In organic chemistry, molecules are dynamic, three-dimensional structures. Flexibility is pronounced around carbon-carbon single bonds, which allow attached groups to spin freely. These temporary spatial arrangements resulting from rotation are known as conformations, or rotational isomers. The stability of a molecule is directly influenced by the conformation it adopts, and this article explores the specific arrangement called the gauche interaction.
Understanding Molecular Conformation
The ability of a molecule to change its shape stems from the cylindrical symmetry of a sigma (\(\sigma\)) bond. This bond permits continuous rotation of the bonded atoms relative to one another without breaking the bond. While a molecule can exist in an infinite number of momentary positions, only a few conformations represent chemically significant energy minimums or maximums.
To accurately describe the spatial relationship between non-bonded groups on adjacent atoms, chemists use the dihedral angle, also known as the torsional angle. This angle is defined by the planes formed by four atoms: the two groups of interest and the two central atoms of the single bond connecting them. The dihedral angle quantifies the degree of rotation and is the primary tool for analyzing conformational stability.
The dihedral angle is most easily visualized using a Newman projection, where the molecule is viewed directly down the carbon-carbon bond axis. This projection represents the front carbon as a dot and the back carbon as a circle, illustrating the angular separation between attached groups. Analyzing the dihedral angle classifies conformations, such as the staggered arrangement, where groups are positioned in the gaps between those on the adjacent carbon. Staggered orientations are generally more stable than the eclipsed orientation, where groups directly line up.
Defining the Gauche Conformation
The gauche conformation is a specific staggered arrangement defined by the spatial relationship between two large substituent groups separated by a carbon-carbon single bond. In this arrangement, the dihedral angle between the two groups is approximately \(60 \text{ degrees}\). This places the two groups close to each other, but they are not directly overlapping. The term “gauche” is French for “awkward,” hinting at the slightly less favorable nature of this arrangement.
The classic example illustrating this interaction is the butane molecule, which has four carbon atoms in a chain. The relevant rotation occurs around the central carbon-carbon bond (between the second and third carbon atoms). The two terminal methyl (\(\text{CH}_3\)) groups are the large substituents whose relative positions define the conformation. When the dihedral angle between these two methyl groups is \(60 \text{ degrees}\), the molecule is in the gauche conformation.
The gauche conformation is contrasted with the anti conformation, which represents the most stable arrangement for butane. In the anti conformation, the two large methyl groups are positioned as far apart as possible, with a dihedral angle of \(180 \text{ degrees}\). Both gauche and anti are staggered conformations, but their difference in spatial separation leads directly to a difference in molecular energy.
Energetic Consequences of Gauche Interactions
The gauche conformation is less favorable than the anti conformation due to steric hindrance. Steric hindrance is a repulsive interaction that occurs when atoms or groups are forced to occupy the same region of space. In the gauche conformation, the two methyl groups are close enough that their electron clouds repel each other, increasing the molecule’s potential energy. This non-bonded repulsion destabilizes the gauche arrangement.
For the methyl-methyl gauche interaction in butane, this repulsive force results in an energy penalty compared to the anti conformation. This difference is quantified at approximately \(3.8 \text{ kilojoules per mole } (0.9 \text{ kilocalories per mole})\) higher than the energy of the anti conformer. This relatively small energy difference means the molecule rapidly interconverts between the more stable anti and the less stable gauche forms at room temperature.
The energy difference determines the equilibrium ratio of conformers present in a solution. Since the anti conformation has the lowest potential energy, the butane molecule spends the majority of its time in this arrangement. The higher energy of the gauche conformation demonstrates how the size and proximity of groups influence the preferred three-dimensional shape of organic molecules. Understanding these energetic preferences is important for predicting the structure and reactivity of larger, more complex biological molecules.