Conformational analysis
Rotation, shape, and energy
Most single bonds are able to rotate continually, which leads to infinite different shapes being possible around that bond axis. Conformational analysis is the study of those shapes; which ones are preferred, and why.
Basics
Four ways to draw the same molecule
Most single bonds are continually rotating, which leads to different shapes being possible around that bond axis. These shapes have different energies depending on the relative placement of attached groups. Conformational analysis is the study of these shapes and is important for assessing what conformations will predominate in the overall makeup of the molecule. We begin simple with ethane and build up to more complex acyclic chains, in which the basics still apply.
In organic chemistry we use several different devices to describe the structures of molecules, each of which brings different value to the discussion. The simple bond-line structure (a) shows how atoms are attached, while the older sawhorse idea (b) attempts to show the relative disposition of atoms in space. The more modern molecular model picture (c) gives a better idea of how atoms are arranged, while the space-filling model (d) helps us remember how big atoms and groups are and how close they can get in space.
Ethane
From wedge-dash to a head-on view
Beginning with ethane, we are able to draw numerous different diagrams that offer information on the molecule's shape. The first is the simple structure (a), which quickly tells us which atoms are involved but not much about the shape. The side-on wedge-dash picture (b) is much more informative, because we can assess how each atom is orientated relative to the rest of the molecule.
If we turn this structure slightly, to give (c), we begin to view the front carbon relative to the back carbon and can assess the relative orientations of all atoms involved. Taking this further, to (d), we begin to view what will become a Newman projection — invaluable in assessing the relative stabilities of shapes that are a consequence of rotation about the central C–C bond.
Newman projections
Anti, gauche, eclipsed, syn
Newman depictions are drawn head-on down a chosen C–C bond axis, so that the front carbon of that bond may be seen but the rear carbon cannot. In projection (a) all of the atoms are staggered and none overlap. If substituents other than hydrogen are attached (X) then this shape is known as anti, with the two larger X groups as far away as possible. This will be the most stable conformation, since there is no interaction between the two large X groups.
When we rotate around the central C–C bond we keep one carbon in place, in this case the one at the back, and move the other. Rotating by 60° gives conformation (b), which is less stable because atoms and groups at the front and back are starting to interact: an eclipsed conformation. Rotating further gives (c), a second staggered shape but less stable than (a) because the X groups are getting closer; a gauche conformation. Rotating to (d) gives the least stable shape, in which both X groups overlap. Rotate further and the same conformations repeat. The rotation is continuous, but there are barriers to it, and staggered conformations are generally preferred.
Energetics
Energy against dihedral angle
If we plot the angle of rotation around the central C–C bond against the potential energy of the resulting shapes we get the graph below, which conveniently shows favoured and unfavoured conformations. Anti is lowest in energy, since the larger methyl groups are far apart. Rotation of the front carbon through 60° then causes destabilizing eclipsing interactions, which are relieved by further rotation to 120° to give the gauche conformation.
Through to 180° causes significant interaction of the methyl groups in the second eclipsed conformer. Carrying on through 360° creates the mirror-image conformations on the way back to anti. If we swap the methyl groups for anything else larger than H we get essentially the same graph, differing only in the size of the energy increments.
Reference
The four conformers of butane
Rotation about the C2–C3 bond, taking anti as the zero point. Energies are approximate and shift with the size of the groups, but the order never does.
Self-check
Six questions before you move on
Work out an answer on paper, then reveal to check. If your reason is right but the answer is wrong, you are closer than you think.
What does a Newman projection show you that a wedge-dash drawing does not?
The relationship between front and back substituents around one bond axis. Looking head-on down the C–C bond puts all six groups in one plane of view, so you can read the dihedral angle directly.
Anti and gauche are both staggered. Why is gauche the higher in energy?
Neither has torsional strain, but in gauche the two large groups sit only 60° apart and crowd each other. Anti puts them 180° apart, as far away as the bond allows.
Why does the energy plot for ethane show three identical maxima rather than one?
All six substituents are hydrogens, so every eclipsed arrangement is the same. Rotating 360° passes through three equivalent eclipsed and three equivalent staggered positions.
Replace butane's methyls with tert-butyl groups. What changes on the graph?
The shape is the same; only the increments grow. Bigger groups raise the eclipsed maxima and the gauche minimum much more than the anti minimum, so anti dominates even more.
If rotation is continuous, why do we talk about conformations at all?
Because the molecule spends most of its time near the energy minima and only passes quickly through the maxima. The named conformations are the shapes worth referencing.
What does the space-filling model tell you that the molecular model does not?
How much room atoms actually occupy. Ball-and-stick shows geometry, but space-filling shows how close groups can get before they clash, which is what drives the energy differences.