Chapter 4 Worked Problem 1

Steric Strain in Cyclohexanes

There are 7 isomers of dimethylcyclohexane. Rank them in order of increasing strain.

Analysis. Identify the seven isomers first. Place one methyl group on cyclohexane; then the possibilities for the second are:

On carbon-1: 1,1-dimethylcyclohexane.
On carbon-2: cis or trans-1,2-dimethylcyclohexane
On carbon-3: cis or trans-1,3-dimethylcyclohexane
On carbon-4: cis or trans-1,4-dimethylcyclohexane

Now, draw each of these in a chair conformation and consider BOTH ring-flip isomers:

From these, estimate the magnitude of the steric strain based on the fact that placing a methyl group in an axial orientation costs 1.8 kcal/mol versus it being equatorial. This provides an initial estimate of strain. Making models is a smart thing to do to help see everything. Then find the amount of strain in the LESS-strained ring flip isomer.

1,1-dimethylcyclohexane: Both ring flip isomers identical: +1.8 kcal/mol.
cis-1,2-dimethylcyclohexane: Both ring flip isomers identical: one axial methyl group = +1.8 kcal/mol. There is a gauche interaction between the two methyl groups that raises this by 0.9 kcal/mol (see Chapter 2.)
trans-1,2-dimethylcyclohexane: Diaxial form would be 2x+1.8 kcal/mol = +3.6 kcal/mol, but the diequatorial form would be 0. However, we should add a little bit back because the two methyl groups are gauche to each other (this is about +0.9 kcal/mol--see Chapter 2.)
cis-1,3-dimethylcyclohexane: The diaxial form would be more than 2 x 1.8 kcal/mol, because the two methyl groups would run into each other (rather than just into an axial hydrogen). The diequatorial form would have no steric interactions, so it would have a strain energy of 0.
trans-1,3-dimethylcyclohexane: Both forms identical, with one axial methyl group. +1.8 kcal/mol.
cis-1,4-dimethylcyclohexane: Both ring flip isomers identical: one axial methyl group = +1.8 kcal/mol.
trans-1,4-dimethylcyclohexane: The diaxial form would be 2 x 1.8 kcal/mol = +3.6 kcal/mol; the diequatorial form would have no interactions and be 0.

So, the order in increasing strain is predicted to be:
trans-1,4-dimethylcyclohexane = cis-1,3-dimethylcyclohexane = 0
trans-1,2-dimethylcyclohexane = +0.9 kcal/mol
trans-1,3-dimethylcyclohexane = 1,1-dimethylcyclohexane = cis-1,4-dimethylcyclohexane = 1.8 kcal/mol
cis-1,2-dimethylcyclohexane = 2.7 kcal/mol

The values calculated based on computational modeling are:

trans-1,4-dimethylcyclohexane E_rel = 0
cis-1,3-dimethylcyclohexane E_rel = 0
trans-1,2-dimethylcyclohexane E_rel = +0.56 kcal/mol The gauche effect isn't quite as big as predicted, but still evident.
1,1-dimethylcyclohexane E_rel = +0.69 kcal/mol This is the oddball since we predicted it to be +1.8 kcal/mol; there is something called the "Thorpe-Ingold effect" that stabilizes geminal dimethyl groups. Discussion of this is beyond the scope of this course.
trans-1,3-dimethylcyclohexane E_rel = +1.69 kcal/mol
cis-1,4-dimethylcyclohexane E_rel = +1.76 kcal/mol
cis-1,2-dimethylcyclohexane E_rel = +2.32 kcal/mol Again, the gauche effect is a little smaller than expected but still evident.

(M06/cc-pVTZ, Spartan'14, Wavefunction, Inc., Irvine, CA)