Overview

In this lesson, we delve into the role of ring conformation and its stability, which determines the spatial arrangement and, consequently, the molecular symmetry and stereoisomerism of cyclic compounds. 1,2-Dimethylcyclohexane is used as a case study to evaluate the possible number of stereoisomers. Here, given the multiple (n = 2) chiral centers, there are 2ⁿ = 4 possible configurations that lack a plane of symmetry, as the ring skeleton exists in a non-planar chair conformation. In addition, the potential for ring-flipping in a cyclohexane ring entails that each of these four possible configurations could further exist as a mixture of two or more conformations.

The effect of conformational flexibility in a ring system on the number of possible stereoisomers is shown using a case study of cis and trans configurations of 1,2-dimethylcyclohexane. While the cis configurations are chiral molecules (non-superposable mirror images) with the enantiomers as potential distinct stereoisomers, the rapid ring-flipping at room temperature renders these configurations interconvertible and inseparable. Accordingly, they represent conformations of the same molecule. On the other hand, the trans isomers are chiral molecules that cannot be superposed by rotation of the molecule or ring-flipping and exist as unique compounds. This proves the presence of three stereoisomers for the chosen example—the cis isomer and the pair of trans enantiomers.

This is further elucidated using another ring structure with a difference of substitutional position: 1,3-dimethylcyclohexane. The cis configuration is achiral due to a molecular plane of symmetry. Consequently, the system with two chiral centers exhibits three stereoisomers—the two trans non-interconvertible enantiomers and an achiral cis configuration. In essence, when a ring structure is evaluated, the two aspects that need to be studied are the ring-flipping and the plane of symmetry to determine the possible number of stereoisomers.

Procedure

Recall that in cyclic compounds, such as cyclohexane, the conformation of the ring predominantly determines the spatial arrangement of the constituent atoms. As such, the conformational stability of the ring influences the molecular symmetry as well as the stereoisomerism of cyclic compounds.

Consider the case of 1,2-dimethylcyclohexane, a disubstituted cyclohexane with two chiral centers and four possible configurations. Here, each configuration lacks a plane of symmetry, as the cyclohexane ring exists in the non-planar chair conformation.

Furthermore, the cyclohexane ring in these molecules can easily undergo ring-flipping at room temperature. As a result, each of the four possible configurations of 1,2-dimethylcyclohexane may exist as a mixture of two or more conformations.

This conformational flexibility of the cyclohexane ring affects the number of possible stereoisomers of 1,2-dimethylcyclohexane.

For instance, the cis configurations of 1,2-dimethylcyclohexane have conformations that are enantiomers of each other. 

However, ring-flipping followed by a 180-degree rotation transforms one configuration into another. Therefore, these configurations simply represent conformations of the same molecule.

The trans isomers of 1,2-dimethylcyclohexane also have conformations that are enantiomers of each other.

These configurations cannot be superposed by rotation of the molecule or by undergoing a ring flip. Accordingly, each trans isomer of 1,2-dimethylcyclohexane exists as a unique compound.

Thus, 1,2-dimethylcyclohexane exhibits three stereoisomers: the cis-1,2-dimethylcyclohexane and the pair of enantiomers of trans-1,2-dimethylcyclohexane.

Similarly, 1,3-dimethylcyclohexane has two chiral centers but only exhibits three stereoisomers. Here, the two trans configurations are enantiomers of each other that cannot be interconverted. The other pair, the cis configurations, have a plane of symmetry and are achiral; that is, they are the same molecule.