Substituent constant values

So for each p-substituent we now have available two, alternative, substituent constants—electron-withdrawing substituents or cTp.x and o-p.x for electron-donating substituents— whose use depends on whether through-conjugation between p-substituent and reaction centre does, or does not, take place in a particular reaction. It would be nice to think that these dual substituent constant values would now take care of all eventualities, and an analysis was therefore made of no less than eighty different... 

In eqn (8.4), k is the rate constant for the hydrolysis of an R substituted ester, and is corresponding constant for the methyl substituted parent, thus all comparisons are made between the substituent and a methyl group. These substituent constant values are used in the same way as the electronic and hydrophobic substituent constants discussed earlier, that is to say they are found in tabulations of substituent constant values, and of course the same problems of missing values apply. In fact, the situation can be even worse for Es as a number of substituents are themselves unstable under the conditions of acid hydrolysis. It has also been argued that this descriptor is not just a measure of steric effects, but that it also includes some electronic information. A number of more or less ingenious fixes were proposed to solve such problems, but a much more popular and generally useful measure of steric effects for both substituents and whole molecules was adopted in the form of molar refraction (MR), as defined by the Lorentz-Lorenz equation [eqn (8.5)]. 

This package includes databases of substituent constant values and (at the time of writing) contains routines for compound selection (various) and the generation of regression models. 

The second method, which was applied in the field of QSAR of corrosion inhibitors, is the Free-Wilson approach (Free and Wilson, 1964). Although by this method it has also been assumed that all the molecules are derivatives of a common parent structure, it is not necessary to collect substituent constant values to derive a regression equation. With this assumption, that inhibition efficiency is the dependent variable to be accounted for the Free-Wilson method is based on the following equation... 

The rate of solvolysis of l-(2-phenyl-5-thiazolyl)ethyl chloride is consistent with the substituent having an electrophilic substituent constant value of cTp = -0.34. This result is accounted for satisfactorily in terms of the coplanarity of the triazole and phenyl rings in this structure. ... 

The term p is a reaction constant and is mathematically evaluated for a particular reaction by plotting log kjkQ against a. The slope of the straight lines is p, and reflects the sensitivity of the reaction under study to effects of substituents. The value of p is obviously affected by temperature, solvent changes, etc. 

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. 

Good to excellent Hammett plots were obtained using substituent constants (see Figure 2.6). Surprisingly, literature examples of good Hammett correlations of stability constants are rare The p-values are shown in Table 2.7. 

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 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. ... 

Hammett and Taft substituent constants and, in particular. Tables 9.1 through 9.4 may also prove useful for estimating values. 

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. 

It is instructive to consider Af-substituted azoles in reverse, i.e. the azole ring as the substituent linked to some other group. Hammett and Taft cr-constant values for azoles as substituents are given in Table 11. The values show that all the azoles are rather weak net resonance donors, imidazole being the strongest. They are all rather strong inductive acceptors, with pyrazole considerably weaker in this respect than imidazole or the triazoles. 

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... 

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. 

Calculations have been done at the STO-3G and 4-3IG levels, and the resulting substituent constants correlate well with empirical values derived from ground-state structural parameters, such as C-NMR chemical shifts and IR absorption frequencies. 

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. 

Some bromination rate eonstants are summarized below. Compare the correlation of the rate data with o and substituent constants. What is the value of p What is the mechanistic significance of these results ... 

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 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 nonspecialist reading Table 7-7 will probably be impressed by the substantial consistency among cti values evaluated by different methods, but the specialist tends to concentrate on the differences. There is one very interesting difference in Table 7-7, that for cti of alkyl groups based on Eq. (7-33) compared with cti based on the ionization of 3, the latter values showing practically no effect of inductive electron release and certainly no trend with increased branching. (The uncertainties associated with these substituent constants can be found in the original literature.) Swain... 

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 ... 

Taft began the LFER attack on steric effects as part of his separation of electronic and steric effects in aliphatic compounds, which is discussed in Section 7.3. For our present purposes we abstract from that treatment the portion relevant to aromatic substrates. Hammett p values for alkaline ester hydrolysis are in the range +2.2 to +2.8, whereas for acid ester hydrolysis p is close to zero (see Table 7-2). Taft, therefore, concluded that electronic effects of substituents are much greater in the alkaline than in the acid series and. in fact, that they are negligible in the acid series. This left the steric effect alone controlling relative reactivity in the acid series. A steric substituent constant was defined [by analogy with the definition of cr in Eq. (7-22)] by Eq. (7-43), where k is the rate constant for acid-catalyzed hydrolysis of an orr/to-substituted benzoate ester and k is the corresponding rate constant for the on/to-methyl ester note that CH3, not H, is the reference substituent. ... 

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. 

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