Newman Projections

Now that we understand that sigma bonds are free to rotate as much as they want, it turns out that there's a unique way to visualize this rotation and that visualization technique is called the Newman projection. Newman projects are all about finding the different energy levels that conformers can make by rotating a sigma bond.
So maybe you recognize this drawing. This drawing is the same drawing that I had before when I was talking about conformers. And I was saying that you could have an s-trans hexane or an s-cis hexane. But it turns out that it's kind of difficult to visualize how those are different in energy. Energy is kind of an abstract concept right now, we haven't really defined it really well. But just think about that if something is very high in energy, that's not going to make it very stable.
In this case, it's not easy to tell which one is lower energy and which one is higher energy and that's why we want to have a new way to visualize this. What we say is, hey, imagine that your eyeball was right on this plane, so imagine that this is your face and this is your nose and those are your lips and obviously you're just an amazing looking dude. Wow. I need to stop what I'm doing because that's really terrible looking.
Imagine that that's a person. Don't imagine that's you, I don't want you to get traumatized. And you're looking at that bond straight down the line, straight down that bond. What you would actually see is you would see a carbon in the front, let's say that's your red carbon. And you would also see a carbon in the back, let's say that's your blue carbon. You'd see them overlapping each other. If you're looking right down that bond, you'd see one in the front, one in the back. So you would see that this would be your front one and then the one in the back would be represented by that circle.
Basically, what Newman projections allow you to do is to visualize where are the groups on the front carbon oriented and where are the groups in the back carbon oriented and how are they related to each other. With Newman projections, you're allowed to rotate around that bond in a three-dimensional way.
Basically, if you were to look down that bond what you would see is that your big groups, this ethyl group here and this ethyl group here would be on opposite sides of these carbons because as you can tell, if you were to draw your dotted line, they're on opposite sides of the fence. Basically, they'd be really far away from each other.
But then if you look at s-cis, s-cis is different. S-cis, if I had the same thing where my eyeball is looking, I would still see one in the front – oh, just a second. Wow. Red. I'd still see one in the front and one in the back, but what I'd also see is that now the big groups are overlapping each other. Instead of being on opposite sides, they're overlapping and that has a huge difference in how stable these molecules are, how stable these conformations are.

So let's go ahead and start off by defining what the dihedral angle is. The dihedral angle is defined by theta. Theta is just a variable that means angle. What it does is it describes the rotation between the two largest groups relative to each other. So basically the largest group in the front, on that front carbon, that largest group on the back carbon, where they are relative to each other, that's going to tell you your dihedral angle.
For example, if my two largest groups are overlapping each other perfectly like that – by the way, I just want to point out that there is a mistake on mine how it says CH3, it should be CH2 and then CH3, so don't let that freak you out. If they're perfectly overlapping, that means that the difference in their angle is zero because as you go further around, your angle gets bigger, but they're perfectly overlapping. So the dihedral angle, in this case, would be zero. And this conformation is called eclipsed.
The eclipsed conformation is the one where both of the groups overlap each other perfectly. This happens to be the conformation with the highest energy. Why would that be? Well, it turns out that large, bulky groups don't like to be next to each other. Why? Because they feel crowded. Remember that big bulky groups, they don't just have atoms, they also have electrons and electrons are negative. So if you put a bunch of these electrons together, they're going to repel each other.
So it's a really bad idea for these groups to overlap each other so perfectly. So this is going to be highest energy and what that means is lowest stability. Energy and stability are inverse of each other. They're opposites.
Then let's look at the next one. The next one would be if the dihedral angle is 60 degrees, 60 degrees just means that they are not perfectly overlapping, but they're also not perfectly far away. They're just kind of like maybe 2:00. At a 60 degree angle that is going to be called a weird word. That's going to be called gauche. Gauche, you can say it's when they're adjacent to each other. They're not overlapping, but they're still not as far away as possible, so in this case you see how its visualized there.
Now this one is not amazing, but it's not as bad as the other one. What I'm trying to say here is that the gauche conformation it's not as unstable as eclipsed, but it's also not as good as it could be. I'm just going to say here it has middle energy. That's a terrible word to use. But middle meaning just that it's not as bad as eclipsed so that would also mean kind of middle stability. Cool.
So now we're going to go on to our last one. Our last one is what if the dihedral angle is 180 degrees. That means that they're perfectly apart from each other. If they're perfectly apart from each other that means they're the furthest away they can get. And that means this is going to be called anti or anti. The anti conformation.
The anti conformation is where your two largest groups are opposite, that one's going to be the lowest energy. And by lowest energy that would obviously mean most stable. 

So, what I want to do is I want to plot an energy diagram with these degrees and I want to show you guys what that means and how that actually translates, OK? Now I know this is going to be your first interaction with an energy diagram or one of your first interactions so I'm just going to explain how this works, alright? Energy is on the Y axis over here and as you go up you basically get less stable, is that cool? And then on the X axis I'm going to have the dihedral angle, OK? so I'm going to go ahead and start off at 0, 0 degrees and then I'm going to go by groups of 60 so I'm going to go 60, 120, 180, 240, 300 and then 360 is that cool? Alright so what I want to do is go ahead and start off we don't have numbers and I don't want you to worry about exact numbers I just want to get a general pattern of what this is going to look like as it rotates so basically what I'm doing is I'm drawing a map of what the energy instability looks like as this bond rotates a full cycle or whether, OK? So, let's go ahead and start off with 0, 0 degrees is what kind of energy? Is it highest, lowest, middle what is it? 0 degrees is eclipsed that means that they're perfectly overlaps which means that this is going to be the highest energy so I want to pick a point that's really high on my energy diagram, do I need to know exactly what energy? No, I just want to take the high point is that cool? Now let's look at 60 degrees, 60 degrees would be gauche we said that gauche is more stable than eclipse so what I should do is I should pick a spot that's lower so I'm going to pick a spot like right here, alright? So that means that as I rotate from 0 to 60 I'm getting better my energy is getting less which means that I'm also getting more stable, is that cool? Alright so then we go to 120, OK? Well actually let's go to 180 first since that's the one that we actually have plotted out and then we'll do the 120, OK? So, for 180, 180 would be that they're perfectly far apart which means that they are the most stable that it's ever going to get so 180 where should I plot that point? I should put that point at the lowest point of my graph that's going to be the most stable point on my graph, alright? Cool so then let's go ahead and plot these again for if we kept going so if I basically if I added another 120 degrees I would get back to the 60-degree spot but I would get the 60 degrees spot the other way and then finally after 360 degrees I would get back to a full cycle where they're overlapping again so then I would pick a high spot, OK? Now I know that it's difficult to visualize what that maybe that second blue spot looked so I'll actually draw it, so remember that this first red one would just be like this it would be let's say I have X and X and they're overlapping, OK? So that would be our and then you have basically all these H, OK? I'm just writing X because I don't want to draw the entire thing, OK? Actually, yes that's fine...Well actually it says here to plot down the C3, C4 bond of hexane, OK? What does that mean? We should actually talk about that I'm sorry I forgot to mention that, OK? What that means is that they want us to show down the bond of the third carbon and the fourth carbon what the different energy levels would be, notice that what's coming off of the first half would be an Ethel group and what's coming up with the second half would be an Ethel group as well because the two in the middle are the part that are in the Newman projection, those two are the front and the back of the Newman projection, OK? So, what that means is that I could just instead of writing X-X I could just write ET ET where ET stands for Ethel, OK? And that's actually a really common abbreviation of Ethel is just to write ET, OK? Now let's go down to 60, 60 would mean that now one of the Ethel's is still facing the top but now the other Ethel is to the side, does that make sense? Cool, so now they're a little bit more stable then 180 would mean that one Ethel is facing up and one of those facing down, OK? Well then where am I getting this other blue spot from? Well the other blue spot would be if I just continued rotating this what I would eventually get is that this ET is still at the top but then now this ET just got 60 degrees away again but now it's on the other side and then finally this one would be if the ETs overlap again, alright? So now you're probably wondering about the 120s, the 120s actually don't have a name that we use often in organic chemistry but you could imagine that what's happening is that at the 120s I'm going to get an ET here and then I'm also going to get an ET here overlapping with an H, H-H so that means that for the 120s everything is overlapping again, OK? So, I mean this is actually going to be a higher energy point so this would actually be up here somewhere and then this would also be up here somewhere, OK? So now we finally got our energy diagram all we have to do is connect the dots and when we connect the dots we're going to get something that looks like this. Basically, down here then up then down then up then down and then back up, OK? And that is your energy diagram as you rotate along the bond, what that basically says is that you start off at the worst spot then you go 60 degrees and it gets a lot better then you go 120 degrees and it gets worse again then you go 180 and it gets the best then you come back and you do 240 and that's pretty bad because everything's overlapping then you do 300 and that is a little bit better than 240 because now things are staggered and then finally 360 is the same as 0, OK? I know it looks silly with me doing the whole clock thing but hopefully that helps you guys relate to this diagram, now the reason I went to such depth with this diagram is that some professors want you to be able to draw this or at least recognize what's going on with these dihedral angle diagrams, OK? So, I just want us to understand that hopefully now you should easily know that Anti is the best, eclipse is the worst and Gauche is in the middle and you should also be familiar with their dihedral angles.