How To Draw A Bond Rotation

How To Draw A Bond Rotation

• Rotation can happen to an infinitesimal extent around carbon-carbon single bonds but for the most part we only really care about showing rotations in 60 degree increments. This keeps two groups in the plane of the page.
• Rotations of +120° or -120° can be shown simply by interchanging any three groups on a carbon. If the carbon is a chiral center, take special care that 3 groups are interchanged, otherwise this will result in inversion of configuration (a “single swap”) on the chiral center.
• Bond rotations never result in flipping the absolute configuration of a carbon from (R) to (S) or vice versa, since that would involve breaking bonds. All that’s happening in a bond rotation is showing the molecule in a different conformation.
• Rotations of 180° are useful because they allow for rotation of the entire carbon chain. When you’re just getting started, applying some simple templates can help with getting things right, as will using a model kit (or even your hands).
• Rotations of +60° or -60° are necessary less often than 180° rotations, but they do use the same template as rotations of 180°.
• For situations where you need to rotate a large number of bonds at the same time, it’s often better to completely redraw the carbon chain and just make sure each chiral carbon has the same configuration in your “new” configuration as it does in the “old” one.

Table of Contents

1. Bond Rotation Basics: Interchanging Any 3 Groups On Carbon Performs A 120° Bond Rotation
2. Bond Rotation Practice
3. 120° Rotations on Fischer Projections
4. 180° Rotations: Two Templates
5. Bond Rotation Practice (180°)
6. 60° Bond Rotations
7. Multiple Bond Rotations
8. Summary
9. Notes
10. Quiz Yourself!
11. (Advanced) References and Further Reading

1. Bond Rotation Basics: 120° Rotations

This article is to guide you through the times in your life when you need to draw a bond rotation.

For most purposes, we are really only going to deal with the rotation of C-C bonds, but it can also apply to the rotation of other sigma bonds.

We will just do rotation of C-C sigma bonds in simple chains here, since 1) bond rotation in small rings is restricted [See Article: Introduction to Cycloalkanes] and 2) pi bonds cannot undergo free rotation.

Furthermore, although bonds can be rotated to an infinitesimal degree, we generally only care about showing bond rotations in increments of 60 degrees.  This makes 3-dimensional molecules easier to depict on a flat piece of paper (or screen) since two of the four groups attached to tetrahedral carbon can be drawn in the plane of the page.

Since the carbon chain is drawn in the plane of the page 99% of the time, it follows from this we will focus on showing how to do rotations about one of the C-C bonds that is in the plane of the page.

Finally,  I’m going to assume that you know that in our convention for drawing tetrahedral carbon,  a wedged bond indicates that a group is pointing out of the page, while a dashed bond indicates a group is going into the page. [See article – The Wedge Dash Convention for Drawing Tetrahedral Carbon]

Also, for our purposes, it’s most important whether a bond is a dash or wedge. Not whether it’s pointing left or right. There are always two different ways of depicting the dashed and wedged groups (one on the right, one on the left) and they are equivalent. It’s just a matter of perspective which one we choose to draw.

With that out of the way, here is the first thing to know about bond rotations.

If you interchange any three groups on a tetrahedral carbon you will have drawn a bond rotation.

That’s it.

• You don’t have to think in 3-D.
• You are really just picking 3 symbols on a sheet of paper and interchanging them.
• You don’t have to even imagine you are doing a bond rotation.
• The net result will be a bond rotation of 120°, either clockwise or counterclockwise.

Let’s illustrate. Here is an isomer of 2-bromobutane. Let’s do a rotation about the C-C bond that connects the chiral carbon (C) with the ethyl carbon (marked by the green circle).

To do a bond rotation of 120°, all we need to do is interchange 3 groups: Br, H, and CH₃ while keeping the fourth group (CH₂CH₃) in the same place.

Woot! That’s it!  We’ve done a bond rotation of 120° clockwise when viewed from the right.

It translates to this:

via GIPHY

Alternatively, let’s start with the same molecule drawn slightly differently and do the same operation. (Note that in this example that the chiral carbon ends up on the “bottom” of the zigzag carbon chain, so the H and Br are pointing down instead of up. Completely identical molecule to the one drawn above,  but a slightly different representation). 

In this case we’ve done a rotation of 120° counter–clockwise (when viewed from the right) which is equivalent to a rotation of 240° clockwise.

(A key thing to notice is that the configuration of the chiral center does not change. It’s (S) on the left and also (S) on the right after bond rotation has occurred.)

That’s equivalent to doing this:

In each case we have performed a rotation of 120° or 240°.

I will leave it as an exercise to the reader to prove that interchanging any 3 groups on carbon leads to a bond rotation. 

There’s just one extremely important thing to watch out for.

Only one group on the carbon should remain in its original position. The other three groups must be exchanged!

If you only exchange two groups, then you have not performed a bond rotation. Instead, you have inverted the configuration (i.e. you have broken some bonds).

Switching two groups on a chiral center will invert the configuration from (R) to (S) and vice versa. While this is also a useful trick of its own accord (See article: How to Draw the Enantiomer of A Chiral Molecule) it’s not a bond rotation.

2. Bond Rotation Practice

Probably the most common instance of using a bond rotation comes up when determining the absolute configuration (R/S) of a molecule and being faced with a #4 ranked substituent (generally H) that is either on a wedge or in the plane of the page.

One way to put the #4 substituent in the back is to do a bond rotation. So let’s do two exercises in that vein.

In this case, the hydrogen is in the front. Show what the molecule would look like when the H is in the back (i.e. on a dash).

Click to Flip

In the case below, the H is in the plane of the page. Do a bond rotation that would put it in the back.

Click to Flip

An alternative to doing a bond rotation is to learn to apply the Single Swap Rule, covered here – How To Draw The Enantiomer of a Chiral Molecule.

3. 120° Rotations On Fischer Projections

The technique of exchanging any three groups also works when the molecule is drawn from alternative perspectives, such as in the Fischer and Newman projections.

For instance, show how to do a bond rotation in this Fischer projection:

Click to Flip

It really is as straightforward as switching around three groups (but not two!)

Do two bond rotations here. Does this reveal anything special about the molecule?

Click to Flip

From doing all the bond rotations it should reveal that the molecule is a meso compound.

Doing bond rotations is one way of determining whether a molecule is a meso compound or not. (For more, see The Meso Trap – Identifying Meso Compounds. )

For an article on how to interchanging Newman projections via bond rotation, see Newman Projection of Butane, among others. 

4. 180° Rotations: Two Templates

Life would be simpler if all bond rotations were 120° rotations.

Alas, there are times when we absolutely must do an 180° or 60° bond rotation. They are slightly more involved than doing a 120 bond rotation, but not by a lot.

The 180° is arguably more important since it results in rotating the carbon chain, so we’ll cover that first. 

A good template to have by your side for these occasions is a simple tetrahedral carbon with 4 different colored atoms attached. 

Just by rotating the tetrahedral carbon you will go a long way towards being able to map these rotations out in your mind.

If you don’t have a model kit handy, you can just use your fingers as a guide, even if it looks a bit like you are making gang symbols.

Any line drawing of a tetrahedral carbon atom will have two groups bonded to carbon that are in the plane of the page. Since we like to make line drawings where everything is flat, those groups are usually carbon atoms,

A 180° rotation is useful because it results in a rotation of the carbon chain.

There are really two key templates to examine for 180° rotations, which I will arbitrarily call the starting point a “peak” or a “valley”.  [Note 1 ]

A 180° bond rotation in the first template, starting from the “peak” looks like this:

If you map out the starting positions and the end positions,

• the group that is in the plane (pointing down) remains in the plane, pointing up.
• the wedged group (pointing up) becomes dashed (pointing down)
• the dashed group (pointing up) becomes wedged (pointing down) 

In practice, this rotation looks like this:

In the second template, we start with the valley (i.e. from the bottom of the zigzag in the line diagram).

Mapping out the starting and end positions here, we get:

• the group that is in the plane (pointing up) remains in the plane, pointing down
• the wedged group (pointing down) becomes dashed (pointing up)
• the dashed group (pointing down) becomes wedged (pointing up)

This is what the rotation looks like with a model.

5. Bond Rotation Practice: 180° Rotations

OK, now let’s try doing some 180° bond rotations.

Click to Flip

Here’s another one:

Click to Flip

6. 60° Bond Rotations

Yes, we can also do 60° bond rotations.

There’s good news, though. If you can do a 180°,  you can certainly do a 60°, since the 60° follows a similar template.

Here’s two templates, starting from a “peak” or a “valley” of the carbon chain:

Here is an example of a 60° rotation starting from the “peak”

Here is am example of a 60° rotation starting from the “valley”:

7. Doing Multiple Bond Rotations

So far so good. We’ve shown how to do bond rotations along one carbon carbon bond. Slap yourself on the back if you’ve been successful at the exercises.

As we know, however, life can inflict cruel punishments.  What if we need to do multiple bond rotations?

Yes, we could apply what we have learned above to do all those bond rotations.

But…. one starts to run into a law of diminishing returns building models, applying templates,  and all that jazz.

So I present to you an alternate solution.

If you have to show the result of multiple bond rotations about a carbon chain, my advice is to do the following:

• Number your carbons.
• Determine the absolute configuration (i.e. (R)/(S)) of all chiral centers
• Redraw your carbon chain to the desired conformation
• Fill in all the substituents on the non-chiral carbons
• Put in all the substituents on the chiral carbons, and then determine (R)/(S) on each. If any of them have the wrong value, swap the dashed and wedged groups to obtain the correct configuration.

It may sound like a lot of work, but trust me, it’s less work than fudging around with models and everything else.

8. Summary

• If there’s one key trick to get out of this article, I’d say it’s just learning that swapping any 3 groups about a carbon gives you the result of a bond rotation. This alone can make the task of determining R/S when #4 is in the front or in the plane of the page significantly easier.
• Bond rotations should never result in changing the configuration about a carbon (i.e. going from (R) to (S) or vice-versa.  One way to check if you’ve done a bond rotation correctly is to determine (R/S) before and after your bond rotation.
• Make sure to swap 3, since swapping two will just flip the configuration.
• Doing 180° bond rotations gets significantly easier with practice.  I may suggest carrying around a single tetrahedral carbon from a model kit with 4 different substituents attached. It can come in handy for doing bond rotations and also for determining R/S. If anyone asks you what it is, just tell them it’s a piece of avant-garde sculpture or something.
• If you don’t have a model kit, just using your hands can be enough. Never forget that molecules are just 3-dimensional objects like anything else.

Notes

Note 1. Only two templates, but four if you consider their mirror images where we are looking from right to left along the carbon-carbon bond. For simplicity we’re just going to omit those cases.

Quiz Yourself!

[90° rotation]

(Advanced) References and Further Reading

References