Probing hyperconjugation experimentally with the conformational deuterium isotope effect

Article abstract of DOI:10.1021/jo3017988

Hyperconjugation underlies many chemical phenomena of fundamental and practical importance. Owing to a great deal of interest in the anomeric effect, anomeric-like hyperconjugative effects have been thoroughly investigated in oxygen-containing systems. However, such interactions in the second- and third-row chalcogens are less well-understood and have generated some controversy. Here, we show that the conformational deuterium isotope effect, in combination with Saunders isotopic perturbation method, permits sensitive and direct experimental probing of the conformational equilibria in dioxane, dithiane, and diselenane analogues by variable-temperature, dynamic NMR spectroscopy. We find that the magnitude of the conformational deuterium isotope effect is 252.1, 28.3, and 7.1 J/mol (±10%) for the oxygen, sulfur, and selenium analogues, respectively. These results reveal the periodic trend for hyperconjugation in the chalcogens, which reflect a decreasing n _x→σ_C-H(D) interaction throughout the period, as supported by IR spectroscopy and in agreement with DFT calculations and a natural bond order analysis.

Full text of DOI:10.1021/jo3017988

Article
pubs.acs.org/joc
Probing Hyperconjugation Experimentally with the Conformational
Deuterium Isotope Effect
Kyle T. Greenway, Anthony G. Bischoff, and B. Mario Pinto*
Department of Chemistry, Simon Fraser University, Burnaby, BC, V5A 1S6, Canada
*
S Supporting Information
ABSTRACT: Hyperconjugation underlies many chemical
phenomena of fundamental and practical importance. Owing
to a great deal of interest in the anomeric effect, anomeric-like
hyperconjugative effects have been thoroughly investigated in
oxygen-containing systems. However, such interactions in the
second- and third-row chalcogens are less well-understood and
have generated some controversy. Here, we show that the
conformational deuterium isotope effect, in combination with
Saunders’ isotopic perturbation method, permits sensitive and
direct experimental probing of the conformational equilibria in
dioxane, dithiane, and diselenane analogues by variable-
temperature, dynamic NMR spectroscopy. We find that the
magnitude of the conformational deuterium isotope effect is 252.1, 28.3, and 7.1 J/mol (±10%) for the oxygen, sulfur, and
selenium analogues, respectively. These results reveal the periodic trend for hyperconjugation in the chalcogens, which reflect a
decreasing n →σ
interaction throughout the period, as supported by IR spectroscopy and in agreement with DFT
C−H(D)
x
calculations and a natural bond order analysis.
INTRODUCTION
■
Structural and conformational phenomena in organic molecules
test theoretical frameworks and underpin many questions of
chemical stability and reactivity. Frontier molecular orbital
(
FMO) theory has been largely successful in attributing these
1
,2
phenomena, such as the anomeric effect, to a limited set of
critical molecular orbital interactions, including hyperconjuga-
3
tive interactions. The concept of hyperconjugation was
originally introduced to explain the effects of alkyl substituents
on electronic properties of unsaturated compounds in terms of
Figure 1. Compounds of interest and one key hyperconjugative
interaction. Compounds are 2-deuterio-5,5-dimethyl-l,3-dioxane (1),
4
,5
σ−π orbital interactions. It was later extended to discuss
various conformational, structural, and reactivity effects in
terms of interactions between sigma-bonding orbitals σ or
nonbonding (lone pair) orbitals n and sigma-antibonding
2
-deuterio-5,5-dimethyl-l,3-dithiane (2), and 2-deuterio-5,5-dimethyl-
l,3-diselenane (3). Depicted orbitals are the n orbitals present on both
x
chalcogens and the σ*C−H(D), in a simple representation (left) and as
calculated by the NBO method (right).
6
7,8
9
orbitals σ*, such as the gauche effect, Saytzeff’s rule, and
10−12
the anomeric effect.
Experimental evaluation is complicated by the difficulty of
positions. Within the Born−Oppenheimer approximation,
hydrogen and deuterium are electronically identical. Therefore,
the major determinant of this equilibrium is molecular
vibration, in which the energy of the molecule is best
minimized when deuterium occupies the stronger bond
owing to its lower zero-point energy. Since hyperconjugation
lengthens and weakens bonds in which antibonding orbital
occupancy is increased or in which bonding orbital occupancy
isolating hyperconjugation from other contributing factors,
1
3,14
often resulting in controversy.
Here we show both
experimentally and computationally that the conformational
deuterium isotope effect (CDIE) can serve as a minimal
perturbation to directly probe the balance of hyperconjugative
interactions in the acetal unit of a series of 2-deuterio-5,5-
dimethyl-1,3-diheterocyclohexanes (X = O, S, Se, Figure 1).
By incorporating a single deuterium at C2 in such cyclic
systems, which undergo rapid ring inversion between otherwise
degenerate conformations, the resultant difference in free
energy ΔG° can be attributed entirely to the competition
between deuterium and hydrogen for axial and equatorial
6
is decreased, a single deuterium atom at the anomeric position
of these systems can translate the balance of the hyper-
Received: August 22, 2012
Published: October 1, 2012
©
2012 American Chemical Society
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Article
Figure 2. 13C room temperature spectra of compounds 1, 2, and 3, in dichloromethane-d at 298 K. Inset shows separated signals for methyl groups
2
at room temperature due to the conformational deuterium isotope effect.
conjugative interactions present into the ΔG° of the
equilibrium. ΔG° can then be determined using low-temper-
ature nuclear magnetic resonance (NMR) via the isotopic
for oxygen. Specifically, early computational work employing
the 6-31G* basis set suggested that the anomeric-like equatorial
21
C−H bond was longer than the axial bond in 1,3-dithiane.
15
perturbation method of Saunders or, alternatively, by direct
Experimental results with 1,3-dithiane further showed that the
1
integration. Here, we report the values of ΔG° for 5,5-dimethyl-
JC−H coupling constants were reversed in magnitude from
23
2-deuterio-1,3-dioxane (1), -dithiane (2), and -diselenane (3)
those of 1,3-dioxane, ΔG° for the equilibrium of 2 in Figure 1
was reported to be essentially zero; IR stretching frequencies
using both methods, permitting evaluation of the balance of
axial versus equatorial hyperconjugative interactions in these
systems.
There is little dispute that hyperconjugation is partly
responsible for the anomeric effect with first-row elements
24
for axial and equatorial C2−D bonds were reported to be
24
24
identical, and it was concluded that no CDIE existed.
However, more recent analyses at higher levels of computation
with a variety of methods and with higher-level basis sets have
(
e.g., O), though the exact magnitude of this contribution
16
found that the axial bond is in fact longer than the equatorial
remains disputed. The dominant interaction is from the p-
11,25
bond.
These differences in axial and equatorial bond
type lone pair on oxygen n to the adjacent axial antibonding
O
lengths and non-equivalent hyperconjugative interactions
should result in distinct axial and equatorial IR stretching
frequencies and a CDIE (by way of comparison, for the oxygen
σ* orbital, although several interactions affecting equatorial and
axial σ* orbitals contribute, and it is their balance that is most
7
,11
relevant.
Experimental support for the dominance of the
−1
analogue 1, stretching frequencies differed by 141 cm and
axial effects over the equatorial effects includes the longer C-
2
6
ΔG° was reported to be 205 J/mol).
substituent axial bonds relative to C-substituent equatorial
1
7
1
It is now also clear that coupling constants are not
bonds, larger JC−H coupling constants for the stronger
1
8,19
straightforward measures of bond strengths since longer and
equatorial bonds (Perlin effect),
stretching frequencies (Bohlmann bands) that further suggest
a weaker axial bond.
and IR C−H(D)
1
weaker C−H bonds can exhibit larger J
coupling constants
C−H
20,21
(
dubbed the “reverse Perlin effect”) as in dioxane, dithiane, and
10
oxathiane. Detailed natural bond order (NBO) analysis has
further shown that sulfur exhibits many of the same
hyperconjugative interactions that contribute to the anomeric
In the case of the heavier congener, sulfur, the picture is less
clear. Numerous studies on conformational preferences in 2-
heterosubstituted thiaheterocycles have demonstrated an
2
2
11
anomeric effect, although some evidence in the parent
effect in oxygen, albeit at a somewhat reduced level, and
heterocycles has led investigators to conclude that hyper-
conjugation plays little or no role, in contrast to the situation
σC−H(D)→σ*S−C interactions are not dominant as previously
postulated in our earlier work.
19
18,21
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In the case of systems containing selenium, several studies
bondeither due to increasing strength of equatorial
interactions, decreasing strength of axial interactions, or
bothbut parity is not reached.
27
have demonstrated anomeric effects in selenium coronands
2
8,29
and diselenanes,
and NBO analysis suggests that hyper-
6
conjugative interactions similar to sulfur exist. It is not known
whether a CDIE or Bohlmann-type bands are present.
The results for C−D stretching frequencies, measured by
infrared spectroscopy, offer further insight into hyperconjuga-
tion. As Table 2 shows, the axial C−D stretching frequency for
In this work, we have re-evaluated the CDIE and IR spectra
for systems containing oxygen (1) and sulfur (2) and extended
the studies to the diselenane (3). We confirm that the CDIE is
an effective probe of hyperconjugation and provide corrected
data for the dithiane system (2), which confirms the presence
of a CDIE. The collective data reveal a consistent periodic
trend for anomeric-like hyperconjugation in the chalcogens,
Table 2. IR C2−D Stretching Frequencies and Computed
Bond Lengths
exptl IR
frequency
computed IR
computed bond
−1
−1
a
a
(cm
)
frequency (cm
)
length (Å)
which reflects a n →σ*
order X = O > S > Se, as supported by DFT calculations and a
natural bond order analysis.
interaction that decreases in the
x
C−H(D)
1
2
3
axial
2089
2230
2153
2196
2185
2202
2086
2238
2182
2224
2213
2233
1.1036
1.0864
1.0903
1.0874
1.0865
1.0860
equatorial
axial
equatorial
axial
RESULTS AND DISCUSSION
The C NMR spectra at low temperature and at 298 K for 1−3
Figure 2) exhibit separated signals due to the CDIE. These
■
(
13
equatorial
a
Results of DFT calculations at the B3LYP 6-311G++(3df,3pd) level,
with a scaling factor of 0.9673.
3
3
separations permitted the determination of ΔG° values, using
Saunders isotopic perturbation method, which are listed in
15
Table 1 along with theoretical results for compounds 1−3. ΔG°
dioxane 1 is 141 cm− less than the equatorial C−D stretching
frequency. This suggests a longer (and weaker) bond, as would
be expected from dominant axial interactions. In dithiane 2,
however, the axial C−D stretching frequency has increased by
1
Table 1. Experimental and Computed Values of ΔG°
a
b
c
d
Δ (Hz)
ω (Hz)
ΔG° (J/mol)
computed ΔG° (J/mol)
1
2
3
116.25
1367.52
1186.35
5.91
7.82
1.70
252.1
28.3
7.1
299.3
36.8
13.1
−1
6
4 cm while the equatorial C−D stretch has decreased by 34
−1 −1
cm , narrowing the gap to 43 cm . This is consistent with the
reduced ΔG° CDIE value being due to both an increase in the
equatorial hyperconjugative interactions and a decrease in the
axial hyperconjugative interactions. In diselenane 3, the gap
between C−D stretching frequencies is further narrowed to just
a
Δ was measured under conditions of slow exchange at 180 K for 1
13
and 2 and 156 K for 3 from the 125 MHz C NMR spectra; value
corrected to 150 MHz 1 C for comparisons. ω was measured under
3
b
13
conditions of fast exchange at room temperature in the 150 MHz
C
c
−1
NMR spectra. ΔG° was determined experimentally via eq 2 and the
17 cm , due to a further increase in the C−D axial stretching
standard relationship ΔG° = −RT ln K for T = 298 K, with an
frequency. The last result corresponds well with the CDIE
results, in which the equilibrium constant is only slightly above
unity, owing to weaker axial hyperconjugative interactions. In
all cases, computed IR stretching frequencies agree well with
experimental values (Table 2), although the discrepancy from
the previous report of equal axial and equatorial C−D IR
stretching frequencies bears addressing. As is evident in our
experimental spectra (Supporting Information Figures S8−
S10) and in our computed IR intensities (Supporting
Information Table S5), the intensities of these stretches are
quite low. Further, they are far lower for the dithiane 2 (and the
diselenane 3) than they are for the dioxane 1. Indeed, the
d
estimated error of 10%. Results of DFT calculations.
is largest for the dioxane 1, reduced for the dithiane 2, and
reduced even further for the diselenane 3, with all systems
exhibiting a preference for an equatorial deuterium atom. This
preference was successfully established by assignment
3
0,31
utilizing the W effect,
T measurements, and predicted
1
3
2
NMR spectra, all in agreement (see Supporting Informa-
tion)and subsequent integration of the H2 signals in the low-
1
temperature H NMR spectra.
Our result of 252 J/mol for the dioxane 1 is similar to the
previously reported value of 205 J/mol. However, our result for
the dithiane 2 of 28 J/mol differs considerably from the
previous report of 0 J/mol. In both cases, we believe our result
intensity of the C−D
stretch for the dithiane 2 is
calculated to be only 4% of that for the dioxane 1 and 2% of the
equatorial
C−D stretch intensity for 1. We therefore suggest that the
axial
second IR stretch peak for the dithiane 2 was missed by the
1
3
to be of greater precision due to our use of C chemical shifts,
24
previous study due to its surprisingly low intensity.
1
rather than H chemical shifts, with Saunders’ isotopic
Finally, our NBO analysis suggests that these observed trends
perturbation method because of the greater spectral dispersion
are consistent with a decreasing n →σ* interaction in the
offered by 13C spectra. This is significant given that, except for
x
C−H
order X = O > S > Se, as summarized in Table 3. The
magnitude of the hyperconjugation effect can be evaluated
within the framework of standard second-order perturbation
the dioxane 1, no conformationally separated signals are visible
1
in the H spectra (Supporting Information Figures S2, S4, and
S6). For the diselenane 3, our results suggest a further
reduction of ΔG° to 7 J/mol, which marks the lowest
measurement of a ΔG° by NMR spectroscopy to our
knowledge. These results (Table 1) suggest that the hyper-
conjugative interactions in dioxane 1 that lengthen the axial
C2−H(D) bond are significantly greater than those lengthening
the equatorial C2−H(D) bond. Moving down the period, the
balance is shifted toward lengthening the equatorial C−H
3
theory. It is directly proportional to the square of the Fock
matrix element F (or to the square of orbital overlap S )
ij
ij
between interacting orbitals i and j and is inversely proportional
to the energy gap ε −ε between these orbitals, as in eq 1.
j
i
2Fi2j
Sij
2
2
ΔE =
∝
εj − ε
i
εj − ε
i
(1)
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Table 3. Calculated Chalcogen−carbon Bond Lengths and
CONCLUSIONS
■
Results of the NBO Analysis
We have shown that the CDIE in combination with IR
spectroscopic studies of monodeuterated dioxane 1, dithiane 2,
and diselenane 3 analogues reveals a simple trend that is
reflective of a decreasing anomeric-like hyperconjugation in the
top three chalcogens. Sulfur exhibits a CDIE that is reduced by
roughly an order of magnitude from oxygen, while the
interaction is reduced by nearly 75% further for selenium.
NBO analysis suggests that a source of this decrease is a
deletion
X−C2 bond
X−C4 bond
energy
Fi,j
(au)
ε −ε
j i
b
a
system
length (Å)
length (Å)
(kJ/mol)
(au)
1
2
3
1.4030
1.8150
1.9609
1.4240
1.8235
1.9761
23.9
17.9
13.8
0.054
0.046
0.041
0.64
0.62
0.64
a
Off-diagonal Fock matrix elements, corresponding to the orbital
b
resonance integral. Difference in orbital energies.
reduction in the anomeric-like n →σ*
interaction due to
x
C−H(D)
the lengthened carbon−chalcogen bond, which decreases the
orbital overlap. These results suggest that hyperconjugative
interactions affecting axial C−H(D) bonds are greater than
those affecting equatorial C−H(D) bonds in second- and third-
row systems, similar to the first-row systems. Finally, we
confirm that modern theory and experiment are in agreement
with respect to the importance of hyperconjugative interactions
in this series of chalcogens.
More accurately, this energy can be assessed using NBO
deletion analysis by setting F = 0 and rediagonalization of the
ij
3
4
Fock matrix, although some have questioned the NBO
35
framework’s validity. Our NBO results indicate that the axial
nx→σC−H(D) interaction decreases down the period, much like
the experimental trends, suggesting that a decreasing anomeric-
like interaction contributes to the observed trend. Of the two6
factors that contribute to the strength of this interaction,
namely, the overlap and the energy difference of the interacting
orbitals, orbital overlap is the major factor, as determined from
examination of the relevant Fock matrix elements. Orbital
overlap is reduced by approximately 15% from dioxane 1 to
dithiane 2 and a further 10% to diselenane 3, corresponding to
a decrease in the energy of the hyperconjugative interactions of
EXPERIMENTAL SECTION
General. Dioxane and its congeners are widely employed model
■
fect.
systems for studying hyperconjugation and the anomeric ef-
6,7,11,17−19,21,22,24,26,28,29
The choice of the specific analogues
utilized in the present study is based on several considerations. The
employment of a single deuterium at the anomeric C2 position is
explained above. The use of two chalcogens in the systems increases
the magnitude of the hyperconjugative effects of interest and
symmetrizes the molecule, simplifying analysis. Finally, the inclusion
of two methyl groups at the C5 position facilitates accurate
measurement of the equilibria using Saunders’ isotopic perturbation
6
and 4 kJ/mol, respectively. The decrease in orbital overlap is
1
5
due to the lengthening of carbon−chalcogen bonds moving
down the period (Table 3), which distorts the ring significantly
for compounds 2 and 3. More thorough NBO analyses in first-
and second-row systems that more closely examine the balance
of the multiple interactions presented have been performed
method.
2
The general retrosynthetic scheme is shown in Scheme 1. The [ H]-
methylene unit for the synthesis of the diselenane 3 was derived from
Scheme 1. Retrosynthetic Analysis
1
1
elsewhere, and factors such as other vibrational modes and
rehybridization may contribute to CDIE magnitudes and the
qualitative agreement between experimental values and NBO
results. However, we note that the experimental trend is well-
described by the key n →σ*C−H interaction. This conclusion is
x
supported by the results in Figure 3, which demonstrate that
the equatorial C2−H(D) bond remains roughly constant
throughout compounds 1−3 while the axial bond length
changes significantly.
[2
2
H]-paraformaldehyde, while the more convenient [ H]-diethoxy-
methane (Scheme 2) was employed for the synthesis of dioxane 1 and
2
2
Scheme 2. Synthesis of [ H]-Methylene Units: [ H]-
Paraformaldehyde (Above) and [ H]-Diethoxymethane
2
(
Below)
Figure 3. Comparison of calculated axial and equatorial C−D bond
lengths with observed IR stretching frequencies.
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2
6H, Me). Low-temperature 13C NMR (125 MHz, CD Cl , 185 K): δ
dithiane 2. Combination of the [ H]-methylene unit with the diol
2
2
equivalents, as shown in Scheme 3, yielded the compounds of interest
in satisfactory yields.
40.95 (s, C4/C6), 31.34 (s, Meeq), 30.89 (1:1:1 t, J = 23.5 Hz, C2),
26.61 (s, C5), 22.29 (s, Meax). Room-temperature C NMR (150
13
MHz, CD Cl , rt): δ 42.41 (s, C4/C6), 31.82 (1:1:1 t, J = 22.9 Hz,
2
2
C2), 27.83 (br s, Me), 27.34 (s, C5). HRMS (EI): m/z calcd for
Scheme 3. Synthesis of Dioxane 1 (Top), Dithiane 2
C H DS [M] 149.0443, found 149.0469. FTIR (ATR): 2196, 2153.
6
11
2
(Middle), and Diselenane 3 (Bottom)
2
5
,5-Dimethyl-[ H ]-1,3-diselenane (3). 4,4-Dimethyl-1,2-disele-
2
28
nolane (150 mg, 0.63 mmol) was added to hypophosphorous acid (7
mL) in a 50 mL round-bottom flask. A condenser fitted with a N
bubbler was attached to a 25 mL two-necked flask containing [ H]-
2
2
paraformaldehyde (78 mg, 1.25 mml), prepared by known
3
proceedures and several drops of both phosphoric acid and
hypophosphorous acid. The two-necked flask served as the receiver
on a distill-head which was purged with nitrogen and quickly attached
to the 50 mL flask. The diselenide mixture was heated with stirring
over 30 min, after which a 2,2-dimethyl-1,3-propanediselenol/water
mixture was distilled over at 90 °C and collected in the receiver. Under
a blast of nitrogen, the two-necked receiver was removed and
stoppered. (Note: the diselenol is extremely sensitive to oxidation by
air back to the diselenide.) The mixture was refluxed for 24 h, cooled,
then extracted with ether (2 × 10 mL). The combined ether extracts
were washed with water (10 mL) and concentrated, leaving a dark-red
liquid. The product was chromatographed on silica (hexane/ethyl
acetate, 100:1) and distilled (bulb-to-bulb under vacuum at 80 °C) to
1
yield the product as an oil (40 mg, 26%). Low-temperature H NMR
(
1
500 MHz, 95:5, CCl F /CD Cl , 158 K): δ 3.81 (s, 1H, H2 , fwhm =
0.9 Hz, T = 706 ms), 3.25 (s, 1H, H2 , fwhm = 12.7 Hz, T = 732
1 eq 1
2 2 2 2 ax
ms), 2.98 (d, J = 11.5 Hz, 4H, H4 /H6 ), 2.37 (d, J = 11.5 Hz, 4H,
ax
ax
H4 /H6 ), 1.31 (s, 6H, Me ), 1.27 (s, 6H, Me ). Room-
eq
eq
ax
eq
1
temperature H NMR (600 MHz, CD Cl , rt): δ 3.54 (1:1:1 triplet,
2
2
1
H, H2,), 2.65 (s, 4H, H2/H4), 1.24 (s, 6H, Me). Low-temperature
1
3
C NMR (125 MHz, 95:5, CCl F /CD Cl , 168 K): δ 35.39 (s, C4/
2
2
2
2
C6), 32.54 (s, Me ), 26.70 (s, C5), 24.70 (s, Me ), 6.34 (1:1:1 t, J =
eq
ax
13
2
3
2.2 Hz, C2). Room-temperature C NMR (CD Cl , 150 MHz, rt): δ
2 2
5.52 (s, C4/C6), 28.28 (d, J = 1.7 Hz, Me), 26.46 (s, C5), 5.82 (1:1:1
+
t, J = 23.5 Hz, C2). HRMS (EI): m/z calcd for C H DSe [M − H]
2
6
12
2
45.9405, found 245.9424. FTIR (ATR): 2202, 2185.
Spectroscopic Analysis. NMR room-temperature spectra were
recorded on a 600 MHz spectrometer equipped with a QNP
cryoprobe with deuteratred dichloromethane as the solvent. Low-
temperature spectra were recorded on a 500 MHz spectrometer in
2
5
1
,5-Dimethyl-[ H ]-1,3-dioxane (1). The synthesis 5,5-dimethyl-
1
[2
H ]-1,3-dioxane (1) has been described previously. Low-temper-
ature H NMR (500 MHz, CD Cl , 185 K): δ 4.92 (s, 1H, H2 , fwhm
4.5 Hz), 4.44 (s, 1H, H2 , fwhm = 4.2 Hz), 3.51 (d, J = 10.9 Hz, 2H,
H4 /H6 ), 3.32 (d, J = 10.9 Hz, 2H, H4 /H6 ), 1.08 (s, 6H, Me ),
36
1
deuterated dichloromethane for 1 and 2 and with CCl F /CD Cl
2
2
eq
2 2 2 2
(90:10) for 3. Axial and equatorial methyl 13C signals were measured
at several temperatures and chemical shifts linearly extrapolated to
room temperature for use in eq 2. Curve fitting, as implemented in the
software program MestReNova 6.2.1, was used to accurately determine
the separation of signals. Assignment of peaks is discussed in
Supporting Information. Theoretical NMR shifts, used as further
support of the spectral assignments, were computed with the gauge-
=
ax
eq
eq
ax
ax
ax
1
0
1
1
9
2
.63 (s, 6H, Me ). Room-temperature H NMR (500 MHz, CD Cl ,
e
q
2
2
85 K): δ 4.72 (s, 2H, H2), 3.46 (s, 4H, H4/H6), 0.94 (d, J = 11.7 Hz,
2H, Me). Low-temperature 13C NMR (125 MHz, CD Cl , 185 K): δ
3.26 (1:1:1 t, J = 24.5 Hz, C2), 76.45 (s, C4/C6), 30.72 (s, C5),
2.28 (s, Me ), 21.63 (s, Me ). Room-temperature C NMR (150
MHz, CD Cl , rt) δ 94.18 (1:1:1 triplet, J = 24.9 Hz, C2), 77.64 (s,
2
2
13
ax
eq
3
2
independent atomic orbital (GIAO) method (Supporting Informa-
tion Tables S1 and S3) as implemented in Gaussian 09. Infrared
spectra were recorded at room temperature on an attenuated total
reflectance Fourier transform IR spectrometer (ATR-FTIR) and were
assigned based on comparison to previous work and by computed IR
stretching frequencies.
2
2
C4/C6), 31.31 (s, C5), 22.84 (d, J = 5.92 Hz). FTIR (ATR): 2230,
089.
,5-Dimethyl-[ H ]-1,3-dithiane (2). [ H]-diethoxymethane was
2
2
2
5
1
37
synthesized by known proceedures, as was the 2,2-dimethyl-1,3-
dithiol. In a 5 mL flask equipped with a micro stirrer and a
condenser, the dithiol (160 mg, 1.17 mmol) was combined with [ H]-
diethoxymethane (150 mg, 1.43 mmol), boron trifluoride etherate
38
2
The standard method of determining equilibrium constants is direct
integration of the NMR spectra at sufficiently low temperatures at
which conformational exchange is slow on the NMR time scale,
yielding the equilibrium populations at that temperature. However, the
CDIE are small in magnitude, as hydrogen/deuterium are “weak”
(
0.18 mL, 1.4 mmol), acetic acid (0.35 mL, 6.1 mmol), and
chloroform (3 mL). The solution was refluxed overnight. The product
was diluted to 10 mL with dichloromethane and washed alternately
with water and 0.1 M NaOH, three times each. The resultant liquid
was dried over sodium sulfate and chromatographed on a silica column
in 99:1 pentane/ethyl acetate. The isolated product was condensed
under rotary evaporation and distilled in a microdistillation apparatus
to yield dithiane 2 as a pale yellow oil (160 mg, 92%). Low-
10
acceptors or donors of the hyperconjugative interactions of interest.
Therefore, only small variations in bond lengths are being probed and
a more sensitive measurement technique is required.
The Saunders isotopic perturbation method is perfectly suited to
this task. With this technique, the symmetrical methyl groups, which
do not affect the equilibrium or the chemical shifts at C2, facilitate
measurement of ΔG° as follows. Given a non-unity equilibrium, one of
the methyl groups at C5 will spend slightly more time in the axial
position and the other slightly more time in the equatorial position.
1
temperature H NMR (500 MHz, CD Cl , 185 K): δ 3.82 (s, 1H,
H2 , fwhm = 4.1 Hz), 3.29 (s, 1H, H2 , fwhm = 5.7 Hz), 2.71 (d, J =
2
2
ax
eq
1
(
0.9 Hz, 2H, H4 /H6 ), 2.27 (d, J = 10.9 Hz, 2H, H4 /H6 ), 1.15
eq eq ax ax
1
s, 6H, Me ), 0.96 (s, 6H, Me ). Room-temperature H NMR (600
ax eq
1
13
MHz, CD Cl , rt): δ 3.60 (s, 1H, H2), 2.55 (s, 4H, H4/H6), 1.15 (s,
Thus, the H and C NMR spectra will exhibit separated signals
2
2
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The Journal of Organic Chemistry
Article
rather than an exchange-averaged signal even at temperatures at which
exchange is fast on the NMR time scale. The magnitude of the
separation will depend on two factors: the chemical shift difference
between the environments and the equilibrium constant. In order to
obtain the latter, the former must be measured at several temperatures
sufficiently low for exchange to be slow on the NMR time scale and
extrapolated to room temperature.
The equilibrium constant can be obtained quantitatively from a
simple expression as a function of the observed separation ω and the
observed separation in the low-temperature signals Δ (derivation in
Supporting Information):
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K = (Δ − ω)/(Δ + ω)
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+
9 software package with B3LYP functional and the 6-311G+
3
9,40
(3df,3pd) basis set.
Justification for this choice is presented in
(
the Supporting Information, section 4. Optimized structures were
identified as minima with zero imaginary vibrational frequencies, and
the coordinates and energies of each are given in the Supporting
Information. Free energies were calculated at 298.15 K, including zero-
point energy and thermal contributions. Isotope substitution was
performed for axial and equatorial deuterium orientations by setting
the appropriate hydrogen’s mass to 2 amu for additional frequency
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34
5
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G09.
(
1
(
5
ASSOCIATED CONTENT
Supporting Information
Derivation of eq 2, description of spectral assignments, C and
H room-temperature and low-temperature NMR spectra, IR
■
*
S
13
1
(
spectra, computational details for basis selection choice and
predicted NMR shifts, computed IR intensities, computed
geometries, and energies. This material is available free of
charge via the Internet at http://pubs.acs.org.
(
2
(
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AUTHOR INFORMATION
Corresponding Author
E-mail: bpinto@sfu.ca.
■
*
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D. J. Org. Chem. 1988, 53, 3766−3771.
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Notes
(
The authors declare no competing financial interest.
(
ACKNOWLEDGMENTS
11683−11700.
■
(
34) Reed, A. E.; Weinhold, F. J. Chem. Phys. 1985, 83, 1736−1740.
The authors thank A. Lewis for technical assistance, N.
Weinberg for helpful discussions, and the Natural Sciences
and Engineering Research Council of Canada for financial
support in the form of a Canada Graduate Scholarship (to
K.T.G.) and a grant (to B.M.P.). This article is dedicated to the
memories of three inspiring individuals, F.A.L. Anet, B.D.
Johnston, and S. Wolfe.
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