Organic Chemistry: Carbocycles

Conformational Analysis of Cycloalkanes

Summary Conformational Analysis of Cycloalkanes

The boat conformation is less stable than the chair conformation because it experiences a number of eclipsing interactions. Whereas the chair conformation resembles two staggered ethanes, the boat conformation resembles two eclipsed ethanes. In addition, there is considerable repulsion between hydrogens on the two "tips" of the boat. These hydrogens are called flagpole hydrogens. The combined effects of torsional strain and steric hindrance between flagpole hydrogens makes the boat conformation less stable than the chair by 6.9 kcal/mol.

Figure %: Eclipsing interactions and steric hindrance in the boat conformation.

We could flip either end of the boat down to regain a chair conformation. The two possible chair conformations that can be obtained are distinct; all of the axial bonds in one chair become equatorial in the other and vice versa. These two chair conformations can be interconverted by going through the boat intermediate. Such a chair-chair interconversion is sometimes called a chair flip. Build a model of cyclohexane with distinct colors for the axial and equatorial hydrogens. Try the chair flip yourself to verify that the colors really do change positions. The effect is really quite startling the first time you see it!

Figure %: Chair flip via a boat intermediate. Notice that axial and equatorial bonds are interchanged. Note also that substituents on the top face remain on the top face of the molecule; the same applies for bottom face substituents.

Substituent Effects

When substituents are placed on the cyclohexane ring, they prefer to take equatorial positions over axial positions. This positional preference is shown for methylcyclohexane. When the methyl group occupies the axial position, there is steric hindrance between it and the axial hydrogens three carbons away. These repulsive effects are called 1,3-diaxial interactions. 1,3-diaxial interactions can also be understood in terms of gauche butane. The highlighted bonds indicate the butane-like structures in the axial conformation of methylcyclohexane. It turns out that the axial methyl conformation is less stable by 1.8 kcal/mol, precisely the cost of two gauche butane interactions.

Figure %: Conformational preference of methylcyclohexane

The amount of energy it "costs" to move a substituent group into the axial position is sometimes referred to as the A-value of that substituent group. For instance, the A-value of a methyl group is 1.8 kcal/mol. The A-values of several substituent groups are listed below. A-values can be useful for estimating the energy difference between the two conformations of a substituted cyclohexane. However, a simple summation of A-values does not always give the right answer, as Problem 9 will show.

Figure %: A-values of common substituent groups

It is useful to know the energy difference between the two chair conformations because it enables you to calculate the relative abundance of each conformation. For instance, the 1.8 kcal/mol A-value of methyl allows us to predict that less than 1 in 20 molecules of methylcyclohexane will occupy the axial position at room temperature. The A-value of the tert-butyl group is so large that any molecule with a tert-butyl substituent is "locked" into the conformation that places the tert-butyl group in the equatorial position.