Carbon kinetic isotope effects reveal variations in reactivity of intermediates in the formation of protonated carbonic acid

Article abstract of DOI:10.1021/jo402180z

Kinetic evidence suggests that acid-catalyzed decarboxylation reactions of aromatic carboxylic acids can occur by a hydrolytic process that generates protonated carbonic acid (PCA) as the precursor of CO₂. Measurements of reaction rates and carbon kinetic isotope effects (CKIE) for decarboxylation of isomeric sets of heterocyclic carboxylic acids in acidic solutions reveal that C-C cleavage to form PCA is rate-determining with significant variation in the magnitude of the observed CKIE (1.018-1.043). Larger values are associated with the more reactive member in each isomeric pair. This variation is consistent with stepwise mechanisms in which C-C cleavage is competitive with C-O cleavage, leading to reversion to the protonated reactant to varying degrees with an invariant intrinsic CKIE for C-C cleavage. Thus, the relative barriers to reversion and formation of PCA control the magnitude of the observed CKIE in a predictable manner that correlates with reactivity. Application of the proposed overall mechanism reveals that carboxylation reactions in acidic solutions will proceed by way of initial formation of PCA.

Full text of DOI:10.1021/jo402180z

Article
pubs.acs.org/joc
Carbon Kinetic Isotope Effects Reveal Variations in Reactivity of
Intermediates in the Formation of Protonated Carbonic Acid
Adelle A. Vandersteen,† Scott O. C. Mundle,‡ Georges Lacrampe-Couloume,‡ Barbara Sherwood Lollar,‡
and Ronald Kluger*,†
†Davenport Research Laboratories, Department of Chemistry, University of Toronto, 80 St. George Street, Toronto, Ontario, Canada
M5S 3H6
‡Stable Isotope Laboratory, Department of Earth Sciences, University of Toronto, 22 Russell Street, Toronto, Ontario, Canada M5S
3B1
ABSTRACT: Kinetic evidence suggests that acid-catalyzed
decarboxylation reactions of aromatic carboxylic acids can
occur by a hydrolytic process that generates protonated
carbonic acid (PCA) as the precursor of CO2. Measurements
of reaction rates and carbon kinetic isotope effects (CKIE) for
decarboxylation of isomeric sets of heterocyclic carboxylic
acids in acidic solutions reveal that C−C cleavage to form PCA
is rate-determining with significant variation in the magnitude
of the observed CKIE (1.018−1.043). Larger values are
associated with the more reactive member in each isomeric pair. This variation is consistent with stepwise mechanisms in which
C−C cleavage is competitive with C−O cleavage, leading to reversion to the protonated reactant to varying degrees with an
invariant intrinsic CKIE for C−C cleavage. Thus, the relative barriers to reversion and formation of PCA control the magnitude
of the observed CKIE in a predictable manner that correlates with reactivity. Application of the proposed overall mechanism
reveals that carboxylation reactions in acidic solutions will proceed by way of initial formation of PCA.
Scheme 1. Prohibitive Decarboxylation Reaction of Pyrrole-
2-carboxylic Acid Leading to Protonated Carbon Dioxide
INTRODUCTION
■
The structure and properties of protonated carbonic acid
+
(C(OH)3 , PCA) have been the subjects of spectroscopic and
theoretical analysis.1−5 We have recently reported that kinetic
analysis of acid-catalyzed decarboxylation reactions of hetero-
cyclic carboxylic acids implicates PCA as an obligatory reaction
intermediate whose role is predicted to be similar in a wide
range of reactions.6−9 The overall process involves addition of
the equivalent of a water molecule and a proton, in analogy to
ester hydrolysis, hence the designation “hydrolytic decarbox-
ylation”.
Scheme 2. Acid-Catalyzed Decarboxylation of Pyrrole-2-
carboxylic Acid via Addition of H+ and H2O
The rate law for specific-acid-catalyzed decarboxylation of a
carboxylic acid requires that the rate-determining transition
state arises from a species with the equivalent of one more
proton than the neutral carboxylic acid. This is clearly
inconsistent with C−C bond cleavage occurring via a simple
dissociative process that produces CO2. Furthermore, while the
formation of the conjugate acid of CO2 (HOCO+) would be
consistent with such a rate law, the exceedingly low proton
affinity of CO2 makes its conjugate acid an inaccessible reaction
intermediate (Scheme 1).10
These results are instead consistent with an alternative
pathway that produces PCA in the step that cleaves the C−C
bond. This is achieved by the initial addition of water to the
carboxyl group and protonation of the ring α to the carboxyl,
leading to a highly reactive precursor of PCA (Scheme 2).6−9
The overall process has been assessed and supported by
independent computational studies that also tested various
alternatives.11,12
In order to specify the role of PCA in the context of reaction
intermediates, we evaluated the kinetic properties of two sets of
isomeric heterocyclic carboxylic acids derived from pyrrole and
indole. While they are expected to undergo hydration with
similar energetics, the reactive intermediates that produce PCA
are energetically distinct, leading to observable effects that
define the nature of the transition states that produce PCA in
competition with those that revert to the reactants.
Received: September 30, 2013
© XXXX American Chemical Society
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On the basis of the overall reaction patterns of these sets of
reactants, we find that the transition state for the step that
produces PCA is partially rate-determining to varying extents.
This information is accessed via measurements that reveal the
magnitudes of the observed carbon kinetic isotope effects (k12/
k13, CKIE) for the reactions in the sets of related compounds
under conditions where a defined single reaction mechanism is
required by the observed rate law (plateau regions of the
acidity-rate profiles). Comparing the results of observed rate
constants and CKIE measurements in the acid-catalyzed
decarboxylation reactions of compounds 1−4 reveals variations
that affect the competing forward and reverse steps from the
hydrated intermediates that are C-protonated (protonated at
the position α to the hydrated carboxyl). The cations differ in
energy depending on the extent to which stabilization by
formation of iminium character is accessible. The range of
observed CKIEs can be understood from considering a
common intrinsic value for the isotope effect that is then
attenuated by the extent to which the formation of PCA is
competitive with reversion to the reactants from the steady-
state reactive intermediate species.
Figure 1. Logarithm of the first-order rate constants for the
○
●
decarboxylation of ( ) indole-3-carboxylic acid, ( ) indole-2-
▼
▽
carboxylic acid, ( ) pyrrole-2-carboxylic acid, ( ) pyrrole-3-
carboxylic acid, as a function of pH and Hammett acidity constants.
▼
▽
● ○
(
/ ) HClO4 solutions at 25 °C and ( / ) HCl solutions at 60 °C.
For indole-3-carboxylic acid, data points higher than pH 1.0 are
buffered solutions.9
Table 1. Maximum Observed First-Order Rate Constants for
Decarboxylation
c
aromatic carboxylic acid
kobs(max) (s‑1)
pKa
a
pyrrole-2-carboxylic acid
pyrrole-3-carboxylic acid
6.2 × 10−4
1.9 × 10−6
1.2 × 10−4
5.0 × 10−3
−1.3
−1.3
−1.5
0.4
b
indole-2-carboxylic acid
RESULTS
b
■
indole-3-carboxylic acid
a
b
c
As was reported for the acid-catalyzed decarboxylation
reactions of pyrrole-2-carboxylic acid6,7 and the indole-
carboxylic acids,9 the observed first-order rate constant for
the decarboxylation of pyrrole-3-carboxylic acid increases with
increasing acidity, reaching a plateau higher than that for the
uncatalyzed reaction. The resulting dependence of the observed
first-order rate constants on acidity (Ho) for all heterocyclic
carboxylic acids fit the calculated titration curves for forming
the conjugate acids of the reactants (Figure 1). In the plateau
regions, there is necessarily a common mechanism for each
species and for which the observed CKIEs were obtained.
While the equation-generated plots of acidity vs first-order
rate constants are similar in shape for the various reactants,
there are significant differences in the values of the high
plateaus as well as for the lowest acidities at which the
maximum values occur (presumably due to the pKa of the
conjugate acid). The fitted values for the maximum observed
first-order rate constants are summarized in Table 1 along with
the apparent macroscopic pKa values that were used to fit the
data to the Hammett acidity function, Ho. For the indole-
carboxylic acids, the rate of decarboxylation is greater where the
carboxyl group is positioned at C-3 of the indole ring, while
carboxyl substitution at the C-2 position leads to a faster
observed rate in the pyrrole-carboxylic acid series.
Reference 6. Reference 9. For monoprotonation of the carboxylic
acids from titration using Ho-defined media.
Table 2. Carbon Kinetic Isotope Effects Observed for Acid-
Catalyzed Decarboxylation Reactions
solution acidity (Ho or pH)
Pyrrole-2-carboxylic Acid
CKIE ( 0.002)
ab
,
Ho = −2.6
Ho = −0.7
1.043
1.027
b
Pyrrole-3-carboxylic Acid
Ho = −2.6
Ho = −0.4
1.036
1.028
c
Indole-2-carboxylic Acid
Ho = −3.8
Ho = −2.7
Ho = −1.3
1.018
1.017
1.002
c
Indole-3-carboxylic Acid
Ho = −3.2
Ho = 0.2
pH 4.4
1.030
1.027
1.003
a
b
c
Reference 7. Conditions: 25 °C, HClO4. Conditions: 60 °C, HCl.
that the rate-determining transition state involves cleavage of
the C−C bond (forming PCA). However, the locations of the
carboxyl group within a series of indole- and pyrrole-carboxylic
acid positional isomers lead to differences in reactivity that
affect the magnitudes of the observed CKIEs. It is likely that the
step involving C−C cleavage is subject to a common intrinsic
isotope effect, while the significant variations in the values of
CKIEs arise from the extent to which the C−C cleavage step is
rate-determining in competition with reversion to reactants.
This is consistent with expectations from theoretical analysis of
The variations of the observed maximum rate constants
demonstrate a pattern that applies to the step leading to
formation of PCA, with additional information provided by the
differential magnitudes of the observed carbon kinetic isotope
effects (CKIEs) (Table 2).
DISCUSSION
■
Previous studies with pyrrole-2-carboxylic acid7 revealed a large
CKIE for the acid-catalyzed decarboxylation which indicates
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Scheme 3. Mechanisms for the Decarboxylation of Indole-3-carboxylic Acid (Upper) and Indole-2-carboxylic Acid (Lower)
carbon kinetic isotope effects from SN2 and E2 reactions which
reveal that, despite significant changes in the transition state (or
bond order), intrinsic CKIEs are essentially invariant.13−17
An instructive example can be found in the heavy-atom
isotope effects for decomposition of substituted benzenediazo-
nium ions.18 The electrons from the cleaved bond are
transferred to nitrogen (forming N2) rather than to the residual
organic species as in decarboxylation reactions. While the
electron transfer is in the opposite sense to that observed in the
acid-catalyzed decarboxylation reactions, substituents also affect
the bond-breaking event. This is apparent in the 100−1000-fold
range in the observed rates for dediazoniation with various
substituents.18 This variation in reactivity might suggest that
there are changes in the position of the transition state for the
carbon−nitrogen cleavage step that lead to the variation in
observed isotope effects; however, the measured nitrogen
kinetic isotope effects are invariant for all derivatives.19,20 Thus,
variations in the observed kinetic isotope effects for breaking
bonds to heavy atoms are not associated with the extent of
bond breaking in the transition state for C−N bond cleavage.
An important study from Hilvert, O’Leary, and co-workers21
determined the CKIEs for the decarboxylation of 5-nitro-3-
carboxybenzisoxazole under a variety of conditions. In this one-
step reaction coupled to decomposition, reversion to reactants
is not possible. Therefore, the magnitude of the observed CKIE
should be identical with the magnitude of the intrinsic isotope
effect. The polarity of the reaction medium was varied
(including the presence of a catalytic antibody), which
produced a large variation in rate; the observed first-order
rate constants vary by a factor as large as 2 × 104. However, a
nearly constant magnitude for the CKIE was observed
(∼1.045). This value is a reasonable expectation for the
intrinsic CKIE. In the present study there are significant
changes in the magnitudes of CKIEs. This is clear evidence that
variations in the CKIEs result from effects of variability in
competition among partially rate determining steps in a
multistep pathway. The invariance of the intrinsic CKIEs is
the result of their arising only from differences in the ground
state vibrational energies where the C−C bond is in place,
whereas in the transition states that bond is broken and no new
bond to either position is in the process of being formed (in
contrast to the case for proton transfers between Brønsted acids
and bases).
CKIE for reaction of the conjugate acid of indole-3-carboxylic
acid (1-SH; Scheme 3) is significantly larger than that for the
conjugate acid of indole-2-carboxylic acid (2-SH) (1.030 vs
1.018). The extent to which the step competes with the
reversion to the reactants controls the magnitude of the
observed CKIE.
In Scheme 3 the magnitude of k2/k−1 must be smaller than
that for k2′/k−1′ to give the observed differential CKIE values,
as expressed in eqs 1−3. The magnitudes of the observed
k1k2
k−1 + k2
kobs
=
(1)
k213
k−1
k212
k−1
k212
k213
1 +
1 +
CKIEobs
=
·
(3)
CKIEs (eq 3) depend on the relative values of k2/k−1 for each
reactant. The smaller the ratio, the larger the value of the
observed CKIE, approaching the intrinsic CKIE for the
unimolecular process as a limit. This follows the analysis
from which Northrop identifies the nature of the effects of
“commitment factors”.22,23
k212
12
k−1 + k212
k
k
obs
CKIEobs
=
=
k213
k−1 + k213
13
obs
(2)
In general, where the magnitudes of k−1 and k2 are
comparable, the CKIE that is observed depends on the ratio
of the values of those rate constants. Where the rate constant
for C−C cleavage is larger than that for the reversion process
(loss of water and a proton), the observed CKIE will be smaller.
For the less reactive substrate in each set (i.e., indole-2-
carboxylic and pyrrole-3-carboxylic acids), protonation at a site
that is more highly energetic than is the case for their paired
isomers leads to a smaller observed rate constant within the pair
of isomers. Therefore, reactions of the less reactive isomer
occur from intermediates that are closer in energy to the
transition state for formation of PCA than in the cases for the
more reactive member. As a result, the larger observed CKIE is
associated with the more reactive substrates, since the barrier
On the basis of the preceding discussion, we assume that the
magnitudes of the observed CKIEs arise from a common
intrinsic CKIE in the C−C bond-breaking steps. The observed
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giving the CKIE is higher relative to the reversion step than it is
with the less reactive substrates.
The sources of these observations can be understood from
mathematical models for these processes. The curves in Figure
2 were generated to illustrate the relationship between
in CKIEs. The rapid decomposition of PCA leads to formation
of CO2, which is the detected product other than pyrrole, as the
proton and water are catalytically cycled.
In all of the reactions that we have presented here, the
species that precedes the cleavage of the C−C bond (to release
PCA) contains a hydrated carboxyl group where protonation at
the position α to the (hydrated) carboxyl carbon has taken
place. These intermediates have a barrier to the transition state
for decarboxylation lower than those in which the proton is
added to the β position, although the latter in some cases are
thermodynamically favored.24−26
The relative energies of the cationic intermediates depend on
the effects of protonation on aromatic stabilization, as the
positive charge is dispersed onto the nitrogen of the
heterocycle, as shown in Scheme 5. In the case of the indole-
Scheme 5. Resonance Stabilization for α Protonation of (a)
Indole-3-carboxylic Acid, (b) Indole-2-carboxylic Acid, and
(c) β Protonation of Indole-2-carboxylic Acid
Figure 2. Theoretical model of observed CKIEs as a function of the
ratio of the rate constants for C−C bond cleavage in comparison to
reversal (k2/k−1) for a range of descending intrinsic CKIE values (1.10,
1.07, 1.05, 1.03, 1.01). Dashed lines indicate the relationship of
commitment factor to observed CKIE as a function of a typical
intrinsic CKIE for cleavage of a C−C bond.
commitment factors and observed CKIEs as derived from the
rate law for the mechanism in Scheme 2. The x axis is the value
of the rate constant subject to the intrinsic CKIE divided by the
effective rate constant for conversion of the same intermediate
to the protonated reactant. The y axis is the resulting observed
CKIE. The value of the observed CKIE is reduced from the
intrinsic CKIE (on the basis of a range of illustrative intrinsic
values for a CKIE) as the rate constant for the C−C breaking
step becomes larger relative to the rate constant for reversion
(the latter increases and the former remains constant). As the
barrier for reversion becomes larger relative to that for the C−
C bond-breaking step, the value for the observed CKIE
approaches a limiting value of 1.0.
carboxylic acids, the pathway for the less reactive isomer
(indole-2-carboxylic acid) proceeds through the structure
shown in Scheme 5b. However, protonation to produce the
structure in Scheme 5c gives a more stable intermediate.25,26 In
other words, protonation of the aromatic ring must occur at the
less basic site in order for the system to be able to lose PCA in
the next step. On the other hand, disruption of aromaticity is
less significant for the pyrrole-carboxylic acid, as there is no
benzenoid moiety as in the indole derivatives. As a result, this
leads to a smaller distinction in the magnitudes observed for the
CKIEs for the pyrrole-carboxylic acid isomers.
The difference between the pKa values for protonation at the
lower energy position vs that which is required for the reaction
pathway of decarboxylation of pyrrole-3-carboxylic acid is about
2.0 pKa units.24 The observed rate constant for decarboxylation
of pyrrole-3-carboxylic acid is about 300 times smaller than that
for pyrrole-2-carboxylic acid (Table 1), suggesting that the rate
differences arise principally from differences in the energies of
the sites for protonation. In pyrrole-2-carboxylic acid, the
required site of protonation for decarboxylation is also the
lower energy site of protonation under the reaction conditions.
The reaction patterns of the indole-carboxylic acids follow the
same trend, leading to differences in the values for the rate
maxima. However, in contrast to the pyrrole derivatives, it is the
isomer with the carboxyl at the 3-position that is preferentially
protonated and that also leads to C−C bond cleavage.
Pathways for the decarboxylation of the isomeric pyrrole-
carboxylic acids are presented in Scheme 4. These provide the
necessary intermediates to understand the basis of the variation
Scheme 4. Mechanisms for the Decarboxylation of Pyrrole-3-
carboxylic Acid (Upper) and Pyrrole-2-carboxylic Acid
(Lower)
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were prepared from combinations of reagent-grade hydrochloric acid
or perchloric acid with purified water.
In typical decarboxylation reactions in neutral solutions,
formation of the residual carbanion is the key rate-controlling
feature and the reaction falls within the realm of carbanion
chemistry. We see from the present study that in acid-catalyzed
decarboxylation reactions which produce PCA, the leaving
group is derived from a cation that becomes neutral and
aromatic upon passing through the transition state involving
C−C cleavage. Since the other product, PCA, is a cation, we
consider the step that produces it will be subject to factors that
parallel the typical rate-determining step in substitution
reactions that proceed by an SN1 mechanism. Where the
intermediate preceding PCA is higher in energy than in the case
of its isomer, the leaving group is thereby activated, reducing
the barrier to C−C cleavage. Although the barrier to that step is
reduced, the overall reaction is slower than in the case where
the pre-PCA intermediate is subject to greater stabilization.
Thus, k2 for the higher energy species will be greater (with a
lower barrier) than k2 for the lower energy species. On the
other hand, in the competing process, loss of water to re-form
the carboxyl group (k−1) should be independent of the nature
of the specific intermediate. As a result, k2/k−1 is larger for the
less reactive species, resulting in a lower value for the observed
CKIE (see eq 3).
Our results show that the protonated carboxylic acid is more
reactive toward decarboxylation than any other protonation
state of the substrate. However, it does not directly produce
CO2 in the C−C cleavage step. This is not because PCA is
formed more easily than CO2; rather, it is due to the ring-
protonated carbocation leaving group being formed to a much
greater extent in acid, as compared to the zwitterion that forms
in neutral solutions to produce CO2.
Thus, we see the importance of PCA in defining the key
intermediates in a major class of readily accessible decarbox-
ylation reactions. Its formation occurs where an aromatic
species acquires a proton to form a carbocation at the position
β to a carboxyl group, even if the site of protonation is not the
site that gives the intermediate that is lowest in energy. Rather,
the key factor is that protonation must occur on the site that
leads directly to the production of PCA. Significantly, the
pattern of observed CKIEs provides the necessary context for
arriving at this understanding and the results also provide
insights into the factors leading to the observed value of a
CKIE.
Kinetics of Decarboxylation. The rates of decarboxylation for
pyrrole-2-carboxylic acid, indole-2-carboxylic acid, and indole-3-
carboxylic acid in acidic solutions have been previously reported.6,7,9
The rate of decarboxylation of pyrrole-3-carboxylic acid was measured
in solutions of perchloric acid of Ho-defined acidity. The reaction was
followed by the decrease in absorbance at 255 nm with a UV−vis
spectrometer at 25 °C, with the cell compartment kept within 0.1 °C
of the reported temperature. Data were collected with an interfaced
computer, and the observed first-order rate constants were calculated
by regression to the apparent first-order rate expression using the
method of initial rates.
Measurement of Carbon Kinetic Isotope Effects. Reactions
were carried out in 125 mL bottles sealed with butyl-blue stoppers.
The acidic reaction solution (50 mL) was placed in the bottle, and the
headspace was purged with helium to remove atmospheric CO2. The
carboxylic acid reactant (16 mg) was dissolved in degassed dimethyl
sulfoxide (0.5 mL) and injected into the vessel to initiate the reaction.
The reactions were maintained at 60.0 °C (indole-carboxylic acids) or
25.0 °C (pyrrole-carboxylic acids) in a circulating water bath. At
specific reaction progress intervals, the bottle was cooled in ice and the
reaction was quenched with 25 mL of degassed acetate buffer (1 M,
pH 5) for reactions taking place in dilute acid solutions or by addition
of 60 mL of degassed acetate buffer (5 M, pH 5) for reactions taking
place in concentrated acid solutions in order to produce a dilute acid
solution (∼0.01 M) appropriate for headspace analysis. Solutions were
kept at 0 °C prior to analysis. The headspace was sampled with a
pressure-lock analytical syringe with a side-port taper needle.7,28,29
Different reaction progress intervals were sampled from the headspace
up to 50% conversion. Reaction progress was approximated by
reaction time and by comparison with the peak area obtained from
mass intensity scans on an isotope-ratio mass spectrometer coupled to
a combustion oven and gas chromatograph (GC-C-IRMS). Samples of
CO2 from complete conversion of the reactants were taken after 10
half-lives for each reaction. As a control, the sequence was repeated
without reactant. In these cases, CO2 was not detected in the
headspace.
The CKIEs were calculated from the measured data using an
equation adapted from Bothner-By and Bigeleisen:29,30
k12/k13 = log(1 − f )/log[1 − f(Nx/Nx0)]
(4)
In eq 4, k12 and k13 are the observed first-order rate coefficients for
reaction of the corresponding carbon isotopes and f denotes the
fractional extent of the decarboxylation process, which varies from 0 at
the start to 1 at completion. The originally defined terms “R” and “R0”
have been replaced with “Nx” and “Nx0” (where the ratio of abundance
of 13CO2/12CO2 from the IRMS has been converted to relative
abundances).
CONCLUSIONS
■
The mechanisms of acid-catalyzed decarboxylation reactions
implicate the formation of PCA from a carbocationic
intermediate that is generated by addition of water to the
carboxyl group and a proton to the α position of the adjoining
unsaturated species, regardless of the relative energy of
protonation at that site. The variation in the observed CKIE
is consistent with a common intrinsic value that depends on the
extent to which hydration is also partially rate-determining. The
key reactive intermediate is one that leads to the formation of
PCA. The principle of microscopic reversibility suggests that
electrophilic aromatic substitution based on PCA should be an
accessible route to carboxylation of aromatic heterocycles.27
AUTHOR INFORMATION
■
Corresponding Author
*E-mail for R.K.: rkluger@chem.utoronto.ca.
Notes
The authors declare no competing financial interest.
ACKNOWLEDGMENTS
■
The Natural Sciences and Engineering Research Council
provided support through an NSERC Strategic Grant to
B.S.L. and Discovery Grant to R.K.
EXPERIMENTAL SECTION
■
Pyrrole-2-carboxylic acid, pyrrole-3-carboxylic acid, indole-2-carboxylic
acid, and indole-3-carboxylic acid were obtained from commercial
sources. All structures were verified spectroscopically, and the
compounds were used without further purification. Acidic solutions
ABBREVIATIONS
■
CKIE, carbon kinetic isotope effect; PCA, protonated carbonic
acid
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