4.4 Substituted cyclohexanes
4.4 Substituted cyclohexanes
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 averaging 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.
