Hammett relation

The approach Taft has presented gives rise to an equation that is obviously more powerful than the Hammett relation. It correlates more reactions and can be extended to include steric parameters. It takes the form... 

It is well known that we usually deal with a mixture of rotamers in chemical reactions. If they are interconverted rapidly at a given temperature (eq. [6]), then the Curtin-Hammett relation (171) (eq. [7]) will explain the product dis-... 

The values for % and 0 are as defined above and used as dimensionless numbers. Property as in Hammett relations should be the logarithm of a rate constant, equilibrium constant, etc. An important refinement for the steric contribution was made after the recognition that below a certain threshold of cone angles the property no longer changed and one should use the value 0 for c [29], Above the threshold a linear relation was found. Thus, for each property a steric threshold 0 was defined and the equation now reads ... 

The polar effect was at first invoked to explain various directive effects observed in aliphatic systems. Methyl radicals attack propionic acid preferentially at the a-position, ka/kp = 7.8 (per hydrogen), whereas chlorine " prefers to attack at the /3-position, ka/kp = 0.03 (per hydrogen). In an investigation of f-butyl derivatives, a semiquanti-tative relationship was observed between the relative reactivity and the polar effect of the substituents, as evidenced by the pK, of the corresponding acid. In the case of meta- and / ara-substituted toluenes, it has been observed that a very small directive effect exists for some atoms or radicals. When treated by the Hammett relation it is observed that p = —0.1 for H , CeHs , P-CH3C6H4 and CHs . On the contrary, numerous radicals with an appreciable electron affinity show a pronounced polar effect in the reaction with the toluenes. Compilation of Hammett reaction constants and the type of substituent... 

Hammett relations, secondary kinetic isotope effects ", pressure studies and viscosity-independent rates ° have all pointed to a two-bond homolysis taking place via TS 3. The rates are, however, insensitive to change of the solvents = —1.18 in CDCI3, p+ = —1.17 in CCLt and p+ = —1.0 in C6H5CI at 80 °C). This may indicate that there is little solvent interaction taking place via 3. The variation of the activation parameters with the substituent can be solely dependent on the formation and cleavage of the bonds a and b in 3. 

Mitigating this situation to some extent are the correlation equations for estimating kHO (water) from kHO (air) or from the Hammett relation (see below), making it possible to tap into the abundant database of measured values for kHO (air) (Atkinson, 1989), the excellent SARs for estimating kHO (air) values (Atkinson, 1987), and the utility of the Hammett equation with its large database of substituent constants (Exner, 1978 Perrin et al., 1981). 

Structure-activity relations (SARs) rest on the extra-thermodynamic principles first expressed in the Hammett relation for reactions of aromatic (benzene) compounds (Hammett, 1940 Exner, 1972) ... 

The key features of the Hammett relation are that (1) o is a portable parameter, independent of reaction type and (2) X, as a para- or meta- substituent, is remote from the reaction center and only electronic effects need be accounted for. A negative p value indicates an electron-deficient reaction center stabilized by electron donating groups, the most common situation for oxidation reactions. 

However, even for the simple methyl transfer reactions, there is considerable confusion and some disagreement about the details of the mechanism. Some authors (Sneen, 1973) have suggested that ionization of RX always precedes attack by the nucleophile, while others have maintained that the nucleophile attacks the covalent substrate. Extensive references to both points of view are given by McLennan (1976). In the present review the application of the Marcus theory of atom transfer (Marcus, 1968a) allows us to deduce values of the parameter a which describes the symmetry of the transition state. We shall compare this information about the transition state with that from changing the solvent, from isotope effects, and from Hammett relations. We shall then attempt to deduce a model for the transition state which is consistent for all the different types of data. 

Fig. 24 Evidence for the transition states in the hydrolysis of methyl halides from the different probes Marcus analysis, a 0.5 charge development, Z. Vi = 0.70, JZ, rjY = 0.46 solvent isotope effect, dotted lines (see Fig. 13) o-deuterium isotope effect, r 1.0 Hammett relations, shaded area (see Fig. 23)...

Similarly the argument from the er-deuterium isotope effect depends on the value one assumes for the fractionation factor for the transition state at r = 1. The simple geometric mean shown in Fig. 20 can only be a plausible guess. Again, for the Hammett relations, one has to make assumptions about the values of p for the transition state at r = 1 (Fig. 23). Furthermore there are also assumptions in separating the kinetic and thermodynamic contributions. 

In cases where B = 1 the Hammett relation also holds for equilibrium constants ... 

Equilibrium or rate constants of protodetritiation of benzenoid hydrocarbons (Scheme 4) can be measured in well-defined experiments with high accuracy [51], Referring to the Hammett-relation (4) (more correctly Hammett-Streitwieser relation) we may define... 

The oxidation of substituted /3-benzoylpropionic acids by PFC follows the Hammett relation with a negative reaction constant. A possible mechanism for the oxidation has been discussed.5 The oxidation of maleic, fumaric, crotonic, and cinnamic acids by PCC is of first order with respect to PCC and the acid. The oxidation rate in 19 organic solvents has been analysed by Kamlet s and Swain s multiparametric equations. A mechanism involving a three-centre transition state has been postulated.6 The relative reactivity of bishomoallylic tertiary alcohols toward PCC, to yield substituted THF products via the tethered chromate ester, is dependent only on the number of alkyl groups. This observation suggests a symmetrical transition state in this intramolecular Cr(VI)-alkene reaction.7 Mechanisms have been proposed for the oxidation of 2-nitrobenzaldehyde with PBC8 and of crotonaldehyde with tetraethylammonium chlorochromate.9... 

Two approximations usually applied in plotting Hammett relations for phenols are the assumed equality of ortho and para positions and an expected additivity of single substituent effects for polysubstituted cases. It is clear that neither of these can be exactly valid, although recent evidence shows that both approximations are fairly good for the acidity of phenols (Bolton et al., 1970 Sucha et al., 1970). 

The Hammett relation, og(hyjko)= pa, has been applied for many years to substituent eifects on reaction kinetics in solution, and has been particularly successful for reactions of benzene compounds. Attempts have also been made to apply Hammett correlations to other phenomena such as infrared (T. L. Brown, 1960), ultraviolet (Jaffe and Orchin, 1962a) and nuclear magnetic resonance absorption frequencies (Bothner-By and Glick, 1956). 

Although the activation energies of aminoazobenzene-type compounds (Ea between 75 and 88 kj moH) are not very different from those of azobenzene-type molecules, therm Z -> E isomerization of aminoazobenzene-type molecules is in general much faster than that of the azobenzene-type compounds. Conventional flash experiments are necessary to monitor the changes. The half-life of the Z-form of dimethyl-aminoazobenzene in toluene at 298 K is 220 s. A Linear Free Energy Rehitionship and Hammett relation is established, which includes azobenzene- and aminoazobenzene type compounds.A linear In vs, n, the Taft parameter of solvent polarity, is also observed. The dependence of the isomerization rate on pressure is weak In most solvents, it increases less than 35% at 2100 bar, AV -1.65 ml moLL Methanol is exceptional, with AV = -17 ml... 

Correlation of the half-wave potentials of meta- and para-substituted phenylarsonic acids with the Hammett substituent constants, cr, has been tried . The equation 1/2 = (0.053 0,010)o- — 0.705 V vs NHE (r = 0.9946) was obtained for a series of five compounds (unsubstituted, 4-OH, 4-NHj, 4-Me, 3-NH2-4-OH) studied in 0.02 M HCl, while under the same conditions the equation jy2 = 0.173(7 — 0.703 V vs NHE (r = 0.9991) was obtained for the second reduction of a series of three N02-substituted phenylarsonic acids using the a value for —NHOH for the reduced nitro group , i.e. apparently two different correlations exist. However, the possible protonation of the amino or hydroxylamino groups under the experimental conditions was not taken into account, and the validity of assigning the a value of the reduced substituent to the combined substituent/arsonic acid reduction taking place at the potential of the second wave was not discussed. It is therefore not surprising that the data cannot be described by a simple Hammett relation. For the simple para-substituted phenylarsonic acids a linear relation (equation 15) was found between the half-wave potential and the value of the arsonic acid. 

For the series of symmetrically substituted compounds ArjP, ArjAs and ArjSb the half-wave potentials for the irreversible oxidations were correlated with the Ecr values and the three Hammett relations, equations 91 -93, in which the potentials are referred to NHE and m is the number of compounds, were found . 

Several approaches have been made (see Reference 96 and references cited therein) to establish a quantitative, empirical scale describing the influence of a large collection of ligands of wide structural diversity on the redox potentials of transition metal complexes. All the approaches are based on the assumption that the relative contribution of each ligand to the redox potential of a transition metal complex is independent of the presenee of other ligands, the identity of the transition metal, the oxidation and spin states of this metal, the solvent etc. . Hence the approaches resemble the empirical use of substituent constants in the Hammett relation in organic chemistry. 

Styphnic acid 193 (I/538-54I) lead salts of 462(ia 213-220) pK deviation from the Hammett relation 191... 

Some characteristics can be found in the monograph by Meyer (1) and attention was paid to chemical properties of picric acid and its substituted derivatives. Thus Pearce and Simkins (86) determined pA a values (by calculation and experiment) of alkyl homologues of picric acid and its methoxy or halogen derivatives. The pA a values fit well with data predicted from the Hammett relation. Styplmic acid however shows a deviation. 

Biggs, A.I. and Robinson, R.A. (1961). The Ionisation Constants of Some Substituted Anilines and Phenols A Test of the Hammett Relation. J.Chem.Soc., 388-393. 

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