Diaxial (larger view)

Diequatorial (larger view)

(How to manipulate JSmol structures)

 

The diaxial conformation of cis-1,3-dimethylcyclohexane, or any cis-1,3-disubstituted cyclohexane for that matter, cannot be calculated by A-values alone. While each axial methyl group has four gauche interactions (3.6 kcal/mol) (think of each axial methyl group as a component of axial methylcyclohexane), there is also an interaction between the substituent axial methyl groups. This interaction is similar to the interaction between the methyl groups in diequatorial trans-1,2-dimethylcyclohexane. This interaction is worth 2.0 kcal/mol. Thus, the total energy of the diaxial conformation is ~5.6 kcal/mol. The equilibrium mixture is greater than 99.99% diequatorial. The five atoms blue-green-green-green-blue form a syn-pentane interaction. The syn-pentane interaction is the highest energy conformation for n-pentane itself. Needless to say, diaxial cis-1,3-dimethylcyclohexane is exceptionally unstable and will conformationally invert to the diequatorial conformer. The diequatorial conformation on the right has both methyl groups equatorial and they do not interact with each other. Therefore, the energy of this conformation is taken as 0 kcal/mol. Note that the atoms red-green-green-green-red are in a low energy zig-zag conformation of pentane.