What is the Relationship Between Isomers?

All right, so now we're going to talk about one of the most important types of problems that you guys are going to get in this chapter and it has to do with identifying the relationship between two different types of isomers.
Maybe you guys remember this flow chart. I made it when we were talking about constitutional isomers. Remember that we talked about how the very first step is to verify that all the atoms are the same. So we would count the non-hydrogen atoms and the IHD in both compounds. We said that if they were not exactly the same, then they were different compounds. Then we said that if they were the same, then you would go to step two.
Then we would talk about connectivity and we said are they all connected the same. We talked about that you look for a landmark atom. This is all review based on what we learned from constitutional isomers.
Then we said if they were not exactly connected the same, then they're constitutional isomers. Then we said if they were – back then we said that if they the same atoms and that if they were connected the same then we were going to say that they were identical.
Usually, when we're talking about constitutional isomers, we would have put identical in this blank. But it turns out that now that we have the possibility of stereoisomers, we actually have to go to step three now. Instead of just assuming that they're identical, now we have to look at the stereoisomers and we have to say stereocenters. We have to say is this an R? Is this an S? Stuff like that. 

So now we have to go to step three. And what step three talks about is chiral centers and trigonal centers. So let's go ahead and go for this.
So now that we've verified that all the atoms are the same and the connectivity is the same, now we're going to look for chiral centers. So if we have basically, if we have zero chiral or trigonal centers present so that means all the items are the same, connectivity is the same and there's zero chiral or trigonal centers, then the two molecules are identical.
So this is that blank that we would have used earlier when we would have said identical, but now we're just verifying that there's no chiral centers or trigonal centers.

But what if we do have one chiral center, which happens all the time? Well, if you have the same chiral center on both, then they're identical. If you have different chiral centers for both, then the relationship is going to be enantiomers.
Let me illustrate this with the following molecules. Let's say that I have 2-butanol and I have another 2-butanol. So I've already verified that these two compounds have the same molecular formula. They have the same IHD everything. And they have the same connectivity. They're both secondary alcohols that are butanols.
Then I go ahead and I figure out the configuration of this and I figure out that this one is R, has one chiral center. And this one is also R. So what do you think that relationship is? Well, that's going to be identical because they're the same molecule and they have the same chiral center.
Now, what if I'm comparing it to instead of R, what if I were comparing it to the same molecule, but now my OH is on a dash? Now instead of being R, this one's going to be S. What do you think is the relationship between these two guys? Well, we have one chiral center and they're different, so then these would be enantiomers or mirror images. Does that make sense?
That's the way this flow chart works, basically we look step-by-step and we say are they the same, are they different, etcetera. 

So let's go on to if we have two or more chiral centers. If we have two or more chiral centers and all of them are identical, all of them are exactly the same, then the molecules are still going to be identical.
For example, if I have a molecule that has three chiral centers and the chiral centers are like this. Let's say it's 2R, 3R and then 5S. And then I'm comparing it to another molecule that has the same molecular formula, same connectivity and it happens to be 2R, 3R, and 5S as well. Then those are going to be identical.
How about if all of them are exactly different. What if I was comparing it to 2S, 3S, 5R? Then what would that relationship be? Well, here what we see is that every single one is opposite. Every single chiral center has flipped, has switched, so because of that this would be the mirror image. So if they're all different that's going to be an enantiomer as well. We've already talked about this a little bit when I talked to you guys about the different types of stereoisomers you could have. Then if everything's completely different, that's an enantiomer.
But what if not all of them are different, but not all of them are the same? So what if we have this middle situation where I have 2R, 3R and then I have 5R? So now I have two of them that are the same, but I have one of them that's different. What kind of situation would that be? Well, that would be right in the middle where it's not the same, it's not different. It's not going to be a mirror image, but it's still different, so this is a diastereomer.
That's the way we think. If they're kind of different but kind of the same, that would be a diastereomer. Does that make sense to you guys? Cool

So then let's go to a few more and then we'll be done. How about if we have two chiral centers that are symmetrical and opposite to each other? This is a special case. If we have two chiral centers that are symmetrical and opposite to each other, that's going to be meso compounds. Remember that we discussed that meso compounds are kind of an exception where they have two chiral centers but they cancel out because they're opposite. Awesome. So those would be meso compounds.
And then finally we've been talking about chiral centers, what about trigonal centers? That's kind of its own thing. For trigonal centers, if I have one or more trigonal center and both of them are the same, then that's going to be identical. So an example of that would be 2-butene versus 2-butene. Notice that I'm doing a cis and a cis and I'm comparing them. If they both have the same arrangement, cis or trans, then they're just going to be identical.
But what if I'm comparing it to that one versus the trans, versus trans-2-butene? What's that relationship going to be? And it turns out that these are definitely stereoisomers, right? They look different, but they're not mirror images. One is not the mirror image of the other, so these are actually going to be diastereomers.
That is always the case when you have double bonds that switch cis and trans, you're always going to get diastereomers as a product, not enantiomers. So don't think of enantiomers because enantiomers are mirror images. But these – basically this one here and this one up here are definitely not mirror images of each other. So they're diastereomers. That's their relationship. Does that make sense?
Cool. So now I want to teach you guys a little secret here. I've given you all these rules. This is your flow chart. I really want you guys to use this a lot, apply it to memory and also just use it as a way of doing your practice problems. Have this out for reference. 

Something that's going to help is that this whole time I've been comparing S and R so that implies that every single time you have to figure out R and S. But it turns out that the same and the different part can actually work without finding R and S.
So for example, if I had a molecule that – if I have two molecules – I was going to draw something but I think I'll just explain it. If I have two molecules that look exactly the same except that the wedges and dashes are different, I don't need to actually calculate R and S. I can just instead say are they the same or are they different. But that only works if my molecules haven't been rotated.
If my molecules are rotated, meaning that your molecules are rotated into different positions when you're comparing them, then you actually do have to figure out R and S. So what I'm trying to say here is that R and S, if you figure that out, you always get it right. That's always the fail-proof way to do it.
But a lot of times we're going to cheat and instead of using R and S, we're just going to look and say are the molecules rotated. No, they're exactly the same position. The only thing that's changed is the bond being towards the front or the back. And in that case I would just say are they the same or are they different and that's going to save me a lot of time.
All right. So with that said let's go ahead and move on to the next page and see if we can figure out these relationships.