Alkanes, seemingly simple molecules, have fascinating spatial arrangements. Rotations around single bonds create different conformations, each with unique energy levels. Understanding these arrangements is key to predicting molecular behavior and stability.

Staggered and eclipsed conformations are the stars of the show. Staggered wins the stability contest by keeping substituents far apart. Anti and gauche conformations in butane further illustrate how spatial arrangements affect energy levels and molecular populations.

Conformations of Alkanes

Alkane conformations: staggered vs eclipsed

• Conformations represent different spatial arrangements of atoms that can interconvert by rotation about single bonds (ethane, butane)
• Staggered conformation arranges substituents as far apart as possible minimizing steric strain and torsional strain resulting in lower energy and greater stability compared to eclipsed conformation (Newman projection)
• Eclipsed conformation arranges substituents as close together as possible maximizing steric strain and torsional strain leading to higher energy and reduced stability relative to staggered conformation (sawhorse representation)
• Dihedral angle measures the angle between two planes each containing one of the C-C bonds with staggered conformations having a dihedral angle of 60° and eclipsed conformations having a dihedral angle of 0°
• Rotational barrier quantifies the energy required to rotate from one conformation to another determined by the energy difference between staggered and eclipsed conformations (rotational energy profile)
  • This barrier is influenced by torsional strain, which arises from electron-electron repulsion during bond rotation

Anti vs gauche conformations in butane

• Anti conformation represents the staggered conformation where methyl groups are positioned 180° apart resulting in the lowest energy conformation of butane by minimizing steric strain and torsional strain (extended zigzag)
• Gauche conformation depicts a staggered conformation where methyl groups are oriented 60° apart leading to higher energy than the anti conformation due to increased steric strain (sickle shape)
• Energy difference between anti and gauche conformations amounts to approximately 0.9 kcal/mol with the gauche conformation being less stable than the anti conformation by this margin
• Population distribution of anti and gauche conformations is determined by the Boltzmann distribution with a ratio of approximately 3:1 anti to gauche conformations at room temperature (entropy)

Strain energy calculations for alkanes

• Strain energy quantifies the energy difference between a given conformation and the lowest energy conformation (ground state)
• Interaction values represent energy contributions from specific interactions between substituents:
  1. Gauche interaction occurs between substituents separated by a dihedral angle of 60° with a typical interaction value of 0.9 kcal/mol (butane)
  2. 1,3-Diaxial interaction arises between axial substituents separated by three bonds commonly observed in cyclohexane and its derivatives with a typical interaction value of 3.0 kcal/mol (cis-1,3-dimethylcyclohexane)
• Calculating strain energy involves summing all interaction values present in a given conformation such as two gauche interactions resulting in a strain energy of 2 × 0.9 kcal/mol = 1.8 kcal/mol
• Comparing strain energies allows predicting the preferred conformation of a given alkane with the conformation exhibiting the lowest strain energy being the most stable (potential energy diagram)

Conformational analysis and equilibrium

• Conformational analysis involves studying the different possible spatial arrangements of a molecule and their relative energies
• Bond rotation allows molecules to interconvert between different conformations
• Steric hindrance, caused by the spatial proximity of atoms or groups, influences the stability of different conformations
• Conformational equilibrium exists between different conformations, with the population of each determined by their relative energies