Conformational studies in the cyclohexane series. 1. Experimental and computational investigation of methyl, ethyl, isopropyl, and tert- butylcyclohexanes

Article abstract of DOI:10.1021/jo990056f

The conformational enthalpy (ΔH°), entropy (ΔS°), and free energy (- ΔG°) of methyl- (1), ethyl(2), and isopropylcyclohexane (3) have been reinvestigated both experimentally and computationally. A novel experimental approach to evaluation of highly biased conformational equilibria is described that obviates the need to measure large axial/equatorial isomer ratios directly in order to determine the equilibrium constant: the natural abundance ¹³C signal for the C(2,6) resonance in the equatorial isomer of an alkylcyclohexane may be used as an internal reference, and the ratio of this band area to that of an enriched ¹³C nucleus in the axial isomer gives K following correction for statistical differences and the differing ¹³C- content of the signals being monitored. The experimental conformational enthalpies (ΔH°), determined at 157 K in independent studies at two laboratories, were found to be (kcal/mol) 1.76 ± 0.10 (Me), 1.54 ± 0.12 (Et), and 1.40 ± 0.15 (i-Pr); the corresponding conformational entropies (ΔS°, eu) were 0.2 ± 0.2 (Me), 1.3 ± 0.8 (Et), and 3.5 ± 0.9 (i-Pr). Computational studies at the QCISD level gave satisfactory agreement with the experimental results, but B3LYP gave energy differences that were too large, whereas MP2 gave differences that were too small. The computed structural data indicates that an axial alkyl substituent leads to local flattening of the cyclohexane ring but there was no evidence of a 1,3-synaxial interaction with the axial hydrogens at C(3,5).

Full text of DOI:10.1021/jo990056f

J . Org. Chem. 1999, 64, 2085-2095
2085
Con for m a tion a l Stu d ies in th e Cycloh exa n e Ser ies. 1.
Exp er im en ta l a n d Com p u ta tion a l In vestiga tion of Meth yl, Eth yl,
Isop r op yl, a n d ter t-Bu tylcycloh exa n es
Kenneth B. Wiberg,*,1a J ack D. Hammer,1a Henry Castejon,1a,d William F. Bailey,*,1b
Eric L. DeLeon,1b and Ronald M. J arret1c
Department of Chemistry, Yale University, New Haven, Connecticut 06520-8107, Department of
Chemistry, University of Connecticut, Storrs, Connecticut 06269-3060, and Department of Chemistry,
College of the Holy Cross, Worcester, Massachusetts 01610
Received J anuary 12, 1999
The conformational enthalpy (∆H°), entropy (∆S°), and free energy (-∆G°) of methyl- (1), ethyl-
(2), and isopropylcyclohexane (3) have been reinvestigated both experimentally and computationally.
A novel experimental approach to evaluation of highly biased conformational equilibria is described
that obviates the need to measure large axial/equatorial isomer ratios directly in order to determine
the equilibrium constant: the natural abundance 13C signal for the C(2,6) resonance in the equatorial
isomer of an alkylcyclohexane may be used as an internal reference, and the ratio of this band
area to that of an enriched 13C nucleus in the axial isomer gives K following correction for statistical
differences and the differing 13C-content of the signals being monitored. The experimental
conformational enthalpies (∆H°), determined at 157 K in independent studies at two laboratories,
were found to be (kcal/mol) 1.76 ( 0.10 (Me), 1.54 ( 0.12 (Et), and 1.40 ( 0.15 (i-Pr); the
corresponding conformational entropies (∆S°, eu) were 0.2 ( 0.2 (Me), 1.3 ( 0.8 (Et), and 3.5 ( 0.9
(i-Pr). Computational studies at the QCISD level gave satisfactory agreement with the experimental
results, but B3LYP gave energy differences that were too large, whereas MP2 gave differences
that were too small. The computed structural data indicates that an axial alkyl substituent leads
to local flattening of the cyclohexane ring but there was no evidence of a 1,3-synaxial interaction
with the axial hydrogens at C(3,5).
Nearly a half-century has passed since Barton’s semi-
nal paper relating cyclohexane conformation to the
physical and chemical properties of cyclohexanoid sys-
tems.2 Over the ensuing years the conformational be-
havior of a large number of monosubstituted cyclohex-
anes has been investigated, the area has been extensively
reviewed,3-5 and conformational energies, -∆G° (or “A
values”),6 as well as conformational enthalpies (∆H°) and
entropies (∆S°), have been determined for a variety of
substituents.7,8 In light of the rapid development of ab
initio computational methods, it was of interest to
determine to what extent modern molecular orbital (MO)
theory might be used to accurately describe the confor-
mational behavior of monosubstituted cyclohexanes.9
Herein we report the results of a computational inves-
tigation of conformational equilibria in methyl- (1), ethyl-
(2), isopropyl- (3), and tert-butylcyclohexane (4) at various
levels of theory.
At the inception of this study it was recognized that
methylcyclohexane (1) is a key compound in the confor-
mational analysis of cyclohexane derivatives: it is the
model against which other substituted-cyclohexanes are
compared,4 and it has been used in the so-called “coun-
terpoise” method,10 employing cis-1-methyl-4-substituted
cyclohexanes, to provide information on the conforma-
tional preference of other groups.4,5,7,8 To the extent that
the methyl group is a benchmark substituent in the
conformational analysis of substituted cyclohexanes, the
ability to quantitatively account for the equatorial prefer-
ence of methylcyclohexane (1) is the sine qua non of a
computational approach to understanding conformational
equilibria in alkyl-substituted cyclohexanes.
(1) (a) Yale University. (b) University of Connecticut. (c) College of
the Holy Cross. (d) Present address: Science Computing, University
of Notre Dame, Notre Dame, IN 46556.
(2) Barton, D. H. R. Experientia 1950, 6, 316.
(3) Eliel, E. L.; Allinger, N. L.; Angyal, S. J . Conformational
Analysis; Wiley: New York, 1965.
(4) Eliel, E. L.; Wilen, S. H. Stereochemistry of Organic Compounds;
Wiley: New York, 1994; pp 665-834 and references therein.
(5) J uaristi, E. Conformational Behavior of Six-Membered Rings;
VCH Publishers: New York, 1995.
(6) Winstein, S.; Holness, N. J . J . Am. Chem. Soc. 1955, 77, 5562.
(7) (a) Hirsch, J . A. Top. Stereochem. 1967, 1, 199. (b) J ensen, F.
R.; Bushweller, C. H. Adv. Alicycl. Chem. 1971, 3, 139.
(8) Bushweller, C. H. In Conformational Behavior of Six-Membered
Rings; J uaristi, E., Ed.; VCH Publishers: New York, 1995; pp 25-58.
(9) (a) Previous ab initio studies of monosubstituted cyclohexanes
have been reviewed and the difficulties attending such calculations
have been discussed; see: Cremer, D.; Szabo, K. J . In Conformational
Behavior of Six-Membered Rings; J uaristi, E., Ed.; VCH Publishers:
New York, 1995; pp 59-135. (b) Salzner, U.; Schleyer, P. v. R. J . Org.
Chem. 1994, 59, 2138 and references therein.
The conformational equilibrium of methylcyclohexane
(1a h 1e) may be observed directly by low-temperature
13C NMR, and several research groups have used this
approach to determine the conformational energy of the
(10) (a) Eliel, E. L.; Kandasamy, D. J . Org. Chem. 1976, 44, 3899.
(b) Eliel, E. L.; Manoharan, M. J . Org. Chem. 1981, 46, 1959 and
references therein.
10.1021/jo990056f CCC: $18.00 © 1999 American Chemical Society
Published on Web 03/04/1999

2086 J . Org. Chem., Vol. 64, No. 6, 1999
Wiberg et al.
methyl group.11-13 The currently accepted “best value”
for the conformational energy of methyl in cyclohexane
(-∆G° ) 1.74 kcal/mol)4,8 was determined by Booth and
Everett from a 13C NMR study of the conformational
equilibrium of 1 in CFCl3-CDCl3 (9:1 by volume) over a
temperature range of 149-172 K using material enriched
to 91 atom % 13C at the methyl carbon.11 These authors
reported a conformational enthalpy (∆H°) of -1.75 ( 0.05
kcal/mol and a conformational entropy (∆S°) of -0.03 (
0.25 eu for the methyl group in 1.11 However, a reexami-
nation of these data led us to question the accuracy of
the derived values. Consequently, we have reinvestigated
the conformational behavior of methyl- (1), ethyl- (2), and
isopropylcyclohexane (3) in conjunction with the compu-
tational study.
Resu lts a n d Discu ssion
Exp er im en ta l Stu d ies. The determination of the
conformational energy difference between the axial and
equatorial isomers of methylcyclohexane (1) by Booth and
Everett involved measurement of the ratio of the intensi-
ties of the enriched 13CH3 resonances in the two isomers
(1a and 1e).11 The conformational equilibrium constants
(K) reported in this study ranged from 426.7 at 149 K to
164.2 at 172 K.14 In an analogous analysis of the
conformational equilibrium of isopropylcyclohexane (3),
Booth and Everett reported that the equatorial/axial ratio
for 3 was 723 at 149 K and 323 at 175 K.14 Clearly, even
under ideal conditions, the accurate determination of an
isomer ratio greater than ∼100 is an extraordinarily
difficult proposition, and it is possible that significant
errors resulted from the measurement of these large
ratios. Indeed, it has been argued that precise and
accurate measurement of sizable equilibrium constants
by integration of NMR peak areas is a futile exercise due
to the very large error inherent in the determination of
such a large ratio;15 better results are obtained when the
ratio of the signals to be examined are in the range of
0.1-10.
F igu r e 1. van’t Hoff plots of the equilibrium data for (a)
methylcyclohexane (1) and (b) isopropylcyclohexane (3) as
reported by Booth and Everett (ref 11).
(11) Booth, H.; Everett, J . R. J . Chem. Soc., Perkin Trans. 2 1980,
255.
A van’t Hoff plot, ln K vs T-1, of the equilibrium data14
reported by Booth and Everett11 for methylcyclohexane
(1) is shown in Figure 1a: it represents a curve rather
than a linear relationship. Nonetheless, a “best” line
through the data leads to ∆H° ) -2.1 kcal/mol, and it is
difficult to see how the reported value (∆H° ) -1.75 (
0.05 kcal/mol)11 could be derived from these data. The
corresponding plot for the isopropylcyclohexane (3) data
of Booth and Everett14 is shown in Figure 1b; here again,
it is not clear how the reported conformational enthalpy
(∆H° ) -1.35 ( 0.49 kcal/mol)11 could be determined
from this nonlinear plot. In light of the uncertainty in
the accuracy of the reported conformational energies of
the methyl, ethyl,16 and isopropyl groups, we have
reexamined the conformational behavior of the alkylcy-
clohexanes in CBrF3-CD2Cl2 (5:1 by volume) solvent by
low-temperature 13C NMR.
(12) (a) The axial conformer of methylcyclohexane (1a ) was detected
at -110 °C in the 13C NMR of a neat sample in an elegantly simple
experiment described by Anet and co-workers. This work, which
represents the first direct determination of K for the axial-equatorial
equilibrium of 1, provided a conformational free energy (-∆G°) of 1.6
kcal/mol. See: Anet, F. A. L.; Bradley, C. H.; Buchanan, G. W. J . Am.
Chem. Soc. 1971, 93, 258. (b) A minimum value of 1.8 kcal/mol for the
conformational free energy of a methyl group was reported by Subbotin
and Sergeyev from a low-temperature NMR study of 1; see: Subbotin,
O. A.; Sergeyev, N. M. J . Chem. Soc., Chem. Commun. 1976, 141.
(13) Eliel and Wilen (ref 4, p 702) note that the energy difference
between cis- and trans-1,3-dimethylcyclohexane should be close to that
of the conformational energy of a methyl group. The experimental
energy difference for the former pair is 1.7 ( 0.6 kcal/mol in the liquid
phase and 1.9 ( 0.6 kcal/mol in the gas phase (Osborne, N. S.;
Giddings, D. C. J . Res. Natl. Bur. Stand. 1947, 39, 453). It is well
recognized that the energy difference between conformational isomers
is often phase dependent (cf. ref 4, pp 600 and 710). The origin of the
solvent effect on conformational energy differences has been inter-
preted in terms of the von Auwers-Skita rule which states that the
isomer of higher enthalpy content has the smaller molecular volume;
see: Allinger, N. L. J . Am. Chem. Soc. 1957, 79, 3443. Since the isomer
of smaller molecular volume will have the higher heat of vaporization,
there is no a priori reason to expect conformational energies determined
in solution to be identical in magnitude to those observed in the vapor
phase.
The approach used in this report to evaluate the highly
biased equilibria of alkyl-substituted cyclohexanes, which
appears not to have been used in any prior study of a
(14) Equilibrium constants (equatorial/axial) reported in ref 11, p
259, for methylcyclohexane (1) and isopropylcyclohexane (3) are as
follows [K (temperature, absolute)]: 1 K ) 426.7 (149), 222.5 (160),
183.0 (167), 164.2 (172); 3 K ) 723 (149), 617 (155), 629 (162), 561
(169), 323 (175).
(16) The conformational enthalpy and entropy of the ethyl group in
ethylcyclohexane (2) reported in ref 11 (∆H° ) -1.60 ( 0.06 kcal/mol,
∆S° ) 0.64 ( 0.35 eu) were determined by the counterpoise technique
using cis-1-ethyl-4-methylcyclohexane.
(15) Sergeyev, N. M. Org. Magn. Reson. 1978, 11, 127.

Conformational Studies in the Cyclohexane Series
J . Org. Chem., Vol. 64, No. 6, 1999 2087
conformational equilibrium, is best appreciated by refer-
ence to the conformational equilibrium for 13CH3-meth-
ylcyclohexane (99 atom % 13C) illustrated below. Deter-
mination of the equilibrium constant for this process by
low-temperature 13C NMR spectroscopy requires evalu-
ation of the area ratio [13CH3-1e/13CH3-1a ]. Fortunately,
it is not necessary to measure this very large equatorial/
axial ratio directly in order to obtain K for the equilib-
rium.
an analytical expression.18 In some cases, the bands were
not strictly Lorentzian due to slight asymmetry, and in
these instances the band areas were corrected as de-
scribed in the Experimental Section. The area ratios (K′)
obtained in this way from the low-temperature 13C NMR
spectra of 1-3 in CBrF3-CD2Cl2 (5:1 by volume) solution
are small and relatively easy to measure. The equilibrium
constants, K, derived from these experiments (eq 1) are
reported in Table 1. It should be noted that experimental
data were obtained both at Holy Cross, using a 300 MHz
spectrometer, and at Yale, using a 500 MHz spectrom-
eter. Studies using different NMR spectrometers at
different laboratories should minimize systematic error
in the measurements. The results obtained at the two
sites are in good agreement (Table 1), and this suggests
that the error in the relative band areas is less than 5%.
A major contributor to errors in measurement of the
temperature dependence of equilibrium constants via
low-temperature NMR is the temperature measurement
itself.19,20 The commonly used methanol thermometer21
does not cover the full range of temperatures used in the
current study, and since it involves two measurements,
one of the sample tube containing methanol and the other
of the experimental sample, there is no guarantee that
the temperature of the NMR probe did not change
between the two measurements. For this reason, we used
neat 2-chlorobutane, contained in a capillary, as an
internal thermometer. It has been found that the 13C
chemical shifts of 2-chlorobutane are temperature sensi-
tive,22 and the variation in chemical shift of C(3) relative
to C(4) with temperature [∆δ ) δC(3) - δC(4)] has been
used as a thermometer.23 The use of neat 2-chlorobutane
to monitor temperature has the advantage that it is an
internal thermometer and responds to the temperature
present during the measurement of interest. The 2-chlo-
robutane thermometer has been calibrated by Kates,24
and a fit to his data from -51 to -127 °C, shown in
Figure 2, is linear (r ) 0.999). The temperature is given
by eq 2, where ∆δ ) δC(3) - δC(4). For the range of
temperatures of interest, there was good agreement
between the 2-chlorobutane and methanol thermometers.
Although the absolute error of the former thermometer
may be 1-2°, it seems reasonable to believe that the
relative error over a small temperature range would be
The 13C resonance for the C(2,6) carbons of the equato-
rial isomer (1e), at δ 36.1 in CBrF3-CD2Cl2 (5:1 by
volume), is well separated from other resonances and
may serve as an internal reference. At a temperature low
enough to allow observation of the conformational iso-
mers by NMR, the intensity of the small signal for the
13C-enriched axial methyl in 1a at δ 17.63 is comparable
in magnitude to the intensity of the natural abundance
(i.e, 1.11 atom % 13C) signal for the C(2,6) resonance of
the equatorial conformer (1e). In the natural abundance
13C NMR spectrum of methylcyclohexane, the relative
areas of the CH3 and C(2,6) resonances are in the
statistical ratio of 1:2 provided that there is no dif-
ferential enhancement due to differences in relaxation
times and/or the nuclear Overhauser effect.17 In view of
the possibility of differential enhancement of the relevant
signals, the relative areas of the methyl and C(2,6)
carbons in natural abundance methylcyclohexane were
measured over a range of temperatures using the acqui-
sition parameters employed in the conformational study
described below: the intensity ratio was found to be
temperature independent and in the statistical ratio of
0.5 within the experimental uncertainty.
Given these preliminaries, the equilibrium constant for
the 1a h 1e equilibrium is easily evaluated. Thus, one
need simply measure the area of the C(2,6) resonance in
1e relative to the area of the enriched 13CH3 nucleus in
1a [K′ ) (C(2,6)-1e/13CH3-1a ] and make the appropriate
corrections to account for the both statistical difference
(0.5) and the differing 13C-content of the carbons being
monitored (i.e., 99%/1.11% ) 89.2). In this way, the
equilibrium constant for the 1a h 1e conformational
equilibrium is given by eq 1.
K ) K′(0.5 × 89.2) ) 44.6K′
(1)
In short, a highly one-sided equilibrium (K ≈ 200 to
500) may be characterized by measurement of a ratio on
the order of K′ ≈ 4-10. An entirely analogous approach
allows determination of K for the conformational equi-
librium of 13C-enriched (99 atom % 13C) samples of 2
and 3.
The relevant 13C area ratios were obtained by fitting
each signal to a Lorentzian line shape and allowing the
center of the band, the band height, and the width at
half-height to be adjusted to give a best fit; the area of
the Lorentzian was derived from these parameters via
(18) NMR bands should have a Lorentzian line shape. The area of
a Lorentzian is given by (height × π)/Γ, where Γ is 2/width at half-
height.
(19) Binsch, G. Top. Stereochem. 1968, 3, 97.
(20) Ammann, C.; Meier, P.; Merbach, A. E. J . Magn. Reson. 1982,
46, 319.
(21) Van Geet, A. L. Anal. Chem. 1970, 42, 679.
(22) Schneider, H.-J ., Freitag, W. J . Am. Chem. Soc. 1976, 98, 478.
(23) Siehl, H.-U.; Fuss, M.; Gauss, J . J . Am. Chem. Soc. 1995, 117,
5983.
(24) Kates, M. R. Ph.D. Dissertation, Yale University, New Haven,
CT, 1978.
(17) (a) Slichter, C. P. Principles of Magnetic Resonance, 3rd ed.;
Springer-Verlag: Berlin, 1992; pp 254-64. (b) Harris, R. K. Nuclear
Magnetic Resonance Spectroscopy; Wiley: New York, 1986; pp 108-
111.

2088 J . Org. Chem., Vol. 64, No. 6, 1999
Ta ble 1. Exp er im en ta l Equ ilibr iu m Da ta for Alk ylcycloh exa n es (Axia l f Equ a tor ia l)a
Wiberg et al.
Yale data
T (K)
Holy Cross data
∆δ (ppm)
K′
K
∆δ (ppm)
T (K)
K′
K
Methylcyclohexane (1)
21.711
21.658
21.604
21.560
21.557
165.7
159.9
153.0
149.0
148.6
4.96
6.61
8.16
9.05
9.78
221
295
364
404
436
21.716
21.667
21.600
166.3
160.9
153.4
5.44
6.36
8.99
243
284
401
Ethylcyclohexane (2)
21.677
21.661
21.588
21.541
162.0
160.2
152.1
146.9
5.29
5.32
6.81
8.16
236
237
304
364
21.689
163.3
159.3
154.7
149.6
5.24
5.96
6.93
8.02
234
266
309
358
21.653
21.612
21.566
Isopropylcyclohexane (3)
21.695
21.688
21.649
21.648
21.595
21.591
164.0
163.2
158.9
158.7
152.9
152.4
9.73
9.58
11.81
10.73
11.77
13.96
434
427
527
479
525
623
21.700
21.652
164.5
159.2
9.56
11.41
426
509
a
δ∆ ) δC(3) - δC(4) for the neat 2-chlorobutane thermometer (eq 2); K′ is the observed ratio of band areas [viz., intensity of the C(2,6)
resonance at natural abundance for the equatorial conformer/intensity of the 13C-labeled resonance of the axial conformer]; K ) 44.6K′
(eq 1, see text).
the plot is -∆H°/R, where ∆H° is the conformational
enthalpy difference between the axial and equatorial
conformers and the intercept is ∆S°/R, where ∆S° is the
conformational entropy difference. The slope of the plot
leads to ∆H° ) -1.74 ( 0.06 kcal/mol, and the intercept
gives ∆S° ) 0.4 ( 0.4 eu.25 The calculations described
below suggest that the entropy difference should be 0.2
eu. Since the calculated entropy difference depends only
on computation of geometry (i.e., moments of inertia) and
vibrational frequencies, it is usually more accurately
determined by calculation than are energy differences,
and this accuracy often exceeds that of an experimental
determination of ∆S° due to uncertainty in the measure-
ment of temperature.19 If the calculated conformational
entropy is included as a constraint in the van’t Hoff plot,
the slope then corresponds to an enthalpy difference of
-1.78 kcal/mol. It seems reasonable to choose the average
of these values, ∆H° ) -1.76 kcal/mol, as the conforma-
tional enthalpy of a methyl group, and we estimate an
uncertainty of 0.10 kcal/mol.
F igu r e 2. Calibration of the 2-chlorobutane thermometer
The conformational equilibrium of ethylcyclohexane
(2a h 2e) was studied in the same fashion as for the
methyl compound. The data are summarized in Table 1:
a van’t Hoff plot leads to ∆H° ) -1.42 ( 0.04 kcal/mol
and the intercept corresponds to ∆S° ) 2.1 ( 0.2 eu.25
The calculated entropy difference (vide infra) was 0.5 eu,
and if this is included as a constraint to the van’t Hoff
plot the slope then gives ∆H° ) -1.66 kcal/mol. Again,
the true enthalpy difference is most likely bracketed by
these values, and it seems appropriate to take the
average, giving ∆H° ) -1.54 kcal/mol as the conforma-
tional enthalpy of an ethyl group in cyclohexane, with
an estimated uncertainty of 0.12 kcal/mol.
Isopropylcyclohexane (3) was studied in the same way,
giving the data presented in Table 1. This compound
presented an additional experimental difficulty in that
one of its NMR bands overlapped a 2-chlorobutane
resonance at lower temperatures, thus limiting the
temperature range that could be used. A van’t Hoff plot
using the data of ref 24; ∆δ ) δC(3) - δC(4).
on the order of 0.5°.
T(°C) ) 111.07∆δ - 2518.8
(2)
A typical 13C NMR spectrum of methylcyclohexane (1)
in CBrF3-CD2Cl2 (5:1 by volume) at -120 °C is shown
in Figure 3. The signals for the 2-chlorobutane thermom-
eter are well separated from the relevant resonances of
1, and equilibrium constants at temperatures from
-107.5 to -124.6 °C were easily extracted from measure-
ment of the areas of C(2,6)-1e and 13CH3-1a using eq 1.
The data are summarized in Table 1. It would be
desirable to carry out the measurement of K over a wider
range of temperatures. However, the methyl signal
begins to broaden at higher temperatures, while the
melting point of the solvents, the decreased solubility of
1, and slow equilibration times restrict the use of lower
temperatures.
Be that as it may, a van’t Hoff plot of the equilibrium
data, shown in Figure 4, demonstrates that the Yale and
Holy Cross results are in good agreement. The slope of
(25) The uncertainties in the slope and intercept were estimated
using the Marquardt algorithm and correspond to one standard
deviation: Marquardt, D. W. J . Soc. Indust. Appl. Math. 1963, 11, 431.

Conformational Studies in the Cyclohexane Series
J . Org. Chem., Vol. 64, No. 6, 1999 2089
F igu r e 3. 13C NMR spectrum of methylcyclohexane (1) at -120 °C in CBrF3 - CD2Cl2 (5:1 by vol).
Ta ble 2. Exp er im en ta l Con for m a tion a l En th a lp y (∆H°),
En tr op y (∆S°), a n d F r ee En er gy (∆G°) for
Alk yl-Su bstitu ted Cycloh exa n es a t 157Ka
-∆H°,
kcal/mol
-∆G°,b
kcal/mol
compound
∆S°, eu
methylcyclohexane (1)
ethylcyclohexane (2)
isopropylcyclohexane (3) 1.40 ( 0.15 3.5 ( 0.9 1.96 ( 0.02
1.76 ( 0.10 0.2 ( 0.2 1.80 ( 0.02
1.54 ( 0.12 1.3 ( 0.8 1.75 ( 0.02
a
b
Data for axial f equatorial equilibrium. Derived directly
from the equilibrium constants.
Com p u ta tion a l Stu d ies. Meth ylcycloh exa n e (1).
Geometry optimizations were carried out for the two
conformers of 1 using the HF, B3LYP, and MP2 theoreti-
cal levels with several basis sets.26 The HF and B3LYP
calculations gave a classical energy difference of 2.1-
2.2 kcal/mol favoring the equatorial isomer, 1e. This is
clearly significantly larger than the experimentally mea-
sured energy difference. It has, however, recently been
found that the B3LYP theoretical model often overesti-
mates conformational energy differences, whereas MP2
appears to give values in better agreement with experi-
ment.27 The energy difference was calculated using MP2
with several different basis sets (Table 3), and with the
larger basis sets, values close to the experimental energy
difference were obtained. Thus, it appears that, in the
present case, B3LYP also overestimates conformational
energy differences. In the subsequent examination of the
dimethylcyclohexanes (see below) it was found that
B3LYP was in error with respect to the observed relative
energies in one direction, while MP2 was in error in the
opposite direction.
F igu r e 4. van’t Hoff plot of the equilibrium data for meth-
ylcyclohexane (1) summarized in Table 1. The open circles
correspond to data obtained at Yale and the closed circles
represent the data obtained at Holy Cross; the circles represent
an estimated error in K and 1/T.
of the equilibrium data leads to ∆H° ) -1.25 ( 0.10 kcal/
mol, and the intercept corresponds to ∆S° ) 4.4 ( 0.6
eu.25 The calculated entropy change (vide infra) is 2.6 eu,
and if this is included as a constraint, the slope of the
van’t Hoff plot corresponds to ∆H° ) -1.55 kcal/mol.
Taking the average of these values gives ∆H° ) -1.40
kcal/mol, with an estimated uncertainty of 0.15 kcal/mol,
as the conformational enthalpy of an isopropyl group in
cyclohexane.
The conformational enthalpy, entropy, and free energy
of methyl, ethyl, and isopropyl groups in cyclohexane
determined in this study are summarized in Table 2.
These values do not differ appreciably from those re-
ported by Booth and Everett,11 but they do stand on a
more secure experimental foundation. With these data
in hand, we may now examine the computational results.
QCISD provides a superior method for correcting for
the effects of electron correlation, and with the dimeth-
ylcyclohexane calculations described below, it gave rela-
tive energies in very good agreement with the experi-
mental values. Therefore, the QCISD/6-311+G** energies
for the 1a and 1e were obtained using the MP2/6-
(26) Additional theoretical levels and details of the thermal correc-
tions to 298 K are given in the Supporting Information.
(27) Karpfen, A.; Choi, C. H.; Kertesz, M. J . Phys. Chem. A 1997,
101, 7426.

2090 J . Org. Chem., Vol. 64, No. 6, 1999
Wiberg et al.
Ta ble 3. Ca lcu la ted En er gies for Meth ylcycloh exa n e (1)
conformer energiesa
axial-CH3 equatorial-CH3 (kcal/mol)b
∆E
basis set
MP2/6-311+G**
MP2/6-311+G (3df,2p) -274.531 58 -274.534 21
-274.367 91 -274.370 62
1.70
1.65
1.81
1.76
QCISD/6-311+G**
-274.451 54 -274.454 42
QCISD/6-311+G(3df,2p) -274.615 21 -274.618 01
energies (kcal/mol)
CH3 rotational barrier
2.42
119.15
5.26
-19.28
82.30
3.01
118.97
5.28
-19.32
82.52
ZPEc
0.18
-0.02
0.04
(H°298 - H°0)
(G°298 - G°0)
S° (cal/mol-deg)
-0.22
a
Total energies, calculated using the MP2/6-311G* geometries,
are given in hartrees (H); other energies are in kcal/mol (1 H )
b
627.51 kcal/mol). Axial-CH3 - equatorial-CH3. c Zero point ener-
gies; HF/6-31G* frequencies were scaled by 0.893. The internal
rotor modes were treated separately and their zero point energies
are included.
311+G** geometries giving an energy difference of 1.81
kcal/mol (Table 3). Pople, in developing his G1 and G2
model chemistries, found that the effects of polarization
functions were additive.28 Thus, the QCISD/6-311+G-
(3df,2p) energies were estimated as follows: QCISD/6-
311+G(3df,2p) ) QCISD/6-311+G** + MP2/6-311+G-
(3df,2p) - MP2/6-311+G**. This procedure led to an
energy difference of 1.76 kcal/mol as our best estimate
of ∆E for the axial-equatorial equilibrium of 1.
To compare the calculated energy difference with the
experimental results, ∆E must first be corrected for the
difference in zero-point energy (ZPE) between the two
conformers, the change in ∆H° on going from 0 K to the
higher temperatures must be computed, and the enthalpy
difference must then be converted to ∆G° using the
calculated entropy difference. These computations re-
quired estimates of the vibrational frequencies, and they
were calculated at the HF/6-31G* level and scaled by the
usual factor, 0.893. One of the modes corresponds to
methyl rotation, and it was treated separately as previ-
ously described.29 The rotational barriers were calculated
at the B3LYP/6-311G* level and are included in
Table 3.
F igu r e 5. Calculated (MP2/6-311G**) structural data for the
axial (1a ) and equatorial (1e) conformers of methylcyclohexane
and for 1,1-dimethylcyclohexane.
The final calculated relative energies (∆H°, ∆S°, and
∆G°) of the axial and equatorial isomers of methylcyclo-
hexane (1a and 1e) at 157 and 298 K are given in Table
4. The data for 157 K correspond to the average temper-
ature used in the experimental study (Table 1). The
calculated enthalpy difference at 157 K, ∆H° ) -1.93
kcal/mol, is in good agreement with the experimental
value of -1.76 ( 0.10 kcal/mol.
It is of interest to note that the calculated rotational
barriers for the axial and equatorial methyl rotamers
(Table 3) are close to that for ethane and the changes in
geometry on rotation parallel those found for rotation
about the C-C bond in ethane. With the equatorial
methyl conformer (1e), the MP2/6-311+G* calculated
CH3-C length increases from 1.527 to 1.542 Å on rotation
and other structural changes were small. Thus, the origin
of this methyl rotational barrier is the same as that for
ethane, where the only significant structural change on
rotation is found in the C-C bond length.29
The difference in energy between the axial (1a ) and
the equatorial (1e) conformations of methylcyclohexane
is often attributed to 1,3-synaxial interactions between
the axial methyl group and the axial hydrogens at
C(3,5),3-8 although the two gauche-butane interactions
present in the axial conformer, but absent in the equato-
rial isomer, must also be important.3-8 One would think
that such steric interactions should lead to some char-
acteristic changes in geometry of the cyclohexane ring
at positions remote from the axial substituent. Structural
parameters for 1e and 1a derived from MP2/6-311+G**
calculations are summarized in Figure 5.30 In both
conformational isomers, the calculated structural param-
eters at the C(3,5) and C(4) positions are quite close to
those found in cyclohexane itself (bond angles: C-C-C
) 111.28°, H-C-H ) 106.65°, C-C-Ha ) 108.83°,
C-C-He ) 110.55°).31 The C(2)-C(3)-Ha angle in 1a
(30) A previous study of methylcyclohexane at the HF/6-31G* level
(Wiberg, K. B.; Murcko, M. A. J . Am. Chem. Soc. 1988, 110, 8029) found
slightly larger C-C(3,5)-Ha angular distortions for 1a . The structural
data obtained in the present study (Figure 5) should be more satisfac-
tory.
(28) Curtiss, L. A.; Raghavachari, K.; Trucks, G. W.; Pople, J . A. J .
Chem. Phys. 1991, 94, 7221.
(29) Murcko, M. A.; Castejon, H.; Wiberg, K. B. J . Phys. Chem. 1996,
100, 16162.
(31) Dommen, J .; Brupbacher, T.; Grassi, G.; Bauder, A. J . Am.
Chem. Soc. 1990, 112, 953 and references therein.

Conformational Studies in the Cyclohexane Series
J . Org. Chem., Vol. 64, No. 6, 1999 2091
Ta ble 4. Ca lcu la ted Con for m a tion a l En th a lp y (∆H°), En tr op y (∆S°), a n d F r ee En er gy (∆G°) for Alk yl-Su bstitu ted
Cycloh exa n esa
-∆H°,kcal/mol
∆S°, eu
-∆G°, kcal/mol
compound
0 K
157 K
298 K
157 K
298 K
157 K
298 K
methylcyclohexane (1)
ethylcyclohexane (2)
isopropylcyclohexane (3)
1.94
1.82
1.60
1.93
1.77
1.53
1.92
1.67
1.46
0.13
0.55
2.56
0.22
0.99
2.92
1.96
1.86
1.94
1.98
1.96
2.33
a
Data for axial f equatorial equilibrium; the energies are based on the corrected QCISD energy differences (see text).
Ta ble 5. Ca lcu la ted En er gies for th e
(110.1°) is somewhat larger than the corresponding bond
angle in 1e (109.1°), but overall, these positions seem
little affected by an axial methyl substituent. The fact
that the axial hydrogens at C(3,5) in 1a are not signifi-
cantly splayed from their positions in 1e by the presence
of the axial methyl is significant: angle bending is not
particularly costly in terms of energy, and one would
expect larger than observed differences in the C(2)-C(3)-
Ha angles of 1a vis-a`-vis 1e if 1,3-synaxial interactions
contributed in a major way to the conformational energy
of the methyl substituent.
In contrast to the small changes in geometry at remote
ring positions engendered by an axial methyl group,
much larger structural perturbations are found at the
substitution site. In the axial methyl conformer (1a ), both
the C(2)-C(1)-CH3 bond angle (112.0°) and the C(1)-
C(2)-C(3) angle (112.5°) are larger than those of the
equatorial isomer (111.4 and 111.9°, respectively). Not
surprisingly, the CH3-C(1) bond length in 1a (1.532 Å)
is longer than that in 1e (1.528 Å). In short, the
structural data for 1e and 1a do not appear to be
consistent with interpretations that attribute the con-
formational energy of a methyl group to 1,3-synaxial
interactions. Rather, the data indicate that repulsive
steric interaction between an axial methyl group and the
ring carbons, including the gauche torsional interaction,3-8
is the major component responsible for destabilization
of the axial methyl group.
Dim eth ylcycloh exa n es. The 1,4- and 1,1-dimethyl-
cyclohexanes are an important set of compounds for
conformational studies. A comparison of the difference
in energy between cis- and trans-1,4-dimethylcyclohexane
with ∆H° for a methyl group provides a test of the
assumption that the conformational energies of substit-
uents at C(1) and C(4) are additive as assumed in the
counterpoise method for obtaining -∆G° values.4,5,8,10 An
examination of the structure of 1,1-dimethylcyclohexane
would be useful in assessing the importance of the so-
called “buttressing” effect in geminally disubstituted
cyclohexanes.4,5 The energies of these compounds were
calculated at several theoretical levels, and the results
are summarized in Table 5 along with experimental heat
of formation data for the 1,1- and 1,4-dimethylcyclohex-
anes.32
Dim eth ylcycloh exa n es
dimethylcyclohexane
trans-1,4- cis-1,4-
1,1-
total energya
MP2/6-311G*
MP2/6-311+G**
-313.447 82 -313.445 21 -313.447 79
-313.570 18 -313.567 75 -313.570 25
QCISD/6-311+G* -313.545 69 -313.542 73 -313.543 64
relative energiesb
MP2/6-311G*
MP2/6-311+G**
QCISD/6-311+G*
ZPEc
0.00
0.00
0.00
135.70
0.00
1.63
1.52
1.86
135.89
2.04
0.02
-0.04
1.29
135.80
1.39
d
∆∆H°0
∆∆H°298
0.00
1.98
1.24
e
experimental ∆Hf
∆∆Hf
-44.1 ( 0.4 -42.2 ( 0.4 -43.2 ( 0.5
0.0 1.9 ( 0.5 0.9 ( 0.6
a
Total energies are given in hartrees (H); 1 H ) 627.51 kcal/
mol. Relative energies are in kcal/mol. c Zero point energies; HF/
b
d
6-31G* frequencies were scaled by 0.893. Based on QCISD
calculated energies. e Experimental heat of formation (kcal/mol)
at 298 K, taken from ref 31.
level (MP2/6-311+G*). The low relative energy of the 1,1-
dimethyl compound presumably arises from the same
interactions that stabilize neopentane relative to the
other pentanes.34
The deficiencies in the MP2 calculated energy differ-
ences led us to obtain the QCISD/6-311+G** energies
using the MP2 geometries. After correcting for the
differences in ZPE, and the change in energy on going
from 0 to 298 K (Table 5), the calculated relative energies
are in remarkably good agreement with the experimental
∆Hf values.
The MP2/6-311+G* difference in energy between cis-
and trans-1,4-dimethylcyclohexane is 2.04 kcal/mol after
correcting for the difference in zero-point energy. The
corresponding difference in energy between the axial and
equatorial isomers of methylcyclohexane, 1a and 1e
(Table 3), is 1.99 kcal/mol. The fact that these energy
differences are virtually identical indicates that the C(4)-
CH3 in 1,4-dimethylcyclohexane does not affect the
conformational energy of a methyl group in cyclohexane.
This result lends strong support to the assumption that
the counterpoise technique for obtaining conformational
energies does not introduce large errors.
In 1,1-dimethylcyclohexane, with two methyl groups
attached to the same carbon, one might expect that the
axial methyl would be moved toward the cyclohexane
ring, which should increase any 1,3-diaxial interactions
that might be present (viz., the buttressing effect).4,5
Structural data for 1,1-dimethylcyclohexane, derived
from MP2/6-311+G** calculations, are summarized in
The relative energies of the isomeric 1,4-dimethylcy-
clohexanes are reproduced by the B3LYP calculations
and, to a lesser extent, by MP2. However, the B3LYP
model does not reproduce the relative energy of 1,1-
dimethylcyclohexane, and it might be noted that it also
does not reproduce the relative energies of n-pentane and
neopentane.33 On the other hand, MP2 does better at
reproducing the relative energy of 1,1-dimethylcyclohex-
ane, although it appears to overcorrect at the highest
(33) The B3LYP/6-311G* energies for n-pentane and neopentane are
-197.813 79 and -197.815 34 H, respectively, giving a calculated
energy difference of only 0.97 kcal/mol, or after correction for the
difference in zero-point energy, 1.6 kcal/mol at 0 K. The experimental
energy difference (ref 31) is 3.4 kcal/mol at 0 K.
(32) Pedley, J . B. Thermochemical Data and Structures of Organic
Compounds; Thermodynamics Research Center, Texas A&M Univer-
sity: College Station, TX, 1994; Vol. 1.
(34) Laidig, K. E. J . Phys. Chem. 1991, 95, 7709.

2092 J . Org. Chem., Vol. 64, No. 6, 1999
Wiberg et al.
F igu r e 6. Potential energy change for rotation of the ethyl group in ethylcyclohexane; the torsional angle is defined by H(1)-
C(1)-CH2-CH3. The upper curves are for the axial conformer (2a ), and the lower curves are for the equatorial conformer (2e).
Legend: axial (2a )/) MM3, 4 ) HF/6-31G*, O ) B3LYP/6-311G*, O ) MP2/6-311+G**; equatorial (2e) ± ) MM3, 2 ) HF/6-
31G*, 9 ) B3LYP/6-311G*, f ) MP2/6-311+G**.
Ta ble 6. Ca lcu la ted En er gies for Eth ylcycloh exa n e (2)
Figure 5. The geometry at C(3), C(4), and C(5) is virtually
unchanged on going from 1a to 1,1-dimethylcyclohexane,
despite the decrease in the C(2)-C(1)-CH3 bond angle
from 112.0° in 1a to 110.6 ° in the geminally disubstituted
cyclohexane. Thus, buttressing of the axial methyl by an
equatorial group does not appear to have an effect on the
geometry at remote ring positions when the axial groups
at C(3,5) are hydrogen. This observation lends further
support to the suggestion made above that interactions
between an axial CH3 and the synaxial hydrogens at
C(3,5) are not an important factor in the determining the
conformational preference of a methyl group.
conformer energiesa
axial-CH3 equatorial-CH3 (kcal/mol)
∆Eb
basis set
MP2/6-311+G*
-313.445 06 -313.447 60
-313.750 47 -313.752 68
-313.538 43 -313.541 33
1.59
1.39
1.82
1.61
MP2/6-311+G (3df,2p)
QCISD/6-311+G*
QCISD/6-311+G (3df,2p)c -313.843 84 -313.846 41
energies (kcal/mol)
CH3 rotational barrier
2.58
136.32
6.16
-21.15
91.58
2.62
136.11
6.31
-21.29
92.57
ZPEd
0.21
-0.15
0.14
(H°298 - H°0)
(G°298 - G°0)
S° (cal/mol-deg)
-0.99
Eth ylcycloh exa n e (2). Whereas methylcyclohexane
has a simple 3-fold rotational barrier for the methyl
group, the rotational barrier for an ethyl group is more
complex. The stationary points on the potential energy
surface for ethyl rotation in the equatorial and axial
isomers of 2 were located at the HF/6-31G*, B3LYP/6-
311G*, MP2/6-31G*, and MP2/6-311+G** levels and are
shown in Figure 6; the torsional angle (τ) is defined by
H(1)-C(1)-CH2-CH3. As might be expected, the rotamer
with a ∼60 torsional angle (i.e., methyl gauche to H) had
the lowest energy for both the axial (2a ) and equatorial
(2e) isomers. The general features of the torsional func-
tion for 2e are the same for the several theoretical levels
with a spread of less than 1 kcal/mol at the two maxima.
Although the relative energies of 2a and 2e differ
significantly on changing theoretical level, the general
features are reproduced at all theoretical levels.
The MM3 molecular mechanics force field has been
well optimized for hydrocarbons, and therefore, it was
of interest to compare the rotational profile calculated
above with that predicted by MM3; the results of these
calculations are also shown in Figure 6. It can be seen
that the MM3 force field gives fairly good agreement with
the ab initio results.
a
Total energies are given in hartrees (H); other energies are in
b
kcal/mol (1 H ) 627.51 kcal/mol). Axial-CH3 - equatorial-CH3.
c Estimated energies as described in the text. Zero point energies;
d
HF/6-31G* frequencies were scaled by 0.893. The internal rotor
modes were treated separately and their zero point energies are
included.
geometry optimization at several theoretical levels. The
results of these calculations are summarized in Table 6.
Here again, the B3LYP model gave larger energy differ-
ences than did MP2. In view of the results described
above, the energy difference between 2a and 2e also was
calculated at the QCISD/6-311+G* level and corrected
to the QCISD/6-311+G(3df,2p) using the MP2 data as
described above, giving ∆E ) 1.61 kcal/mol. Thermo-
chemical correction for internal rotation was made using
the MP2/6-311+G** energy profile. The final calculated
relative energies for 2 are summarized in Table 4. At 157
K, ∆H° for ethylcyclohexane is calculated to be -1.85
kcal/mol, which is in reasonable agreement with the
experimental value of -1.54 ( 0.12 kcal/mol (Table 2).
Isop r op ylcycloh exa n e (3). The rotational profile for
isopropylcyclohexane (3) was calculated at the HF/6-
31G*, B3LYP/6-311G*, MP2/6-31G*, and MP2/6-311+G*
levels, and they are compared with that predicted by
MM3 in Figure 7 (τ is defined as the H(1)-C(1)-C-H
The energies of the lower energy rotamers of axial and
equatorial ethylcyclohexane were also calculated by

Conformational Studies in the Cyclohexane Series
J . Org. Chem., Vol. 64, No. 6, 1999 2093
F igu r e 7. Potential energy change for rotation of the isopropyl group in isopropylcyclohexane; the torsional angle is defined by
H(1)-C(1)-C-H. The legend is the same as for Figure 6.
Ta ble 7. Ca lcu la ted En er gies for Isop r op ylcycloh exa n e (3)
conformer energiesa
axial-CH3
equatorial-CH3
∆Ec (kcal/mol)
basis set, torsional angleb (τ, °)
MP2/6-311G*, 180°
MP2/6-311G*, 60°
MP2/6-311+G**,d 180°
MP2/6-311+G**,d 60°
QCISD/6-311+G*, 180°
QCISD/6-311+G(3df,2p), 180°
energies (kcal/mol)
CH3 rotational barrierd
τ ) 60° (inner methyl)
τ ) 60° (outer methyl)
τ ) 180°
-352.622 05
-352.615 88
-352.760 71
-352.754 62
-352.731 56
-352.623 84
-352.623 92
-352.762 13
-352.762 22
-352.733 97
1.12
5.05
0.89
4.77
1.51
1.31e
3.74
2.99
2.43
171.70
6.88
2.83
2.96
2.75
171.41
7.02
ZPEf (τ ) 180°)
0.29
-0.14
0.73
(H°298 - H°0)
(G°298 - G°0)
-21.81
96.20
-22.54
99.12
S° (cal/mol-deg)
-2.92
a
b
Total energies are given in hartrees (H); other energies are in kcal/mol. The torsional angle, τ, is defined as the H-C-C-H angle.
c Axial-CH3 - equatorial-CH3. Calculated using the MP2/6-311G* geometries. e Estimated value, see text. f Zero point energies; HF/6-
31G* frequencies were scaled by 0.893. The internal rotor modes were treated separately, and their zero point energies are included.
d
angle). There are three low-energy rotamers for the
equatorial conformer, 3e, corresponding to torsional
angles of ∼60°, 180°, and ∼300°. Although there are
minima at the corresponding torsional angles for the
axial conformer, only the 180° rotamer of 3a has a low
enough energy to be significantly populated. For the case
of the 3e, all theoretical levels give essentially the same
potential energy curve, and that derived from MM3 is
not very different. The spread of calculated potential
energies for 3a is greater, but this is mainly the result
of differences in the relative energies of the axial and
equatorial isomers.
The calculated energies for isopropylcyclohexane are
summarized in Table 7. The QCISD/6-311+G* energies
were calculated using the MP2 geometries, giving 1.51
kcal/mol as ∆E for the axial and equatorial isomers.
Making the same correction for added polarization func-
tions as found appropriate in the ethylcyclohexane case,
the “best” estimate of the energy difference between 3a
and 3e becomes 1.31 kcal/mol. The thermochemical
correction for internal rotation was made using the MP2/
6-311+G** energy profile, and the final calculated rela-
tive energies at 157 and 298 K are given in Table 4. The
calculated ∆H° for an isopropyl group at 157 K is -1.53
kcal/mol, in good agreement with the observed value of
-1.40 ( 0.15 kcal/mol (Table 2).
It is of some interest to note that the 180° and “60°”
rotamers of 3e, depicted below with torsional angles
derived from MP2/6-311G* calculations, have essentially
the same energy (Figure 7) despite the fact that the latter
conformation is subject to an additional gauche-butane
interaction not present in the former. This seeming
paradox is reminiscent of that in 2,3-dimethylbutane
where the anti and gauche conformations are nearly
equal in enthalpy.35 As noted elsewhere,35 this behavior
arises from constraints on the torsional angles imposed
by the larger than tetrahedral C-C-C bond angles found
in congested molecular frameworks such as 2,3-dimeth-

2094 J . Org. Chem., Vol. 64, No. 6, 1999
Wiberg et al.
Ta ble 8. Ca lcu la ted En er gies for
Con clu sion s
ter t-Bu tylcycloh exa n e (4)
The results presented above demonstrate that it is
possible to obtain a fairly accurate measurement of the
conformational equilibrium constant for alkyl-substituted
cyclohexanes by low-temperature 13C NMR of samples
having 13C-enriched alkyl groups if one uses one of the
cyclohexane ring resonances as an internal standard. The
-∆H° values for methyl- (1), ethyl- (2), and isopropylcy-
clohexane (3) were found to be 1.76 ( 0.10, 1.54 ( 0.12,
and 1.40 ( 0.15 kcal/mol, respectively. Ab initio calcula-
tions at the QCISD level reproduced the experimental
values fairly satisfactorily, but B3LYP gave energy
differences that were too large, whereas MP2 gave
differences that were too small. It should be noted that,
although the computed enthalpy differences are some-
what larger (by ∼0.2-0.3 kcal/mol) than those observed
in solution, this may well be a consequence of the fact
that the experimental conformational enthalpies were
determined in solution whereas the computational results
are referred to the gas phase.13 An analysis of the
structural data derived from the calculations indicated
that an axial substituent affected only the local geometry;
consequently, 1,3-diaxial interactions between a methyl,
ethyl, or isopropyl group and a synaxial hydrogen are
apparently not an important contributor to the energy
difference between axial and equatorial alkyl groups.
conformer energiesa
equatorial
axial
twist-boat
basis set
MP2/6-31G*
MP2/6-311G*b
-391.660 15 -391.651 22 -391.651 47
-391.807 25 -391.798 58 -391.799 33
MP2/6-311+G**b -391.961 16 -391.953 01 -391.953 22
relative energies
MP2/6-31G*
MP2/6-311G*
MP2/6-311+G**
ZPEc
0.00
0.00
0.00
5.60
5.44
5.11
5.45
4.97
4.98
169.92
170.18
170.00
a
Total energies are given in hartrees (H); relative energies are
in kcal/mol. Calculated at the MP2/6-31G* geometries. c Zero
b
point energies; HF/6-31G* frequencies were scaled by 0.893. The
internal rotor modes were treated separately, and their zero point
energies are included.
ylbutane and 3e. Consequently, the anti rotamer has two
small torsional angles (τ ) 56.6°); moreover, if one of the
small angles were to be increased so as to reduce steric
interactions, the other would of necessity have to de-
crease. In sum, the 180° rotamer of 3e is effectively
destabilized via enhanced steric repulsion enforced by
small torsional angles between the methyl groups and
the C(2,6) positions.
Exp er im en ta l Section
Ma ter ia ls. Methylcyclohexane enriched to 99 atom % 13C
at the methyl carbon (1) was prepared by the catalytic
hydrogenation of 13CH3-toluene (99 atom %; Cambridge Isotope
Laboratories) using Adam’s catalyst in acetic acid (room
temperature, 30 psi hydrogen pressure).37 Ethylcyclohexane-
R-13C (2) was prepared by the catalytic hydrogenation of
1-phenylethanol. The alcohol was obtained by LiAlH4 reduction
of acetophenone, which was prepared by the reaction of acetyl-
1-13C chloride (99-atom %; Cambridge Isotope Laboratories)
with benzene and aluminum chloride. Isopropylcyclohexane-
R-13C (3) was obtained by the catalytic hydrogenation of
2-phenyl-2-propanol prepared by the reaction of methylmag-
nesium bromide with acetophenone-13CdO.
NMR Mea su r em en ts. NMR spectra were obtained at 11.8
T at Yale using a Brucker AM-500 spectrometer and a dual-
channel 1H/13C probe. A 4.0 µs pulse width (∼35° tip angle)
was used with a recycle delay of 6.0 s to ensure complete
relaxation of the sample. The spectra were obtained using 64K
of points and sweep widths of 12-15 kHz to give an acquisition
time of ∼2.4 s and a resolution of ∼0.4 Hz per point.
Approximately 200 scans gave sufficient signal-to-noise for
each compound. At Holy Cross the spectra were obtained at
7.1 T using a Bruker AC-300 spectrometer and a dual-channel
1H/13C probe. The same parameters as noted above were
employed except that the sweep width was ∼7 kHz and 32K
of points were collected to give the same acquisition time and
spectral resolution.
ter t-Bu tylcycloh exa n e (4). A more limited compu-
tational study of the highly biased conformational equi-
librium of tert-butylcyclohexane was conducted at several
levels of theory (Table 8). The equatorial preference of
tert-butyl is so large (-∆G° ) 4.9 kcal/mol)36 that it has
long been used as an anchoring substituent.6 Nonethe-
less, there are three conformational isomers that must
be considered in an analysis of tert-butylcyclohexane. The
lowest energy form of 4 clearly has an equatorial tert-
butyl group.3,4,6,8,36 However, when the group is placed
in the axial position, the molecule may escape the severe
steric interactions by conversion to a twist-boat form that
places the tert-butyl group in a pseudoequatorial position.
The energies of the three relevant conformers of 4 were
calculated, giving the data summarized in Table 8. The
axial and twist-boat conformations were found to have
virtually the same energy albeit with a slight preference
for the nonchair conformation. After correction for dif-
ferences in the zero point energies, the calculated con-
formational enthalpy of an axial tert-butyl group at the
MP2/6-311+G* level (∆H° ) -5.4 kcal/mol) is in reason-
able agreement with the accepted value (-∆G° ) 4.9 kcal/
mol)36 for the conformational energy of a tert-butyl
substituent in cyclohexane.
Dilute solutions, approximately 10% by volume, of 1-3 in
CBrF3-CD2Cl2 (5:1 by volume) solvent were used in the low-
temperature NMR studies; neat 2-chlorobutane contained in
a capillary placed in the NMR tube was used as an internal
thermometer (eq 2). It should be noted that the spectrometer
temperature controllers were found to be in error by a
considerable amount, and there were discrepancies of up to
13 °C between the internal temperature and the setting of the
temperature control.
(35) (a) Bartell, L. S.; Boates, T. L. J . Mol. Struct. 1976, 32, 379. (b)
Heinrich, F.; Lu¨ttke, W. Chem Ber. 1977, 110, 1246. (c) For a concise
discussion of the conformational analysis of 2,3-dimethylbutane and
related molecules, see ref 4, p 605-606 and references therein.
(36) (a) Manoharan, M.; Eliel, E. L. Tetrahedron Lett. 1984, 25, 3267.
(b) Allinger, N. L.; Hirsch, J . A.; Miller, M. A.; Tyminski, I. J .; Van-
Catledge, F. A. J . Am. Chem. Soc. 1968, 90, 1199. (c) van de Graaf, B.;
van Bekkum, H.; van Koningsveld, H.; Sinnema, A.; van Veen, A.;
Wepster, B.; van Wijk, A. M. Rec. Trav. Chim. Pays-Bas 1974, 93, 135.
Following FT transformation, spectra were transferred in
digital form to another computer. Relevant band areas were
obtained in two independent ways. The first method consisted
(37) Adams, R.; Marshall, J . R. J . Am. Chem. Soc. 1928, 50, 1970.

Conformational Studies in the Cyclohexane Series
J . Org. Chem., Vol. 64, No. 6, 1999 2095
of fitting the NMR bands to a Lorentzian curve. The area was
then obtained from the height and width at half-height.18 In
some instances, the bands were not precisely Lorentzian due
to slight asymmetry; in these cases the small difference
between the experimental and calculated curves was inte-
grated using Simpson’s rule, and the area was added to that
of the Lorentzian curve. The second procedure for obtaining
band areas involved the venerable “cut-and-weigh” method:
the appropriate bands were adjusted to the same size using a
known scaling factor and printed. Areas were then determined
by cutting out the bands, weighing them, and correcting for
the scaling factor. The two methods gave essentially the same
relative areas in every instance. The areas obtained by
integration were used for the van’t Hoff plots; errors were
determined using the Marquardt algorithm.25
carried out using locally developed programs. The rotational
barriers were treated by calculating the energy and the
reduced moment of inertia as a function of the torsional angle
and then calculating the energy levels.29 The partition function
was obtained from the energy levels and the other terms were
obtained using the usual statistical mechanics formalism.39
Ack n ow led gm en t. We thank Martin Saunders for
suggesting the use of the 2-chlorobutane thermometer.
The work at Yale was supported by a grant from the
National Science Foundation; the work at UCONN was
supported by a grant from the Connecticut Department
of Economic Development; the work at Holy Cross was
supported by a grant from the National Science Foun-
dation.
Ca lcu la tion s. The ab initio calculations were carried out
using Gaussian 95.38 The thermochemical corrections were
Su p p or tin g In for m a tion Ava ila ble: Summary of the
calculations, including additional theoretical levels and details
of the thermal corrections to 298 K, and calibration of the
2-chlorobutane thermometer. This material is available free
of charge via the Internet at http://pubs.acs.org.
(38) Frisch, M. J .; Trucks; G. W.; Schlegel, H. B.; Gill, P. M. W.;
J ohnson, B. G.; Robb; M. A.; Cheeseman, J . R.; Keith, T.; Petersson,
G. A.; Montgomery, J . A.; Raghavachari, K.; Al-Laham, M. A.;
Zakrzewski, V. G.; Ortis, J . V.; Foresman, J . B.; Cioslowski, J .; Sefanov,
B. B.; Nanayakkara, A.; Challacombe, M.; Peng, C. Y.; Ayala, P. Y.;
Chen, W.; Wong, M. W.; Andres, J . L.; Replogle, E. S.; Gomperts, R.;
Martin, R. L.; Fox, D. J .; Binkley, J . S.; Defrees, D. J .; Baker, J .;
Stewart, J . P.; Head-Gordon, M.; Gonzalez, C.; Pople, J . A. Gaussian
95, Development Version (Rev. D); Gaussian, Inc.: Pittsburgh, PA, 1995.
J O990056F
(39) Cf. J anz, G. J . Estimation of Thermodynamic Properties of
Organic Compounds; Academic Press: New York, 1958.