In the past, chemists believed that cycloalkanes, including cyclohexane, were planar, like benzene (see below). Since the ∠C-C-C bond angle of sp3 hybridized carbon chain is 109o28', cycloalkanes will suffer from some strain if these are to be planar. All cycloalkanes, except for cyclopentane, become unstable because of this strain (Baeyerﾕs strain theory). According to this theory, the most stable cycloalkane is cyclopentane, and cyclohexane is the next.
Although this theory could explain the high reactivity of cyclopropane,
it gradually turned out that cyclohexane could be more stable
if the nonplanar structure was assumed. By taking the nonplanar
structure, the ∠C-C-C bond angle of cyclohexane could maintain
the tetrahedral angle. Because of the cyclic nature, the number
of structures cyclohexane can take is much less as compared with
its acyclic analog hexane. There is, however, flip-flop of the
ring as the rotation about the C-C bond of cyclohexane takes place.
The movement of the ring can most conveniently revealed by the
torsion angle made by four successive carbon atoms (butane unit)
arbitrarily chosen. If we choose C1~C4 (1) as the butane
unit, the torsion angle can be defined as is shown in 2.
You should confirm the discussion above by using a molecular model.
If the torsion angle-energy diagram for C1～C4 "butane unit" of cyclohexane is essentially identical with that of butane (Fig. 2.4), the staggered form 3 (which is referred to as "butane gauche form") should be more stable than the eclipsed form 4. If a given cyclohexane contains six butane-gauche units, it should be the most stable conformer in which all bond angles are tetrahedral.
The conformer of cyclohexane 5
or 5’is named chair form,
which is the most stable one.
There is another conformer of cyclohexane 6 or 6’in
which all bond angles are tetrahedral. This conformer is named
boat form.
go to S4.1 Cyclohexane: chair form and boat form.
Now let us pay attention to twelve hydrogen atoms of cyclohexane. Of the two C-H bonds from each carbon atom, one is perpendicular to the pseudo-plane made by six carbon atoms, and the other parallel to it. If we admit that cyclohexane resembles the earth, the chain of six carbon atoms may be accepted as the equator. Based on this analogy, the C-H bond perpendicular to the equator (hence parallel to the axis of the earth) is named an axial bond, and that parallel to the equator to an equatorial bond. An atom or a group of atoms bonded to the these bonds are referred to an axial atom (group) or an equatorial atom (group), respectively.
there are two way of writing a cyclohexane in the perspective view. In one way, the C2-C3-C5-C6 plane is horizontal (as 5). This way is advantageous when comparison with a boat form is attempted. In the other way, the C2-C3-C5-C6 plane is slightly tilted so that the axial bonds are perpendicular (as 9). This method is convenient when the differentiation between axial and equatorial is important.
The relation between a chair cyclohexane and a boat cyclohexane can most conveniently examined with the aid of a molecular model (Fig. 4.1). If you lift up the leg of 11 (i.e., C1) gently, you will obtain a boat cyclohexane 12 (process i). You will notice that the rotation about C-C bonds takes place at the same time. This chair-boat interconversion is referred to as the ring inversion of cyclohexane. This phenomenon is a type of chemical exchange.
In addition to process (i) (11→12), there is
another process (v) with equal probability to lead the other boat
form (11→14). The boat form 12 can be reconverted
to 11 by pulling down the bow (or the stern) (C1)
(process viii)or converted to another chair 13 by pulling
down the stern (or the bow) (C4) (process
ii).
The second chair 13 can be converted to the boat 14
by pulling down the support C1 (process iii) or to the boat 12
by lifting up the leg C4 (process vii). The
boat form 14 can similarly be converted to two chairs 11
or 13 (processes iv and vi). Since the energy barrier of
the boat �ﾌ chair interconversion is low, the process
Q4.6 takes place easily.
In the case of cyclohexane, the two chair forms 11 and 13 obtained by the ring inversion were proved identical as far as the shape of carbon skeleton is concerned. Can we say, however, that these two are strictly identical? Our belief will waver if we make a chair form with six axial hydrogen atoms 15. By inversion you notice that the second chair form 16 has six equatorial hydrogen atoms rather than six axial hydrogen atoms. Similarly, a chair form with six equatorial hydrogen atoms 17 is converted to the second chair form with six axial hydrogen atoms 18.
A chair form of cyclohexane is not converted to the exactly identical chair form. If we neglect hydrogen atoms, 11 and 13 are identical. However, 15 or 17 are not identical with 16 or 18 if hydrogen atoms are taken into consideration. If we can differentiate axial hydrogen atoms from equatorial hydrogen atoms, cyclohexane 19 is not identical with cyclohexane 20 which is formed from 19 by ring inversion. This fact will more clearly demonstrate when we learn substituted cyclohexanes.
go to S4.2 Ring inversion of cyclohexane
Methylcyclohexane, which is obtained by replacing one of the hydrogen atom of cyclohexane with a methyl group, is a very intriguing compound. The two chair forms of methylcyclohexane are not identical as is the case with cyclohexane itself. The equatorial methyl derivative 21 and the axial methyl derivative 22 form a pair of stereoisomers (Fig. 4.3)
Two chair forms of cyclohexane 11 and 13 are
identical, but two chair forms of methylcyclohexane 21
and 22 are stereoisomers. Then, how we can characterize
the difference between 21 and 22? Let us return
to cyclohexane and examine twelve hydrogen atoms preferably with
the aid of a molecular model. The interatomic distances among
three axial hydrogen atoms bonded to C1,
C3 and C5 are relatively
short. If one of the three hydrogen atoms, e.g., the hydrogen
atom bonded to C1, is substituted by a large
group such as a methyl, the distance between the methyl group
and the axial hydrogen atoms bonded to C3
or C5 become much shorter to generate severe
interaction. This will make the energy of the axial methylcyclohexane
higher than that of the equatorial one and this interaction is
referred to as 1,3-diaxial interaction.
go to S4.4 1,3-diaxial interaction
If we neglect the ring inversion, or if we assume the conformers
are averaged by ring inversion, there is only one isomer for methylcyclohexane.
If we do not neglect the effect of ring inversion, there are two
isomers for methylcyclohexane, axial and equatorial isomers. Thus,
the number of isomers of substituted cyclohexanes will vary whether
or not the ﾒaveragingﾓ by the ring inversion is taken into consideration.
If we admit averaging of cyclohexane ring by inversion, we need
not worry about the chair and boat forms of cyclohexane. Cyclohexane
may be regarded as a planar molecule. Methylcyclohexane can be
written as 25 or 26. We may differentiate the upper
and lower sides of the plane, but this procedure is to admit that
one side is the axial side and the other equatorial side.
If we admit averaging, there is one isomer 27 for 1,1-dimethylcyclohexane, and there are two isomers 28 and 29 for 1,2-dimethylcyclohexane. 28 is the cis isomer and 29 is the trans isomer.
1,1-dimethyl 1,2-dimethyl
However, if the averaging by ring inversion is not accepted, or if 21 and 22 of methylcyclohexane are regarded as isomers, the situation will be different. The case of 1,1-dimethylcyclohexane is rather special. For this compound, the number of isomers is one whether or not the averaging is accepted. By ring inversion 27ae is converted to the identical molecule 27ea (for notation see below).
The situation is different for 1,2-dimethylcyclohexane. There are two trans isomers; one with two equatorial methyl groups (34ee; hereafter designated as 1,2-ee), which, by ring inversion, turn into the other isomer with two axial methyl groups (34aa). 34ee and 34aa are different compounds in the same sense that 21 and 22 are different compounds. Hence the population should not be 1 : 1, and it is expected that 34aa has much larger energy due to the double 1,3-diaxial interaction of two axial methyl groups, and the equilibrium below should largely be shitted to the left side.
How about the cis isomer? How 35ea is related to 35ae? As for the conformation of methyl groups is concerned, the two compounds have the same stereochemistry and hence the same energy. The equilibrium below should be 1 : 1. Detailed analysis of the structure of two compounds with the aid of a molecular model will reveal an important point. This point will be discussed later.
Among cycloalkanes CnH2n, all of these with C = 3～5, that is,
cyclopropane 42, cyclobutane 43 and cyclopentane
44, have ∠C-C-C bond angle deviated from the tetrahedral
angle.
Cyclopropane 43 has a high chemical reactivity, but its
ring is rigid and there is no ring inversion. For 1,2-dimethylcyclopropane,
there are two stereoisomers.
For instance, 1,2-dimethylcyclopropane has two isomers, the cis isomer 45 and the trans isomer 46.
For many years cyclobutane 43 was regarded as a square molecule. It is now known that at least in the gas and liquid phase, 43 has a folded structure, and consequently a ring inversion 43a �ﾌ 43b, similar to that of cyclohexane, takes place.
Cyclopentane 44 is also nonplanar molecule, and like cyclobutane, it has a folded, envelop type structure 52 or half-chair structure 53. For 52, there is no flip-flop of the triangle part, and instead, a process in which the carbon at the tip of the triangle alternate one after the other. In the envelope form, four carbon atoms, and in the half-chair form, three carbon atoms define a plane.
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