A substituent effect is the change in a molecule’s reactivity when a substituent on the molecule is changed. In 1935, Louis Hammett designed a scale to measure influence of various substituents (X) at the meta- or para- positions on the acidity of benzoic acid. Contributed by: Erika Aoyama and Megan Browning, University of Utah, 2016

1. Organic Pedagogical Electronic
Network
Hammett plots in the world of
enzymes
Erika Aoyama and Megan Browning
Figure 1: A Hammett plot from Louis Hammett’s original 1935 paper in which he described Hammett plots.
Reference: Hammett, L. P. Chem. Rev. 1935, 17 (1), 125–136.

2. A substituent effect is the change in a molecule’s reactivity when a substituent on the molecule
is changed. In 1935, Louis Hammett designed a scale to measure influence of various
substituents (X) at the meta- or para- positions on the acidity of benzoic acid. He measured
equilibrium constants of deprotonation of substituted benzoic acids and compared them to the
equilibrium constant with X = hydrogen (unsubstituted benzoic acid).
He called the log of this comparison sigma (σ). Either K (equilibrium constant) or k (rate
constant) can be used in the equation:
𝑙𝑜𝑔
𝐾𝑥
𝐾 𝐻
= 𝑙𝑜𝑔
𝑘 𝑥
𝑘 𝐻
= 𝜎𝑥
Electron donating groups (EDG) have negative σ values (reduce acidity); electron
withdrawing groups (EWG) have positive σ values (increase acidity). The relationship between
reaction (or activation) free energy change and the character of the substituent is linear on a
graph, so σ is called a linear free energy relationship (LFER).
σ (sigma)
References: Hammett, L. P. Chem. Rev. 1935, 17 (1), 125–136. Eric V. Anslyn; Dennis A. Dougherty. Modern
Physical Organic Chemistry; University Science Books, 2006.

3. Hammett plots and ρ (rho)
References: Hammett, L. P. Chem. Rev. 1935, 17 (1), 125–136. Eric V. Anslyn; Dennis A. Dougherty. Modern
Physical Organic Chemistry; University Science Books, 2006.
In general, if:
ρ>0, negative charge is building (or positive charge is decreasing)
• ρ>1: new reaction is more sensitive to substituents than benzoic acid reference reaction
• 0<ρ<1: new reaction is less sensitive to substituents than the benzoic acid reference reaction
ρ<0, positive charge is building (or negative charge is decreasing)
in the reaction or the rate-limiting step (r.l.s.) of the reaction.
For example, in this hydrolysis of an ester
(see right), the 𝜌 value is 2.54. The positive
sign indicates that the reaction creates
negative charge like the deprotonation of benzoic acid, and the fact that 𝜌 is higher than 1 indicates it
is more sensitive to substituents than benzoic acid.
𝜌 values have been used to elucidate mechanisms in all branches of chemistry. On the next few pages are
two examples where Hammett plots were used to probe mechanisms for an enzyme-mimic- and enzyme
catalyzed reactions.
σ can be used to study substituent effects of other reactions
by comparing 𝑙𝑜𝑔
𝑘 𝑥
𝑘 𝐻
of the new reaction to 𝜎𝑥 , to see if the
new reaction is more or less sensitive to substituents than
benzoic acid deprotonation. A graph of 𝑙𝑜𝑔
𝑘 𝑥
𝑘 𝐻
vs 𝜎𝑥 is called a
Hammett plot. The slope of the Hammett plot is defined as 𝜌 (rho):
𝑙𝑜𝑔
𝐾 𝑥
𝐾 𝐻
= 𝑙𝑜𝑔
𝑘 𝑥
𝑘 𝐻
= 𝜌𝜎𝑥

4. In this paper, the researchers (Hoffmann et al.) used 𝜎+ to elucidate a
mechanism for an enzyme mimic. They designed a catalyst to mimic
tyrosinase, a copper containing enzyme that catalyzes the hydroxylation of
phenols using dioxygen, a notoriously difficult reaction to catalyze synthetically.
Hoffmann et al. made an synthetic catalyst enzyme-mimic that hydroxylates
a variety of phenols at room temperature. They created a Hammett plot of their
catalyst to compare it to the enzyme to see if their catalyst proceeded through
a mechanism similar to tyrosinase. Using 𝜎+ for their Hammett plot, they
calculated 𝜌 = -0.99, indicating that at the transition state, there is an increase
in positive charge. This is consistent with the electrophilic aromatic substitution
mechanism that is accepted for tyrosinase, and is also consistent with the
trend of 𝜌 values published for tyrosinase: -1.8 to -2.2. The Hammett plot
supported their claim that their catalyst acts through the same mechanism
as tyrosinase.
𝜎+ and Biology example 1: Enzyme-mimic
References: Eric V. Anslyn; Dennis A. Dougherty. Modern Physical Organic Chemistry; University Science Books, 2006. Okamoto, Y.;
Brown, H. C. J. Org. Chem. 1957, 22 (5), 485–494. Hoffmann, A.; Citek, C.; Binder, S.; Goos, A.; Rübhausen, M.; Troeppner, O.; Ivanović-
Burmazović, I.; Wasinger, E. C.; Stack, T. D. P.; Herres-Pawlis, S. Angewandte Chemie International Edition 2013, 52 (20), 5398–5401.
Sigma only describes inductive charge stabilization/ destabilization effects (including indirect resonance effects). Other LFERs
have been defined that describe other effects as well. In 1957, Herbert C. Brown sought an LFER that described effects of direct
resonance charge stabilization. They used a new reference reaction in which the direct resonance stabilization of a positive
charge far outweighs any inductive stabilization effects:
This LFER is called 𝜎+.
𝜎+ is defined so that ρ<0 still means positive charge is building.

5. Biology example 2: Kynureninase-catalyzed reaction of β-benzoylalanine
References: Kumar, S.; Gawandi, V. B.; Capito, N.; Phillips, R. S. Biochemistry 2010, 49 (36), 7913–7919.
Kynureninase, an enzyme found in bacteria, catalyzes the following reaction, which is an important step in
L-tryptophan catabolism:
Kynureninase can catalyze a similar reaction involving β-benzoylalanine instead of L-kynurenine as the
substrate:
The rate-limiting part of the process is the release of the product L-Alanine.
However, in this new reaction, the formation
of the first product (benzoate) was found to
be rate-limiting.
To probe the mechanism of this new reaction, the authors synthesized derivatives
of β-benzoylalanine with various substitutents (X) attached to the aromatic ring,
used these derivatives as substrates for the kynureninase reaction, and created a
Hammett plot from the rate data obtained (plot shown on next page).

6. References: Kumar, S.; Gawandi, V. B.; Capito, N.; Phillips, R. S. Biochemistry 2010, 49 (36), 7913–7919.
Hammett plot for kynureninase-catalyzed
reaction of substituted β-benzoylalanines.
The break in the plot shows 2 different rate-limiting
steps (r.l.s.) in benzoate formation, depending on X.
Positive slope ρ on the left side of the plot shows that
negative charge is building (or positive charge is
decreasing) in the r.l.s. when X = EDG. Negative
slope ρ on the right side of the plot shows that
positive charge is building (or negative charge is
decreasing) in the r.l.s. when X = EWG.
Part of the proposed mechanism for
benzoate formation.
Step A has negative charge building, whereas Step
B has a decrease in negative charge. This is
consistent with the Hammett plot.
The authors conclude that their Hammett plot
provides support for a gem-diolate intermediate in
the formation of benzoate, with Step A being the
r.l.s. for X = EDG, and Step B being the r.l.s. for X =
EWG.
Step A
Step B

7. Problems
1. Would X= MeO have a
a. zero σ value
b. positive σ value
c. negative σ value
2. Why was σ insufficient and σ+ invented?
a. σ described only resonance, and parameter including induction was needed
b. σ described only induction and indirect resonance, and a parameter including direct resonance was needed
c. σ described resonance and induction, and a parameter describing only induction was needed
d. σ described direct resonance, and a parameter describing indirect resonance was needed
3. Is 𝜌 value positive or negative when the reactant containing the aromatic ring is acting as an electrophile?
a. negative
b. positive
c. neither
For 4 and 5 use the reaction to the right:
4. Which LFER parameter would best represent the reaction?
a. σ-
b. σ
c. σ+
d. None of the above
5. For the reaction is 𝜌
a. Negative
b. Positive
c. Zero

8. This work is licensed under a
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License.
Contributed by:
Erika Aoyama and Megan Browning
University of Utah, 2016