No contribution of an inductive effect to secondary deuterium isotope effects on acidity

Article abstract of DOI:10.1002/anie.201102125

Effect and cause: Secondary deuterium isotope effects on the acidity of the deuterated compounds 1-4 were measured by using an NMR titration method applicable to a mixture and capable of very high accuracy. Variable-temperature experiments show that these isotope effects are due only to changes in vibrational frequencies. These findings refute an inductive origin for these isotope effects. Copyright

Full text of DOI:10.1002/anie.201102125

Communications
DOI: 10.1002/anie.201102125
Isotope Effects
No Contribution of an Inductive Effect to Secondary Deuterium
Isotope Effects on Acidity**
Charles L. Perrin* and Agnes Flach
Isotope effects are observed when a reaction rate or
equilibrium constant changes as a result of isotopic substitu-
tion.[1] They continue to be used as valuable tools to provide
insight into molecular structure and reactivity.[2] Secondary
isotope effects are those in which the bond to the isotope
remains intact. Their origin continues to be an area of
investigation.[3] Herein we address the origin of secondary
deuterium isotope effects on acidity.
donation or withdrawal, or, equivalently, to electrostatics.
Inductive effects are well established for substituents such as
ꢀ
Cl, where the C Cl dipole withdraws electrons, stabilizes a
nearby anion, and increases the acidity of chloroacetic acid
relative to acetic acid. Loosely speaking, deuterium is then
proposed to be electron-donating. A more rigorous explan-
ation proposes an electrostatic interaction between the ionic
[10]
ꢀ
ꢀ
charge and the dipole moments of C H or C D bonds.
Deuterium isotope effects on acidities are expressed as
Dipole moment is the product of charge separation and bond
D
KaH/Ka or as DpK = ꢀlog10(KaH/KaD), where Ka is the acid-
length. Owing to anharmonicity, the average C H bond is
ꢀ
ꢀ
dissociation constant. Deuteration at a bond that is not
broken reduces acidity, and it is generally accepted that
changes in vibrational frequencies and zero-point energies
(ZPEs) are responsible.[4] In support, the isotope effect in
formic acid could be reproduced from the observed infrared
longer than the C D, and thus has a larger dipole moment
that more effectively stabilizes the negative charge of the
carboxylate anion, as (exaggeratedly) suggested in 4H
relative to 4D.[11] Two estimates of
the difference in dipole moments vary
frequencies of HCOOH, HCO2ꢀ, DCOOH, and DCO2
.
widely, 0.0086 D versus 0.0001 D.[10b,6]
ꢀ
[5]
Moreover, many calculations, including recent DFT calcula-
tions on isotope effects in carboxylic acids and phenols,[6]
ammonium ions,[7] and pyridinium ions,[8] support an origin in
This is an unresolved issue, and emi-
nent researchers continue to invoke an
inductive effect to account for secon-
C H stretching frequencies and ZPEs that decrease upon
dary deuterium isotope effects.[12]
ꢀ
deprotonation.
The focus of the current work is to test whether there is a
contribution to the isotope effect on acidity due to an
inductive effect. Such a contribution is generally manifested
in entropy. An established example is the comparison of
formic and acetic acids. Their enthalpies of dissociation in
water at 258C are nearly the same, 0.01 ꢁ 0.05 and ꢀ0.02 ꢁ
0.05 kcalmolꢀ1, respectively, whereas the entropies are ꢀ17.1
and ꢀ21.9 calKꢀ1 molꢀ1.[13] The unfavorable DG8 for dissoci-
ation of either thus arises from the entropy, which is more
negative for the less acidic acetic acid. Similarly, although the
dissociation of p-methylbenzoic acid is more exothermic than
that of benzoic, the acid-weakening effect of a p-methyl
group, attributed to its electron-donating ability, appears in
the entropy.[14] The importance of entropy is generally
attributed to solute-solvent interactions, specifically the
orienting of water molecules around the anion.[15] Indeed, in
the context of isotope effects Halevi and co-workers proposed
that “it should be noted that DH8 of ionization of weak
carboxylic acids in water at 258 is generally close to zero.
Therefore, if inductive effects determine acidity at all, they do
so via changes in entropy, presumably entropy of solva-
tion”.[16] According to this reasoning, the smaller dipole
These decreases are generally attributed to delocalization
ꢀ
of lone pairs into an antibonding C H orbital (1,2). A
stereoelectronic origin was demonstrated by computation of
ꢀ
the C D stretching frequency in rotamers of DCH2NH2 (2-D)
and by experimental measurement of the relative basicities of
the two isotopomers of 2,2,6-[D3]1-benzyl-4-methylpiperidine
(3).[7] For higher carboxylic acids, beyond formic, it is more
difficult to assign frequency changes to electron delocaliza-
tion, and an alternative interpretation of the isotope effect has
been proposed.[9]
A long-standing question is whether there is also a
contribution from an inductive effect, due to electron
[*] Prof. C. L. Perrin, A. Flach
Department of Chemistry & Biochemistry
University of California—San Diego
La Jolla, CA 92093-0358 (USA)
E-mail: cperrin@ucsd.edu
ꢀ
moment of the C D bond (4D) would be less effective than
ꢀ
that of the C H (4H) at stabilizing a negative charge. As a
result, a deutero anion would require more solvation and a
greater degree of solvent organization, and it would show a
more negative entropy than the protio anion.
[**] This research was supported by NSF Grant CHE07-42801. Purchase
of the NMR spectrometer was made possible by NSF Grant CHE-
0741968.
To assess the entropy, it is necessary to measure the
temperature dependence of the isotope effect. Early attempts
to do so were unsuccessful, owing to large experimental
Supporting information for this article is available on the WWW
under http://dx.doi.org/10.1002/anie.201102125.
7674
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Angew. Chem. Int. Ed. 2011, 50, 7674 –7676

error.[17] Later work showed that the b-deuterium isotope
effect on amine basicity is undeniably temperature depen-
dent,[7] contrary to some previous claims, but the experimen-
tal error was still too large to evaluate the entropy contribu-
tion. We have therefore undertaken to investigate this
problem further.
A powerful NMR spectroscopy titration method makes it
possible to measure relative acidities,[18] and thus to measure
isotope effects on acidity with great accuracy. The method
involves titrating a mixture of isotopologues (which differ
only in isotopic composition, or number of isotopic substitu-
tions) with small aliquots of base. Equation (1) shows how the
The enthalpy and entropy contributions to the isotope
effect were evaluated from a plot of ln(KaH/KaD) versus 1/T,
which gives a slope of ꢀDDH8/R and an intercept of DDS8/R,
À
Á
À
Á
where DDSꢂ ¼ SHꢂ ꢀ ꢀ SHꢂ 0 ꢀ SDꢂ ꢀ ꢀ SDꢂ 0 , and similarly for
DDH8. Figure 1 is the plot for formic acid. Plots for all other
compounds studied are included in Supporting Information.
The correlation coefficients for these plots are all greater than
0.99.
ꢀ
ꢁ
KaH
KaD
ð1Þ
ðdH0 ꢀ dHÞðdD ꢀ dDꢀ Þ ¼
ðdH ꢀ dHꢀ ÞðdD0 ꢀ dDÞ
ratio of acidity constants can be obtained as the slope of a
linear plot involving the chemical shifts dH0 and dD0 of the acid
forms at the beginning of the titration, dHꢀ and dDꢀ of the
deprotonated forms at the end of the titration, and dH and dD
during the titration. This method was applied to carboxylic
acids and phenols,[6] ammonium ions,[7] and pyridinium ions.[8]
Secondary deuterium isotope effects were measured for
the following four deuterium-substituted acids: [D]formic (5)
by 13C NMR, [D]acetic and [D2]acetic (6,7) by 1H NMR, and
2,4,6-[D3]3,5-difluorophenol (8) by 19F NMR spectroscopy.
Figure 1. Temperature dependence of secondary deuterium isotope
effect on acidity of [D]formic acid.
The enthalpy and entropy contributions to the isotope
effects are presented in Table 1, along with TDDS8 at 208C, to
convert the entropy contribution into Jmolꢀ1 for easier
comparison with the enthalpy contribution. Errors reported
are standard deviations, from the linear fits. All DDH8 values
are negative, corresponding to a secondary deuterium isotope
effect where the enthalpy contribution decreases the acidity
of the protio acid more than that of the deutero acid and
Instead of a complete titration for each sample, only three
titration points, obtained from three samples prepared at
room temperature, were used for each acid. Two of the points,
corresponding to the fully protonated and fully deprotonated
samples, lie at the origin in the plot of Equation (1). The third
point was obtained from a 50%-neutralized sample. Little
accuracy is sacrificed by this simplification, because the slope
of a line is largely determined by its extremities. Thus the
isotope effect at each temperature could be measured from
the same three samples.
D
thereby leads to a KaH/Ka greater than one.
Table 1: Enthalpy and entropy contributions to secondary deuterium
isotope effects on acidities.
Acid
DDH8 [Jmolꢀ1
]
DDS8 [Jmolꢀ1 Kꢀ1
]
TDDS8, 208C
[D]formic
[D]acetic
[D2]acetic
ꢀ156ꢁ5
0.037ꢁ0.017
ꢀ0.024ꢁ0.006
ꢀ0.042ꢁ0.009
ꢀ0.035ꢁ0.017
11ꢁ5
ꢀ33ꢁ1.7
ꢀ63.5ꢁ2.6
ꢀ6.9ꢁ1.7
ꢀ12ꢁ2.6
ꢀ10.4ꢁ5
[D3]3,5-difluoro- ꢀ117ꢁ5
D
For each acid the isotope effect KaH/Ka at each temper-
phenol
ature was evaluated from measured chemical shifts, according
to Equation (1). The data are presented in Table S2 in the
Supporting information. For all of the compounds studied and
According to the data in Table 1, the isotope effects
appear in the enthalpy, as had been observed before for
similar acids. This contribution is expected if the origin of the
isotope effects lies in ZPEs of isotope-sensitive vibrations.
Moreover, comparisons of the DDH8 with TDDS8 values in
Table 1 show that the dominant contribution to the isotope
effect comes from the enthalpy, not entropy.
The principal new conclusion from the data in Table 1 is
that there is no entropic contribution to the isotope effect. For
acetic acid and difluorophenol DDS8 is negative, whereas an
inductive contribution would require a positive DDS8 value
D
at all temperatures, the values of KaH/Ka are greater than
one, demonstrating a detectable deuterium isotope effect on
the acidities, with the acid dissociation constant for the
deutero acid smaller (less acidic) than that of the protio. This
agrees with the results of many previous studies.
Table S2 in the Supporting Information includes the
temperature dependence of the isotope effects, which
decrease with increasing temperature. The effects are small,
and the temperature dependences even smaller, but the NMR
titration makes them measurable.
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7675

Communications
Physical Organic Chemistry, University Science Books, Sausa-
lito, CA, 2006.
(to reinforce the negative DDH8 value). As for the remaining
acid, formic, for which DDS8 is positive, the entropy
contribution is not significantly different from zero (at the
95% confidence level, according to Studentꢀs t test,[19] which
also rejects the negative DDS8 for difluorophenol). The
unreliability of apparently significant compensating relation-
ships between enthalpy and entropy is well established.[20] We
therefore conclude that none of the entropy contributions in
Table 1 is significantly different from zero. The absence of an
entropy contribution to the isotope effect refutes an inductive
effect.
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After over 50 years, this result finally settles the question
of whether there is an inductive contribution to the isotope
effect on acidity. There is none. Instead, the findings are
consistent with the proposal not only that isotope effects
originate from changes in vibrational frequencies upon
deprotonation but also that they originate only from changes
in vibrational frequencies, with no need to invoke anharmo-
nicity of those vibrations. Besides, this conclusion lends
[4] C. L. Perrin, Adv. Phys. Org. Chem. 2010, 44, 123.
[5] R. P. Bell, J. E. Crooks, Trans. Faraday Soc. 1962, 58, 1409.
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support to the later estimate of 0.0001 D for the difference in
[6]
ꢀ
ꢀ
dipole moments between C H and C D bonds. This
difference would be manifested in an inductive contribution
to the isotope effect, but it is too small to be detected even by
the sensitive NMR titration method used herein.
[11] This direction of the dipole, Cd+Hdꢀ, is opposite to the usual
direction based on electronegativities of the elements, but this
was an assumption required to account for the direction of the
isotope effect only in this particular case.
In summary, our findings show that the isotope effects on
the acidities of the carboxylic acids and phenol studied
originate only in changes in vibrational frequencies and ZPEs
upon deprotonation. No evidence for an inductive contribu-
tion or electron-donation effect was found.
[12] S. Toyota, M. Oki, Bull. Chem. Soc. Jpn. 1992, 65, 2215; A.
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Biology (Eds.: A. Kohen, H. H. Limbach), CRC, Boca Raton,
2005, pp. 955 – 974.
[13] J. J. Christensen, R. M. Izatt, L. D. Hansen, J. Am. Chem. Soc.
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[15] L. P. Fernandez, L. G. Hepler, J. Am. Chem. Soc. 1959, 81, 1783.
[16] E. A. Halevi, M. Nussim, A. Ron, J. Chem. Soc. 1963, 866.
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[18] C. L. Perrin, M. A. Fabian, Anal. Chem. 1996, 68, 2127.
[19] W. J. Youden, Statistical Methods for Chemists, Wiley, New York,
1951.
Received: March 25, 2011
Revised: May 5, 2011
Published online: June 24, 2011
Keywords: acid–base equilibria · deuterium · isotope effects ·
.
NMR spectroscopy · thermodynamics
[1] L. Melander, W. Saunders, Reaction Rates of Isotopic Molecules,
Wiley, New York, 1980; E. V. Anslyn, D. A. Dougherty, Modern
[20] O. Exner, Coll. Czech. Chem. Commun. 1973, 38, 799.
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