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Lecture 1
Conformational Analysis in Acyclic Systems
Learning Outcomes: by the end of this lecture and after answering the associated problems, you will be able to:
- use Newman and saw-horse projections as 3D representations of different conformational isomers;
- use the terms, staggered, eclipsed, anti , and gauche to describe different conformers;
- calculate the energetic costs of a range of simple eclipsing interactions;
- explain why different conformers have different energies;
- recognise a syn pentane interaction;
- calculate the equilibrium constant, and therefore the relative populations of two conformers, for a simple conformational equilibrium.
Some definitions:
conformation conformation relates to the different spatial arrangements of the atoms in a molecule that arise through rotation about the bonds linking the atoms.
torsion or dihedral angle
Conformation of Alkanes
Let's consider the possible conformations of one of the simplest acyclic alkanes, ethane. We can identify two types of conformational isomer, namely staggered and eclipsed conformers.
Ethane
Rotating about the C−C bond, we see that ethane has three low-energy conformational isomers. They are identical or degenerate (same energy) and are described as staggered conformers. The H−C−C−H dihedral angle in these conformers is 60°. We can identify a second high-energy conformational isomer in which the H−C−C−H dihedral angle is 0°. For obvious reasons, this is described as an eclipsed conformer. Since eclipsed conformers are higher in energy than staggered conformers, there is clearly restricted rotation about the C−C single bond (although the energy barrier to rotation is relatively small).
θ = 0° (^) θ = 60° θ = 120° θ = 180°
(^0 60 120 180) θ
potential energy (kcal mol -1^ )
In contrast, when a filled molecular orbital overlaps with an unfilled molecular orbital this is an energetically favourable process. This is most efficient when the molecule adopts a staggered conformation. We can see this by constructing a molecular orbital diagram:
- sterics (Van der Waals interactions)
Since the H atoms are barely within van der Waals distance this effect is not very important in this case (estimate that sterics contribute to 10% of the energy barrier in this instance).
Note Van der Waals' repulsions become much more significant contributors to the energy barrier when the substituents on the carbon atoms are large, e.g. in hexachloroethane.
Cl
Cl Cl
Cl
Cl Cl Cl Cl
Cl Cl
Cl
Cl
Calculating the Populations of Different Conformers
Consider the two staggered conformers of butane:
H
H Me
Me
H H Me
H H
Me
H H
Recall that the equilibrium constant, K, is related to the Gibb's free energy according to the following equation:
and
We know that ∆H° = kcal mol -
Thus to evaluate ∆G°, and therefore the equilibrium constant, K, we need to incorporate an entropy contribution. Since there are two enantiomeric gauche conformers and only one anti conformer.
∆S° = -R ln2 (R = gas constant; 1.9872 10 -3^ kcal K-1^ mol -1^ )
Substituting this information into equation 2 (see above),
∆G° = -0.9-(−RT ln2).
Thus at 298 K, ∆G° = -0.9 + 0.41 = -0.49 kcal mol -
but from equation 1, ∆G° = -RT lnK
K = = 2.
This corresponds to a distribution of 70% anti and 30% gauche conformers.
Energy difference between gauche and anti conformers of 1,2-dichloroethane:
phase dielectric constant ε energy difference (kcal mol -1^ )
1,2-Difluoroethane
1,2-Difluoroethane seems anomalous; the gauche conformer is favoured even in the gas phase.
To rationalise this observation we need to consider:
- statistical factors ( i.e. an entropic contribution to ∆G° (remember there are two degenerate gauche conformers, whereas only one anti conformer).
- dipole-dipole interactions - these are repulsive and will be high in the gauche conformer especially in the gas phase.
- van der Waals repulsions (steric effects) - the small size of the F atom (van der Waals radius = 1.5 - 1.6 Å) means that this not too important; (this factor is very important for 1,2-dichloroethane, and even more so for 1,2-dibromoethane).
- stereoelectronic or hyperconjugative effects. In the gauche conformer, both C−F bonds can benefit from the most favourable σ σ* orbital overlap (most compatible HOMO-LUMO set). [Remember that a filled MO interacting with an unfilled MO leads to an energetically favourable interaction.]
