β-deuterium Isotope Effects on Amine Basicity, Inductive and Stereochemical

Article abstract of DOI:10.1021/ja038343v

Secondary β deuterium isotope effects on acidity constants of ammonium ions are measured using a remarkably precise NMR titration method. Deuteration is found to increase the basicity of methylamine, dimethylamine, benzylamine, and N,N-dimethylaniline. The effect is attributed to a lowered zero-point energy of a CH bond adjacent to an amine nitrogen. The method permits a determination of the stereochemical dependence of the isotope effect in a locked piperidine, and it is found that deuteration is more effective when antiperiplanar to a lone pair. The values are consistent with a cos² dependence on dihedral angle, with no detectable angle-independent inductive effect. Copyright

Full text of DOI:10.1021/ja038343v

Published on Web 11/15/2003
â-Deuterium Isotope Effects on Amine Basicity, “Inductive” and
Stereochemical
Charles L. Perrin,* Brian K. Ohta, and Joshua Kuperman
Department of Chemistry 0358, UniVersity of California, San Diego, La Jolla, California 92093-0358
Received September 4, 2003; E-mail: cperrin@ucsd.edu
Isotope effects (IEs) are characteristic features of rates and
equilibria.1 Primary IEs arise when a bond to the isotope is formed
or cleaved. Secondary ones arise when that bond remains intact.
Those due to an isotope one or two bonds distant from the reaction
site are called R or â, respectively. They continue to provide
mechanistic information regarding organic2 and enzymatic reac-
tions.3 We now report definitive data regarding secondary deuterium
IEs on amine basicities.
Alpha secondary IEs usually arise from a change in hybridization.
Historic examples come from solvolyses,4 where the reacting carbon
changes from sp3 to sp2. Since the out-of-plane bending frequency
ν of an sp2 CH bond is unusually low, the zero-point energy
()1/2hν) is reduced in the transition state. The reduction is less for
CD because zero-point energy is inversely proportional to square
root of mass. Consequently, the protium substrate reacts faster than
the deuterated one.
charge separation in a nonpolar CH bond and the difference due to
anharmonicity are small. Thus their product, the IE, ought to be
vanishingly small. Since such IEs were crucial to assessing the
symmetry of NHN hydrogen bonds,11 we have reinvestigated them.
A new titration method permits precise measurement of relative
basicities.12 Successive aliquots of acid are added to a mixture of
bases. Acid will preferentially protonate the more basic species,
whose NMR chemical shift will move ahead of that of the less
basic one. The acidity constants Ka and chemical shifts δ can be
related through eq 1, where δ+ or δ0 is for the protonated or de-
protonated form, measured at the beginning or end of the titration.
+
Therefore, a plot of the quantity on the left vs (δ1 - δ1°)(δ2
-
δ2) should be linear with the zero intercept and with a slope equal
to the ratio of acidity constants.
0
0
(δ1+ - δ1)(δ2 - δ2 ) ) (Ka1/Ka2)(δ1 - δ1 )(δ2+ - δ2) (1)
Beta effects are more subtle. In solvolyses they are generally
associated with hyperconjugation, whereby the CH bond delocalizes
its electrons to stabilize a developing carbocation. Delocalization
from the stronger CD bond, of lower zero-point energy, is then
less effective. This cannot be an inductive effect, whereby protium
is simply more electron-donating than deuterium, since according
to the Born-Oppenheimer Approximation, the electronic wave
function is independent of nuclear mass.5 Instead, it must be
attributed to a change of vibrational frequencies.
Our interest is in â deuterium IEs on amine basicity. IEs
involving filled orbitals are less common, and they are usually
equilibrium effects. Deuteration consistently increases the basicity
of amines, but the effects are small and opposite to deuterium’s
reduced electron-donating power in solvolyses. For benzylamine-
R-d2, the IE, expressed as ∆pKa () -log KaD + log KaH, where Ka
is the acidity constant of the conjugate acid), is 0.054 ( 0.001,
which was subsequently revised to 0.032, and 0.056 ( 0.001 for
2,4-dinitro-N-methylaniline-d3.6 The error estimates are only mea-
sures of precision, and they are overoptimistic if systematic error
arises from an impurity in one of the samples.
This method is capable of exquisite precision, since it is based
only on chemical-shift measurements, not pH or volume or molarity.
Since the titration is performed on a mixture of the two bases, under
conditions guaranteed identical for both, it avoids systematic error
due to possible impurities.
IEs are now measured for deuterated methylamine (1-d0-3),
dimethylamine (2-d3), benzylamine (3-d), and N,N-dimethylaniline
(4-d3).13 Mixing each of these last three with unlabeled material
produces a 1H NMR spectrum with resolvable signals due to
different isotopologs, from reporter nuclei that are depicted in
boldface in the molecular structures. The ratio of acidity constants
for the isotopomers of 1-benzyl-4-methylpiperidine-d3 (5-d3) is also
determined.14
Similarly, ∆pKa is 0.056 for methylamine-d3 and 0.12 for
dimethylamine-d6, but these are surprisingly temperature-indepen-
dent,7 as would be consistent with impurities. For trimethylamine-
d9, ∆pKa is 0.185,8 well beyond experimental error, but this could
be due to steric repulsions, which flatten trimethylamine-h9.
These cases differ from solvolyses in that there is no rehybrid-
ization, neither of the carbon bearing the isotope nor of the nitrogen,
which remains nominally sp3 on deprotonation. The IE was therefore
attributed to an electrostatic interaction between the positive charge
on the NH+ and the dipole moment of the CH or CD bond.9 Since
dipole moment is charge times distance and since the average CH
bond is longer than CD, because of anharmonicity, deuterium could
be effectively electron-donating. This sort of inductive effect is
consistent with the Born-Oppenheimer Approximation, and it
seems to be accepted as the source of these IEs.10 Yet both the
1
Samples were subjected to H NMR titration in D2O or D2O-
CD3OD and analyzed according to eq 1. Signals of deuterated 1-4
were assigned from samples of known stoichiometry. The isoto-
pomers of 5-d3 are specified by the orientation of deuterium, so
that Keq is for 5-deq, which shows a 12-Hz doublet due to Hax,
whereas 5-dax shows an Heq multiplet further downfield.
Excellent linearity was achieved, with correlation coefficients
typically >0.999. A typical titration is shown in Figure 1. Individual
titrations produced smaller errors than the variability among
titrations, and they were therefore averaged. Table 1 lists the IEs.
The IEs are small but accurately measurable. This is because
the method is comparative; therefore, any minute imbalance of
basicities can be detected. For 1, the IEs are linear in the number
of deuteriums, and for 1-3 the IE per D is nearly constant.
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10.1021/ja038343v CCC: $25.00 © 2003 American Chemical Society

C O M M U N I C A T I O N S
isotopomers show a ∆pKa of 0.025, and the one with deuterium
trans to the methyl group, and therefore axial, is the more basic,
exactly as required. It is remarkable that basicities of isotopomers
can be distinguished. These are stereoisomers that differ only in
the position of an isotope.
The secondary â deuterium IEs on amine basicity can be fit to
a cos2 dependence on the dihedral angle between the CD and the
lone pair. As in solvolyses, calculations indicate a cos2 dependence
of such IEs on dihedral angle.18 The average value from 1 and 2 is
the 2:1 sum of contributions at 60° and 180°, and the value from
5 is the difference between these two. The resulting equation is
∆∆G° (cal/mol) ) (45.7 ( 4.5) cos2 θ + (1.8 ( 2.6). This equation
is imperfect since it does not distinguish antiperiplanar from
synperiplanar, and studies are underway to generate amines with
deuterium at other dihedral angles. However, the fit shows that
there is a stereochemical dependence of the IE on amine basicity.
This is the first such report because basicity differences between
isotopomers are small and beyond most measurements.
Figure 1. Plot (eq 1) from titration of 3 plus 3-d.
Table 1. Isotope Effects on Amine Basicities
Moreover, there is no angle-independent term. Within an
exceedingly small experimental error, <3 cal/mol, this is not
significantly different from zero. This is the term that would arise
from an electrostatic interaction between a positive charge and a
bond dipole.9 We therefore conclude that an inductive effect does
not contribute to the observed IE.
0
amine
KH/KD
∆pK
∆∆G (cal/mol)a
a
1
1.040 ( 0.006
1.081 ( 0.004
1.144 ( 0.005
1.0419 ( 0.0009
1.1051 ( 0.0018
1.060 ( 0.006c
0.017 ( 0.003
0.034 ( 0.002
0.058 ( 0.002
0.0178 ( 0.0004
0.0434 ( 0.0007
0.0253 ( 0.0025
23.2 ( 3.4
23.1 ( 1.1
26.6 ( 0.9
24.4 ( 0.5
19.7 ( 0.3
34 ( 3
1b
2
3
4
5
Acknowledgment. This research was supported by NSF Grants
CHE94-20739 and CHE99-82103. Purchase of the spectrometers
was made possible by grants from NIH and NSF.
c
a Per D. b -d2. Keq/Kax (Keq is for isotopomer with equatorial D).
The key result is that deuterium increases the basicity. The ∆pKa
data in Table 1, converted to a per deuterium basis, confirm some
previous reports on 2 and 3,6,7 and our value for 4 agrees with the
∆pKa for N-methyl- and N,N-dimethyl-p-fluoroaniline, measured
with a single-point version of eq 1.15 However, these values are
significantly lower than that reported for 2,4-dinitro-N-methyl-
aniline,6 which is likely to be erroneous because the IE ought to
be lower for a nitroaromatic amine, where the lone pair is
delocalized. Regardless, all these values are smaller than the KH/
KD of ∼1.2 per D observed in solvolysis, since filled-filled orbital
interactions are weaker than filled-vacant ones.
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2700-2800 cm-1 16 lower than the 2900 cm-1 of a typical CH
,
stretch. Upon N-protonation, these bands revert to a typical
frequency. Therefore, the zero-point energy of the CH increases
on protonation, but the increase is less for CD. Indeed, a ∆ν of
100 cm-1 would produce a ∆pKa of 0.03, comparable to the IEs
observed.
The reduction of frequency is generally attributed to negative
hyperconjugation, or delocalization of the lone pair into the vacant
σ*CH orbital.17 This is supported by calculations on carbanions and
alcohols,18 by the ∆pKa of 0.056 in trifluoroethanol-d2,19 and by
the preference for equatorial deuteriums in 1,3,5,5-tetramethyl-
hexahydropyrimidine-2-d and cis-N-methylpiperidine-2,6-d2.20 In-
deed, the stereochemical dependence of the IE on basicity could
have been inferred on the basis of these latter results.
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The involvement of orbital interactions implies a stereochemical
requirement. Only if there is overlap between lone-pair and CH-
bond orbitals can the IE operate. We have tested this with 1-benzyl-
4-methylpiperidine-2,2,6-d3 (5-d3), also listed in Table 1. The two
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