- Hammett equation
; 1935; 17(1); 125-136 [http://pubs.acs.org/cgi-bin/abstract.cgi/chreay/1935/17/i01/f-pdf/f_cr60056a010.pdf Abstract] ] .
The basic idea is that for any two reactions with two aromatic reactants only differing in the type of substituent the change in free energy of activation is proportional to the change in
Gibbs free energy"Advanced Organic Chemistry Part A" Second Edition F.A. Carey, R.J. Sundberg Plenum Press ISBN 0-306-41198-9] . This notion does not follow from elemental thermochemistryor chemical kineticsand was introduced by Hammett intuitively [The opening line in his 1935 publication reads: "The idea that there is some sort of relationship between the rate of a reaction and the equilibrium constant is one of the most persistently held and at the same time most emphatically denied concepts in chemical theory"] .
The basic equation is:
equilibrium constantK for a given equilibrium reaction with substituent R and the reference K0 constant with R=H to the substituent constant σ which depends only on the specific substituent R and the reaction constant ρ which depends only on the type of reaction but not on the substituent used.
The equation also holds for
reaction rates k of a series of reactions with substituted benzene derivatives:
In this equation k0 is the reference reaction rate of the unsubstituted reactant and k that of a substituted reactant.
A plot of log(K/K0) for a given equilibrium versus log(k/k0) for a given reaction rate with many differently substituted reactants will give a straight line.
The starting point for the collection of the substituent constants is a
chemical equilibriumfor which both the substituent constant and the reaction constant are arbitrarily set to 1: the ionizationof benzoic acid(R and R' both H) in water at 25°C.
Having obtained a value for K0, a series of equilibrium constants (K) are now determined based on the same process but now with variation of the para substituent for instance
p-Hydroxybenzoic acid(R=OH, R'=H) or 4-aminobenzoic acid(R=NH2, R'=H). These values combined in the Hammett equation with K0 and remembering that ρ = 1 give the para substituent constants compiled in table 1 for amine, methoxy, ethoxy, dimethylamino, methyl, fluorine, bromine, chlorine, iodine, nitroand cyanosubstituents. Repeating the process with meta-substituents afford the meta substituent constants. This treatment does not include ortho-substituents which would introduce steric effects.
The σ values displayed in table 1 [These values are the original values obtained by Hammett in his1937 publication and may differ from subsequent publications by others. The following review contains more commonly accepted substituent constants: C. Hansch, A. Leo and R. W. Taft
Chem. Rev.; 1991; 91; 165-195 [http://pubs.acs.org/cgi-bin/abstract.cgi/chreay/1991/91/i02/f-pdf/f_cr00002a004.pdf Abstract] ] reveal certain substituent effects. With ρ = 1 the group of substituents with increasing positive values, notably cyanoand nitrocause the equilibrium constant to increase compared to the hydrogenreference meaning that the acidityof the carboxylic acid (depicted on the left of the equation) has increased. These substituents stabilize the negative charge on the carboxylate oxygen atom by an electron-withdrawing inductive effect(-I) and also by a negative mesomeric effect(-M).
The next set of substituents are the
halogens for which the substituent effect is still positive but much more modest. The reason for this is that while the inductive effectis still positive, the mesomeric effectis negative causing partial cancellation. The data also that for these substituents the meta effect is much larger than the para effect and this is due to the fact that the mesomeric effect is cancelled in a meta substituent.
This effect is depicted in "scheme 3" where in a para substituted arene 1a, one
resonance structure1b is a quinoidwith positive charge on the X substituent releasing electrons and thus destabilizing the Ysubstituent. This destabilizing effect is not possible when X has a meta orientation.
Other substituents like
methoxyand ethoxycan even have opposite signs for the substituent constant as result of opposing inductive and mesomeric effect. Only alkyl and aryl substituents like methylare electron-releasing in both respects.
Of course when the sign for the reaction constant is negative (next section) only substituents with a likewise negative substituent constant will increase equilibrium constants.
With knowledge of substituent constants it is now possible to obtain reaction constants for a wide range of
organic reactions. The archetypal reaction is the alkaline hydrolysisof ethyl benzoate(R=R'=H) in a water/ethanol mixture at 30°C. Measurement of the reaction ratek0 combined with that of many substituted ethyl benzoates ultimately result in a reaction constant of +2.498 .
Reaction constants are known for many other reactions and equilibria, a selection of those provided by Hammett himself (with their values in parenthesis):
* the hydrolysis of substituted
cinnamic acidester in ethanol/water (+1.267)
* the ionization of substituted
phenolsin water (+2.008)
* the acid catalyzed
esterificationof substituted benzoic esters in ethanol(-0.085)
* the acid catalyzed bromination of substituted
acetophenones ( Ketone halogenation) in an acetic acid/water/hydrochloric acid (+0.417)
* the hydrolysis of substituted
benzyl chlorides in acetone-water at 69.8°C (-1.875).
The reaction constant, or sensitivity constant, "ρ", describes the susceptibility of the reaction to substituents, compared to the ionization of benzoic acid. It is equivalent to the slope of the Hammett plot. Information on the reaction and the associated mechanism can be obtained based on the value obtained for "ρ". If the value of:
# "ρ>1", the reaction is more sensitive to substituents than benzoic acid and negative charge is built during the reaction.
# "0<ρ<1" , the reaction is less sensitive to substituents than benzoic acid and negative charge is built.
# "ρ=0", no sensitivity to substituents, and no charge is built.
# "ρ<0", the reaction builds positive charge.
These relations can be exploited to elucidate the mechanism of a reaction. As the value of "ρ" is related to the charge during the rate determining step, mechanisms can be devised based on this information. If for example, the mechanism for the reaction of an aromatic compound is thought to occur through one of two mechanisms, the compound can be modified with substituents with different "ρ" values and kinetic measurements taken. Once these measurements have been made, a hammett plot can be constructed to determine the value of "ρ". If one of these mechanisms involves the formation of charge, this can be verified based on the ρ value. Conversely, if the hammett plot shows that no charge is developed, i.e. a zero slope, the mechanism involving the building of charge can be discarded.
Hammett plots may not always be perfectly linear. For instance, a curve may show a sudden change in slope, or "ρ" value. In such a case, it is likely that the mechanism of the reaction changes upon adding a different substituent. Other deviations from linearity may be due to a change in the position of the transition state. In such a situation, certain substituents may cause the transition state to appear earlier (or later) in the reaction mechanism. ["Modern Physical Organic Chemistry" E.V. Anslyn, D.A. Dougherty. University Science Books ISBN 1-891389-31-9]
Other equations now exist that refine the original Hammett equation: the
Swain-Lupton equation, the Taft equationand the Yukawa-Tsuno equation. An equation that address stereochemistry in aliphatic systems is also known [M. Bols, X. Liang, H. H. Jensen “Equatorial contra axial polar substituents. The Relation of a Chemical Reaction to Stereochemical Substituent Constants.” "J. Org. Chem." 2002; "67"; 8970-74. [http://pubs.acs.org/cgi-bin/abstract.cgi/joceah/2002/67/i25/abs/jo0205356.html Abstract] ] .
Quantitative structure-activity relationship
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