Conformations of Alkanes

In the last chapter, we saw that it was possible to describe the complete 3-dimensional shape of methane by specifying its bond angles and bond lengths. Ethane, which is comprised of two methyl groups attached to each other, has properties very similar to those of methane. However, the complete 3-dimensional shape of ethane cannot be specified by these bond lengths and bond angles alone because ethane can internally rotate about its C-C bond.

To understand why ethane has this extra degree of freedom, consider the cylindrically symmetric nature of $\sigma$ bonds. The $\sigma$ bond can maintain a full degree of overlap while its two ends rotate. Hence, the energetic barrier to rotation about sigma bonds is generally very low. Unlike $\pi$ bonds in alkenes, the C-C sigma bond does not hold the two methyl groups in fixed positions relative to one another. The different spatial arrangements formed by rotations about a single bond are called conformations or conformers.

Several methods are used by organic chemists to help them visualize the conformations of molecules. One of these methods uses wedges to denote bonds that are extending out from the plane of the page toward the reader and dashes to indicate bonds that are going into the plane of the page away from the reader. This notation is frequently used to represent the tetrahedral geometry of $sp^3$-hydridized carbons.

A Newman projection can be used to specify the conformation of a particular bond with clarity and detail. A Newman projection represents the head-on look down the bond of interest. The circle in the Newman projection represents the atom in front of the bond, and the lines radiating from the center are the bonds of that atom. The bonds of the rear atom emerge from the sides of the circle.

Newman projections can be characterized by the angles formed between bonds on the front atom and bonds on the rear atom. Such angles are called dihedral angles. The full 3D shape of any molecule can be described by its bond lengths, bond angles, and dihedral angles.

While there are an infinite number of conformations about any sigma bond, in ethane two particular conformers are noteworthy and have special names. In the eclipsed conformation, the C-H bonds on the front and back carbons are aligned with each other with dihedral angles of 0 degrees. In the staggered conformation, the C-H bonds on the rear carbon lie between those on the front carbon with dihedral angles of 60 degrees.

Energetically, not all conformations are equally favored. The eclipsed conformation of ethane is less stable than the staggered conformation by 3 kcal/mol. The staggered conformation is the most stable of all possible conformations of ethane, since the angles between C-H bonds on the front and rear carbons are maximized at 60 degrees. In the eclipsed form, the electron densities on the C-H bonds are closer together than they are in the staggered form. When two C-H bonds are brought into a dihedral angle of zero degrees, their electron clouds experience repulsion, which raises the energy of the molecule. The eclipsed conformation of ethane has three such C-H eclipsing interactions, so we can infer that each eclipsed C-H "costs" roughly 1 kcal/mol.

Eclipsing interactions are an example of a general phenomenon called steric hindrance, which occurs whenever bulky portions of a molecule repel other molecules or other parts of the same molecule. Because such hindrance causes resistance to rotation, it is also called torsional strain. The 3 kcal/mol needed to overcome this resistance is the torsional energy. Note that this figure is very small compared to the energy required to rotate around double bonds, which is 60 kcal/mol (the bond energy of a C-C $\pi$ bond). At room temperature, ethane molecules have enough energy to be in a constant state of rotation. Because of this rapid rotation, it is impossible to isolate any particular conformation in the way that cis- and trans- alkenes can be individually isolated. Although the term "conformational isomer" is sometimes used as a synonym for conformations, conformations of a molecule are not considered true isomers because of their rapid interconversion.