The Substituent Constant

A further complication arises with Ingold s suggestion that both the inductive and resonance effects are composed of initial state equilibrium displacements that reveal themselves in equilibrium properties like dipole moments and equilibrium constants and of time-dependent displacements produced during reaction by the approach of an attacking reagent, observed rate effects being resultants of both types of electronic effects. Hammett, however, claims that it is not necessary or possible to make this distinction. 

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. 

The reasonable extension of these ideas is to express o- as a sum of contributions from the inductive and resonance effects. Branch and Calvin suggested this, and much of the research on LFER of the past three decades has been concerned with 

Taft and Lewis S began with Eq. (7-30), adding the assumptions that the inductive effect is identical from the meta and para positions and that the resonance effect from the meta position is some fraction a of its effect from the para position. These assumptions give Eq. (7-31)  

The constants oi were taken equal to a scaled value of the aliphatic polar substituent constants a (which are defined in Section 7.3), and a was set at 3 (or a = in for substituents capable of through resonance). The resulting plots of Eq. (7-32) gave good LEER, which was interpreted to justify the approach. Refinements, - of this treatment showed that a depends upon the reaction, although most values fell  

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Herein is the rate constant for a dienophile with substituent x ko is the corresponding rate constant for unsubstituted 2,4c Ox is the substituent constant for substituent x and p is the reaction constant, defined as the slope of the plot of log (k / ko) versus Ox. The parameter p is a measure of the sensitivity of the reactions towards introduction of substituents. Figure 2.3 and Table 2.4 show the results of correlating the kinetic data for the reaction of 2.4a-e with 2.5 with a. ... 

The suitability of the model reaction chosen by Brown has been criticised. There are many side-chain reactions in which, during reaction, electron deficiencies arise at the site of reaction. The values of the substituent constants obtainable from these reactions would not agree with the values chosen for cr+. At worst, if the solvolysis of substituted benzyl chlorides in 50% aq. acetone had been chosen as the model reaction, crJ-Me would have been —0-82 instead of the adopted value of —0-28. It is difficult to see how the choice of reaction was defended, save by pointing out that the variation in the values of the substituent constants, derivable from different reactions, were not systematically related to the values of the reaction constants such a relationship would have been expected if the importance of the stabilization of the transition-state by direct resonance increased with increasing values of the reaction constant. 

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,... 

One underlying physical basis for the failure of Hammett reaction series is that substituent interactions are some mixture of resonance, field, and inductive effects. When direct resonance interaction is possible, the extent of the resonance increases, and the substituent constants appropriate to the normal mix of resonance and field effects then fail. There have been many attempts to develop sets of a values that take into account extra resonance interactions. 

The chemical information available through LFER is primarily the reaction constant p. but this value depends upon the substituent constants selected for the construction of the LFER. The o values available are cr, cr, , a" or ct , and Oi ... 

The substituent constant cr is defined at a given temperature. If 8rA// and 8rAS are independent of temperature, p should be linearly related to 1/7" if all other conditions are held constant. (The constancy of other conditions is not strictly possible, however, because the dielectric constant is a function of temperature.) Data are in reasonable agreement with this prediction. 

Some authors use O] instead of cr as the substituent constant in such correlations.) An example is provided by the aminolysis of phenyl esters in dioxane the substrates RCOOPh were reacted with -butylamine, and the observed first-order rate constants were related to amine concentration by = k2 [amine] kj [amine]. The rate constants kz and k could be correlated by means of Eq. (7-54), the reaction constants being p = +2.14, b = + 1.03 (for A 2) and p = -1-3.03,8 = -1-1.08 (for ks). Thus, the two reactions are about equally sensitive to steric effects, whereas the amine-catalyzed reaction is more susceptible to electronic effects than is the uncatalyzed reaction. 

In Section 8.4 we will encounter many empirical measures of solvent polarity. These are empirical in the sense that they are model dependent that is, they are defined in terms of a particular standard reaction or process. Thus, these empirical measures play a role in the study of solvent effects exactly analogous to that of the substituent constants in Chapter 7.)... 

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. 

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). 

The diazonio group is a somewhat more complex substituent for such evaluations because it is charged, in contrast to the majority of substituents on which the Hammett treatment is based. The electrostatic interaction of the diazonio and other charged groups was calculated by Hoefnagel et al. (1978) and by Exner (1978). The substituent constants they obtained, including the effects of coulomb interactions, are only slightly different from those of Lewis and Johnson (1959). 

The changes in the substituent constants and in the parameters F and R on going from the diazonium ion to various addition products provide a useful probe for understanding the mechanism(s) of addition of these nucleophiles to arenediazonium ions. Such constants and parameters are listed in Table 7-4. All values are taken from the relevant tables in the paper by Hansch et al. (1991). With the exception of the last three entries, which we shall discuss later, the products of nucleophile additions are arranged in a sequence of decreasing electron-withdrawing capability, as estimated from the values of <7m and op for the substituent corresponding to the nucleophile added. ... 

The similarity of the substituent constants and the parameters for the tert-butyl-azo group to those for the phenylazo group is interesting, but not easily understandable. 

The quantity on the right-hand side of Eq. (10-8) can be written in simplified form. This expression defines the substituent constant rr in terms of the m- and / -substituted benzoic acids, relative to benzoic acid itself. The value of <7 is given by... 

The symbol k or K is the rate or equilibrium constant, respectively, for a side-chain reaction of a meta- or para-substituted benzene derivative, and k° or K° denotes the statistical quantity (intercept term) approximating to k or K for the parent or unsubstituted compound. The substituent constant a measures the polar (electronic) effect of replacing H by a given substituent (in the meta- or para-position) and is, in principle, independent of the nature of the reaction. The reaction constant p depends on the nature of... 

Taft (21) has suggested that the electrical effect of a substituent is composed of localized (inductive and/or field) and delocalized (resonance) factors. Thus we may write the substituent constant of the group X as... 

Values of Pr for the substituent constants commonly used with eq. (1) are given in Table I. When correlations are made with eq. (1), the substituent constant used determines the composition of the electrical effect. 

AS can be obtained. In most practical applications, the parameter is the solvent composition (41-44, 192-194) however, the functional relationships are of complicated form and have not been expressed algebraically. A slightly different approach makes use of the relationship between log k and the parameter usually the substituent constant a—at different temperatures. From the temperature dependence of the slope—the reaction constant p—the value of /3 is then obtained indirectly (3, 155). Consider the generalized Hammett equation (9, 17) in the form... 

It appeared to the author some years ago that, irrespective of the mechanism of the toxic action of DDT, there might be a correlation of structure and toxicity in analogous compounds. Hammett (13) has shown that the rate and equilibrium constants of over 50 side-chain reactions of meta and para substituted aromatic compounds may be correlated with the so-called substituent constant a, according to the equation log k — log k0 = pa, where k and k0 are rate (or equilibrium) constants for substituted and unsubstituted compounds, respectively, p is the reaction constant giving the slope of the linear relationship, and a is the substituent constant, which is determined by the nature and... 

The substituent constants have also been associated with the ability of the substituent group to alter the charge density at the reaction site. 

Very high a values have been recorded for m- and p-NMe3+, about 1.0 and 0.9 respectively. However, as already remarked, the significance of the substituent constants of unipolar groups is a matter of debate234. 

The ion pairing between the enolate of 5 and the catalyst should make the asymmetric induction sensitive to the electronic effects of substituents on the N-benzyl group. A Hammett plot of log ee/eeQ vs the substituent constant o of the para N-benzyl substituted catalysts (R = CH3O, CH3 H, F, Cl, CF3) gave a reaction constant of p - 0.21 + 0.02 with ee s in the range of 60% to 92% demonstrating that substituents with increasing... 

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