Question: Draw a graph, similar to Figure 3-11, of the torsional energy of $2-\text{methylbutane}$ as it rotates about the$\mathbf{\text{C2}}\mathbf{-}\mathbf{\text{C3}}$ bond.

Newman projections are often used in drawing conformations. In Newman projection, one is viewing the $\text{C}-\text{C}$ bond end on along the axis of connection. The front carbon is represented by the intersection of bonds from it, while the rear carbon appears as a circle.

Dihedral angle$\text{(}\theta \text{)}$gives the identity of any conformation. Itmay be defined as the angle between $\text{C}-\text{H}$ bonds on the front carbon atom and $\text{C}-\text{H}$the bonds on the back carbon atom in the Newman projection. Eclipsed conformation has a dihedral angle, $\theta = 0^0$and the staggered conformation has a dihedral angle, $\theta = {60}^0$. Any other intermediate conformation is known as skew conformation. When two methyl groups are pointed in same direction $(\theta = 0^0)$, they eclipse with each other and this conformation is known as totally eclipsed. Also, when two methyl groups are toward left and right of each other at $\theta = {60}^0$, then this conformation is known as gauche conformation.Another staggered conformation takes place at $\theta = {180}^0$,where the two-methyl groups are pointing in opposite direction known as the anti-conformation.

The potential energy of a molecule increases when it rotates toward an eclipsed conformation, and also there is a resistance to the rotation. The resistance to twisting (torsion) is known as torsional strain and the energy required is known as torsional energy.

totally eclipsed gauche eclipsed anti

Torsional energy of as it rotates about bond

Both the staggered conformations (gauche and anti) are lower in energy than any other eclipsed conformation. The bulky methyl group are placed in opposite directions (far apart) in anti-conformation. Gauche conformation in which the methyl groups are separated by a dihedral angle of just is higher in energy than anti-conformation since their electron clouds begin to repel each other. Totally eclipsed conformation due to the presence of two methyl groups so close to each otherexperiences a strong repulsion in their electron clouds.