Or + substituent constant

The effect of a substituent on the aromatic substitution reaction is similar to its effect on electrophilic side chain reactions, but not precisely parallel. Thus the Hammett relationship using the usual sigma or substituent constants gives considerable scatter when applied to aromatic substitution. The scatter is probably due to an increased importance of resonance effects in the nuclear substitution reaction as compared with the side chain reactions. 

Based on the earlier work of Meyer and Overton, who showed that the narcotic effect of anesthetics was related to their oil/water partition coefficients, Hansch and his co-workers have demonstrated unequivocally the importance of hydrophobic parameters such as log P (where P is, usually, the octanol/water partition coefficient) in QSAR analysis.28 The so-called classical QSAR approach, pioneered by Hansch, involves stepwise multiple regression analysis (MRA) in the generation of activity correlations with structural descriptors, such as physicochemical parameters (log P, molar refractivity, etc.) or substituent constants such as ir, a, and Es (where these represent hydrophobic, electronic, and steric effects, respectively). The Hansch approach has been very successful in accurately predicting effects in many biological systems, some of which have been subsequently rationalized by inspection of the three-dimensional structures of receptor proteins.28 The use of log P (and its associated substituent parameter, tr) is very important in toxicity,29-32 as well as in other forms of bioactivity, because of the role of hydrophobicity in molecular transport across cell membranes and other biological barriers. 

Decades of work have led to a profusion of LEERs for a variety of reactions, for both equilibrium constants and reaction rates. LEERs were also established for other observations such as spectral data. Furthermore, various different scales of substituent constants have been proposed to model these different chemical systems. Attempts were then made to come up with a few fundamental substituent constants, such as those for the inductive, resonance, steric, or field effects. These fundamental constants have then to be combined linearly to different extents to model the various real-world systems. However, for each chemical system investigated, it had to be established which effects are operative and with which weighting factors the frmdamental constants would have to be combined. Much of this work has been summarized in two books and has also been outlined in a more recent review [9-11]. 

The importance of all this work lies in the fact that it established for the first time that chemical reactivity data for a wide series of reactions can be put onto a quantitative footing. With continuing research, however, it was found that the various chemical systems required quite specific substituent constants of their own, leading to a decline in interest in LEER. Nevertheless, substituent constant scales are still in use and methods for calculating or correlating them are still of interest [12]. 

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,). 

The ability of partial least squares to cope with data sets containing very many x values is considered by its proponents to make it particularly suited to modern-day problems, where it is very easy to compute an extremely large number of descriptors for each compound (as in CoMFA). This contrasts with the traditional situation in QSAR, where it could be time-consuming to measure the required properties or where the analysis was restricted to traditional substituent constants. 

The applicability of the two-parameter equation and the constants devised by Brown to electrophilic aromatic substitutions was tested by plotting values of the partial rate factors for a reaction against the appropriate substituent constants. It was maintained that such comparisons yielded satisfactory linear correlations for the results of many electrophilic substitutions, the slopes of the correlations giving the values of the reaction constants. If the existence of linear free energy relationships in electrophilic aromatic substitutions were not in dispute, the above procedure would suffice, and the precision of the correlation would measure the usefulness of the p+cr+ equation. However, a point at issue was whether the effect of a substituent could be represented by a constant, or whether its nature depended on the specific reaction. To investigate the effect of a particular substituent in different reactions, the values for the various reactions of the logarithms of the partial rate factors for the substituent were plotted against the p+ values of the reactions. This procedure should show more readily whether the effect of a substituent depends on the reaction, in which case deviations from a hnear relationship would occur. It was concluded that any variation in substituent effects was random, and not a function of electron demand by the electrophile. ... 

For the nine substituents m- andp-methyl, p-fluoro, m- and p-chloro, m- and p-bromo, and m- and p-iodo, using the results for nitration carried out at 25 °C in nitromethane or acetic anhydride - (see tables 9.1, 9.5), a plot of logjoA/ j against cr+ produced a substituent constant p = —6-53 with a standard deviation from the regression line i = 0-335, 2 correlation coefficient c = 0-975. Inclusion of... 

The color and constitution of cyanine dyes may be understood through detailed consideration of their component parts, ie, chromophoric systems, terminal groups, and solvent sensitivity of the dyes. Resonance theories have been developed to accommodate significant trends very successfully. For an experienced dye chemist, these are useful in the design of dyes with a specified color, band shape, or solvent sensitivity. More recendy, quantitative values for reversible oxidation—reduction potentials have allowed more complete correlation of these dye properties with organic substituent constants. 

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... 

Substituent constants calculated in this way are in good agreement with empirical Of values. The same system was used to calculate values by determining charge accumulation or depletion on the a and p carbons of substituted ethylenes using the 4-3IG method. 

The most common manifestation of extrathermodynamic relationships is a linear correlation between the logarithms of rate or equilibrium constants for one reaction series and the logarithms of rate or equilibrium constants of a second reaction series, both sets being subjected to the same variation, usually of structure. For illustration, suppose the logarithm of the rate constants for a reaction series B is linearly correlated with the logarithm of the equilibrium constants for a reaction series A, with substituent changes being made in both series. The empirical correlation is... 

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 ... 

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 ortho effect may consist of several components. The normal electronic effect may receive contributions from inductive and resonance factors, just as with tneta and para substituents. There may also be a proximity or field electronic effect that operates directly between the substituent and the reaction site. In addition there may exist a true steric effect, as a result of the space-filling nature of the substituent (itself ultimately an electronic effect). Finally it is possible that non-covalent interactions, such as hydrogen bonding or charge transfer, may take place. The role of the solvent in both the initial state and the transition state may be different in the presence of ortho substitution. Many attempts have been made to separate these several effects. For example. Farthing and Nam defined an ortho substituent constant in the usual way by = log (K/K ) for the ionization of benzoic acids, postulating that includes both electronic and steric components. They assumed that the electronic portion of the ortho effect is identical to the para effect, writing CTe = o-p, and that the steric component is equal to the difference between the total effect and the electronic effect, or cts = cr — cte- They then used a multiple LFER to correlate data for orrAo-substituted reactants. 

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.)... 

Probably the most important development of the past decade was the introduction by Brown and co-workers of a set of substituent constants,ct+, derived from the solvolysis of cumyl chlorides and presumably applicable to reaction series in which a delocalization of a positive charge from the reaction site into the aromatic nucleus is important in the transition state or, in other words, where the importance of resonance structures placing a positive charge on the substituent - -M effect) changes substantially between the initial and transition (or final) states. These ct+-values have found wide application, not only in the particular side-chain reactions for which they were designed, but equally in electrophilic nuclear substitution reactions. Although such a scale was first proposed by Pearson et al. under the label of and by Deno et Brown s systematic work made the scale definitive. 

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. 

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). 

Sets of homo- and hetero-nuclear substituent constants for the alkoxy-dechlorination of 4-chloroquinolines have been recently obtained from preliminary values of the p-constants and can be extended and improved on the basis of the more extensive data now available. A detailed discussion on substituent constants would extend beyond the scope of this review. In general, it can be stated that unless enhanced resonance interaction occurs with the reaction center in the transition state (i.e., para-, cata-, amphi-N02 groups) or with the aza... 

In Scheme 7-1 kx and kn refer to the rate constants for a benzene derivative, in our case the benzenediazonium ion, bearing a substituent X in the 3- or 4-position, and the corresponding unsubstituted benzene derivative respectively. The term p is Hammett s reaction constant for the reaction, and o is Hammett s substituent constant which is, at least in principle, independent of the nature of the reaction but different for the 3- and 4-positions. A plot of log kx (or log kx - log kH) versus o should give a straight line. Its slope (positive or negative) corresponds to the reaction constant p. Equilibrium relationships are treated analogously. 

In summary we think that, on a superficial basis, a comparison of the effects of different nucleophilic species added covalently at the (3-nitrogen atom of an arenedi-azonium ion yields results that are almost trivial. Of more interest are unexpected results such as those of Exner and Lakomy for the substituent -N = CHC6H5. A possible explanation for the latter results emerged when the twisted structure of the substituent became known. We emphasize, however, that definitive explanations on the basis of Hammett or related substituent constants are not found very frequently. 

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... 

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. 

However, the duality of substituent constants and the attempt to deal with crossconjugation by selecting cr+, a or a in any given case is somewhat artificial. The contribution of the resonance effect of a substituent relative to its inductive effect must in principle vary continuously as the electron-demanding quality of the reaction center is varied, i.e. whether it is electron-rich or electron-poor. A sliding scale of substituent constants would be expected for each substituent having a resonance effect and not just a pair of discrete values a and a for — R, or o and a for + R substituents55. 

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