T-Butyl Cyclohexane

From WikidChem

Axial Methylcyclohexane (aka T-butylcyclohexane)

When the methyl group is perfectly axial (parallel to the 3-fold axis), the molecule has a total energy of 16.55 kcal/mol. Though there is no stretch or bend energy in this molecule, there is torsion and significant vanderwaals repulsion.

When the molecule relaxes, the formerly axial groups (such as methyl) rotate outwards slightly - becoming a little bit more equatorial. The total energy decreases to 8.66 kcal/mol because the van-der-waals repulsions decrease dramatically.

Here, McBride made the point that strain concentrates in weak "springs" (aka "bonds") because they deform more. This is because strain energy is the product of force times distance. The distance over which a force can act on a weak spring is greater than the distance over which a force can act on a strong spring.

One can view axial-methylcyclohexane as being composed of 8 gauche butanes. The slide highlights one such butane in red. Look at this as if the bond between the Carbon labeled 13 and the Carbon labeled 11 goes into the plane of the page. From this perspective, the Carbon labeled 3 protudes from Carbon 13 at 10 o'clock, while the Carbon labeled 14 protrudes from Carbon 11 at 12 o'clock. This is a gauche butane.

When the methyl group becomes equatorial, it now protrudes at 4 o'clock from Carbon 11. This is now an anti butane (4 o'clock is directly opposite from 10 o'clock).

The energy for CH3 to change from axial to equatorial is consequently 1.8 kcal/mol, twice the energy change from gauche to anti conformation. The 2 derives from the fact that 2 of the 8 gauche butanes are affected when CH3 changes position.