Conformational Energies

CONFORMATIONAL ENERGIES

The energetic consequences of chair – chair interconversions in substituted cyclo-hexanes are related to the interconversion of axial and equatorial valences. Because axial groups undergo 1,3 diaxial interactions which increase the energy of the molecule, the obvious energy preference is for groups larger than hydrogen to occupy equatorial positions. The relative energies of various chair conformers of multisubstituted cyclohexanes can thus be evaluated by noting the numbers of 1,3 diaxial interactions in each of the conformers.

For example, trans-1,2-dichlorocyclohexane has diaxial and diequatorial chair forms. The diaxial conformer should be less stable because it has two sets of 1,3 diaxial interactions between the chlorines and the axial protons. Knowing the equatorial– axial preference for a single chlorine substituent on a cyclohexane is 0.52 kcal/mol (2.2 kJ/mol), one can predict that the diequatorial isomer is favored by 1.04 kcal/mol (4.4 kJ/mol). cis-1,3-Dichlorocyclohexane has two chair forms with two equatorial chlorines and two axial chlorines, respectively. The diaxial isomer should be more than 1 kcal/mol higher in energy than the diequatorial isomer because the 1,3 diaxial interactions between two axial chlorines should be more severe than the 1,3 diaxial interactions between an axial chlorine and axial hydrogens. In contrast, trans-1,3-dichlorocyclohexane has a single axial chlorine in either chair conformer; thus the two chair forms are of the same energy.

Similarly trans-4-methylcyclohexanol has diequatorial and diaxial substituted chair forms. It is thus predicted that the former should be about 2.7 kcal/mol (11 kJ/mol) more stable than the latter because an axial methyl is less stable by 1.8 kcal/mol (7.3 kJ/mol) and an axial OH group is less stable by 0.9 kcal/mol (3.8 kJ/mol) than their equatorial counterparts.

Similar qualitative assessments can be made for more highly substituted cyclo-hexanes. It is found that cis,cis-1,3,5-trimethyl cyclohexane exists in only one chair form. This must be the triequatorial isomer because the other chair form has three axial methyl groups interacting on the same side of the ring. This should cause severe steric interactions and be much less stable than the all-equatorial isomer. In fact, the energy difference between the all-equatorial and the all-axial isomer should be greater than 5.4 kcal/mol (3 × 1.8 kcal/mol). This can be esti-mated by noting that an axial methyl group is less stable by 1.8 kcal/mol when the other axial valences with which it interacts are protons. The 1,3 diaxial inter-actions should be even greater if the other axial valences hold groups larger than protons; thus the energy difference should be greater than for three axial methyl groups or greater than 3 × 1.8 = 5.4 kcal/mol.

Since 1,3 diaxial interactions are the major factor which increases the energy of conformations with axial substituents, it is reasonable to expect that larger groups would have more severe steric interactions, causing the energy difference between the axial and equatorial position to increase. That is, the larger the group, the larger is the 1,3 diaxial interactions with axial protons and the greater is the energy difference between the axial and equatorial forms.

This effect is clearly seen by comparing methylcyclohexane and t-butylcyclohexane. The axial– equatorial energy difference is 1.8 kcal/mol for the methyl group while it is 4.9 kcal/mol for the t -butyl group. This is because the t -butyl group is much larger than a methyl group, and 1,3 diaxial interactions are much stronger. In fact, these interactions are so large that the t -butyl group has been employed to anchor the particular chair conformation that has the t -butyl group equatorial. The other chair form would be much higher in energy and virtually unpopulated; thus the chemistry that is observed arises from reactions of a single conformation of the t -butyl-substituted ring.