Let’s recap what we’ve talked about so far. Sawhorse cat and Freaky Sawhorse cat are constitutional isocats. But Freaky Sawhorse Cat has a mirror image of himself crawling around somewhere – a cat that is not exactly the same, but in fact a non-superimposable mirror image. An enantiocat, in other words.
Sawhorse cat does not have an enantiocat. Why is this? We’re going to need to look at the Cat Line Diagrams in more detail. Let’s do that.
So far with the Cat Line Diagrams we’ve neglected to mention any discussion of the “connectors” – the points where all the limbs meet. Let’s add another letter to our Cat Line diagram and label those points C. C can stand for connector, but if you want anatomical justification it can also stand for collarbone (the front half) or coccix (the tailbone) if you like.
Looking at Freaky Sawhorse Cat, the front C is attached to H, T, F and CT3, whereas the back C is attached to T,T,T and CHTF.
Look closely at C1. There’s something special about this C : it has no plane of symmetry. There’s no way we can find a mirror plane that cuts through this connector. This is because there are 4 different substitutents attached to it. It must be this C which is the reason why Freaky Sawhorse Cat is not superimposable on his mirror image, because if we look at C2, we can easily find a mirror plane due to the identical T substituents. Furthermore, if you look at the Cat Line Diagram of Sawhorse Cat, you’ll see that the substituents of each C also have a plane of symmetry.
We should give this property of Freaky Sawhorse Cat’s C1 a name, so let’s call it an “asymmetric center” or “chiral center” to provide the necessary Greek gravitas (chiral meaning “handedness”, referring to the fact that our hands possess a similar property).
If you compare the configuration of C1 between Freaky Sawhorse Cat and his mirror image you will see that their configurations at C1 are the opposite.
So we can also call a chiral center a “stereocenter” since it is the C1 on Freaky Sawhorse Cat that gives rise to the possibility of another cat with a mirror image configuration on C1 – his stereoisomer.
What about Larry, Doug, and Moe? This applies to them too.
Looking at the Cat Line Diagrams, notice how each of these cats share the formula C2H2T2F2 but differ in the orientation of their limbs in space (they are therefore stereoisocats). If you look at their cat line diagrams, you’ll see that each of them actually has two stereocenters.
Looking at the stereocenters we can start to understand their relationships.
Larry and Doug are enantiomers, because their configurations are opposite at both C1 and C2.
In contrast, the configuration at C1 and C2 of Moe is not the mirror image of the configurations of C1 and C2 of Larry or Moe. In each case, one C is the same and one is different. Therefore they are not enantiomeric, but diastereomeric. Remember: “diastereomers” is what we call cats that are “stereoisomers, but not enantiomers”.
There’s just one last piece of the puzzle that I can’t figure out. Why can’t I find an enantiocat for Moe? I guess I’ll just have to keep looking.
Bottom line: When comparing stereoisocats, enantiocats always have the opposite configurations at all of their stereocenters. If any of the stereocenters have the same configuration, they will be diastereocats.