I want to spend the next three lectures, three classes talking really closely about first order coupling and the reason is that there is so much to be gained by deeply understanding NMR spectra.

As I said, a lot of what one's going to be doing is asking specific questions about stereochemistry and being able to ask those questions is intimately linked to understanding what's going on.

Also, just in general for solving structures, being able to read spectra, really read them at a level that goes beyond the level of sophomore organic chemistry involves intimately understanding coupling. So we're going to take a relatively slow path through this and in fact are going to through the midterm exam only have 1D spectra

on our exam so that we really focus on understanding things. So I want to start by kind of making the bridge between last time's lecture where we talked about magnetic equivalents and we talked about non-first order systems and so last time was sort

of the bad and today is going to be the good. So the bad is that I said a lot of the rules that you learned in simple sophomore organic chemistry really are oversimplifications. There are very few systems that truly behave in the way

that you learn they should behave. These are the first order systems. So first order systems are anything like AX systems, AMX systems, A2MX, in other words they're anything

where your coupled protons, protons within a spin system are far apart in chemical shift and if you do have 2 protons that are chemically equivalent like we have

in an A2MX system that those protons are both chemically equivalent and magnetically equivalent. We divided this and separated it from non-first order systems

and these are systems in which you either have magnetically in equivalent protons that are chemically equivalent or you have protons that are similar in chemical shift. So for example of non-magnetically equivalent protons we saw for example AA prime, X prime systems

and we talked about just how ugly those systems could be. Those were like the phthalate system where I said no matter how far apart, no matter how high a magnetic field you look at,

dioctyl phthalate or ortho dichlorobenzene is never going to get better than this complex pattern of lines. Then I said we have other systems like AB systems where the protons are similar in chemical shift and ones that are related to this for example ABX systems.

The good news about many of these types of systems is that many of these non-first order systems behave very much like first order and that you can start to apply some type

of simple rational understanding to them which is more than I can say for an AA prime system, XX prime system or an AA prime, BB prime system. Now sometimes these systems will look like first order which is great because sometimes you can analyze these

types of systems as first order and many times you can but what I tried to show you last time was how there are ones that simply defy a simple reduction.

So let me show you exactly and let's take the AB system because I think this is a great starting point and what's nice is the AB system is going to be an archetype for many sorts of systems that although they're not first order we can apply first

order analysis to and we can start to see the distortions that occur. So a pure AX system is one in which you have a doublet so it's two hydrogens that are J coupled

so I'll say and again that's going to be the whole spin system so I'll just put on XX and YY to represent some other nuclei that aren't going to couple and not of course something with a hydrogen on it where it's J coupling. So you would have a doublet and then a big,

big span between it and then another doublet. This little squiggly is just a break in the spectra and if those two doublets are far apart in chemical shift then you're going to see them each

as a simple one to one doublet. Now as the distance between them becomes smaller, in other words either you have different substituents that instead of having them be very far apart they're closer together in PPM or you simply went

to a lower field spectrometer. Now you start to see a distortion that we would call an AB pattern where the inner line and so now instead of saying these are effectively very, very far apart now I'm saying they are far apart like so.

In other words this means one here and one way over there. Okay, now the typical way in which one characterizes this is the distance between these lines is the J value.

The distance between these doublets and technically one takes not the dead center of the doublet but the weighted average because technically with a multiplet the position of the multiplet is not at its average but at its weighted average.

In other words since this line is a little bit bigger we take the center as just a hair over. It's the weighted average. In other words if this line is 4 times, if these lines are in a 4 to 3 ratio and they're separated by .07 PPM we'd say,

alright you're .4 of the way over there, just a little hair. So if we call this distance delta nu typically if delta nu over J is much, much greater than 10 we're

in a situation like this and if delta nu over J is less than or equal to 10 and those are approximations then we're sort

of into this AB situation. By delta nu I mean the difference in position in hertz so in other words let's say the center

of this line was at 7.30 PPM and the center of this line was at 7.10 PPM and let's just say here

that our J value is let's say our, what will work out? What will work out? Well let's say that our J value equals 17 hertz. Now imagine for a moment you're on a very low field spectrometer.

Imagine you're on a 100 megahertz spectrometer. What's delta nu at that point?

What? 730 hertz. Does everyone agree? Delta nu is 20 hertz.

So at 20 hertz these guys would be hugely close together. In fact we'd have a situation that looked like this.

At this point delta nu actually would be just a hair further apart because it's the weighted average so I'm going to shift it over just a hair,

make the outer lines just a little bit bigger. This would be a situation where delta nu over J is very small. Where delta nu is about 20 hertz and J is about 17 hertz. If we had the same system at 500 megahertz what would the difference in,

what would delta nu be for 500 megahertz? A 100 hertz, right? So at 500 hertz, 500 megahertz delta nu is equal

to 100 hertz. So you look at this situation and at 500 megahertz you'd be more like this. At 100 megahertz you'd be more like this. So this is your AB pattern and if they were even closer they'd be

like what I sketched out before where the inner line would be huge and the outer line would be very tiny. Well that might, it would be like a 60 megahertz spectrometer

like one of the freshman or sophomore and we actually have like 100 or maybe it's 60 in the sophomore lab it would be like this. Or imagine the situation that instead of having substituents that put these apart at .2 PPM imagine they were separated

by .1 PPM but the main thing to keep in mind is for any given doublet no matter what the center of this peak whether I looked at it at a 500 megahertz spectrometer or at a 100 megahertz the center

of this peak is going to be 7.30 and the center of this peak, again weighted average center, is 7.10. Now 17 hertz is more characteristic of a trans alkene which was actually what I was doing when I was drawing this.

For something like this we'd be more like about 7 hertz for our J value. Thoughts or questions at this point? Okay, will the center move so if you improve the equipment

so here we've gone from this is our 100 megahertz, this is our 500 megahertz and the point is the center of this peak for this whatever hypothetical compound this is, the center of this peak is always at 7.3 PPM whether I'm

at 500 megahertz or at 100 megahertz but the distance between the peaks because the number of hertz per PPM is much smaller at 100 than at 500 the distance between the peaks here is very

far, it's 100 hertz apart or relatively far and over here it's only 20 hertz apart. The bigger, the inner one, the closer they are together the more

they tend into each other and that really is the difference between the AX, the center is related to the ratio of the bigger and the smaller, absolutely, absolutely.

Well here the bigger one is at 7.29 PPM or 7.28 PPM, the smaller one is at 7.31 PPM and by here we've got these 2 lines and one of them is at 7.2 PPM and the other is at 7 point whatever the number is.

Now what's valuable about looking at an AB pattern and understanding it is it really becomes an archetype for all sorts of systems that behave very near to first order.

So we were talking before about phenylalanine and I guess the example I gave when we were talking about spin systems was acetyl phenylalanine methyl amide

and I pointed out that we had one, so this is like a spectrum and chloroform solution so I'll say in CDCL3

and we decided that we had one spin system over here and the multiplicity of this proton of the NH is a doublet because it's split by one coupling partner. Each of these protons they're non-chemically equivalent

so they split each other but they're going to be similar in chemical shift. They're similar in environment so they'll both be at about 2-1-2, 3 parts per million. Why do I say about 3 parts per million? Well, they're off of a phenyl group so if we were a methyl group off

of a phenyl I'd say 2 parts per million. It's a methylene so that pushes it to like 2-1-2 parts per million. They're beta to a couple of electron withdrawing groups. They're beta to a nitrogen. They're beta to a carbonyl so that's going to shift them down field by about another half of PPM. So we'd expect them to both be at about 3 parts per million

but probably not to be on top of each other. So each of these is going to show up as a DD and that DD is going to be part of what looks like an ABX pattern

because this is part of an ABMX system. M is something that's far apart from either A and B

and C and so forth and X. So we have 1 proton that's going to be way down field. Amid nitrogen protons are typically at about 7 parts per million. 1 proton that's going to be moderately down field because it's next to an electron withdrawing group and it's alpha to a carbonyl and beta to a phenyl group

so this is going to be about 4 and a half parts per million and then these guys that are both going to be close to 3 parts per million. So we have far apart from this and H far apart from alpha and the alpha is far apart from the beta.

So this guy here is going to be split by 3 different protons so he's going to be a DDD if all of the Js are different or a TD where I will talk more

about these or DT if 2 of the Js are the same or a quartet if all 3 Js are the same within the limits

of experimental error. So the one I really want to draw our attention

to then is these 2 hydrogens here because now this type of AB pattern really can serve as an archetype for more complex patterns that are non-first order but are close to first order. So an ABX pattern is something where you have the AB pattern

in which each line is further split. So imagine this type of pattern here with some level of separation but now with each of these 2 lines split into a doublet. So what you see is line, line, line, line and then line,

line, line, line for these 2 protons.

This is for the ABX system so this is what we're seeing right

at about 3 PPM.

Which of them is which? So okay so stereochemically one of these protons is pro R

and the other proton is pro S. They're diastereotopic protons. If we can go ahead and so for example if I replace this with a deuterium in the thought experiment then the ranking

of the carbons, the ranking of the 4 substituents on here becomes highest rank, next rank, next ranked and so that would become an S center so this is a pro S proton and this proton is pro R.

If I knew the geometry here for example if I knew the phenyl group preferred to point in one way or another or I could by nuclear over house or effect experiments and the like detect certain proximities then I would be able to get an experimental correlation

or a predicted correlation based on say proximity to anisotropic groups of 1 proton and 1 peak. So right now I don't know which is which but with additional experiments, this is obviously just a sketch but with additional experiments in context yes you can figure

out which diastereotopic proton is which. Other thoughts and questions? Do they ever look the same height? Great question. So right now I've made a sketch for a situation in which these are relatively near to each other.

In other words maybe they're separated by a 10th of a PPM and so if they're separated by a 10th of a PPM the JAB here is going to be about 14 hertz. At 500 megahertz that would be a separation if they're separated by a 10th of a PPM about 50 hertz

and so delta nu over J would be about 50 to 14 about 3 but if they were very, very far apart, if something held these in very different magnetic environments then you would see the outer lines getting bigger

and the peaks becoming more like a regular doublet

of doublets so if they were further apart it would look more like this, these guys would be bigger. They would be tinting into each other less.

Other questions? These are really important and this is one of the reasons I'm going really slow over this. Coupling is always going to be mutual and so if we call this, let's name our peaks 1, 2, 3 and 4

and let's name our peaks 1 prime, 2 prime, 3 prime and 4 prime. So the JAB is going to be 1 minus 3 and 2 minus 4.

They will within the limits of experimental error be the same and JAB here will be the same within the limits of experimental error.

It will be 1 prime minus 3 prime and 2 prime minus 4 prime. In this case since it's an ABX pattern the coupling with the other proton, so the coupling with the remote partner, we'll call it AX.

JAX equals 1 minus 2 and 3 minus 4 and again those will be the same with an experimental error so let's say for a moment this is 14 hertz, that's also 14 hertz, let's say for a moment

that this is 6 hertz, actually it looks the way I've drawn it, it looks more like about 9 hertz so let's say this is 9 hertz, that's going to be about 9, that's going to be 9 hertz within the limits of experimental error. Here this distance will also be 14 hertz as will

that distance, this distance the way I've drawn it looks like it's about 12 hertz and that looks like it's about 12 hertz. Ah, where, oh no, no, no, 1 minus 2 will not equal to 2 minus 3.

And so over here JBX equals 1 prime minus 2 prime and 3 prime minus 4 prime and yeah if you look at this pattern and you draw a splitting tree diagram we split into a doublet so that's our big J and then each

of those lines is further split with a small J

and so you get this pattern of line, line, line, line and if I call my lines 1, 2, 3 and 4, 1 minus 2 is the small

J, 3 minus 4 is the small J, 1 minus 3 is the big J, 2 minus 4 is the big J. From the AB coupling, the geminal coupling in this particular case,

and the source of the small J is from the coupling to, in this case, this nucleus over here. That's going, beautiful question, that's going to depend on the geometrical relationship

on the Karpeles curve. So typically you will not have exactly the same coupling between one of the 2 protons, let's say the pro S and this proton versus the other proton and this proton and so rather than my, let me put up some real data.

You'll see exactly the same thing but at least it'll be a nice chance for you to have a real spectrum and I know I passed this out before but we didn't look as deeply at this spectrum. Now let's look at it with a fresh pair of eyes. Let's look at it more deeply.

So I didn't use this exact compound, I just grabbed this right off of the Aldrich webpage and remember you can go to SIAL.com, www.SIAL.com to get yourself lots of spectra.

It's a great way to check out your ideas and your understanding of things and so here we see a real compound. I've shown you this before. This is phenylalanine in D2O so unlike the example

that I, the hypothetical example I gave in chloroform, this one doesn't have an amide here, it has an amine here and it has a carboxylic acid. In D2O those exchange and so this becomes ND2

and you essentially see no coupling and don't see it and actually there's DCL here so this really becomes ND3 plus and you don't see coupling and this becomes D. So this system here what remains are the 2 methylenes and the methines so this is an ABX system

and so you see coupling here and this is your phenyls and this is your HOD and this is your alpha proton

and these are your beta protons and so this is a very real example of what I've sketched out and you'll notice the distance between these 2 lines does indeed match the distance between those 2 lines. In other words, the 1 to 3 or 2

to 4 distance does match the 1 prime to 3 prime or 2 prime to 4 prime distance and you'll also notice that the 2 couplings with the alpha proton are a little bit different, a little bit different from each other so it looks like if I had to eyeball it here

that our coupling here, this distance between 1 and 2 or 3 and 4 is about 6 hertz and the distance here, the distance between 1 prime and 2 prime or 3 prime and 4 prime is about 8 hertz and so you'll notice now the alpha proton is split

into a doublet of doublets so each of these is a DD ABX pattern and then you'll notice that our alpha proton is a DD and the doublet reflects the 2 different couplings.

In other words, the distance between lines 1 and 2 or 3 and 4 corresponds to this coupling to the 6 hertz coupling and the distance between lines 1 and 3 and 2 and 4 corresponds to this coupling to the 8 hertz coupling.

Thoughts or questions?

Well, a great question. So the question is if the alpha proton is a doublet of doublets, shouldn't it be leaning a lot more? You notice these guys are really tenting into each other and this one is just barely tenting in.

So now look, this is a 300 megahertz spectrum so the distance between these 2 looks like it's about a tenth of a PPM so they're separated by about maybe it's 2, let's say 2 tenths.

So the distance between these 2 is about 60 hertz, right, because it's 300 megahertz so it's 300 hertz per PPM so they're separated by about 60 hertz and the J value is about 14 hertz so that's a case where delta new

over J is about 4 or 5. Whereas here the difference between the alpha proton and the beta protons is about 1 hertz, about 1 PPM, about 300 hertz and the J value is 6 and 8. So this is a case, remember I said the big difference

between the AB and AX type of situation, this is a case where delta new over J is very big, 300 versus 6 or 8 is a factor of well over 10. So they're effectively far apart and you get very little tenting inward.

Other thoughts? So the high, so great question. So this is in D2O the most hydrogens

on heteroatoms exchange and so most hydrogens on heteroatoms. As a matter of fact I will say, I can give you exceptions but I will say hydrogens on nitrogen, oxygen are replaced

with D so they get replaced with deuterium. Deuterium shows up completely, shows up not at 500 megahertz

but at about 80 megahertz so they don't show up in the same spectrum and the J values are so small that for all intents and purposes you don't see coupling plus they're exchanging very quickly. Even without DCL they will exchange.

Because of DCL the amine is protonated so the amine is an ammonium group and because of DCL it dissolves whereas phenylalanine in just pure water wouldn't be nearly as soluble.

So I've started to hint that different types of coupling relationships have different coupling constants and what I'd like to do at this point is to talk about typical coupling constants

and see how we can use them to enhance our understanding. So, this whole coupling constants generally if you needed just one number to keep

in your head you could keep 7 hertz or 6 to 8 hertz. Let's say so we're talking SP3 to SP3 right now and if I needed a number, actually I'm going to just put this as a general CH to CH.

I'll show you double bonds in a second but if you need one number to keep in your head 6 to 8 hertz or 7 hertz is a great number to keep in your head without conformational preference.

I'll say without a conformational bias. What do I mean by a conformational bias? Well, if there's a strongly held relationship, for example, if 2 hydrogens are locked in an antiperiplanar relationship

so here we have 180 degree dihedral angle now our J value is going to be bigger. It's going to be about 8 to 10 hertz so for example if you have 2 axial protons so I'll put this

as JXX that would be a typical example for 8 to 10 hertz where you're locked into an axial relationship. If you have something locked into an equatorial relationship

where now you have axial equatorial or equatorial equatorial now you're talking about a 60 degree dihedral angle and so a typical JX equatorial or J equatorial equatorial is

on the order of 2 and I'll put little tildes, little squigglies here just to indicate that that's approximate 2 to 3 hertz. This is based exactly off of the Karpeles curve.

So a general way of thinking about coupling is that coupling comes from interaction of the nuclei with electrons in the bond that polarize the next bond, that polarize the next bond. If at one extreme you have a 90 degree dihedral relationship

between those 2 bonds you get no overlap of orbitals. If at the other extreme you have 180 you get very good overlap, an antiperiplanar relationship and at 0 you also get a good overlap

and so you see very large coupling constants at 180 or at 0 and very small at 90 or 60 and so Karpeles relationship is basically a relationship between theta, your dihedral angle and J and a sort

of a general relationship would be if we go from 0 to 90 to 180 that we go at 0 it's about 8 hertz.

We have kind of a cosine wave going down at 90 to a minimum and up at to about 10 at 180 hertz, at about 180 degrees.

Now this is sort of for general kind of plain vanilla carbon it's modulated. The coupling constants are modulated by electronegativity and hybridization. In general electronegative substituents lead

to a smaller coupling constant. In general if you've got an SP2, SP2 bond between the 2 atoms like a double bond you have bigger J values. So let me show you a couple of examples. So as I said first number to keep in your head is about 7 hertz. But now if you want to think about some oddball situations you

can think of like an aldehyde where now you have an electronegative oxygen and you have an SP2 carbon here and aldehydes are very funny in that your coupling constant is on the order of 2 to 3 hertz so that's sort of unusual.

Alkenes it's good to keep. These are numbers that really are worth keeping at your fingertips. For a cis alkene we're talking typically on the order of say 7 to 12 hertz with let's say 10 hertz being typical.

For a trans alkene we're talking maybe 12 to 18 hertz or 14 to 18 hertz, let's say 14 to 18 hertz with maybe 17 hertz being typical.

So these are all examples of vicinal couplings. One more example falling right in that sort of general 7 hertz range let's take on a benzene as an example.

On a benzene as an example we're talking maybe for ortho coupling maybe 6 to 10 hertz with maybe 8 hertz or 7 hertz typical.

Two bond couplings tend to show more variation than 3 bond couplings so for example

if you have 2 carbons on a methylene group on an SP3 hybridized carbon with different substituents on the carbon you can see anything from say 5 to 20 hertz depending on the electronegativity.

If it's just sort of carbons on here maybe 14 hertz is typical.

If you have an SP2 carbon on a double bond you're talking maybe 0 to 2 hertz, maybe 1 hertz being typical.

So all of these are example of vicinal and geminal coupling.

In other words 2 bond and 3 bond coupling. These are J2HH couplings, these are J3HH. If you have anything more than that, if you have greater than

or equal to 4 bond coupling we're talking long range coupling so for example J4HH would be an example of long range coupling. Normally in saturated systems you don't see coupling

but if you have a system where you have certain geometrical relationships then you may see it so we're talking about say a carbon not with its neighbor but with a carbon 1 over. So where does this come up? Usually if you have intervening double bonds so for example allylic systems, we talked a little bit

about this in discussion section. Typically let's say 0 to 3 hertz depending on the geometrical relationship. Metacoupling on a benzene, same type of thing. Let's say 1 to 3 hertz and the only real situation

that you can actually see a visible splitting where you have just SP3 carbons is if you have a locked relationship, what's sometimes called W coupling

and so usually you need a locked relationship where you have a series of antiperiplanar bonds. This occurs for example in the norbornane ring system. They call it W coupling because you have a W like relationship so say these 2 hydrogens and a norbornane you can see you have this series

of antiperiplanar relationships that make a W. Norbornane actually is loaded with W coupling so you have another W relationship

across the ring like this and there's even a third geometrical W relationship hiding in the molecule like so.

So I want to pass out, there's one table that's really useful in your book and I want to pass it

out just because the stuff that's in the back of your book is so much better when it's passed in front of your eyes rather than it's simply waiting there in the back of the book undiscovered and uncared about. So this is the appendix F I mentioned before

and I just want to show you how many good things are hiding in this one little appendix here. So everything we've talked about and more is hiding

in this appendix so we have our allylic coupling and this is all going to come up on Homeworks. If you're wondering what your typical allylic couplings are

you'll find answers here. If you're wondering what happens if you have a double bond next to a double bond you'll find answers here. If you're wondering we've already seen in the homework we've already seen coupling across the acetylenes and so how many bond coupling is that?

Four bond coupling, right? So 1, 2, 3, 4 bond coupling but if you ask

as many people do when they come up with some of the homework assignments here, well can you couple further? Can you get 5 bond coupling? The answer is right here waiting for you to read about it right over here.

Typically you see a little coupling across there. Coupling on pyridines is going to come up on the homework and already I think we see that very soon. Now all of this is given in more detail in pretz

so pretz has wonderful examples for pyridines, for thiophenes, for all these types of systems off of real compounds and off of typical examples but here distilled into really one little appendix and really one page of the appendix is so much different good stuff that's going to help you

out with some of the problems that you're working on. So I think this is where I'd like to wrap it up today. We're going to talk more about first order splitting next time and we're going to walk through some examples of doublets of doublets and triplets of doublets and doublets of triplets

and doublets of doublets of doublets and that will prepare you for a workbook assignment that comes later on.