Conformations of simple acyclic alkanes
Introduction
The shape of molecules is often overlooked. It is easier and neater to draw stylistic two-dimensional representations of molecules. Unfortunately, these drawings hide the true beauty of organic molecules, which frequently have complex three-dimensional shapes. And these shapes are important when we start to think about a molecules reactivity and physical properties. Stereochemistry is the discussion of three-dimensional shape of a molecule. In an earlier post, you were introduced to shapes fixed by the configuration of an atom, and we discussed these under the umbrella term of stereoisomers. Today’s post looks at the conformation of simple molecules. Conformation describes how a molecule’s shape changes as a single bond rotates (rotation around a σ bond). Each conformation is a different shape but is still the same molecule. This is different to the stereoisomers of the previous posts, where change of configuration results in a new molecule or isomer.
Analogy comparing conformations and configurations to the human body
A common analogy explaining the difference between conformation and configuration involves our bodies. A human can adopt many different shapes by moving our limbs. These different shapes are conformations. We haven’t changed who or what we are, we have just changed our shape. Some of these shapes are more comfortable than others, lying down is more comfortable than balancing on one leg. In other words, some shapes or conformations are more stable than others. Similarly, some conformations of a molecule are more favorable or stable than others. To stretch the analogy to breaking point, if we wanted a change the configuration of our bodies, we would need to swap limbs, perhaps a left leg with a right arm. Now our body would still have all the same parts but they would be in a very different shape. This would be a change in configuration. Summarizing, different conformations are all the same body/molecule, different configurations are different bodies/molecules.
Which Bonds Rotate?
Only single covalent bonds (σ bonds) can rotate. Double bonds (π bonds) are unable to rotate, and add rigidity to a molecule. Hold one pen between two hands and you can rotate it. Hold two pens on top of each other and rotation is impossible as can't wrap around each other. Double bonds are exactly the same. They can’t twist around each other and the atoms can’t rotate. A poor analogy but it works.
Valence bond theory can explain why σ bonds rotate but π bonds don’t. Consider rotating the right-hand atom of the molecule below. The σ bond is formed from the head-to-head overlap of two sp3 hybrid atomic orbitals (HAO). Look along the axis connecting the atoms and the orbital looks identical or has a symmetrical cross section. Rotating one atom rotates one sp3 HAO but this doesn't change the overlap with the second HAO. The bond doesn’t change, and, more importantly, there is always a constructive bonding overlap of the two orbitals. This means rotating the atom does not break the bond.
Rotation around a single σ bond has no effect on the orbital
Rotation around a double bond is different. The π bond is formed by the side-to-side overlap of two 2p atomic orbitals. Such orbitals are dumbbell shaped and overlap only occurs when they are parallel. Rotate one of the atoms and you cause the 2p atomic orbital to skew to one side. It no longer overlaps the second 2p atomic orbital and the bond breaks. It takes a lot of energy to break a bond and this only occurs in a chemical reaction. In other words, a double bond cannot rotate unless you react it and cause it to become a single bond first (and the atoms ions or radicals).
Rotation of a π bond would cause the 2p atomic orbitals to become skewed & no longer overlap. The bond would break. You cannot rotate a π bond.
Representations of Conformations
Before discussing the various conformations of simple molecules, a couple of minutes looking at how you can represent the three-dimensional shape of a molecule is useful. The three most common drawings are shown below:
Three representations of a molecule all showing the same conformation. One atom is marked with an asterisks for clarity.
The skeletal representation is the standard drawing for an organic molecule. The three-dimensional quality of a tetrahedral atom is indicate by bold wedges (or lines) and dashed lines. The bold bonds are pointing towards the viewer or coming out of the plane of the page while the dashed lines go away from us. Such drawings a simple, clean and very common. As a negative, they are highly stylized, often confuse the unwary, and don't do justice to true beauty of the shape of organic molecules.
The sawhorse representation is the least used of the drawings. Effectively, it shows the skeletal representation pulled towards the viewer through roughly 45°. It almost gives a forced perspective view of a molecule.
The Newman projection looks along the axis (bond) connecting two atoms. In the diagram above the Newman projection is viewing the molecule along the C–C bond. This projection flattens the molecule with the front atom represented by the point connecting three bonds and the back atom represented by the large circle. The Newman projection makes the spatial relationship between two groups on the two atoms very clear. In this example, the blue and green groups are clearly next to each other at an angle of 60°.
Being able to convert between the three representations is a useful skill, especially if you take chemistry beyond first year. Arguably, the diagram above shows one method to achieve this. If you held the asterisked atom in the skeletal representation and pulled it upwards towards you on a slight angle, with the other carbon atom remaining in the plane of the page, you would arrive at the sawhorse projection. Continue to pull the atom towards you until it overlaps the the back atom and that is the Newman projection. A second example is given below. This includes a final nudge of the Newman projection to highlight the bond that is ‘hidden’ and how the Newman projection relates to the sawhorse.
Rotating a molecule between skeletal, sawhorse and Newman projections (then nudging the Newman projection to one side to highlight the relationship between Newman & sawhorse).
The more traditional method to convert between a skeletal representation and a Newman projection is outlined in the scheme below. Here we want to draw the molecule looking along the central C–C bond indicated by the eyeball and arrow.
The traditional way to convert between a skeletal representation and the Newman projection.
To draw the Newman projection, start by drawing the front atom as a dot. This is where the three bonds coming off the front tetrahedron will meet to give a triangle (the fourth bond is invisible as you look along it). As you look at this atom from the position of the eyeball, the bromo substituent is vertically upwards in the plane of the screen. This is drawn as the vertical line from the dot. The hydrogen is coming out of the screen, but your eye is in the screen, looking along the glass. The hydrogen atom is to the right of your eye, so is draw as the right-hand corner of the triangle. Finally, for the front atom, the methyl group is going into the screen. This is to the left of the eyeball, so it fills the left-hand corner. The front atom is complete.
You then move along the C–C bond to the back atom. This is indicated by the big circle. Looking at the molecule, the right-hand methyl group is in the same plane as the bromine atom, they are both connected to the molecule with normal lines but it is on the opposite side of the central C–C bond. Add this by a vertical line downwards. The bond/line starts at the big circle. It cannot cross this circle as that would imply a fifth bond to the front carbon.
The fluorine atom attached to the back carbon is on the same side as the hydrogen atom on the front atom; they are both pointing upwards out of the screen. This means they will be on the same side of the Newman projection. Similarly, the hydrogen atom of the back atom is on the same side as the methyl group of the front atom and so they are both drawn on the same side of the Newman projection. And there you are, a completed Newman projection.
Many students struggle going from a Newman projection back to the skeletal representation. In my experience the easiest way to do this to simply nudge the front atom to one side. This gives you a sawhorse projection that can then be flattened onto the page to give the skeletal drawing.
Converting a Newman projection to a skeletal drawing via a sawhorse representation.
This gives you the skeletal representation of the conformation shown in the Newman projection. Organic chemists had a nasty habit of converting such representations into tidier, idealized line diagrams that have the longest carbon chain in the plane of the screen. This means rotating C–C bonds or manipulating the drawing. In this case, I’ve pushed the ethyl group back into the plane of the screen and rotated the methyl group up. If you don’t believe me that these are the same compounds, buy some wine gums and toothpicks and make a model.
Modern chemical drawing apps can give reasonable approximations of the shape of a molecule. This, in combination with more ready access to x-ray crystallographic data, has led to more realistic drawings of molecular shape becoming the norm. An example taken from a recent Journal of American Chemical Society article (J. Am. Chem. Soc. 2022, 144, 7457) shows the classic ‘flat’ representation of a molecule and the more modern 3D drawing. The second shows the beauty of molecules but can be hard to interpret, making it difficult to ‘see’ the relationship between adjacent groups. The stylized diagrams above can make it easier to visualize.
Two drawings of a natural product taken from the work of David Proctor at the University of Manchester, UK
It’s about time we actually looked at how the shape changes. As with all good textbooks, I’ll start with the simplest molecules and then increase the complexity.
Conformation of Ethane
Rotating the C-C bond of ethane leads to different shapes of the molecule. These can be defined by the relationship between a hydrogen atom on each of the carbon atoms. The angle between the two C-H bonds, readily seen in the Newman projection, is called the dihedral angle.
There are infinite number of shapes or conformations of ethane depending on how minutely you rotate the bond, but only two conformations are important. These are the two extremes. The first has all the bonds and hydrogen atoms as far from each other as possible. This is the staggered conformation. It is the most favorable or stable or lowest energy conformation. In terms of the analogy to out bodies, it is a conformation that has us comfortably sitting down. The three representations below highlight this.
The three representations (& the ball and spoke model) of the favored, staggered, conformation with the analogy of a comfortable person
The other conformation is the eclipsed conformation. In this conformation all the bonds are overlapping or are aligned with each other. It is disfavored, high in energy or unstable. It is the same as a human trying to balance on our hands, it isn’t comfortable. The three representations are below. By convention we cheat when drawing the Newman projection and move the atoms to one side so that the three hydrogen on the back atom are visible. They should be directly behind the front hydrogen (and hence out-of-sight).
The three representations of the disfavored eclipsed conformation (& ball and spoke model) with the analogy of an uncomfortable person.
The Barrier to Rotation
Ethane is constantly rotating, so what do we mean by the most stable, low energy or favored conformation? This is the shape ethane would prefer to adopt. Or the shape more molecules of ethane are at any one moment in time. The least favored conformation is the equivalent of a brake on rotation of the bond. It is the energy required to make ethane rotate all the way around. It is called the barrier to rotation, and is the equivalent of the transition state between two staggered conformations.
Returning to the analogy of the human body. The most stable conformation sees us comfortably sat in a chair. If we want to change chair, moving to another comfortable position (conformation), we must pass through a high energy, less comfortable, standing position. This is the barrier to moving. It is equivalent to the barrier of rotation.
An analogy for the barrier to rotation. Standing up takes energy. This is equivalent to the high energy disfavored conformation. It is the barrier to moving between conformations.
A second analogy is to consider a marble next to a hill. The marble is happiest, most stable or in its favored position at the bottom of the hill. This is equivalent to the favored or stable conformation. To move the marble to the other side of the hill, the equivalent of rotating a bond between staggered conformations, you must give the marble energy so that it passes over the top of the hill. The top of the hill is the same as the disfavored, eclipsed conformation, as the marble has the most energy. This hill is the barrier to movement or is the same as the barrier to rotation.
A second analogy showing a marble being pushed up a hill. The top of the hill is the barrier and is equivalent to the least favored conformation.
This second analogy is useful as it is possible to determine how the energy of a molecule changes with dihedral angle as you rotate around a single bond. The plot looks very similar to the hill above.
Energy profile for the rotation of the C–C bond of ethane (sorry the style doesn’t match the rest of the pictures but I didn’t feel like re-plotting the data so just pinched the excel plot I use at first year).
This plot shows the most stable conformation, the staggered conformation, occurs when the dihedral angle is 60°, 180° and 300° (or –60°) or the bonds are far apart. The energy minima or favored conformation is known as a conformer. Conformers are stable conformations and are often considered to be stereoisomers. The disfavored, eclipsed conformation occurs when the bonds overlap and this gives the barrier to rotation at approximately 12 kJ/mol.
More Information about Stability and Barriers to Rotation
Two arguments explain the stability and/or instability of the staggered and eclipsed conformations of ethane. The first states that the staggered conformation is more stable as it minimizes the repulsion between the electrons of the C–H bonds. When the bonds are eclipsed, the electrons cause maximum repulsion as they are close to each other. This is the maximum torsional strain.
Torsional strain, the repulsion between electrons of a bond, causes the eclipsed conformation to be less stable.
The second argument requires a knowledge of antibonding orbitals. This suggests that the staggered conformation is favored due to a stabilizing interaction between the C–H σ bonding orbital and the adjacent C–H σ* antibonding orbital. This can only occur when the bonds are parallel and lowers the energy by allowing the electrons to spread out (hyperconjugation). This is a weak version of the anomeric effect found in sugars (and molecules with electronegative atoms).
The staggered formation is more stable due to interactions between the σ bonding orbital and the adjacent σ* antibonding orbital due to better alignment of the orbitals.
It is hard to visualize a barrier to rotation of 12 kJmol-1. What does it actually mean? It means a hydrogen atom is making approximately 1 x 1010 rotations per second. Basically, at room temperature, it is free to rotate.
It takes a barrier of approximately 75 kJmol-1 to slow rotation to once per second. Such a barrier is found in amides like DMF (dimethylformamide). Here delocalization of the nitrogen lone pair means the C(O)–N bond has some double bond character and this hinders rotation (see our discussion at the top of the page).
Structural features alter the barrier to rotation.
Conformations of Propane
Rotation of the C–C bond of propane is the same as ethane. There are two conformations, the staggered and the eclipsed. The barrier to rotation is slightly higher, the torsional strain caused by the overlap of a C–C bond and a C–H bond is a little greater (and the central carbon isn’t a perfect tetrahedron but let’s ignore that for the time being!).
The conformations of propane.
Conformations of Butane
Rotation around the two end C–C bonds of butane leads to the same two conformations as ethane and propane. Rotation around the central C–C bond is different, it leads to new conformations and a new form of strain. Compared to ethane, butane has replaced two hydrogen atoms with methyl groups. These methyl groups are big enough to interact with each should they get close enough. The repulsive interaction of atoms is known as steric strain and it causes one of the staggered conformations (with no torsional strain) to be strained.
The conformations of butane
The most stable conformation of butane is the antiperiplanar (or sometimes anticoplanar) conformation. It is staggered with no torsional strain and the two methyl groups opposite each other. It is one of the conformers, a theoretically isolatable arrangement of butane. If you draw the skeletal representation of butane as the standard zig-zag, it would look like this conformation (that is why we draw the carbon chains like this).
Rotating the central bond by 60° leads to the first eclipsed conformation, the anticlinal conformation. This is disfavored due to torsional strain and is a barrier to rotation. Rotation through another 60° leads to the second staggered conformation. The synclinal or gauche conformation is another conformer. It is theoretically isolatable as any rotation leads to one of the disfavored barriers to rotation. It is less favored than the antiperiplanar conformation as the two methyl groups are close enough for steric interactions to be an issue.
Gauche conformation of butane showing steric hindrance.
Rotating by yet another 60° leads to the least favored synperiplanar conformation. It is the biggest barrier to rotation. It has the maximum torsional strain and the maximum steric strain. Further rotation takes you back to the other conformations but with the methyl group found on the other half of the molecule.
The Conformation of Larger Molecules
It is funny how most textbooks jump directly to cyclohexane at this point. There is a good reason for this, it is difficult to draw out the conformations of larger molecules without the aid of a computer. From pentane onwards, there are two, or more, C–C bonds that can rotate independently of one another but at the same time. Pentane has nine conformations, and a plot of the potential energy versus two different dihedral angles looks like a contour map than a simple graph.
The conformations of pentane.
Most undergraduates never have to worry about systems this complex, and, for pentane, I just want to draw you attention to the central conformation. This is the favored conformation with all the bonds staggered conformation and each group antiperiplanar. As you can see, it is identical to our standard drawing of an alkane. We naturally tend to draw the most stable conformers.
The most stable conformation of pentane, drawn as a skeletal representation, an extended sawhorse and the Newman projection along the C3–C4 bond.
So, if you can only determine the conformations of small molecules like butane, what was the use of any of this discussion? Why do we bother? Well, the principles covered can be used to rank various conformations around a single bond within any molecule. While it would be hard to determine all the conformations of the molecule below it is possible to predict which conformation is the most favored and which the least for rotations around the bond highlighted.
What is the most stable and least stable conformation around the bond highlighted in blue?
To determine this, first draw the Newman projection of the molecule along the bond in question. I’ve drawn it looking from the right-hand end of the bond.
To answer the question you need to draw the Newman projection.
The most stable conformation will be staggered, minimizing torsional strain. There are three staggered conformations about the bond. To determine which is preferred compare the potential steric interactions. The most favorable conformation has the least steric interactions. In other words, the large groups are far apart.
The largest groups on each atom are marked in red.
The first conformation has the two largest groups gauche to each other. This causes steric strain. The second conformation has the large group on the front atom bisecting or gauche to both groups on the back atom. This is less favorable than the first conformation as there are more steric interactions. The final conformation is the most stable. While two groups are gauche to one another, the ethyl group on the front atom is next to the smaller (when compared to the branched isopropyl group) ethyl atom on the back atom. So the most stable conformation around this bond is the third one.
The least favored conformation can be determined in a similar manner. This time, you need to look at the eclipsed conformations. These are all disfavored due to torsional strain. To identify the least favored conformation look for the one with the most steric strain.
The least favored conformation has the the most steric interactions - here it is the largest substituent on each atom eclipsed.
The least favored conformation will have the most steric strain. It will have the largest groups overlapping. But even a system like this might not be clear cut; is there more steric strain from the two largest groups eclipsing or would multiple examples of smaller interactions cause greater strain? There is a reason textbooks don’t look at more complex systems.
Conclusion
Single bonds can rotate. This changes the shape of a molecule. These different shapes are known as conformations. Some of these conformations are more stable or favored than others. These are known as conformers and are considered by some to be examples of stereoisomers (although it should be stressed that they are actually the same molecule … it gets more complex if we enter the murky area of atropisomers ... so we will not). Other conformations are disfavored and act as a barrier to rotation. These are effectively the transition state the molecule passes through as it changes conformer. The shape of a molecule is important in some reactions, such as E2 eliminations, or the reactions of enzymes.
Attached are a number of practice questions focusing on Newman projections. HERE