Rotamer

In chemistry, rotamers are chemical species that differ from one another primarily due to rotations about one single bond. Various arrangements of atoms in a molecule that differ by rotation about single bonds can also be referred to as conformations. Conformations, which represent local minima on the potential energy surface, are called conformers. Conformers can differ from one another due to rotation of multiple bonds; rotamers are a subset of conformers. Conformers/rotamers usually differ little in their energies, so they are almost never separable in a practical sense. Rotations about single bonds are subject to small energy barriers. When the time scale for interconversion is long enough for isolation of individual rotamers (usually arbitrarily defined as a half-life of interconversion of 1000 seconds or longer), the species are termed atropisomers. The ring-flip of substituted cyclohexanes constitutes a common form of conformers. The study of the energetics of bond rotation is referred to as conformational analysis. In some cases, conformational analysis can be used to predict and explain product selectivity, mechanisms, and rates of reactions. Conformational analysis also plays an important role in rational, structure-based drug design.

Types

Rotating their carbon–carbon bonds, the molecules ethane and propane have three local energy minima. They are structurally and energetically equivalent, and are called the staggered conformers. For each molecule, the three substituents emanating from each carbon–carbon bond are staggered, with each H–C–C–H dihedral angle (and H–C–C–CH3 dihedral angle in the case of propane) equal to 60° (or approximately equal to 60° in the case of propane). The three eclipsed conformations, in which the dihedral angles are zero, are transition states (energy maxima) connecting two equivalent energy minima, the staggered conformers. The butane molecule is the simplest molecule for which single bond rotations result in two types of nonequivalent structures, known as the anti- and gauche-conformers (see figure). For example, butane has three conformers relating to its two methyl (CH3) groups: two gauche conformers, which have the methyls ±60° apart and are enantiomeric, and an anti conformer, where the four carbon centres are coplanar and the substituents are 180° apart (refer to free energy diagram of butane). The energy separation between gauche and anti is 0.9 kcal/mol associated with the strain energy of the gauche conformer. The anti conformer is, therefore, the most stable (≈ 0 kcal/mol). The three eclipsed conformations with dihedral angles of 0°, 120°, and 240° are transition states between conformers. Note that the two eclipsed conformations have distinct energies: at 0° the two methyl groups are eclipsed, resulting in higher energy (≈ 5 kcal/mol) than at 120°, where the methyl groups are eclipsed with hydrogens (≈ 3.5 kcal/mol).

Mathematical analysis A rough approximate function can illustrate the main features of the conformational analysis for unbranched linear alkanes with rotation around a central C–C bond (C1–C2 in ethane, C2–C3 in butane, C3–C4 in hexane, etc.). The members of this series have the general formula C2nH4n+2 with the index n = 1, 2, 3, etc. It can be assumed that the angle strain is negligible in alkanes since the bond angles are all near the tetrahedral ideal. The energy profile is thus periodic with 2 π / 3 {\displaystyle 2\pi /3} (120°) periodicity due to the threefold symmetry of sp3-hybridized carbon atoms. This suggests a sinusoidal potential energy function V ( θ , k ) {\displaystyle V(\theta ,k)} , typically modelled using a Fourier series truncated to the dominant terms:

V ( θ , k ) = ∑ k = 0 ∞ V k ( n ) 2 [ 1 − cos ⁡ ( k θ ) ] {\displaystyle V(\theta ,k)=\sum _{k=0}^{\infty }{\frac {V_{k}(n)}{2}}[1-\cos(k\theta )]}

Here:

θ {\displaystyle \theta } is the dihedral angle in degrees,

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