Variable-temperature study of hydrogen-bond symmetry in cyclohexene-1,2-dicarboxylate monoanion in chloroform-d

Article abstract of DOI:10.1021/ja500174y

The symmetry of the hydrogen bond in hydrogen cyclohexene-1,2-dicarboxylate monoanion was determined in chloroform using the NMR method of isotopic perturbation. As the temperature decreases, the ¹⁸O-induced ¹³C chemical-shift separations increase not only at carboxyl carbons but also at ipso (alkene) carbons. The magnitude of the ipso increase is consistent with an ¹⁸O isotope effect on carboxylic acid acidity. Therefore it is concluded that this monoanion is a mixture of tautomers in rapid equilibrium, rather than a single symmetric structure in which a chemical-shift separation arises from coupling between a desymmetrizing vibration and anharmonic isotope-dependent vibrations, which is expected to show the opposite temperature dependence.

Full text of DOI:10.1021/ja500174y

Article
pubs.acs.org/JACS
Variable-Temperature Study of Hydrogen-Bond Symmetry in
Cyclohexene-1,2-dicarboxylate Monoanion in Chloroform‑d
Charles L. Perrin* and Kathryn D. Burke
Department of Chemistry, University of CaliforniaSan Diego, La Jolla, California 92093-0358, United States
S
* Supporting Information
ABSTRACT: The symmetry of the hydrogen bond in hydrogen
cyclohexene-1,2-dicarboxylate monoanion was determined in
chloroform using the NMR method of isotopic perturbation. As
the temperature decreases, the 18O-induced 13C chemical-shift
separations increase not only at carboxyl carbons but also at ipso
(alkene) carbons. The magnitude of the ipso increase is
consistent with an 18O isotope effect on carboxylic acid acidity.
Therefore it is concluded that this monoanion is a mixture of
tautomers in rapid equilibrium, rather than a single symmetric
structure in which a chemical-shift separation arises from
coupling between a desymmetrizing vibration and anharmonic
isotope-dependent vibrations, which is expected to show the
opposite temperature dependence.
INTRODUCTION
■
Hydrogen bonds contribute to the shape and function of
molecules such as water, proteins, and DNA. The principles of
H-bonding are so basic that they are taught in every general
chemistry course, yet so complex that they continue to be
actively studied.1
for selectivity of deuterium over protium.8 X-ray and neutron
Hydrogen-bonding is an attractive force between a proton
donor A−H and a proton acceptor B. The attraction arises
from a combination of interactions, including electrostatic,
induction, electron delocalization, exchange repulsion, and
dispersion.2 For most H-bonds the primary contributor is
electrostatic,3,4 whereby the positive end of the A−H dipole
stabilizes the negative charge on B. In addition, A and B must
be similar in basicity to provide maximum stability to the H-
bond.5
Symmetry of Hydrogen Bonds. A fundamental structural
question is whether one or two minima exist on the potential-
energy surface for motion of a hydrogen between two donor
atoms. If there is one minimum, the hydrogen is centered
between the two donor atoms, creating a symmetric H-bond 1.
If there are two, the hydrogen is at any instant closer to one of
the atoms, resulting in an asymmetric H-bond 2a ⇄ 2b in a
double-well potential.
diffraction studies have shown that some crystals exhibit
centered H-bonds,9 although there are others that do not,
owing to different environments surrounding the two
carboxyls.10
When these low-barrier H-bonds are associated with both
short donor separations and added strength, they are also called
short, strong H-bonds. The basis for expecting a relation
between distance and strength is largely due to one influential
graph,11 where the apparent correlation is due to the fact that
all the very strong H-bonds are gas-phase, where ion-dipole
forces are strong. The basis for expecting symmetric H-bonds
to be strong may have arisen from viewing H-bonds as
resonance hybrids (2a ↔ 2b).12 Maximum stabilization should
occur when both resonance forms have identical energy,
although symmetry is not guaranteed.13 There has been
substantial interest in such H-bonds, owing to their proposed
stabilization of intermediates or transition states in some
enzyme-catalyzed reactions.14
O‐‐‐H‐‐‐O
1
Isotopic Perturbation and Isotope Shifts. The NMR
method of isotopic perturbation can distinguish symmetric
structures from mixtures.15 It is applicable to H-bonds. The
OH‐‐‐‐O ⇄ O‐‐‐‐HO
2a
2b
n
method involves measurement of the isotope shift Δ, defined
The monoanions of the dicarboxylic acids maleate 3 and
phthalate 4 are classic examples that can show symmetric H-
bonds. These ions exhibit characteristic features: a low barrier
to hydrogen transfer, O−O distances of 2.4−2.5 Å,6 a 1H NMR
signal around 20 ppm,7 and fractionation factors greater than 1
as the chemical shift of a reporter nucleus X positioned n atoms
Received: January 7, 2014
Published: February 14, 2014
© 2014 American Chemical Society
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K − 1
K + 1
K − 1
K + 1
away from a heavy isotope, relative to the chemical shift in the
presence of the light isotope (eq 1, with n sometimes omitted).
It usually has a negative value,16 including 18O-induced 13C
NMR shifts.17 In general, the observed isotope shift Δ consists
of both an intrinsic shift Δ0 and a shift Δeq induced by the
perturbation of an equilibrium (eq 2). The mere presence of an
isotope is responsible for Δ0,18 while Δeq is due to differences in
the mass-dependent vibrational frequencies and the ZPEs of the
two species in equilibrium.19 If the H-bond is symmetric, there
is no equilibrium to perturb, and Δ must equal Δ0.
n
−
Δeq
=
D =
(δCOOH − δCO )
2
(3)
D ΔG° 1
2
Δ = Δ0 −
(4)
R T
Previous Results. Isotopic perturbation, including the
temperature dependence, was initially used by Saunders and
co-workers to distinguish a mixture of equilibrating carbocat-
ions from a static symmetric structure.21 Those studies had the
advantage of large chemical-shift differences (D in eqs 3 and 4)
of up to 200 ppm between carbocationic and sp3 carbons and
consequently a large variation with temperature.
Δ = δX(heavy) − δX(light)
(1)
Δ = Δ0 + Δeq
(2)
For many years Perrin and co-workers have been using
isotopic perturbation to explore the symmetry of H-bonds. A
wide range of dicarboxylate monoanions were found to show a
small but significant Δeq, indicative of a mixture of tautomers,22
even though these are symmetric in crystals and show single-
well potentials according to high-level calculations.23 The
asymmetry was initially attributed to the polarity of aqueous
solution, which stabilizes a localized negative charge more than
a delocalized one,24 Indeed, computer simulations supported
that interpretation.25 Yet a Δeq is detectable even in nonpolar
organic solvents.26 The asymmetry was therefore attributed
more generally to the disorder of solvation and to the presence
of solvatomers (isomers that differ in solvation).27 Computer
simulations support this interpretation too.28 The asymmetry
need not be restricted simply to a pair of tautomers, since it is
also possible that the hydrogen is distributed across the O−O
distance, with a structure determined by the instantaneous
solvation.29 In support of the role of solvation, it has recently
been found that difluoromaleate monoanion too is asymmetric
in aqueous solution and in dipolar apritic solvents but is
symmetric in the crystal and in an isotropic liquid crystal
phase.30 Other examples show that asymmetry is not restricted
to dicarboxylate monoanions but is also seen in N−H−N and
N−H−O H-bonds.31
This method can be illustrated with the monoanion of a
mono-18O-labeled dicarboxylic acid, such as 18O-maleate
(3-18O). The 13C NMR spectra of both the corresponding
diacid and dianion show an 18O-induced intrinsic shift,
measured as the difference between the chemical shifts of
13C−18O and 13C−16O. These two intrinsic shifts happen to be
equal. Moreover, the diacid is more shielded than the dianion.
If the monoanion were present as a single symmetric structure
(3-18Os, in rapid equiilibrium with a second conformational
isotopomer, of essentially the same energy, but with 18O in the
carbonyl), only an intrinsic isotope shift would be observed. In
contrast, if there are two rapidly equilibrating tautomers
(3-18O− ⇄ 3-18OH, each in rapid equiilibrium with a
conformational isotopomer that has 18O in the carbonyl), the
isotopic substitution favors one tautomer over the other. Each
of the observed chemical shifts is then a weighted average of the
more shielded carboxylic-acid-like carbon and the more
deshielded carboxylate-like carbon. Consequently the
13C−18O and 13C−16O signals are separated by an additional
Δeq. This method succeeds even when rapid equilibration
coalesces NMR signals.
This method depends on the fact that isotopic substitution
favors one tautomer over the other. The equilibrium constant K
(= [3‑18OH]/[3‑18O−]) is equal to Ka16/Ka18, the ratio of the
acidity constants of the [16O]carboxylic acid and the [18O]-
carboxylic acid. This is ∼1.01, owing to ZPE differences.20 As a
result, the proton resides on the 18O more often than on the
16O, and the chemical shift of the 13C−18O resembles more that
of the shielded diacid while the 13C−16O chemical shift
resembles more that of the deshielded dianion.
These results have been supported by other studies that
found double-well potentials in succinate monoanions,32 and in
phenol-carboxylate complexes.33 Even the proton-bound dimer
1
of pyridine is asymmetric, despite a strongly deshielded H
NMR signal at δ 21.73.34 Studies of homoconjugated anions of
carboxylic acids, (RCO2)2H−, at 110−120 K found that they are
tautomeric, but that maleate and phthalate anions are
symmetric, and the symmetrization was attributed to solvent
ordering at these very low temperatures.35
In summary, we and others have been unable to find
evidence for low-barrier H-bonds in solution (except at very
low temperature).35,36 If they were unusually strong, they ought
to be more readily detectable. The lack of evidence for them
implies that there is no substantial energetic favorability
associated with symmetric H-bonds, and that the disorder of
solvation is sufficient to disrupt the symmetry that is calculated
to characterize the isolated ion.37 One of us has therefore
deplored the common custom of considering short, low-barrier
H-bonds as unusually strong.38 In support of this conclusion, it
was found that compression, to produce a “short, strong” H-
bond, does not contribute to catalysis of enolization.39
Moreover, a network of H-bonds can provide the stabilization
to account for enzyme catalysis, rather than one short, strong
H-bond.40
Equation 3 relates Δeq to K and D, the difference between
−
2
the chemical shifts δCOOH and δCO of the carboxyl and
carboxylate carbons in the monoanion. This parameter cannot
be measured directly, but it can be approximated as the
chemical-shift difference between the diacid and the dianion. (It
should be noted that not only Δ0 and Δ but also D and ΔG°
are <0.) Then, by converting to a Gibbs-energy difference ΔG°
= −RT ln K and expanding the exponential, eq 2 becomes eq 4.
Therefore, if the perturbation of an equilibrium contributes to
the observed isotope shift, then that isotope shift depends on
temperature.
An Alternative Interpretation. Bogle and Singleton
recently published an alternative interpretation of those NMR
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data that were presented as evidence for asymmetric
tautomers.41 They used gas-phase calculations of quasiclassical
trajectories of hydrogen across the highly anharmonic potential-
energy surface in isotopically labeled hydrogen phthalate anion
and averaged the 13C NMR shifts over those trajectories. They
concluded that an 18O can produce a significant intrinsic
isotope shift, whose magnitude is sufficient to account for the
results obtained by Perrin and co-workers. Then there is no
need to propose equilibrating tautomers.
Bogle and Singleton carried out similar calculations on
tetramethylbromonium ion, which Ohta and co-workers had
assigned as asymmetric on the basis of isotopic perturbation by
CD3 groups.42 This ion, with its C−X+−C, is similar to N−X+−
N species with halogen bonds,43 which are found to be
symmetric in CD2Cl2,44 perhaps because both N−X bonds are
fully covalent, as are the C−X bonds in a bromonium ion, and
as distinct from O−H−O or N−H−N H-bonds. This
controversy was resolved upon modeling the disorder of
solvation in SO2 and discovering that an oxygen from SO2 adds
to one carbon of the bromonium ion, producing an
indisputably asymmetric species.45
Proposal. We do not deny that the intrinsic isotope shift
due to an 18O can be substantial when there is coupling
between a desymmetrizing mode and anharmonic isotope-
dependent modes. The question remains whether this
calculated isotope shift accounts fully for the isotope shifts
we have measured.
An intrinsic isotope shift should be largely independent of
temperature. In contrast, the dependence of isotope shift on
temperature was key to Saunders’s evidence for a mixture of
carbocations.21 Likewise, the carboxyl and ipso isotope shifts of
aqueous hydrogen phthalate monoanion decrease with
increasing temperature, whereas the carboxyl isotope shift of
phthalate dianion, which must be intrinsic, hardly varies with
temperature.22 Bogle and Singleton seem to accept the disorder
of the water environment as strong enough to produce
asymmetric ions, but they reject asymmetry in aprotic organic
solvents.41
cyclohexene-1,2-dicarboxylate monoanion 5 is larger at lower
temperature.
EXPERIMENTAL SECTION
■
Instrumentation. All mass spectral data were obtained using ESI-
MS, negative ion mode on a Thermo LCQdeca-MS spectrometer.
NMR spectra were obtained on a JEOL ECA500 FT-NMR
1
spectrometer (500.2 MHz H, 125.8 MHz 13C) with CDCl3/CHCl3
as internal standard.
Synthesis of 5-18O0−4. A mixture of 18O isotopologues of
cyclohexene-1,2-dicarboxylic acid 6 was synthesized by combining
the anhydride with H218O and anhydrous THF (to increase solubility).
The reaction mixture was stirred at room temperature for 20−24 h.
The extent of hydrolysis was monitored by thin-layer chromatography.
The solid tetrabutylammonium salt of the monoacid monoanion 5 was
then obtained by adding 1 equivalent of tetrabutylammonium
hydroxide to 6 and removing the solvent.
Negative-ion mass spectrometry of 18O-labeled diacid 6 was used to
measure the 18O content and distribution of ion 5. The values are
presented in Table 1, expressed as P(n), the fraction with n = 0, 1, 2, 3,
18
Table 1. Masses and Fractional Amounts of
Isotopologues of Diacid 6
O
0−4
m/z
n(18O)
P(n)
169.17
171.17
173.17
175.16
177.20
0
1
2
3
4
0.089
0.422
0.366
0.117
0.006
or 4 18O’s. Although each preparation produced slightly different
ratios, they were all very similar, and this table is representative.
NMR Sample Preparation. NMR samples were prepared as 0.1 M
5-18O0−4 in CDCl3, and the presence of 5 was confirmed by 1H NMR.
RESULTS
■
18O-Induced 13C NMR Isotope Shifts of Diacid 6. A 13
C
NMR spectrum of the diacid 6-18O0−4 in CDCl3 shows
chemical-shift separations of 26, 49, and <5 ppm for the
monosubstituted carboxyl, disubstituted carboxyl, and ipso
signals, respectively. Because there is no tautomeric equilibrium
possible in the diacid these must be intrinsic isotope shifts.
These values thus serve to calibrate expected values of intrinsic
isotope shifts at carboxyl and ipso carbons.
We therefore must evaluate the temperature dependence of
an isotope shift in an aprotic organic solvent. If the isotope shift
is due to perturbation of an equilibrium, it ought to increase at
lower temperature. If the isotope shift is due to the
desymmetrizing effect of isotopic substitution on a symmetric
H-bond, then we infer that it is not necessarily temperature-
independent, as asserted above. Instead we expect that it will
decrease at lower temperature, because the vibrational
amplitudes will decrease and vibrations will become more
harmonic.
18O-Induced 13C NMR Isotope Shifts at Carboxyl
Carbons of Monoanion 5. The H NMR evidence for 5 is
1
presented in Figure S1 (Supporting Information). Figure 1
shows the 13C NMR signals at 293.9 K for the carboxyl carbons
in a mixture of 18O-labeled isotopologues of 5 with 1.0 Hz
additional line broadening. Signals can be assigned tentatively
as unlabeled (A0), mono-18O-labeled (A1), and di-18O-labeled
(A2), based on the general result that an intrinsic isotope shift
due to a heavy atom is shielding.16 This assignment was
confirmed by the addition of authentic unlabeled 5, which
increased the A0 intensity. Moreover, the relative intensities are
consistent with the 18O distribution in Table 1.
The goal of this work is to measure the 18O-induced isotope
shifts at the carboxyl and ipso positions (properly designated as
alkene, but ipso preserves parallelism to previous studies) in the
13C NMR spectrum of 18O-labeled hydrogen cyclohexene-1,2-
dicarboxylate 5. Monoanion 5 was chosen because it had been
At increased resolutionand with no applied line broad-
eningthe three signals of 5-18O0−4 in Figure 1 separate into
additional signals, as shown in Figure 2. The fine structure
arises from a four-bond isotope shift due to 18O in the carboxyl
on the opposite side of the ion. The signals are designated so
that the first subscript is the number of 18O’s attached to a
carboxyl carbon, as in Figure 1, while the second subscript
represents the number of 18O’s attached to the other carboxyl
found to exhibit a large perturbation shift in water.26 The
experiments are run at a series of low temperatures in
chloroform-d, with the tetrabutylammonium salt for solubility.
We now report that the 18O-induced isotope shift in
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intensities are consistent with the probabilities derived from the
18O distribution in Table 1. The assignments were further
supported by the addition of authentic unlabeled monoanion,
which resulted in an increase in the intensity of the A00 signal.
Temperature Dependence of Carboxyl Chemical
Shifts. As the temperature decreases, the chemical shifts of
the carboxyl carbons of 18O-labeled 5 move apart, but only
slightly, as can be seen in the spectra in Figure S2. At low
temperatures the resolution deteriorates, so that the eight
signals coalesce to three. Table S3 lists the chemical shifts of the
three signals at lower resolution. Table S4 lists the chemical
shifts of the eight carboxyl signals at temperatures where the
signals are resolvable.
To better reveal that temperature dependence, isotope shifts
Δ at the carboxyl carbons can be evaluated as differences
between appropriate pairs of chemical shifts from Table S2.
They, with their temperature dependence, are presented in
Table 2. Because isotope shifts due to heavier atoms are
Figure 1. 13C NMR spectrum of the carboxyl region of a mixture of
18O-labeled isotopologues of 5 in CDCl3 at 293.9 K with 1.0 Hz line
broadening.
Table 2. Chemical-Shift Differences and 18O-Induced
Isotope Shifts (ppb) for the Carboxyl Signal of 18O-Labeled
5 in CDCl3
difference
type
at 293.9 K at 264.1 K at 254.1 K
4
−(A11 − A00)
−(A10 − A01)
−(A21 − A12)
−(A20 − A02)
−(1Δ0 + Δ0)
27.3
34.0
34.2
68.1
28.4
35.8
35.8
71.2
28.8
35.9
36.9
72.5
4
−(1Δ − Δ)
4
−(1Δ − Δ)
4
−2(1Δ − Δ)
negative, they are tabulated for simplicity as −Δ, the negative of
the isotope shift. According to the structures in Figure 3, the
chemical-shift difference −(A11 − A00) is the negative of the
Figure 2. 13C NMR spectrum of the carboxyl region of a mixture of
18O-labeled isotopologues of 5 in CDCl3 at 293.9 K with no applied
line broadening.
1
sum of a one-bond isotope shift, Δ, and a four-bond isotope
shift, 4Δ. Because there can be no perturbation of a tautomeric
equilibrium when both carboxyls have identical isotopic
substitution, this sum must be an intrinsic shift, labeled as
1Δ0+4Δ0. Similarly, according to the structures in Figure 3, the
differences −(A10 − A01) and −(A21 − A12) represent −(1Δ −
4Δ), while −(A20 − A02) represents −2(1Δ − 4Δ). These three
are written without subscripts because they are not necessarily
intrinsic shifts.
carbon, which is responsible for the additional splitting in
Figure 2.
Figure 3 shows all six possible 18O-labeled isotopologues of
5, including two distinct isotopomers with two 18O labels.46
18O-Induced 13C NMR Isotope Shifts at Ipso Carbons
of Monoanion 5 and Chemical-Shift Assignments. Figure
4 shows five 13C NMR signals for the ipso carbons of the 18O
Figure 3. 18O-Labeled isotopologues of 5 with 0, 1, 2, 3, or 4 18O’s
●
( ) and designation of distinguishable carbons.
Isotopologues 5-18O1, 5-18O2s, and 5-18O3, which have carboxyl
groups with one 16O and one 18O, exist as a 1:1 mixture of two
rapidly equilibrating conformational isotopomers, but for
brevity only the one with 18O involved in the H-bond is
shown, and the justification for this simplification is presented
in the Supporting Information. The correspondence between
these six species and the signals in Figure 2 is justified in the
Supporting Information, where it is shown that the relative
Figure 4. 13C NMR signals of the ipso carbons of the 18O
isotopologues of 5 in CDCl3 at room temperature, with an applied
line broadening of 1 Hz.
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isotopologues of 5 at room temperature, with an applied line
broadening of 1 Hz. The ipso (B) labeling nomenclature is the
same as that used for the carboxyl carbon (A) in Figure 3. The
first subscript represents the number of 18O’s on the carboxyl
carbon adjacent to the ipso carbon of interest, and the second
subscript represents the number of 18O’s on the opposite
carboxyl. The justification for these assignments is presented in
the Supporting Information. It depends on the agreement
between the relative intensities in Figure 4 and the intensities
calculated from the mass-spectrometric data in Table 1, divided
among the contributions from each of the ipso carbon types of
Figure 3, as presented in Table S5.
Table 3. Temperature Dependence of Chemical-Shift
Differences (ppb) of Ipso Carbons of 18O-Labeled 5 in
CDCl3, Relative to the B00/11 Signal, along with Chemical-
Shift Differences between Carbons in the Same Ion
at
at
at
at
at
difference
−(B10/21
type
−2Δ
293.9 K 264.1 K 254.1 K 244.2 K 224.3 K
−
22.8
23.2
46.0
25.8
25.4
51.0
25.8
26.3
51.2
26.7
26.8
52.8
28.6
26.8
57.6
B00/11
)
B01/12 − B
00/11
3Δ
−(B20 − B
−22Δ
)
00/11
B02 − B00/11
23Δ
47.2
46.0
50.3
51.1
52.1
52.1
54.5
53.5
57.9
55.4
The widths of the signals in Figure 4 are ≤3 ppb. Thus B00
and B11 appear as one signal and are designated as B00/11. The
same is true for B01 and B12 as well as for B10 and B21, and they
are designated as B01/12 and B10/21, respectively. The
(unresolvable) chemical-shift separation B11 − B00 represents
B01/12
−
−(2Δ −
3Δ)
−2(2Δ −
3Δ)
B10/21
B02 − B20
93.2
101.3
103.4
107.3
115.5
2
3
the sum of 18O-induced isotope shifts Δ and Δ. However, as
with A11 − A00 this is an isotope shift between two structures
with identical isotopic substitutions at both carboxyls and with
no tautomeric equilibrium to perturb. This must therefore be
to perturbation of an equilibrium. Indeed, it was concluded
above that the intrinsic isotope shift is negligible. The
2
alternative possibility, that the two intrinsic isotope shifts Δ0
3
and Δ0 have opposite signs and nearly identical magnitudes,
2
3
an intrinsic isotope shift, Δ0 + Δ0. Then, because there is no
resolvable difference between the chemical shifts of B11 and B00
within the signal labeled B00/11, this intrinsic isotope shift is
negligible, just as in diacid 6 and as expected from phthalate
monoanion 4.22 Moreover, the width of 3 ppb is an upper
bound for this intrinsic isotope shift .
2
3
was rejected as unlikely. In contrast, isotope shifts Δ and Δ
arising from perturbation of an equilibrium can have opposite
signs and nearly identical magnitudes because the isotopic
perturbation shifts the two carbons in opposite directions.
Equation 4 expresses the temperature dependence of an
isotope shift due to perturbation of an equilibrium. A linear plot
of the ipso isotope shifts Δ (= 3Δ − 2Δ or 2(3Δ − 2Δ)) versus
1000/T is displayed in Figure 6. The slopes are 8.8 1.2 and
Temperature Dependence of Ipso Chemical Shifts.
Similar to the carboxyl shifts, the chemical shifts of the ipso
carbons of 18O-labeled 5 move apart as the temperature
decreases. Figure 5 shows the variations, which are much more
Figure 5. Temperature dependence of the 13C NMR signals of the
ipso carbons in 18O isotopologues of 5 with an applied line broadening
of 1 Hz.
Figure 6. Linear fit (, two-parameter; ---, one-parameter) of isotope
shifts Δ vs 1000/T for the ipso carbons in the 18O isotopologues of 5
in CDCl3.
apparent than those of the carboxyl shifts. Table S6 lists the
chemical shift of each signal at various temperatures. Table 3
lists differences between the chemical shifts in Table S6, relative
to that of the center signal, B00/11. These can be assigned as
two-bond and three-bond isotope shifts, as indicated in Table 3.
The differences B01/12 − B10/21 and B02 − B20 between ipso
carbons in the same ion are also included in the table. These
latter represent differences between the two-bond (2Δ) and
three-bond (3Δ) isotope shifts. We next consider whether these
isotope shifts represent an intrinsic shift, a perturbation shift, or
a combination of the two.
21.0 0.7, respectively. The intercepts are 17 5 and 22 3.
The correlation coefficients R are 0.973 and 0.998, respectively.
The good linearity and correlation coefficients close to unity
support a temperature-dependent perturbation of an equili-
brium.
This plot also provides an estimate of the energy associated
with the isotope effect on the equilibrium. With a reasonable
estimate for the value of D, as defined in eq 3, the slope in
Figure 6 leads to a ΔG° of −5.1 cal/mol for B01/12 − B10/21 and
−12.3 cal/mol for the B02 − B20 separation, corresponding to
Ka16/Ka18 values at 293 K of 1.009 and 1.011 per 18O,
respectively.
If the isotope shifts in Table 3 were entirely intrinsic, they
would remain essentially constant when the temperature is
changed. Because they do vary, these isotope shifts must be due
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These ΔG° and Ka16/Ka18 values are in good agreement with
the typical 18O isotope effect of ∼1.01 on acidity.20 However,
the intercepts, 17 and 22 ppb, which ought to equal the
intrinsic isotope shifts, are much higher than the maximum of 3
(or 6) ppb estimated from the width of the B00/11 signal.
Moreover, the intercepts fail to differ by a factor of 2, and the
errors in the intercepts are quite large.
This failure of the intercepts is a consequence of the
inaccuracy in extrapolating the data to infinite temperature. To
remedy this, the intercepts can be fixed at 3 and 6 ppb. One-
parameter linear plots of the isotope shifts Δ with fixed
intercepts are also displayed as the dashed lines in Figure 6.
The slopes are 12.3 0.2 and 24.9 0.2, corresponding to
Ka16/Ka18 values per 18O of 1.012 and 1.013, respectively, which
are also reasonable.
18O. These values are remarkably close to the 1.01 per 18O
generally observed for 18O isotope effects on the acidity of a
carboxylic acid.20 Such a good quantitative agreement is
fortuitous, but it is not as pertinent as the qualitative, order-
of-magnitude agreement, owing to the uncertainty in D and the
presence of dianion. Therefore the temperature dependence
supports the attribution of the observed NMR isotope shifts to
an 18O-induced perturbation of an equilibrium between
tautomers that differ in whether the proton is attached more
firmly to an 18O-labeled or unlabeled carboxyl.
Comparison of Carboxyl and Ipso Patterns. It may be
puzzling that the carboxyl and ipso carbons show such different
patterns. The pattern of the ipso carbons is symmetric about
the B00/11 signal, but the carboxyl pattern is asymmetric. In
essence this difference arises because the intrinsic shifts
dominate the carboxyl signals whereas the perturbation shifts
dominate the ipso signals. The central B00/11 signal is assigned
to structures with identical isotopic substitutions at both
carboxyls and with no tautomeric equilibrium to perturb. The
other four ipso signals are paired. They are assigned to
structures with unequal isotopic substitutions at their two
carboxyls. The isotopic substitutions perturb the tautomeric
equilibrium, favoring proton attchment to one carboxyl over
the other, and shifting the components of each pair in opposite
directions. In contrast, the carboxyl signals are split by the
intrinsic isotope shift into three main signals, as in Figure 1, and
with a small additional splitting from a perturbation shift, as
seen in Figure 2.
Asymmetry of 5. The temperature dependence of the
isotope shifts suggests that the dominant origin of those isotope
shifts is the perturbation of an equilibrium by 18O substitution.
The only conceivable equilibrium is between tautomers that
differ in whether the proton resides on the 18O-labeled carboxyl
or the unlabeled one. This is the same tautomeric equilibrium
that was described in previous results from our laboratory.
Although the H-bond is intrinsically symmetric, with a single-
well potential, asymmetry arises from the disorder of solvation
and the presence of solvatomers. Thus we conclude that the H-
bond in hydrogen cyclohexene-1,2-dicarboxylate monoanion 5
is asymmetric not only in water but also in chloroform.
DISCUSSION
■
Temperature Dependence of Carboxyl Carbon Iso-
tope Shifts. Although the first entry of Table 2 is an intrinsic
isotope shift that appears to increase from 293.9 to 254.1 K, in
the Supporting Information it is concluded that this increase is
due to poor spectral resolution and that the intrinsic isotope
shift is nearly constant. The other three entries in Table 2 are
isotope shifts −(1Δ − Δ) in asymmetrically substituted ions.
4
They are substantially larger than the intrinsic isotope shift.
1
4
Therefore Δ and Δ must have opposite signs to make their
difference smaller than their sum. This is consistent with
perturbation of an equilibrium, which shifts the two signals in
opposite directions.
Not only are these isotope shifts larger than the intrinsic
isotope shift but also they show a greater dependence on
temperature. While this variation with temperature is small, it
does suggest that there is not only an intrinsic isotope shift, but
also a perturbation of an equilibrium.
Temperature Dependence of Ipso Carbon Isotope
Shifts. Although the increase of 13C NMR isotope shifts with
decreasing temperature is tenuous for the carboxyl carbons, it is
quite firm for the ipso. Table 3 lists the 18O-induced shifts for
the ipso carbons of 5 at various temperatures in CDCl3. The
2
intrinsic isotope shift is Δ0 + 3Δ0, as might be measured from
the separation between signals B00 and B11, which are due to
symmetrically substituted ions. Unlike the carboxyl carbons,
this separation is not resolvable because the width of the single
CONCLUSIONS
■
According to the NMR method of isotopic perturbation,
monoanion 5 has been found to exist in CDCl3 as a mixture of
tautomers, in an equilibrium that can be perturbed by 18O
substitution. The evidence is an isotope shift that is not merely
intrinsic and that increases as the temperature decreases. In
either of those tautomers the H-bond is asymmetric, with the
proton more firmly attached to either the 18O-labeled carboxyl
or the unlabeled one. A symmetric H-bond would have only an
intrinsic isotope shift, which is largely independent of
temperature. We therefore dispute the conclusion that the
isotope shift is only intrinsic,41 and we reaffirm the conclusion
that the monoanions of dicarboxylic acids such as 5 are
asymmetric not only in aqueous media but also in organic
solvents.
B
00/11 signal is <3 ppb. We therefore conclude that the intrinsic
isotope shift at the ipso carbons is negligible.
The absence of an intrinsic isotope shift implies that the
chemical-shift differences, B01/12 − B10/21 and B02 − B20,
between signals from asymmetrically substituted ions, are due
2
3
to an isotope shift Δ − Δ arising from perturbation of an
equilibrium. This conclusion is further supported by the
temperature dependence of the peak separations. As can be
2
3
seen in Figure 5 and Table S6, the magnitude of Δ − Δ
increases as the temperature decreases. Moreoever, as can be
seen in Figure 6, the dependence is adequately linear in 1/T.
These qualitative results support the conclusion that these
isotope shifts arise from the perturbation of an equilibrium.
Not only are the isotope shifts larger at lower temperature
but also the magnitude of the temperature dependence is
consistent with an origin in the perturbation of a tautomeric
equilibrium. The slopes in the plots of Figure 6 can be
converted to a Gibbs-energy difference ΔG° and to an isotope
effect on an equilibrium constant. The data from the two-
parameter plots correspond to Ka16/Ka18 = 1.009 and 1.011 per
We do not deny that the H-bond is intrinsically symmetric,
with a single-well potential. Nor do we deny that coupling
between a desymmetrizing mode and anharmonic isotope-
dependent modes can contribute to the isotope shift. The
question is whether this is the dominant contribution, or
whether the dominant contribution is the perturbation by the
instantaneous local environment of an equilibrium between
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Journal of the American Chemical Society
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ASSOCIATED CONTENT
* Supporting Information
Experimental methodology; Figures S1 and S2; justification for
chemical-shift assignments; Tables S1−S6. This material is
available free of charge via the Internet at http://pubs.acs.org.
■
S
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AUTHOR INFORMATION
Corresponding Author
cperrin@ucsd.edu
(26) Perrin, C. L.; Nielson, J. B. J. Am. Chem. Soc. 1997, 119, 12734−
12741.
■
(27) Perrin, C. L.; Lau, J. S. J. Am. Chem. Soc. 2006, 128, 11820−
11824. Perrin, C. L.; Lau, J. S.; Kim, Y.-J.; Karri, P.; Moore, C.;
Rheingold, A. L. J. Am. Chem. Soc. 2009, 131, 13548−13554. Perrin, C.
L.; Lau, J. S.; Kim, Y.-J.; Karri, P.; Moore, C.; Rheingold, A. L. J. Am.
Chem. Soc. 2010, 132, 2099−2100.
Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS
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Chem. Soc. 1999, 121, 9198−9207. Dopieralski, P.; Perrin, C. L.;
Latajka, Z. J. Chem. Theory Comput. 2011, 7, 3505−3513.
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This research was supported by NSF Grants CHE07-42801 and
CHE11-48992, by a grant from the UCSD Academic Senate,
and by NSF Instrumentation Grant CHE97-09183,
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