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Conformational Analysis in Mobile Cyclohexane Systems.

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ton, while on the other it shows that the molecule passes
through all the possible valence-isomeric structures.
Table 4. N M R signals of the bullvalyl protons and average rates of
isomerization in monosubstituted bullvalene derivatives 1461.
7 = chemical shift, 7 = 10 for tetrarnethylsilane as internal standard.
1 Preferred
- __
from the temperature-dependent NMR spectra of
monosubstituted bullvalenes (see Table 4); for a discussion cf. [l].
The isomers of monosubstituted bullvalenes in which
the substituent occupies an olefinic position (0, and 0,)
are preferentially formed. This is mainly due to the fact
that substituents are more firmly bonded to an olefinic
than to an aliphatic carbon atom (bond effect).
In the compounds (35), (62), (63), and (64), 0, is
strongly preferred owing to the possibility of conjugation between the substituent and the vinylcyclopropyl
system of the bullvalene skeleton. In (61), 0, and 0,
are present in approximately equal quantities. Owing to
steric hindrance, the bulky t-butyl group in this case is
twisted into a configuration which does not favor optimum conjugation, so that the conjugation effect is subordinate to the bond effect. It cannot be decided whether
0, and O,, or 0, alone predominate in the equilibrium
mixture in (59).
__ 2.p.s.
[a] Cf. Scheme 3
IV. Conclusion
The line width of the singlet and the average rate of isomerization I; at a given temperature depend on the
substituent (see Table 4).
If all seven rate constants were equal, 30 % of the molecules on the average would be in each of the C, O,, and
0, structures, while 10% would have the B structure.
Certain valence isomerizations, however, are at a disadvantage with respect to others, so that the distribution
of the positional isomers depends on the rate constants.
Information 011 rate constants kl-k7 can be obtained
1461 E is that rate constant which, in the case of bullvalene,
would give the same line width a s the one observed for the
derivative studied.
We speak of molecules with fluctuating bonds when
the valence isomers have a mean lifetime of less than
about 100 sec at 0°C. Such molecules can so far be
unambiguously recognized and studied only by NMR
spectroscopy. The study of the bond shifts in substituted cyclooctatetraeiies and bullvalenes is particularly
interesting since the rate of shift depends on the substituent. This gives information on the relative importance af bonding, conjugation, steric, and inductive
[A 4691245 IE]
Received: June 9th. 1965
German version: Angew. Chem. 77, 774 (1965)
Translated by Express Translation Service, London
Conformational Analysis in Mobile Cyclohexane Systems
By “Conformational Analysis” is meant the analysis of the physical and chemical properties
of a compound in terins of its preferred“conformations”, i. e. rotational arrangements about
single bonds. This particular review deals with cyclohexanoid compounds capable of existing
in two or more stable conformations.
1. Historical
That cyclohexane is a puckered, chair- (or boat-)shaped
molecule was first suggested by Sachse [l] 75 years ago.
Because of a lack of appreciation of the restrictions to
rotation about single bonds and other misunderstandings, Sachse’s theories were rejected for nearly 30 years,
[I] H. Sachse, Ber. dtsch. chem. Ges. 23, 1363 (1890); Z. physik.
Chem. 10, 203 (1892).
Angew. Chem. internat. Edit.
VoI. 4(1965)
1 No. 9
to be revived only in 1918 by Mohr 121 and soon to be
confirmed by the classical work of W. Huckel on decalin
[3] and of Boeseken and coworkers on the acetone and
boric acid derivatives of cyclic diols [4].Still the ideas
[2] E. Mohr, J. prakt. Chem. [2] 98, 315 (1918); Ber. dtsch. chem.
Ges. 55, 230 (1922).
[3] W. Huckel, Liebigs Ann. Chem. 441, 1 (1925).
[4] J. Boeseken and J. van Giffen, Recueil Trav. chirn. Pays-Bas
39, 183 (1920); J. Boeseken, ibid. 40, 553 (1921); Ber. dtsch.
chem. Ges. 56, 2409 (1923).
76 1
gained only slow acceptance, being used but occasionally
by carbohydrate chemists [ S ] ; however, during this
period a better understanding of rotational barriers was
gained, first in the biphenyls 161 and later in ethane [7],
which is now known to exist in the “staggered” rather
than the “ec1ipsed”conformation. This phase of development culminated with some very significant work by
Mizushinm 181 on spectroscopic studies of substituted
ethanes, by Hassel[9] on X-ray and electron diffraction
of simple substituted cyclohexanes, and by P i t z r r [lo]
on the shape and thermodynamic properties of cyclohexane derivatives. However, the real breakthrough in
the field did not come until 1950 when D. H . R. Barton,
in a pioneering paper [ll], pointed out the consequences
of conformationdl differences on stability and reactivity. This was an area of great interest to organic
chemists, first those engaged in natural products research and then also those investigating fundamental
molecular behavior, and Barton’s ideas were absorbed,
utilized and further developed rapidly and intensively.
The resulting mushrooming growth of the subject has
carried it, within less than 15 years, to the point where a
comprehensive review requires the format of a book and
two such books have recently appeared 112, 131. A
number of earlier review articles have been listed elsewhere [14, 151.
rl. Scope
Clearly only a limited review is within the scope of the
present article [16]. Conformational concepts play a part
in acyclic, alicyclic and heterocyclic systems; among the
cyclic ones, rings from four-membered on are nonplanar and therefore of particular interest in conformational analysis. We shall confine ourselves here to
six-membered and, in most instances, carbocyclic rings.
[5] See, for example, 0. L. Sponsler and W. H . Dore, Colloid
Sympos. Monogr. 4, 174 (1926); H . S. IsbrN, J. Res. nat. Bur.
Standards 18, 505 (1937); 20, 97 (1938); R. E. Reeves, J. Amer.
chem. SOC. 71, 215 (1949); 72, 1499 (1950); Advances Carbohydrate Chem. 6, 107 (1951).
[6] F. Bell and J. Kenyon, Chem. and Ind. (London) 4, 864
(1926); W. H. MiNs, ibid. 4,884 (1926); E. E . Turner and R . J. W.
LeFkvre, ibid. 4, 831, 883 (1926).
[7] J. D . Kemp and K. S. Pifzer, J. chem. Physics 4, 749 (1936);
3. Amer. chem. SOC.59,276 (1937); K. S . Pitzer, J. chem. Physics
5 , 473 (1937); J . B. Howard, Phys. Review 51, 53 (1937).
[8] a) S. Mizushima and K. Higasi, J. chem. SOC.Japan 54, 226
(1933), and subsequent papers; cf. b) S . Mizushima: Structure of
Molecules and Internal Rotation. Academic Press, New York
1954; c) S. Mizushima, Pure appl. Chem. 7, 1 (1963).
[9] 0. Hassel, Tidsskr. Kjemi, Bergves. Metallurgi 3, 32 (1943);
0. Hasseland B. Ottar, Acta chem. scand. 1, 929 (1947); 0. Hassel, Quart. Rev. (chem. SOC., London) 7, 221 (1953).
[lo] C.W. Beckett, K. S . Pitzer, and R . Spitrer, J. Amer. chem.
SOC.69, 2488 (1947).
[I11 D. H . R . Barton, Experientia 6 , 316 (1950).
[12] E. L . Eliel, N. L. Allinger, S. J. Angyal, and G . A . Morrison:
Conformational Analysis. Wiley, New York 1965.
[I31 M. Hanack: Conformation Theory. Academic Press, New
York 1965.
[I41 E.L.Elie1: Stereochemistry of Carbon Compounds. McGrawHill, New York 1962, Chapters 6, 8.
[I51 E. L . Eliel: J. chem. Educat. 37, 126 (1960).
1161 For a previous review in this journal see H . H . Lau, Angew.
Chern. 73,423 (1961).
Of the two possible puckered forms of cyclohexane, the
chair and the boat, the chair is the more stable because
its bonds are a11 staggered. (In contrast, the boat has
four pairs of eclipsed hydrogen plus other unfavorable
interactions.) Tn the chair form, there are two types of
bonds, those pointing up and down, called ‘‘axial” and
those pointing outward, called “equatorial”. The two
types of bonds are readily distinguished in a model.
I n the following discussion, we shall refer, primarily, to
“mobile systems” which are defined as systems which
can alternate between two or more stable conformations.
The monosubstituted cyclohexane ( I ) provides an
example; it can exist in two conformations, one with
the substituent equatorial, the other one with the substituent axial. The two confarmations are readily interconvertible (see below) and the equatorial conformation
is more stable. Systems of this type are of particular
interest because their reactivity depends i;n the population of the various pertinent conformations.
In contrast to mobile systems are rigid systems, such as
trans-decalin (2) or the steroids - in which ring inversion is impossible because the alternate chair form would
be excessively strained - or biassed systems, such as a
(3). X = halogen - in which
ring inversion is possible but the molecule exists in one
conformation almost to the complete exclusion of the
other(s), because of a large difference in stability. In
the case of t-butylcyclohexane, it is estimated that the
conformation with the equatorial t-butyl group (3a,c ) ,
X = H, predominates over that with the axial t-Duty1
g r m p (3b,d), X = H, by a factor of at least loo00 at
room temperature, because the compression of nonbonded atoms in the t-butyl-axial conformation raises
the potential energy of this form by over 5 kcal/mole
117, 181. There are not many other groups which have
a similar “reluctance” to occupy the axial position.
[I71 S. Winstein and N . J . Holness, J. Amer. chem. SOC. 77, 5562
[181 N. L. Allinger and L. A . Freibet’g, 3. Amer. chem. SOC.82,
2393 (1960).
Angew. Chem. internat. Edit. / Vol. 4 (1965)
No. 9
It should be pointed out that, although we tend to
think of cyclohexanoid molecules as perfectly puckered
chairs with tetrahedral angles, such models are oversimplified. In cyclohexane itself the C C -C bond angle
has been found [19] to be 111.5 ’, somewhat larger than
the tetrahedral angle of 109 28’ and it has been pointed
out [20] that the resulting slight flattening of the chair
significantly influences the physical and chemical properties of certain cyclohexane derivatives. Moreover, the
existence of deformed chairs [21] and even boat forms
[22, 231 especially in some substituted cyclohexanones
[23a], but also in a few saturated systems [18, 23 b] is
becoming increasingly recognized. Major deviations
from chair geometry probably do not occur in the
molecules to be discussed in this review, but the minor
flattening of the cyclohexane ring does affect them and
will be returned to later.
111. Terminology
The terminology of conformation analysis is now generally known and has been reviewed recently [14]. We
wish to introduce only twonew terms here [12]. The term
“conformational energy” will denote the free energy of a
conformation above that of the conformation of minimum energy. For example, the negative of the free
energy AGO for the process ( l a ) + ( l b ) is the conformational energy of the axial form (la). - The term
“syn-axial” groups will be used to denote axial groups
on the same side of a cyclohexane ring and therefore in
close spatial proximity (and frequently steric interaction).
IV. Aims
Monosubstituted cyclohexanes (1) can exist in two
conformations, one with the substituent equatorial, the
other with the substituent axial. The two conformations
are readily interconverted through rotations about
single bonds attended with slight angle deformations.
The potential energy diagram for the interconversion
process is shown in Fig.1. Here, AG; represents the
difference in free energy (i.e. the conformational
energy) of the two chair forms.
The high energy valley between the more stable chair
conformations corresponds to a form in which one side
of the chair has been flipped up but the other has not
yet been flipped down; this form was originally [I]
[19] M . Davisand 0.Hassel, Actachem. scand. 17, 1181 (1963).
[20] R . A . Wohl, Chimia 18, 219 (1964).
[21] See, for example, K. L. Williamson and W . S . Johnson, J.
Amer. chem. Soc. 83, 4623 (1961).
[22] M . Svoboda, M . Tichb, J. FajkoS, and J. Sicher, Tetrahedron
Letters 1962, 717; J . Klinor and A. V.vstrc?l, Chem. and Ind.
(London) 1963, 738.
[23] a) D . H. R . Barton, D . 4 . Lewis, and J . F. McChir, J. chem.
SOC. (London) 1957, 2907; see also ref. [12], pp. 476-481;
b) R . D . Stolow and M . M. Bonaventura, J . Amer. chem. SOC. 85,
3636 (1963).
Angew. Chem. internal. Edit.
1 Vol. 4(1965) / No. 9
Skew boat
Fig. I . Potential energy diagram f o r t h e chair-chair interconversion of
monosubstituted cyclohexanes (schematic). T h e n u m b e r s a r e energies
i n kcallmole.
called the “flexible form” and was later labelled “boat
form”. In fact, this form (in contrast to the chair) is
flexible ; model considerations show that various possible boat forms can be interconverted by minor contortions of the molecule. The boat form, however,
suffers from unfavorable bond eclipsings [7] on the side
of the boat and van der Waals interactions between the
hydrogen atoms at the “bowsprit” and “flagpole” positions, and it has been calculated [24] that the most stable
conformation of the flexible form is one in between two
boat forms, now commonly called the “twist form” or
“skew boat”. The potential energy of this form has been
estimated by computer calculation [24] to be 1.6 kcal/
mole less than that of the classical boat but about
5.5 kcal/mole more than that of the chair (cf. Fig. 1);
the latter value has been confirmed both through
equilibration [ 181 and heat of combustion 1251 measurements involving molecules which, for steric reasons,
exist predominantly in the twist form. The energy barrier
between the chair and twist forms (Fig. 1) has also been
calculated; it is 10-11 kcal/mole above the chair and
corresponds to a conformation in which four adjacent
atoms of the ring are in a plane (“half-chair”). The
value of 10-1 1 kcal/mole has been confirmed by nuclear
magnetic resonance measurements [26,27] and a
similar value was obtained by ultrasonic measurements
[28]; it is small enough so that at room temperature
substituted cyclohexanes rapidly pass from one chair
form into the other by virtue of the thermal excitation
of the molecules.
For the remainder of this review, we shall concentrate on
a discussion of the conformational energies -AG O for
cyclohexanes with different groups X, their rationale
and the ways in which they may be obtained.
V. Results
The -AG values for all the groups so far studied are
given in Table 1. This table represents a summary of
data found in about 75 original papers. It is seen that the
1241 J. B. Hendrickson, J. Amer. chern. SOC.83, 4537 (1961).
G. Baufista, R . L. Clarke,
and W. S . Johnson, J. Amer. chem. SOC.85, 546 (1963).
1261 F. R. Jensen, D. S . Noyce, C. H . Sederholm, and A. J. Berlin, J. Amer. chem. SOC.84, 386 (1962).
[27] F. A. L. Anet, M . Ahmad, and L. D . Hall, Proc. chern. SOC.
(London) 1964, 145; F. A. Bovey, F. P . Hood, E. W. Anderson,
and R . L. Kornegay, ibid. 1964, 146.
[28] M . E. Pedinoff;J. chem. Physics 36, 777 (1962); J . E. Piercy,
J. acoust. SOC. Amer. 33, 198 (1961).
[25] J . L. Margrave, M . A. Frisch, R .
conformationat free-energy values are not monotonous
functions of atom or group size. For example, there is
little progression in -AG value in the halogens from
chlorine to iodine; bromocyclohexane has a much
smaller conformational energy than methylcyclohexane
(although both substituents are ordinarily considered
isosteric) ; the value for cyclohexanecarboxylic acid is
smaller than that for methylcyclohexane which is not
much smaller than that for isopropylcyclohexane.
Tosyloxycyclohexane has about the same conformationa1 energy as cyclohexanol.
Table 1. Conformational free energy differences -AGoX
substituents X in cyclohexanes [a].
Substituent X
1 -AGox
for various
[kcal/molel Ibl
0.0-0.5; 0.4
0.2-0.7; 0.4
0.40-0.45; 0.4
0.25-1.25; 0.5 [cl, 0.9 Id1
0.6-0.75; 0.7
0.9-1.0; 0.9
0.4-1.5; 0.7
0.6-1.7; 0.7
-0.4-0.9: 0.9
1.1-1.8, 1.2 [cl, 1.8 [dl
1.8-2.0; 1.9
0.9-1.1; 1.0 Icl
2.1 [dl
1.5-2.1; 1.7
1.65-2.25; 1.8
1.8-2.5; 2.1
2.0-3.1; 3.1
0.7-1.7; 1.2
2.1-2.3; 2.2
1.0-1.2; 1.1
0.15-0.25; 0.2
ca. 0
[a] References, individual values, methods of determination (see below),
and conditions of temperature, solvent, and phase are given in a lengthy
table in ref. [12], pp. 436-444, as well as in table 1 in 182aI.
[b] Author’s recommended values in italics.
[cl In aprotic solvent.
[d] In hydrogen donor solvent.
[el Ref. 1351.
[f] Ref. [93b].
[g] Ref. 193al.
[h] Ref. 1461.
In principle, the conformational energy can be calculated
from first principles, taking into account the repulsive
(or attractive) energy for the atoms in question (or for
all the atoms of a group such as methyl) with salient
carbon and hydrogen atoms in the ring both in the
equatorial and in the axial position and taking the
difference. Such calculations [29,30] have shown that
the main interactions are of the equatorial group with
adjacent hydrogens (at carbon atoms 2 and 6) and of
the axial group with adjacent hydrogens, syn-axial
1291 J. B. Hendrickson, J. Amer. chem. Soc. 84, 3355 (1962).
[30] Cf. Ref. 1121, pp. 446-457.
hydrogens, and carbon atoms 3 and 5. Other interactions are either negligible or cancel out. Unfortunately, because of insufficient knowledge of the van der
Waals potential functions which form the basis of the
calculations, the results are not very accurate, which is
particularly unfortunate in view of the fact that the
differences one looks for are only of the order of 0-2
kcal/mole (Table 1). Therefore at the moment the experimental approach seems to be the only one feasible;
and while the calculations are sometimes valuable to
indicate trends, it is also worthwhile to acquire some
intuitive ideas about conformational energies, based on
existing data. It is with this aim in mind that the data
will now be discussed.
As already mentioned, there is not a one-to-one correlation between conformational energies and group
sizes as inferred, for example, from the ease of racemization of ortho-substituted biphenyls [31]. Thus the
halogenocyclohexanes have similar - AG values although the size of the halogens certainly increases in
the order fluorine < chlorine < bromine < iodine.
While the value for fluorocyclohexane is somewhat
smaller than that for chlorocyclohexane, the value for
iodocyclohexane is hardly any larger than that for
bromocyclohexane and the latter value is actually
slightly but significantly smaller than that for chlorocyclohexane [32]. One reason for this lack of parallel is
seen from formulae ( 4 ) and ( 5) : whereas in the case of
ortho-substituted biphenyls the interfering groups point
toward each other and the interference will become more
severe as the bond lengths of the atoms or groups involved increase, the contrary is true in axially substituted
cyclohexanes. Here, the longer the bond to the axial
substituent, the further the substituent will be away
from the syn-axial hydrogens and the carbon atoms 3
and 5 which cause the axial crowding. This, to some
extent, compensates for the larger van der Waals radius
of the bigger substituents. By the same token, the flattening of the ring [20] leads to a bending outward of the
axial substituent, and this motion, by a simple leverage
principle, will provide most effective steric relief to the
substituents with the longest bonds, i.e. the large substituents. These two factors may explain in part why
bromocyclohexane (van der Waals radius of Br 1.95 A)
has a much smaller conformational energy (0.4kcal/mole)
than methylcyclohexane (1.7 kcal/mole; van der Waals
radius of the methyl group: 2.0 A).
[31] R . L. Shriner and R. Adams in H . Gilman: Organic Chemistry. Wiley, New York 1943, Vol. 1 , p. 362.
[32] a) E. L. EIieZ and R . J. L. Martin, unpublished data; b) J.
Reisse, J. C. Celotti, and G. Chiurdoglu, Tetrahedron Letters
1965, 397.
Angew. Chem. internat. Edit. 1 Val. 4 (1965) 1 No. 9
There is probably, however, a third reason: the larger
atoms such as bromine tend to be more polarizable and
therefore the attractive London forces are more important for such atoms. London forces are particularly
important just within (and just outside) the van der
Waals radial distance. As shown in Figure 2, they would
lead to a deeper and shallower well in the van der
Waals potential function.
room temperature. In fact, the difference will always be
less than that.
An exception occurs with a substituent with three attached groups, such as t-butyl, C(CH3)3. In this case
one cannot avoid having one group (methyl) point into
the ring when the substituent is axial; this results in a
very sizeable compression with the syn-axial hydrogens
and accounts for the great reluctance of the t-butyl
group to occupy the axial position (trans-1,3-di-t-butylcyclohexane actually prefers the skew-boat conformation to one with axial t-butyl[18]).
In this context, the relatively small conformational energy
of cyclohexyl phenyl sulfone (2.5 kcal/mole) comes as a
surprise; in the series of cyclohexanes with SR, S(O)R,
S(0)zR as substituents, the big jump in -AGocomes between
sulfide and sulfoxide, not between sulfoxide and sulfone.
This may be a consequence of the difference in hybridization
and in bond angle between -SR, -S(O)R, and -S(Oz)R.
Distance H-X
Fig. 2. Potential curves (schematic) for (-1
CH3-H interactions
and (. . . .) Br-H interactions. R = van der Waals radius, A = distance
between an axial substituent and syn-axial hydrogen atoms in monosubstituted cyclohexanes, B = distance between orrho-substituents in
biphenyl derivatives of type ( 4 ) .
Since axial atoms and groups usually find themselves
just within the van der Waals distance from the offending syn-axial hydrogens, etc. (point A, Fig. 2), the shape
of the curve at this point is quite significant and a group
of low polarizability such as methyl (analogous to a
hard or wooden sphere) finds much less steric relief due
to London attraction than a polarizable group, such as
bromine (analogous to a soft or rubbery sphere). In
biphenyls (4) these considerations are much less important because the interatomic distance of the orthosubstituents is much less, and the groups find themselves
in a strongly repulsive part of the van der Waals curve
(point B, Fig. 2) where attractive London forces
(E a l/r6) are no longer important compared to the
repulsive force (E = l/rl2).
Another point of interest in Table 1 is that the atom
next to the cyclohexane ring in large measure determines
the conformational energy; other atoms attached to the
first one are much less important. Thus OH, OAc,
OCH3, OC2H5, OTosyl all have very similar conformational energies, as have SH, SCH3, and SC6H5 or CH3,
C2H5, and CH(CH&. Model considerations quickly
show the reason for this finding; the group may be so
rotated that any atom attached to the first points away
from the ring. This wilI, in essence, leave the conformational energy unaffected except for a small decrease in
entropy of mixing in the case of the axial substituents
because of the elimination of one or two alternate
rotational conformations of the axial substituent in
which the attached group would point into the ring.
In the extreme case, where the equatorial substituent
has three equally probable conformations and the axial
one has only one, this difference would amount to
Rln 3 or 2.2 cal. mole-1 deg.-1, corresponding to a conformational free energy difference of 0.65 kcal/mole at
Aitgew. Chem. internat. Edit./ VoI. 4 (1965) / No. 9
A comparison of R-COOH with R-COO-, R-SH
with R-S- and R-NH2 with R-NH; (R = cyclohexyl)
suggests that the ions are always apparently larger than
the parent groups. Presumably this is to be ascribed to
solvation which leads to a “swelling” of the ionic
The effect of hydrogen bonding on group size is evident
when one compares the conformational energies of
cyclohexylamine in aprotic and protic solvents; the
former value is 1.1 kcal/mole, the latter 1.5-1.8 kcal/
mole [33]. The size of the hydroxy group is also increased by hydrogen bonding [15, 341; thus -AG ’ for
cyclohexanol is 0.6 kcal/mole in cyclohexane but 0.9
kcal/mole in isopropyl alcohol [35]. On the other hand,
the size of the halogen atoms appears to be largely independent of solvent [32], indicating that hydrogen
bonding is too weak to make a difference except possibly in trifluoroacetic acid. While it has not yet been
established whether hydrogen bonding affects conformational enthalpy or conformational entropy, the chances
are that with a group which has two or three free pairs
of unbonded electrons (such as hydroxy) entropy is
mainly involved and that the higher conformational
energy of an axial substituent capable of hydrogen bonding in a protic solvent is due to the fact that the hydrogen
bond forms preferably on the outside of the ring and
thus interferes with certain rotational conformations of
the axial substituent. However, with a group which has
only a single pair of unbonded electrons, e.g. NH2 (6),
hydrogen bonding may force the axial group into an
unfavorable rotational conformation (7).
Besides varying with solvent, conformational free energies
may also vary with phase. For example, in polymethylcyclohexanes the axial isomers not only have the higher enthalpies
[33] E. L. E M , E. W. Della, and T. H. Williams, Tetrahedron
Letters 1963, 83 1.
[34] J . Reisse, J. C. Celoffi,D. Zimmermann, and G. Chiurdoglu,
Tetrahedron Letters 1964, 2145.
[35J E. L. Eliel and S. H . Schroeter, J . Amer. chem. SOC., in the
but also the higher latent heats of vaporization. This means
that the excess energy content of the axial isomer over the
equatorial is greater in the vapor phase than in the liquid
a n d , in fact, the best experimental value for the conformational energy of methylcyclohexane is 1.7 kcal/mole in
the liquid phase and 1.9 kcal/mole in the vapor.
The figures in Table 1 are free energy differences. As yet,
few careful experimental apportionments of these free
energies between enthalpy and entropy terms have
been made. It might be expected that no conformational
entropy differences would be found for spherically or
cyclindrically symmetrical groups, such as methyl, halogen, cyano, ethynyl. In fact, however, experimental
differences have been claimed for methyl [36], cyano
[37], chlorine, and bromine [32b]. The significance of
these findings is somewhat uncertain in view of the difficulty of measuring entropy differences to better than
0.5 cal.mole-1-degree-1, but a possible explanation in
terms of rotational entropy has been offered [32b]. In
the case of non-symmetrical groups, entropy differences
would definitely be expected; thus the differences in
for methyl-, ethyl-, and isopropyl-cyclohexanes
are adequately accounted for by entropy considerations
[38]. Careful measurement has recently been made [39]
of the thermodynamic parameters for the equilibrium
(8a) $ ( S b ) which, presumably, corresponds to the
conformational equilibrium of the carboxyl group (see
Section VII). Determinations of equilibrium from 212 to
333°C in dodecane as a solvent indicates AH" =
-1.63 & 0.05 kcal/mole, ASo = -0.8 & 0.2 cal.mole-1.
degree-', and A G O = -1.4 i 0.1 kcal/mole (extrapolated to 25°C). The negative value of AS" is surprising at first, as one might have expected an equatorial
COOH group to have more conformational freedom
than the corresponding axial group. It appears, however, that the equatorial acid is more strongly associated
in dodecane solution with a resultant greater loss in
translational entropy [*I.
As yet, little definite i s known about conformational
equilibria in di- and poly substituted cyclohexanes, e.g.
(9), X + Y. It is generally assumed that theconformational energies are additive, i.e. A G O = AG+ - A G ~
for the compounds (9a) and (9b). Some support for
this assumption has been obtained for 1,3- and 1,4disubstituted qclohexanes [15,40,41] although there
[36] R.J. Armitage, G. W. Kenner, and M. J. T. Robinson, Tetrahedron 20, 747 (1964).
[371B. Rickborn and F. R.Jensen, J. org. Chemistry 27,4606 ( 1 962).
[38] N . L. Allinger and S E . Hn, J . Amer. chem. SOC.84, 370
(1962); J . org. Chemistry 27, 3417 (1962).
1391 E. L. Eliel and M . Reese, unpubIished work.
[*] Note added in proof: The negative AS' may indicate that
the axial COOH group exists in two (mirror-image) CO/C
eclipsed conformations whereas the equatorial COOH exists
mainly in a single CO/H eclipsed conformation.
1401 E. L. E l i d a n d C. A. Lukarh, J. Amer. chem. SOC.79, 5986
[41] E L . Elidand R . S. Ro, J. Amer. chem. SOC.79, 5995 (1957).
are also difficulties [I 51. In 1,2-disubstituted cyclohexanes, the principle of additivity cannot be expected
to hold for two reasons: one is that, because of the
flattening of the ring, cis-substituents (equatorial-axial)
are closer together and therefore have a greater steric
interaction than trans-substituents (eyuatorial-equatorial) [20,42,43]; the other is that substituents which are
not spherically symmetrical may be forced into different rotational conformatians by adjacent substituents
[44, 451. Thus in a cis-2-isopropylcyclohexanol,the ehydroxy,a-isopropyl conformation is unfavorable by
much more than the difference in -AGO values of
cyclohexanol and isopropylcyclohexane (1.4 kcallmole
[42]). The reason is that the axial isopropyl group cannot readily assume its normal conformation (methyls
out of the ring) since this leads to strong steric interaction with the OH group (equivalent to a hydroxymethyl syn-axial interaction) [44].
In 1,I-disubstituted cyclohexanes, it has been assumed
[46] that the -AGO values are additive. This assumption
seems to be justified in 1-chloro-1-methylcyclohexane in
which - A G O (1.1 kcal/mole in favor of the a-chlorine,
e-methyl conformation) [47] is close to the difference of
the conformational energies of methylcyclohexane
(1.7 kcal/mole) and chlorocyclohexane (0.4 kcal/mole).
VII. Methodology
Since the equilibrium (la) + (Ib) is established in a
fraction of a millisecond at room temperature, direct
measurement of the position of equilibrium is possible only by physical methods (see below). However,
there are various indirect chemical approaches to the
A. Thermochemical Method
In the simplest approach, the conformational eyuilibrium (la) + ( I b ) is replaced by a configurational
equilibrium - hypothetical or actually- achievable
for example (lOa) + (IOh). Since a cis-l,3-disubstitutcc:
[42] T. J . Brett, Ph. D. Thesis, University of Notre Dame, 1963;
E. L. E l k / and T . J.Brett, J. Amer. chem. SOC.,in the prcss.
[43] J . C . Richer, L. A. Pilato, and E. L. Eliel, Chem. and Ind.
(London) 1961, 2007.
[44] R . D . Stolow, J. Amer. chem. SOC.86, 2170 (1964).
[45] J . Sicher, unpublished observations.
[46] R. J. Ouellette, J . Amer. chem. SOC. 86, 3089 (1964).
[47] Anna Fang, M. S. Dissertation, Massachusetts Institute of
Technology, 1965.
Angew. Ciiem. internat. Edit. / Vol. 4 (1965) No. 9
cyclohexane exists virtually exclusively in the diequatorial form (the diaxial conformation has a severe 1,3-synaxial steric interaction of the substituents) and each
enantiomer of the trans-isomer necessarily exists in one
of two superimposable equatorial-axial conformations,
the enthalpy difference between the two configurational
isomers may be equated to the enthalpy difference between equatcrial and axial X (assuming that the second
substituent does not exert a disturbing influence). The
enthalpy difference may be found directly by accurate
determination of the heats of combustion of the cisand trans- isomers and this approach has been used
successfully in the case of the 1,3-dimethylcyclohexanes
[48]. The heat of combustion of the trans-isonier is
1256.75 kcal/mole and that of the cis-isomer 1254.79
kcal/mole (gas phase); the difference of 1.96 kcal/mole
thus represents the greater stability of equatorial methyl
over axial in the gas phase. The corresponding value in
the liquid phase similarly determined is 1.72 kcal/mcle.
It is clear that in order l o achieve an accuracy of approximately .= 10 % in the conformational energy difference
required an accuracy of nearly 1 part in 10000 in the heat-ofcombustion data themselves. Such accuracy is extraordinarily
difficult t o achieve, requiring not only very careful measurement but also extremely pure samples. The attendant difficulties have discouraged wide-spread use of the method.
In the case of the 1,3-dimethylcyclohexanesthe entropies
of the cis- and trans-(&)-isomers have also been rneasured [49] and the difference is found to be 1.24 cab
mole-1-degree-1 in f a v x of the trans-form, in gcod
agreement with the expected value of 1.38 ca1.mole-l.
degree-1 calculated on the assumption that the only
entropic difference between the cis- and trans-isomers
stems from [he fact that the trans-isomer is a ( ~ l - p a i r
and is therefore favored by an entropy Gf mixing of
R In 2. From the experimental values of AH" and AS" for
the 1,3-dirnethylcyclohexanesone may calculate AGO
at 25 to be -- 1.59 kcal/mole for the equilibrium trans +
cis (gas phase). It must be recognized that this value
bears no direct relation to the conformational energy of
methylcyclohexane. To obtain AG" for the conformational equilibrium (la) + (Ib), X = CH3, it is best to
assume that A S o = 0 and therefore AH" AGO
-1.96 kcal/mole in the gas phase. The assumption that
ASo between equatorial and axial methylcyclohexane
is zero is best justified by the observation (vide supra)
that the entropy difference for the dimethylcychhexane
is completely accounted for (within limits of experimental error) by the entropy-of-mixing term (which does
not enter into the methylcyclohexane conformaticnai
B. Equilibrium Methods
An alternative and usually experimentally easier approach is to establish the equilibrium ( 1 0 ~ +
) (IOb)
directly and to measure the equilibrium constant K (e.g.
1481 E. J . Prosen, W. H . .Johi!son, and F. D. Rossirii, J. Rcs. nat.
Bur. Standards 31, 173 (1947); J. E. Kilpatrick, H . G. Werner,
C. W . Bec-kett, K. S.Pirzer, and F. D. Rossini, ibid. 39, 523 (1947).
[49] H . M. Huffinom, S. S . Todd, and G. D. Oliver, J . Amer.
chem. SOC. 71, 584 (1949).
Chen?. in/:r.;wt. Edit. / Vol. 4 (1965)
by gas chromatographic determination of the equilibrium position); then A G O = -RT In K. In principle,
AHo can be measured from the temperature dependence
of K, but to effect such measurements with the required
degree of accuracy is quite painstaking, and some of the
data in the literature in this regard must be viewed with
reserve. Short of performing a really careful measurement of AH", it is probably better, for a spherically
symmetrical group such as methyl, to a s s u m e that
ASo for the process (IOa) + ( l o b ) is -Rin 2 and
then to calculate AHo at the desired temperature. An
even safer approach, applicable to all groups, is to assume that -AG$ for the equilibrium (la) + ( l b ) may
be obtained from - 4 G O for the process (IOa) F (lob)
by adgdin RT In 2. This, in essence, entails the assumption that the prccess (IOa) + (IOb), but for the
equilibrium (optically active trans) + (meso-cis)
daes, in fact, have the same equilibrium constant as
( l a ) F' (lb). These principles were applied to the
equilibration of the diethyl hexahydroisophthalates ( l o ) ,
X = C02C2H5, [50] for which equilibrium at 78 "Ccorresponds to 71 % cis- and 29 7; trans-isomer, -AG
being 0.63 kcal/mole. From this, applying the RT In 2
correction, -AG 3C0,C2Hs is 1.1 1 kcal/mole.
An alternative but related approach is to measure the
equilibrium position for cis- and trans-4-t-butyl isomers (8).
Thus, for example, for ( S ) , X 5 COzCzHs, equilibrium
corresponds t o 84.7 + 0.6 % trans-isomer [51], whence
- A G O C O ~ C ~ may
H ~ be directly calculated to be 1.2 kcal/mole.
In some cases, where groups cannot readily be equiiibrated
directly at temperatures in the vicinity of 25"C, some indirect means of equilibration may be resorted to. For
example, the equilibrium constant for the equilibrium
( I r a ) + ( I l b ) has been shown to be close to unity [52]. Since
it was known from other measurements [531 that -AGOOR =
0.7 kcal/mole, it may be inferred that -AGOSR is of the
same order of magnitude.
A somewhat more intricate method of indirect equilibration is shown by formulae (12a)-(I2c). It is known
1541 that equilibration of 4-t-butylcyclohexano1 with
in ether (probably
an oxidation-reduction type of equilibration involving
the complex ROAICl2, cf. [55]) leads to an equilibrium
mixture containing over 99.5 "/, of the trans-complex.
Therefore, for any R in (12) which is appreciably
smaller than t-butyl, virtually all the cis-isomer exists in
the conformation C' ( I ~ c ) ,and what is chemically an
[50] A'. L. Allinger and R. J . Curbj,, J . org. Chemistry 26, 933
[51] E. L. Eliel, H . Houbetrstoc-k, and R . V. Acliar..~o, J . Amer.
chem. SOC.83, 2351 (1961); N. L. A/lin,qer, L . A . Freiberg, and
S.-E. Hu, ibid. 84,2836 (1962).
[52] E. L. Hieland L . A . Pilrrto, Tetrahedron Letters 1962, 103;
E. L . EIieI, E. W . Dello, and M. R o g i i , J. org. Chemistry 30, 855
[53] E. L. Elk1 and M . H. Giuniii. Tetrahedron Letters 1962, 97.
[54] E. L. Eliel and M . Rerick, J. Amer. chem. SOC. 82, 1367
[ 5 S ] E . L. Eliel and D. Nasipuri, J . org. Chemistry, in the press.
OA 1x2
equilibration between T (I2a) and C (12b), thermodynamically may almost be considered as an equilibration of T and C' so that the measured equilibrium constant Kepi leads directly to AG;. More exactly, we
have an equilibrium between T and (C + C'). Therefore
completely and is out of line with other values of
-AG& The difficulty here may be due to a strong
distortion of the cyclohexane ring, although this point
has not been clearly established.
C. The Kinetic Method
One of the earliest methods to assess conformational
equilibria, discovered independently in Winstein's
laboratory [17] and in the present author's [40] is based
on rate measurements. As suggested in formulae
(14 a) -( I4d), the reaction
of a mobile substituted cyclohexane may be looked at as
really being two reactions: that of the axial conformational isomer and that of the equatorial conformational
Unfortunately, although the method has been successfully applied to alkylcyclohexanes 154,561, complications
of various kinds [42,57] seem to prevent its application
to cyclohexanes containing more polar substituents.
Among other indirect equilibration methods, one which
seems to be quite widely applicable involves equilibration
(at C-5) of 3P-substituted 6-ketosteroids 1581. Since in a 3Psubstituted 5a-ketosteroid the 3-substituent is equatorial but
in the corresponding 5P-ketosteroid it is axial, equilibration
of the two ketones leads to the -AG"x value of the 36substituent after a correction is applied for the equilibrium
of the unsubstituted 5a- and 5P-ketosteroids.
In yet another interesting indirect equilibration method,
-AGOCO~CH, is correlated with - h G 0 c o 2 ~through
measurement of esterification equilibria [36].
Implicit in the application of the equilibration method,
e.g. to the process (8a) + (8b), is the assumption that
the 4-t-butyl substituent does not affect the position of
equilibrium. The only available justification for this assumption lies in the fact that -AG; determined by
the equilibrium method using either 4-t-butyl-substituted
models (8) or 1,3-disubstituted compounds of the type
(10) agrees with values obtained by other methods. In
the case of cyclohexanols, it has been found [59] that
-AG& determined by equilibration of the cis-3,Sdi-
( 1 4 ~ [El
( I r a ) , [A1
If the concentration of the axial conformer is [A] and its
rate constant ka, and if the concentration and rate
constant for the equatorial conformer are [El and k,, it
follows that
rate of reaction
ke[E] P
+ kafA1 P,
where P is the product of all other concentration terms
entering into the rate equation. Experimentally one
rate of reaction
k[C] P,
where [C] is the total concentration of the monosubstituted cyclohexane and k is the observed rate constant. It follows that
+ ka[A]
Remembering that
K = [EI/[Al,
one obtains
+ ka
This equation, in the form
methylcyclohexanols (13a) and (13 b) agrees perfectly
with the value (0.93 kcal/mole) derived from similar
equilibration of 4-t-butylcyclohexano1; the value of
1.23 kcal/mole derived from equilibration of the 3-tbutylcyclohexanols [42] on the other hand, disagrees
156) E. L. Eliel and T. J. Brett, Abstracts, 145th Meeting Amer.
chem. Soc., New York 1963, p. 19Q. See also [421.
[57] E. L. Elid and T.J. Brett, J. org. Chemistry 28, 1923 (1963).
[58] D . N. Jones and D . E. Kime, Proc. chem. SOC.(London)
1964, 334; see also J. F. Biellman and W. S. Johnson, Proc. nat.
Acad. Sci. U S . A. 53, 89 (1 965).
[59] E. L. Eliel and F. Biros, unpublished work.
k = (keK
k (K
+ 1).
+ ka)/(K + 1)
provides a heuristic relationship permitting evaluation
of the empirical-rate constant k in terms of the rate constants k, and k, for the pure conformational isomers and
the equilibrium constant K becween them. Alternatively,
the equation may be regrouped to give
and, in this form, may serve to assess the conformational
equilibrium constant K, if the rate constants k, ke and
ka are known. It is, of course, simple to determine k: it
Angew. Chem. internat. Edit.1 Vol. 4 (1965) 1 No. 9
is only necessary to provide a reaction suitable for the
substituent under consideration for which a convenient
rate measurement is available, e.g. saponification for
the ester group C02C2H5. The determination of k, and
k, is much more difficult in principle. Witzsfein has
suggested [ 171 that conformationally biassed systems
such as (3) will provide suitable models for the determination of k, [= ktrans,(3a)l and k, [= kcis, (3c)I;
thus the rate constant for the hydrolysis of ethyl trans4-t-butylcyclohexanecarboxylate is k, = 8 . 5 0 ~10-4
I.mole-1.sec-1; k, for the cis-isomer is 0.428 x 10-4
1.mole-1.sec-1 and k, the saponification rate of ethyl
cyclohexanecarboxylate is 7.25 x 10-4 1.mole-1.sec-1,
corresponding to
5.45 a t 25 "C
I .OO kcal/mole.
Although the equation
+ ka)j(K + 1) [401
or its equivalent
Nekef NaKa 1171
(N, and N, = mole fractions of the mobile compound
in the equatorial and axial conformations)
is rigorously correct, the hypothesis that k, and k, can
be measured using the appropriate 4-t-butyl analogues
is strictly an assumption, which, in turn, involves four
1) The 4-t-butylcyclohexyl compounds exist virtually
exclusively in the conformation with equatorial t-butyl.
2) The t-butyl group exercises n 3 polar effect on the
3 ) The t-butyl group exercises no steric effect on the
4) The t-butyl group does not distort either the ground
or transition state of the reaction or, if it does, at least
the distortion is compensated in such a way that the
activation energy is not affected.
Postulate 1 ) is well justified by the fact that the conformational energy of the t-butyl group is in excess of
4.4 kcal/mole [42]. Most substituents are small compared
to that and it is probably safe to assume, therefore, that
the 4-t-butyl-substituted molecules do, in fact, Exist in
conformations (3a) and (3c).
Postulate 2) (absence of polar effects) seems to be
justified by the similarity in pKa of cyclohexanecarboxylic acid (7.82 in aqueous dimethylformamide) and of
trans-4-t-butylcyclohexanecarboxylicacid (7.79). If
there were a major polar effect, it should certainly affect acidity. It must be said, however, that more extensive experimental data [60] suggest that substituents
at carbon atom 3 may, in fact, exercise some polar
effect, in contrast to those at C-4.
Postulate 3) (absence of dfmct steric effects) is best
justified on the basis of molecular models.
[60] H.van Bekkum, P. E. Verkade, and B. M . Wepster, Proc.,
Kon. nederl. Akad. Wetcnsch., Ser. B 64,161 (1961).
Angew. Chem. infernat. Edit. / Vol. 4 (1965)
/ No. 9
Postulate 4) (absence of distortive effects) is probably
a weak one; since transition states are of relatively high
energy, appreciable distortions are likely to occur in
them and, especially when the reaction occurs at the
ring itself (oxidation of alcohols, sN1 or sN2 displacement of cyclohexyl tosylates) the assumption that these
distortions affect the ground state and transition state
equally in the unsubstituted and 4-t-butyl-substituted
homologues may not be warranted. In fact, criticism has
been leveled at the kinetic method largely on this
ground [61] and it has been pointed out that an analysis
of activation parameters in the solvolysis of cyclohexyl
tosylates indicates that whereas the free energy of
activation of the unsubstituted compound is intermediate between that of the cis- and trans-4-t-butylsubstituted homologues, the same is not true of the
enthalpy and entropy of activation,and the success of
the Winstein-Holness (or Eliel-Lukach) relationship
therefore is, in this case, a fortuitous circumstance of
The difficulty in tosylate solvolysis is underscored by
recent studies [62] of secondary isotope effects in the
solvolysis of [2,2,6,6-D4]-cyclohexyl tosylates and
brosylates [*I. These studies have been interpreted to
indicate that the cis-4-t-butyl-substituted compound
reacts through a chair-shaped transition state whereas
the trans-isomer reacts through a boat-shaped transition
state; most surprisingly, the unsubstituted compound
seems to react through a boat-shaped transition state
also. Complications have also been found in the reaction of cyclohexyl tosylate and its cis- and trans-4-tbutyl analogues with thiophenolate [63]; whereas the
overall rate constant of the unsubstituted compound
(1 8.8 x 10-5 1.mole-lsec-1)
is appropriately intermediate between that of the 4-t-butyl-substituted
prototypes (cis: 7 3 . 4 ~10-5; trans: 1 . 7 2 ~lO-5), the
fraction of elimination (as compared to substitution) is
g r e a t e r (0.60) for the unsubstituted compound than
either for the cis- (0.45) or trans- (0.39) 4-t-butylsubstituted one.
Complications of this type are probably exacerbated in
the (high-energy) transition states and are therefore
more serious in the kinetic method than in other methods; nevertheless, the kinetic method, using 4-t-butylsubstituted models, gives -AG values in accordance
with those obtained by other methods so frequently that
it appears to be more than a matter of coincidence. As
in the case of the equilibrium method, the same is n o t
always true when one uses 3-substituted models which
suggests, once again, that any distortion which occurs
in the monosubstituted cyclohexane also occurs in the
4-t-butyl- or other 4-alkylcyclohexanes but not necessarily in a 3-alkylcyclohexane. Some pertinent data from
recent work [59] are shown in Table 2; clearly the
acetylation rates of variously substituted cyclohexanols
[ * ] Tosyl = p-toluenesulfonyl; brosyl =p-bromobenzene-sulfonyl.
[61] H. Kwart and T.Takeshita, J . Amer. chem. SOC. 86, 1161
(1964); see also W. Hiickeland M . Hanack, Liebigs Ann. Chem.
616, 18 (1958).
[621 V . J . Shiner and J . Jewett, J. Amer. chem. SOC.87, 1382,
1383 (1965); W. H. Saunders and K . T . Finley, ibid. 87, 1384
[631 E. L. Elid and J . W e s t , unpublished observations.
of analogous conformation are not constant and it
turns out that a value for AGgAcconsistent with other
values in the literature may be obtained from the 4-tbutyl-substituted i n ~ i e l but
s not, for example, from the
cis-3,5-dimethyl-substituted models (which would give
= 0, an unreasonable value).
Table 2. Rate constants for the acetylation of substituted cyclohexanols
a t 25 O C I591. Acetylating agent: acetic anhydride/pyridine. The rate
constant for the acetylation of cyclohexanol is k
8.6:. 10-5 I.rnole-1.
sec- 1 .
k'/ 105
[l.rnole -J.sec-I]
Equatorial alcohols
Axial alcohols
Apart from the intrinsic difficulty involved in the kinetic
method there is a technical difficulty which is evident
from the case of ethyl cyclohexanecarboxylate given
earlier. If k is close to either ke or ka, either the numerator or the denominator in the equation yielding K will
be a small difference of large numbers and the accuracy
of K thus determined will be low. In general, this difficulty arises when the monosubstituted cyclohexane
exists extensively in the equatorial conformation (ie. if
the substituent is relatively large) since in that case k
will be close to k,; the ethoxycarbonyl group is an
example. Clearly, better results would be obtained in a
system where k is nearly midway between ke and ka.
Formulae ( I S a ) and (1Sb) show such a system; here
the ethoxycarbonyl group is counterpoised by the
methyl group [*I and equilibrium will lie near 50: 50.
From the saponification rate constant for this system
(k = 2.65 x 10-4 1-mole-1sec-1) one may readily compute
the equilibrium constant
K = (ka-k)/(k-ke)
whence A G O for this system is +0.57 kcal/mole. Assuming now additivity of conformational free energies
(see Section VI for the limitations of this assumption)
one has
AG'co~c~H.- Xi
[ *] A group c f this type is called a "cotiformation-rcstorinF
group" by J. Siche?-(personal communication; see also ref. 181I).
AG'co~c,H~ = AG'I t AG'cH;.
Taking AGLe as -1.7 kcal/mole, this gives
~ G ' C O ~=
C 1.13
~ H kcaliinole
in very good agreement with the values given earlier.
Some reflection will show that, with AG& = -1.7
kcal/mole, cis-4-methyl-substituted cyclohexanes will
give more accurate conformational energies than monosubstituted cyclohexanes when the conformational
energy is in excess of 0.85 kcal/mole. Some conformational energies obtained by the kinetic method, e.g. that
for the amino group in protic solvents [33], could not
have been obtained without resorting to the cis-Cmethylsubstituted model.
A n approach similar t o the kinetic method but using
equilibrium constants instead of rate constants (K = N e K e
N a K a , where K, Ke, a n d Ka a r e equilibrium constants for
appropriate chemical equilibria for monosubstituted and
trans- a n d cis-4-t-butyl-substituted compounds) has also been
used occasionally; t h e derivation of - A G " c o z ~from p K
d a t a (in essence dissociation equilibrium constants) described
in the next Section is of this type.
D. Physical Methods
Since a number of physical properties of substituted
cyclohexanes are affected by the equatorial or axial position of the substituent, physical measurements can, in
turn, be used to infer conformation. Thus electrm diffraction studies have been used to ascertain the position
of conformational equilibrium in chloro- [64] and
fluorxyclohexane [65]; and the conformational equilibrium of cylohexanes carrying carboxy and carboxylate grmps 136, 60 661, amino, dimethylamino. ammonium, and dimethylammonium groups [67], and
mercaptan and mercaptide groups [68] have been
deduced from pK measurements. Measurements of
dipole moments served in the assignment of conformation to trans-l,2-dibromocyclohexane[69] and the 2halogenocyclohexanones [70]; optical rotatory dispersion 1711 and ultraviolet 1721 measurements have
also been applied to the latter compounds. Kerr con[64} Y. A. Atkinson, Acta chem. scand. 1.5, 599 (1961).
[65] P. Andersen, Acta chem. scand. 16, 2337 (1962).
[66] R. D. Stolow, J . Amer. chem. SOC.81, 5806 (1959); M.Tich.P,
J. Jonuf, and J . Sicher, Collect. Czechoslov. chem. Commun. 24,
3434 ( I 959).
[67] J.Sicher, J . JonaS, and M . Tich.6,Tetrahedron Letters 1963,825.
[68] H . Boaz, unpublished observations; cf. B. P . Thill, Ph. D.
Thesis, University of Notre Dame, 1964.
[69] W . Kwestroo, F. A. Meijer, and E. Havinca, Recueil Trav.
cliim. Pays-Bas, 73, 717 (1954); K. Koziina, K. Sakashita, and
S. Mae&, J. Amer. chem. SOC. 76, 1965 (1954); P. Bender, D. L .
Flowers, and H . L. Goering, ibid. 77, 3463 (1955); E. C. Wessels.
Doctorate Dissertation, University o f Leiden, Wetherlands, 1960.
1701 a) W. D. Kuni/er and A . C. Huitrir, J . Amer. chern. SOC. 78,
3369 (1956); b) N . L. Allinger, J. Allinger, L. A . Freiberg, R . F.
Czaja, and N . A . LeBel, J. Amer. chern. SOC. 82, 5876 (1960);
c) A. S. Kende, Tetrahedron Letters 1959. No. 14, p. 13.
[71] C. Djerassi, L. E. Geller, and E. J . Eisenhraun, J. org.
Chemistry 25, I (1960).
I721 J. Allinger and N . L. Allinper, Tetrahedron 2, 64 (1958);
N . I-. Allinger and J . AIlinger, J. Amer. chem. SOC.80,5476 (1958);
see also ref. [7Ob].
Angew. Chem. interiicrt. Edit.
1 Vol. 4 (1965) 1 N o . 9
stant measurements have been utilized [71] in the determination of conformational equilibrium in bromocyclohexane but seem to be less reliable than other
physical methods.
Whereas these methods are limited in applicability to
special cases, two fairly general methods of conformational assignment are available in infrared and nuclear
magnetic resonance spectroscopy. The infrared spectrum of a substituted cyclohexane C ~ H I I X
in general
varies with the equatorial or axial nature of the substituent X. In particular, if bands can be assigned to the
C-X stretching freqoenzy, equatorial C-X will be
found at higher frequency (by 10-55 cm-1) than axial.
In a mobile system, e.g. ( l a ) + ( l b ) , because of the
oneration of the Franck-Condon principle (time of
vibrational transition
time of conformational interconversion), axial and equatorial C-X stretching
frequencies will both be found and the ratio of intensities
of the equatorial and axial C-X stretching band will
devend on the conformational equilibrium constant K.
Two methods are available to obtain K quantitatively
from infrared data.
a) In one, the temperature is varied and the ratio of
extinctions (integrated band intensities) of the equatorial
and axial C-X stretching bands, A,/A,, is determined
as a funclion of temperature. Then, assuming that the
extinction coefficients for the axial and equatorial
stretching bands d o not vary with temperature and applying the vant'Hoff relationship, one may deduce [74]:
RT1Tz[ln(AdAdT2-ln (Ae/Aa)T,l/[Tz -TI]
Unfortunately, since AH is generally not very large (less
than 1 kcal/mole for most polar substituents), the band
intensity ratio changes rather slowly with temperature
and application of the above method requires large
temperature intervals and accurate measurements of
band intensity. As a result, the method is not experimentally very attractive and has been used relatively
infrequently .
b) In principle, one could deduce conformational
population ratios and, hence, free energies directly from
band intensities if one knew the extinction coefficients,
The temperature-dependent infrared method as applied
to cyclohexanols [78] gives a value of 0.31-0.41 kcal/
mole for AH '. This value may n o t . however, be too
low, since ASo for OH is probably not zero. If one assumes, in the extreme, that an equatorial hydroxy group
has three rotational conformations of equal energy,
whereas an axial hydroxy group has only two conformations of equal energy (the third conformation, with the
hydrogen pointing into the ring, being considered of
sufficiently higher energy to be disregarded), then the
entropy difference is Rln3 - Rln2 or 0.81 cal.mole-1.
degree-1 in favor of the equatorial isomer and
AGOOH = A H & - - T A S O ~ ~ {
would then be calculated to be 0.55-0.65 kcal/mole, in
good agreement with values obtained by other methods
in aprotic solvents.
Application of the second infrared method to chloro- [32a]
and bromocyclohexane [79] gives conformational energy
values (0.40 kcal/mole for the chloride, 0.46 kcal/mole for the
bromide) which are in good agreement with other values for
these atoms; the first infrared method (temperature dependence of intensities) gives reasonable AH values for chlorine
[78a,80] but a somewhat low value (0.2 kcal/mole) for
bromine [78a]; it seems unlikely that entropy differences
between equatorial and axial bromine could account for the
discrepancy in this case.
A particularly valuable and apparently reliable application of infrared spectroscopy consists in the measurement of the relative intensities of bonded and unbonded
OH-stretching frequencies in appropriately 2-substituted
cyclohexanols; this method has been used to assess the
position of conformational equilibrium in rvans-1,2cyclohexanediols and trans-2-amiriocyclohexanoIs (16)
where E, and za are the molar extinction coefficients for
the equatorial and axial C-X stretching mode, respectively. It has been suggested [75] that E, and za can be
measured from the intensity of the C-X stretching
bands in the canformationally homogeneous trans- and
models. For the moment, this
suggestion (which amounts to saying that the 4-t-butyl
group does not affect the extinction coefficient for the
C-X band, X at C-1) must remain an assumption, since
the method has not been applied extensively. In its first
application to cyclohexanol [75a] the method failed
[73] C. G. Le Fi.vre, R . J . W. Le F2vre, R . Roper, and R . K . PieProc. chem. SOC.(London) 1960, 1 17.
[74] Ref. 1141, p. 130, also ref. [Sb].
[75] a) R . A. Pickering and C. C. Price, J. Amer. chem. SOC.80,
4931 (1958); b) G. R . Haber, personal communication.
Auyrw. Cliem. inlernnt. Edit. } Vol. 4 (1965)
when the axial C - 0 stretch was considered, and even
application to the supposed equatorial C - 0 stretching
band [75a, 761 gave a range of conformational energies
for OH of 0.29-0.41 kcal/mole, well below the now
accepted value of 0.6 kcal/mole in solvents which are
not hydrogen donors. It has been suggested [77] that
the difficulty lies not necessarily in the method but in
the problem of discerning a pure equatorial C - 0
stretching frequency in cyclohexanol : presumably the
band at 1069cm-1 which was used has a skeletal
vibrational mode mixed in with it.
No. 9
1761 G. Clriurdoglrr and W. MrrJdreleiir, Bull. SOC. chim. Belges
69, 154 (1960); 70, 29 (1961).
[77] Anita H . Lewin, Ph. D. Thesis, University of California,
Los Angeles, 1963.
I781 a) G. Chiurdoglu, L . Kleiner, W . Massche/riri, and 1. Reissr,
Bull. SOC.chim. Belyes 69, 143 (1960); b) J . Massclielein, .I.
molecular Spectroscopy 10, 161 (1963).
1791 F. R. Jensen and L . H . Gale, J. org. Chemistry 25, 2075
[SO] K . Kozirrtrr and K . Snknshitn, Bull. chem. SOC. Japan 31,
796 (1958).
[81] J. Pit'liu, J . Siclier, I;. S i p o i , M . Ticli?:, and S . Va.itkovd,
Proc. cheni. SOC.(London) 1963, 301.
77 1
Nuclear magnetic resonance is one of the most powerful tools to give direct insight into both the structure and
stereochemistry of an organic compound. It is therefore
no wonder that the technique has been applied extensively in conformational problems - so extensively,
in fact, that its application forms the subject of a
separate review in this journal [82]. For this reason we
shall discuss here only one application of NMR - that
in determining conformational equilibria.
Axial and equatorial protons (similar principles apply to
other nuclei susceptible to NMR detection, such as
fluorine) generally differ in chemical shift of their NMR
signals by 20 -40 cps (at 60 Mc) if the chemical environment is otherwise the same. The signal of the axial
proton usually appears at higher field. Spin-spin splitting also differs between the two types of signals since
axial protons are subject to coupling with both adjacent
axial or anti (Ja,a M 9 cps) and equatorial or gauche
(J,,, = 3 cps) protons whereas equatorial protons
couple only with gauche protons. As a result, the halfwidth of an equatorial proton signal (ca. 7cps) is
appreciably less than that of an axial proton signal (ca.
22 cps). It might be expected, then, in analogy with the
situation in infrared spectroscopy, that a mobile cyclohexane system would show two signals for a given
proton (e.g. the >CHX proton in C ~ H I ~ Xone
) : for the
axial proton of the equatorial isomer and one for the
equatorial proton of the axial isomer. However, this
is not the case. Because the frequency interval between
the two proton signals is only about 30 cps, whereas the
rate of interconversion of the two chair forms is well in
excess of lo00 sec-1 at room temperature, the chair will
flip many times in the interval between an equatorial and
an axial transition and these transitions will therefore
merge into an average signal.
Nevertheless there are two ways in which NMR can be
utilized to establish conformational equilibria. It is
possible to slow down the equatorial-axial interconversion by lowering the temperature; at about -67 “C,
the rate of chair interconversion in cyclohexane is of
the same order of magnitude as the chemical shift between the signals of equatorial and axial protons and so
the original single peak will begin to split into two
separate peaks. (It is from the signal shape at temperatures near this “coalescence point” that the activation
parameters for chair-chair interconversion given earlier
have been obtained.) At temperatures much below the
coalescence point, two clearly divided peaks are found,
and from the areas of these peaks, the relative population of equatorial and axial conformations at the temperature in question may be directly computed. This method is theoretically sound but experimentally difficult for
two reasons: accurate NMR measurements at definite
temperatures much below room temperature are hard
to effect (because of difficulty in obtaining and measuring the temperatures required, because of viscosity
[82] H . Feltkamp and N . C. Franklin, a) Angew. Chem. 77, 798
(1965); Angew. Chern. internat. Edit. 4, 774 (1965); b) Liebigs
Ann. Chern. 683, 55 (1964).
[83] a) A. J. Berlin and F. R . Jensen, Chem. and Ind. (London)
1960,998; b) L . W. Reeves and K . 0 . Stremme, Canad. J. Chem.
38, 1241 (1960).
broadening of the signals, and because of solubility
problems) and the conformational equilibrium at the
low temperatures needed is biassed very much in favor
of the equatorial isomer (e.g. an equilibrium constant
of 4 at room temperature corresponds to one of 11 at
--I00OC,assuming AG to be temperature invariant).
Nevertheless the low-temperature NMR method has
been used with good results for halogenocyclohexanes
An experimentally simpler method is to base the
estimate of the conformational equilibrium on the
p o s i t i o n of the average proton signal at room temperature. This position will depend directly on the positisn
of equilibrium; in fact, it can be shown [84] that
where N, and N, are the mole fractions of axial and
equatorial conformers, as before, and v, and v, are the
shifts for salient protons (e.g. the > CHX proton) in
these conformers whereas v js the shift for the corresponding proton in the mobile system. Clearly, this
equation is entirely analogous to the Winstein-Holness
equation for rate constants (vide supra) and may be
transformed [53,85] into the form
In order to apply this equation to the evaluation of K,
it is necessary to establish the values of v, and v,. This
can be done in two ways, either bq effecting measurements at very low temperatures [83a, 861 where the
signals of the two conformations are separate, or by
using model compounds, such as 4-t-butyl-substituted
cyclohexanes, to fix the appropriate conformations
[32-34,53,85,87,88]. The use of such modelcompounds
now entails the assumption that the 4-t-butyl substituent does not affect the chemical shift. Contrary to
recent assertions [89], this assumption seems to be valid
for cyclohexanone dimethyl ketal and 4-t-butylcyclohexanone dimethyl ketal : the (average) signal of the
methyl groups in the former (-183.9 cps at 60 Mc) occurs, as exactly as the accuracy ot the measurements
permits one to say, exactly half-way in between the
(resolved) signals of the methyl groups in the latter
(-182.9 and -184.9 cps) [90]. Other data, concerned
with the shift of the carbinol proton signal in variously
substituted cyclohexanols [91], while inconclusive, are
not so encouraging as regards the complete absence of a n
effect of a 4-t-butyl group. The data for the pair chloro[84] H . S. Gutowsky and A . J . Saikn, J. chem. Physics 21, 1688
IS51 E. L. Eliel, Chem. and Ind. (London) 1959, 568.
[86] E. A . Allan, E. Premuzic, and L. W. Reeves, Canad. J. Chern.
41, 204 (1963).
[87] A . H . Lewin and S. Winstein, J. Amer. chern. SOC.84, 2464
I881 E. L. Elieland B . P . ThiN, Chem. and Ind. (London) 1963,88.
[89] M . Anteunis and L).Tavernier, Tetrahedron Letters 1964,
[90]E . L. Eliel, M . Gianni, and R . J. L. Martin, unpublished
[91] E. L. Eliel, M . Gianni, T. H . Williams, and J. B. Stothers,
Tetrahedron Letters 1962, 741.
A n g e w . Chem. internat. E d i t . 1 Vol. 4 (1965)
I No. 9
Table 3. Conformational equilibrium of chlorocyclohexane in carbon
system and the subscripts a and e refer to the axial and
equatorial models, respectively, then, in many cases :
X = NeXe f NaXa,
(--81 'C)
(-81 "C)
0.48 [a]
0.74 [b]
which simply means that the property of the mobile
system is the weighted average of the properties of its
constituent conf ormational isomers. It follows that the
desired equilibrium constant is
[a] Extrapolated value, unspecified process of extrapolation
[bl Raw value.
cyclohexane/4-t-butylderivative summarized in Table 3
indicate that though there is a shift, surprisingly, more
reasonable AG ' values are obtained from the data for
the 4-t-butyl compound than from the low-temperature
data on the unsubstituted compound.
One of the difficulties inherent in the N M R method lies in
the fact that the salient peaks are broad (due to extensive
coupling) making accurate measurement of signal position
problematic. This difficulty has been obviated t o a considerable extent by employing [2,2,6,6-D,&cyclohexanes (17)
in which the splitting is reduced by a factor of six [32b, 34,871.
An attempt [32a] to achieve the same end more simply by
employing double resonance (saturation of the ring protons
other than the ;CHX one) was unsuccessful since it was
found that the chemical shift of the signal of the ;CHX
proton depended o n the amount of RF-power used to
saturate the remaining protons; and while it was possible to
extrapolate a set of data obtained a t varying RF to zero RF,
the inaccuracy introduced by this extrapolation is of the
same order of magnitude as the inaccuracy in peak measurement in a simple NMR experiment.
It might be mentioned here that the most accurate measurements of the cyclohexane inversion barrier [271 similarly
While the spin-spin splitting would thus appear t o be a
nuisance in measurements of conformational equilibria, it
has, on the other hand, also been employed to assess such
equilibria [92,93]. The principle here is that just as the signal
position averages in a rapidly flipping substituted cyclohexane, so does the splitting, and if the splitting of both the
equatorial and axial conformers is known, the position of
conformational equilibrium may, in principle, be deduced
from the splitting in the mobile system. This method is
discussed in detail in the accompanying review [82].
E. S u m m a r y
In reviewing the methods availablc for determining conformational equilibria, one finds a certain amount of
unity in them. In most cases some property of the mobile
system (reaction rate, equilibrium constant, appropriate
physical property) is compared to a similar property of a
rigid or biassed system. IF X is the property of the mobile
[921 F. A . L. Anet, J. Amer. chem. SOC.84, 1053 (1962).
I931 a) H . Feltkamp and N . C. Franklin, J. Amer. chem. SOC.87,
1616 (1965); b) H . Feltkamp, N . C. Franklin, K . D.Thomas, and
W . Briigel, Liebigs Ann. Chem. 683, 64 (1965).
Angew. Chem. infernat. Edit./ Vol. 4 (196s) 1 No. 9
To obtain correct results it is necessary to select appropriate models to obtain the axial and equatorial
values Xa and X,. In many instances 4-t-butyl-substituted systems have been chosen for this purpose with
results which, in general, show a remarkable amount of
consistency. However, there is no inherent gclarantee
that the choice of such model systems is sound in all
cases. The only theoretically unobjectionable approach
is to use the mobile system itself and "freeze" it, either
by slowing the interconversion of conformational isomers at low temperatures (low-temperature NMR method) or by using a method which is inherently fast compared to the velocity of ring inversion (such as infrared
frequency measurements).
it is of interest that a method has recently been developed
[94] in which it is not necessary to determine the properties
Xa and Xe of the pure conformers but rather AH" is obtained
by measurement of the change of the averaged property X
(in the case cited, optical rotatory dispersion amplitude)
with temperature. The accuracy and generality of this
method remain to be established.
VIII. Future Work
It may be well (if risky) to conclude this brief review on
conformational analysis in mobile systems by trying to
foresee likely future problems (in the absence of any
fundamental new breakthroughs).
On the theoretical side, it is likely that the availability of
more accurate data on van der Waals radii from molectllar beam experiments on one hand and the increasing
availability of high-speed computers on the other will
lead to more accurate calculations of conformational
equilibria in a variety of systems.
In a semi-theoretical area, it is likely that an increasing
number of assessments of AH" and ASo (as distinct
from A G O ) will be made and that, in the process, a better
understanding of entropy differences between equatorially and axially substituted cyclohexanes will be gained. A
word of caution is in order in this connection: since the
thermodynamic differences between conformational
isomers are in general quite small, accurate measurements of AH" and AS" will be difficult. It is deceptively
easy to obtain such data from measurements of AGO
at two temperatures, and, no doubt, a number of data
will be turned out in this way and later found to be
wanting. Reliable measurements of conformational
AH"s and AS'S will probably require a c c u r a t e
equilibrium measurements at at least four and possibly
[94] A . Moscowitr, K. Welleman, and C. Djerassi, J. Amer.
chem. SOC. 85, 3515 (1963).
as many as six different temperatures over a range of
preferably not less than 100°C. In any case, a careful
error treatment is called for in publications of such data.
On the more practical side, we may look forward to see
measurements on additional groups (such common
groups as -CHO, -COR, -CH=CH2 have not yet had
AG '-values assigned to them). New methods, such as
that based on measurement of the chemical shift of the
OH NMR signal [46] may be expected to be devised.
A more careful study of the solvent dependence of a
number of conformational equilibria, especially those
involving polar and hydrogen-bonding groups, may be
looked forward to. Conformational equilibria of disubstituted cyclohexanes (1,l- as well as 1,2-, 1,3- and
1,4-disubstituted ones) will be siudied to test additivity
relationships in AG (vide supra).
One very large area which has barely been scratched is
that of conformational equilibria in heterocyclic
systems. There has recently been much interest in the
conformation of the basic piperidine and N-methylpiperidine systems [95] with the finding that the unshared electron pair is smaller than hydrogen and much
smaller than a methyl groug. Nothing is known yet on
C-substituted piperidines and only a limited amount of
information has been brought to bear on tetrahydroI951 N . L. Allinger and J . C.Tai, J. Amer. chem. SOC. 87, 1227
(1965); N . L . Allinger, J . G. D. Carpenter, and F. M . Karkowski,
ibid. 87, 1232 (1965); R. J. Bishop,L . E. Surton, D. Dineen, A. Y .
Jones, and A . R. Katritzky, Proc. chem. SOC. (London) 1964,257;
K. Brorvn, A . R. Katritzkv, and A. J . Waring, ibid. 1964, 257.
pyrans [96] - the parent skeleton of the pyranose
sugars - and 1,3-dioxanes [97a]. A number of heterocyclic systems have been considered only from the point
of view of the chair-chair interconversion barrier [97b,
981 if at all and there is obviously much scope for further
work in this area. Chemists interested in the behavior
of natural products, such as sugars, will no doubt continue to consider the conformational implications in
these systems; some studies on hexopyranoses and
cyclitols [99] are already at hand.
The author wishes to acknowledge with pleasure the stimulation and ideas derived from many conversations with
colleagues and coworkers as well as financial support of'
his research by the Petroleum Research Fund of the
American Chemical Society, the National Science
Foundation ( U S A . ) , the Office of Ordnance Research,
U.S. Army, and the U S . Air Force Office of Scientific
Research. Special thanks are due to Dr. J . Sicher whose
detailed and constructive criticism has been most helpful
in the preparation of this manuscript.
Received: June 3rd, 1965
[A 464/241 I € ]
German version: Anpew. Chem. 7 7 , 784 (1965)
1961 J.T. Edwardand I. Puskas, Canad. J. Chem. 40, 71 I (1962);
C. B. Anderson and D. T. Sepp, Chem. and Ind. (London) 1964,
2054; E. L. Eliel and C . Glza, unpublished observations.
1971 a) E. L. €lie/ and C. Knoeber, unpublished observations;
b ) H . Friebolin, S. Kabuss, W . Mnier, and A . Liittringlinrfs. Tetrahedron Letters 1962, 683.
[98] Ref. 1121, p p . 248-252.
[99] Ref. [12], Chapter 6.
Conformational Analysis of Cyclohexane Derivatives by Nuclear Magnetic
Resonance Spectroscopy
Nuclear Magnetic Resonance is today one of the best methods available for the conformational analysis of cyclohexane derivatives. It is possible with this technique to investigate the
spatial orientation of the substituents in fixed molecules, as well as the equilibrium positim
in mobile systems. For these determinations the areas under the signals, the chemical shifts,
the coupling constants, and the band widths of particitlar signals can be used.
I. Basic Principles
1. Energetic Considerations
In a flexible molecule, the individual groups of atoms
can take up different positions with respect to each
other. Arrangements which differ from one another by
rotations about single bonds are known as the conformations of the molecule. In most cases only a very small
amount of energy is required in order to move the molecule from one conformation into the other, and for this
reason one is often dealing with mixtures, in which many
conformations may be in equilibrium with each other.
The cyclohexane system is particularly suitable for
studies of conformational equilibria, as it possesses two
favorable conformations, which correspond to the two
chair forms of cyclohexane. These two forms can interconvert, but a relatively high energy (about 11 kcal/mole>
is required to overcome the torsional rigidity and also to
change the bond angles during the intermediate states.
During this interconversion, cyclohexane passes
through an energy minimum (ca. 5.0 kcal/mole),
known as the twist (or skew) form [l], which is
however considerably above the energy level of the two
[ l ] W . S. Johnson, V. J. Bauer, J . L. Margrave, M . A. Friscl~,
L. If. Dredger, and W . N . Hubband, J. Amer. chem. SOC. 83, 605
Angew. Chem. internnt. Edit.
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