The starting point for the collection of the substituent constants is a
chemical equilibrium for which the substituent constant is arbitrarily set to 0 and the reaction constant is set to 1: the deprotonation of
benzoic acid or
benzene carboxylic 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, or . 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,
nitro and
cyano substituents. 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 the Table above reveal certain substituent effects. With ρ = 1, the group of substituents with increasing positive values—notably
cyano and
nitro—cause the equilibrium constant to increase compared to the
hydrogen reference, meaning that the
acidity of 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 effect is still negative, the
mesomeric effect is positive, causing partial cancellation. The data also show that for these substituents, the meta effect is much larger than the para effect, due to the fact that the mesomeric effect is greatly reduced in a meta substituent. With meta substituents a carbon atom bearing the negative charge is further away from the carboxylic acid group (structure 2b). This effect is depicted in
scheme 3, where, in a para substituted arene
1a, one
resonance structure 1b is a
quinoid with positive charge on the X substituent, releasing electrons and thus destabilizing the Y substituent. This destabilizing effect is not possible when X has a meta orientation. Other substituents, like
methoxy and
ethoxy, can even have opposite signs for the substituent constant as a result of opposing inductive and mesomeric effect. Only alkyl and aryl substituents like
methyl are 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.
The σp− and σp+ constants Because the carbonyl group is unable to serve a source of electrons for −M groups (in contrast to lone pair donors like OH), for reactions involving phenol and aniline starting materials, the
σp values for electron-withdrawing groups will appear too small. For reactions where resonance effects are expected to have a major impact, a modified parameter, and a modified set of
σp− constants may give a better fit. This parameter is defined using the ionization constants of
para substituted phenols, via a scaling factor to match up the values of
σp− with those of
σp for "non-anomalous" substituents, so as to maintain comparable ρ values: for ArOH ⇄ ArO− + H+, we define \sigma_p^- = \frac{1}{2.11}\log_{10}\left(\frac{K_\ce{X}}{K_\ce{H}}\right). Likewise, the carbonyl carbon of a benzoic acid is at a nodal position and unable to serve as a sink for +M groups (in contrast to a carbocation at the benzylic position). Thus for reactions involving carbocations at the α-position, the
σp values for electron-donating groups will appear insufficiently negative. Based on similar considerations, a set of
σp+ constants give better fit for reactions involving electron-donating groups at the
para position and the formation of a carbocation at the benzylic site. The
σp+ are based on the
rate constants of the SN1 reaction of cumyl chlorides in 90% acetone/water: for , we define \sigma_p^+ = -\frac{1}{4.54}\log_{10}\left(\frac{k_\ce{X}}{k_\ce{H}}\right). Note that the scaling factor is negative, since an electron-donating group speeds up the reaction. For a reaction whose Hammett plot is being constructed, these alternative Hammett constants may need to be tested to see if a better linearity could be obtained. ==Rho value==