an arenediazonium ion, and to answer the question, raised several times in Chapters 5 and 6, why the ratio of (Z)- to ( -additions is so different — from almost 100 1 to 1 100 — depending on the type of nucleophile involved and on the reaction conditions. However, before we do that in Section 7.4, it is necessary to give a short general review of the Hammett equation and to discuss the substituent constants of the diazonio group. 

In our opinion the reliability of the basis of the Hammett equation and of the parameters F, R, R+, and R is now clearly sufficient for practically all physical organic purposes. A compilation of all substituent constants and the four parameters F, R, R +, and R was published by Hansch et al. (1991). In the main table of that paper the constants om and ap as well as the parameters F and R are listed for no less than 530 substituents ... 

Substituent effects as evaluated on the basis of the Hammett equation and its extended forms, are - this has to be emphasized again — empirical results. Nevertheless, it is very soothing to know that theoretical approaches, i. e., calculations of substituent effects using ab initio molecular orbital theory (Topsom, 1976, 1981, 1983 Taft and Topsom, 1987, STO-3G and 4-31G level), give results that are consistent with the experimental data. However, it is not recommended to use only theoretically calculated substituent constants and values for F, R, and other parameters for the interpretation of experimental data. 

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). 

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... 

Jaffe (1953)52 showed that while many rate or equilibrium data conform well to the Hammett equation (as indicated by the correlation coefficient), many such data are outside the scope of the equation in its original form and mode of application. Deviations are commonly shown by para-substituents with considerable + Rot — R effect53. Hammett himself found that p-NOz (+ R) showed deviations in the correlation of reactions of anilines or phenols. The deviations were systematic in that a a value of ca. 1.27 seemed to apply, compared with 0.78 based on the ionization of p-nitrobenzoic acid. Other examples were soon discovered and it became conventional to treat them similarly in terms of a duality of substituent constants . 

The special substituent constants for + R para-substituents are denoted by a, and those for — R para-substituents are denoted by a+ 54. They are based respectively on the reaction series discussed above. Selected values are given in Table 1. Characteristic a or a+ values are sometimes distinguished for meta-substituents also, but only for a minority of substituents which show very marked + R or — R effects do these differ significantly from ordinary a values. The range of applicability of the Hammett equation is greatly extended by means of a and cr+, notably to nucleophilic (by a ) and to electrophilic (by cr+) aromatic substitution. 

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