4.7 Conformations of Monosubstituted Cyclohexanes

Conformations of Monosubstituted Cyclohexanes

When you attach a substituent to cyclohexane, it can sit in either an axial or equatorial position. These two chair conformations interconvert through a ring flip, but they're not equal in energy. The equatorial conformation is almost always more stable, and understanding why comes down to steric and torsional strain.

Energy of Cyclohexane Conformations

A monosubstituted cyclohexane exists as two chair conformations that interconvert via a ring flip. In one chair, the substituent is axial (pointing up or down, roughly perpendicular to the ring plane). In the other, it's equatorial (pointing outward, roughly along the ring's "equator").

The energy difference between these two conformations is:

$\Delta G° = G°_{\text{axial}} - G°_{\text{equatorial}}$

A positive $\Delta G°$ means the equatorial conformation is more stable. Two factors drive this energy gap:

• Steric strain: Bulky substituents in the axial position crowd against axial hydrogens on the same side of the ring (1,3-diaxial interactions). Moving to equatorial relieves this crowding.
• Torsional strain: An axial substituent is gauche to the two adjacent ring C–C bonds, creating eclipsing-like interactions. The equatorial position places the substituent anti to those bonds, which is lower in energy.

The magnitude of $\Delta G°$ depends on the substituent's size. Bigger, bulkier groups have a stronger preference for equatorial. This preference is quantified by the A-value, which is simply the $\Delta G°$ between axial and equatorial conformations for a given substituent. Some representative A-values:

Effects of 1,3-Diaxial Interactions

1,3-Diaxial interactions are the steric repulsions between an axial substituent and the axial hydrogens at the C-3 and C-5 positions (two carbons away on the same face of the ring). These are the main reason axial substituents are less stable.

Think of it this way: when a substituent sits axial, it's forced into close contact with two other axial hydrogens across the ring. This is analogous to a gauche interaction in butane. In fact, each 1,3-diaxial interaction with hydrogen is roughly equivalent to one gauche butane interaction (~0.9 kcal/mol of strain).

For methylcyclohexane, there are two such interactions when the methyl is axial, giving about 1.7 kcal/mol of total destabilization. That matches the measured A-value for methyl.

For larger substituents, the repulsion is much worse:

• Methyl ($-CH_3$): moderate 1,3-diaxial strain, A-value = 1.70 kcal/mol
• tert-Butyl ($-C(CH_3)_3$): severe 1,3-diaxial strain, A-value > 4.5 kcal/mol. The three methyl groups on the tert-butyl can't rotate out of the way, making the axial conformation extremely crowded.

Preferred Conformations of Substituted Cyclohexanes

The preferred conformation is whichever chair places the substituent equatorial, since this minimizes 1,3-diaxial interactions. How strong that preference is depends on the substituent:

Size matters most:

1. Large groups like tert-butyl and isopropyl have a very strong equatorial preference. tert-Butylcyclohexane exists almost exclusively in the equatorial conformation at room temperature.
2. Smaller groups like methyl and ethyl still prefer equatorial, but the energy difference is modest enough that a measurable fraction of molecules have the substituent axial at equilibrium.

Polarity plays a secondary role:

1. Polar substituents like $-OH$, $-NH_2$, and $-C \equiv N$ also prefer equatorial, but their A-values are often smaller than you'd expect from size alone. The oxygen in $-OH$ is relatively small, so its equatorial preference (0.52 kcal/mol) is much less than that of a methyl group.
2. The equatorial position reduces torsional strain by placing the substituent anti to the adjacent C–C bonds rather than gauche.

Conformational Analysis Techniques

The chair conformation is the most stable form of cyclohexane because all bonds are perfectly staggered, eliminating torsional strain. Every conformational analysis of cyclohexane derivatives starts with drawing accurate chairs.

A ring flip interconverts the two chair conformations. During a ring flip, every axial position becomes equatorial and every equatorial position becomes axial. The substituent itself doesn't move; the ring changes shape around it. The ring flip passes through higher-energy twist-boat and half-chair intermediates, but the barrier is low enough (~10 kcal/mol) that interconversion is rapid at room temperature.

Newman projections are a useful tool for seeing why equatorial is preferred. If you sight down a C–C bond of the ring:

• An equatorial substituent appears anti to the C–C bond across the ring (low energy, like anti butane).
• An axial substituent appears gauche to that same bond (higher energy, like gauche butane).

Drawing these projections makes the connection between 1,3-diaxial interactions and gauche butane strain much more concrete.