Hammett plots/equations

Fig. 2. Hammett equation plot of relative k. values vs.

Fig. 5. Hammett equation plot of relative k values vs. a for hydrogen abstraction from substituted toluenes by the undecyl radical at 3S4 K. The least-squares treatment gives p = 0.50(2) (r = 0.97) [74 Pry 1]. /, 4-methyltoluene 2, 3-methyltoluene S, toluene 4, 4-fluorotoluene 5, 4-chlorotoluene 6, 3-fluorotoluene 7, 3-chlorotoluene 8, 3-cyanotoluene 9,4-methoxytoluene /0,4-r-butyltoluene //, 3-methoxytoluene 12,3-bromotoluene.

The Hammett equation is said to be followed when a plot of log k against a is linear. Most workers take as the criterion of linearity the correlation coefficient r, which is required to be at least 0.95 and preferably above 0.98. A weakness of r as a statistical measure of goodness of fit is that r is a function of the slope p if the slope is zero, the correlation coefficient is zero. A slope of zero in an LEER is a chemically informative result, for it demonstrates an absence of a substituent... 

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 first reaction series to be considered are the basicities of the various quinolines. Baciocchi and Illuminati have demonstrated that the pK values of quinolines substituted in the B-ring follow the Hammett equation well if ApK, i.e., the difference between the pK values of substituted and unsubstituted compounds, is plotted against a, the quinoline points fall on the same line as the pyridine points, as shown in Fig. 5, so that the p-values for the two series are identical. 

This shows that the assumption made in Eqs. (18) and (19), i.e., that the Hammett equation is separately applicable to the component reactions, does not imply linearity of a plot of vs. a. The assumption of the applicability of the Hammett equation to the component series seems undeniable since these reactions are extremely closely related to series which follow the Hammett equation very well. This assumption also implies... 

A typical Hammett plot is shown in Figure 8-1. The very large scatter indicates clearly that the Hammett equation cannot be applied. Dickson and Eaborn (1959) were the first to point out that the rates of these dediazoniations could be described... 

Hammett equation. Consider the reaction39 of a series of benzenediazonium ions with OH" and CIST. Construct Hammett plots, calculate the p s, and discuss their signs and magnitudes. 

Miller226 applied the Hammett equation to the rate constants for the reaction of 4-substituted l-chloro-2-nitrobenzenes with OMe in methanol at 50°C. a values (denoted ct in accordance with the practice briefly in vogue at that time, 1956) were used for + R substituents, and S02Me conformed well at a a value of 1.04952. Act value of 1.117 for S02Ph was derived from the Hammett plot, intermediate between the values based on phenol and anilinium ionizations by Szmant and Suld88 at about the same time. 

It is, however, important to resist the temptation to introduce new parameters into the Hammett equation merely to achieve a better fit with the experimental data. This is particularly true where, as in some cases, it may be difficult to ascribe real significance, in physical terms, to the new parameter anyway. It is in fact possible, as we shall see, to obtain much highly relevant information about reaction pathways using simple Hammett plots only. 

The Hammett equation is the best-known and most widely studied of the various linear free energy relations for correlating reaction rate and equilibrium constant data. It was first proposed to correlate the rate constants and equilibrium constants for the side chain reactions of para and meta substituted benzene derivatives. Hammett (37-39) noted that for a large number of reactions of these compounds plots of log k (or log K) for one reaction versus log k (or log K) for a second reaction of the corresponding member of a series of such derivatives was reasonably linear. Figure 7.5 is a plot of this type involving the ionization constants for phenylacetic acid derivatives and for benzoic acid derivatives. The point labeled p-Cl has for its ordinate log Ka for p-chlorophenylacetic acid and for its abscissa log Ka for p-chloroben-zoic acid. The points approximate a straight line, which can be expressed as... 

ACIDITY FUNCTION BUNNETT-OLSEN EQUATIONS DECREE OF DISSOCIATION HAMMETT EQUATION HAMMOND PRINCIPLE/POSTULATE LEFFLER S ASSUMPTION REACTING BOND RULES HANES PLOT... 

A number of substrates having a benzylic ether moiety were reacted with 51 to afford the corresponding benzylic esters in good yields (equation 84). For evaluating the effects of p-substiments on the oxidation of a series of benzylic ethers, a competitive oxidation of p-substimted benzylic propyl ethers with 51 was carried out. The Hammett correlation plot for the oxidation reaction gave a better correlation of the relative ratio factors with the a rather than with the a+ substituent constants and afforded a reaction constant p+ = —0.57 (r = 0.99). This p+ value shows that 51 is an electrophilic species and appears to be comparable to the p+ value of —0.65 for benzylic hydrogen abstraction from dibenzyl ethers by the benzoyloxy radicaP . 

Haloform reaction, 237, 296 Halogenation alkanes, 300, 323 alkenes, 179,186, 313 benzene, 138,316 ketones, 295 Hammett equation, 362 additional parameters, 374, 388, 395 derivation of, 362 deviations from, 375 empirical nature of, 395 implications of, 394 reaction pathway, and, 375 solvent effects and, 388 spectroscopic correlations, 392 standard reaction for, 362, 395 steric effects and, 361, 383 thermodynamic implications of, 394 Hammett plots, 359 change in rate-limiting step and, 383 change in reaction pathway and, 378... 

Pyridines are also well known as ligands in transition metal complexes, and if the equilibrium constants for the formation of such complexes can be related to base strength, it is expected that such constants would follow the Hammett equation. The problem has been reviewed,140 and a parameter S, formulated which is a measure of the contribution of the additional stabilization produced by bond formation to the stabilization constants of complexes expressed in terms of a.141 The Hammett equation has also been applied to pyridine 1 1 complexation with Zn(II), Cd(II), and Hg(II) a,/3,y,<5-tetraphenylporphins,142 143 the a values being taken as measures of cation polarizing ability. Variation of the enthalpy of complexation for adducts of bis(2,4-pentanediono)-Cu(II) with pyridines plotted against a, however, exhibited a curved relationship.144... 

The Hammett equation (26-6) states that the relative reactivity (expressed in logarithmic form) of a substituted benzene derivative is proportional to the substituent constant a. For a given reaction, a plot of log (/c//c0) or of log (K/Ka) versus cr should be linear with slope p. Some idea of the validity of the Hammett equation can be gained from Figure 26-4, which shows plots of log kjko) or of log (KjKa) against a for several different reactions. For the examples given, the fit to the Hammett equation is fair. A number of p values (slopes) are listed separately in Table 26-7. It can be seen that p values vary... 

Then the differences in rate caused by the electronic effect of the substituent are correlated by the Hammett equation log(kz/kH) = poz, where kz is the rate constant obtained for a compound with a particular meta or para substituent, ku is the rate constant for the unsubstituted phenyl group, and crz is the substituent constant for each substituent used. The proportionality constant p relates the substituent constant (electron donating or wididrawing) and the substituent s effect on rate. It gives information about the type and extent of charge development in the activated complex. It is determined by plotting log(kz/kQ) versus ov for a series of substituents. The slope of the linear plot is p and is termed the reaction constant. For example, the reaction shown above is an elimination reaction in which a proton and the nosy late group are eliminated and a C-N n bond is formed in their place. The reaction is second order overall, first order in substrate, and first order in base. The rate constants were measured for several substituted compounds ... 

These data were plotted according to the Hammett equation to give the plot in Figure 5.17. The first thing to note is that the Hammett plot is linear. The linearity of die plot implies that the substituent constants determined for the ionization of... 

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