Freshman Organic Chemistry II

CHEM 125b - Lecture 22 - Medical MRI and Chemical NMR

Chapter 1. Tomography, Field Gradients, and Magnetic Resonance Imaging [00:00:00]   

Professor J. Michael McBride: OK, welcome back. I hope you had a good break. Can you remember back to when we, before break, what we were talking about? The last thing we did was this gyroscope bicycle-wheel precession to show what would happen to a nucleus that was spinning in a magnetic field, or an electron for that matter. Just to rehearse it a little bit, remember the idea of a pulse, a 90° pulse, that if you have a big magnetic field– the blue one there, really enormous– and then the little magnet of the nucleus precesses at 100 MHz, for example, in a certain field. And that gives rise to a constant vertical field, but a rotating horizontal field from that one.

So the question is whether that rotating horizontal field, which as you see it will be going back and forth and back and forth, will act as an antenna and give you a signal. You should be able to pick up a radio signal at 100 MHz. Indeed, you should be able to, except that there’s not just one proton. There are lots of protons, and they’re in different phases of precession. So although they all add vertically, and you have a substantial vertical magnetism from those, their horizontal components cancel, so you don’t see anything.

In fact, the energy is so small, of the interaction of each of these magnets with the field, that there are ones pointing the opposite direction, with higher energy, almost exactly the same population. Just a tiny, tiny difference. But we’ll look just at the excess. Obviously, ones down will cancel ones up. But if we look just at the net ones up, even they cancel, because they’re at different phases of rotation or precession about that axis.

But you can do a trick, remember. We could consider that we’re rotating with them, so that they look like they’re standing still. And then in our frame we’ll put on a little bit of a magnetic field that’s horizontal, a very weak field. And now, as far as we can see, we don’t care about the big field anymore, because we’ve compensated for it by orbiting around this thing as we’re looking at it.

But what we see is that these will begin to precess in our frame around that horizontal field, so they’ll do a slow precession, all of them, in that direction. So they’ll be going like this. They’ll start here, they’ll go there, then they’ll go down, then they’ll go back, and then back up again. But we’re going to put on a pulse only long enough, of this field, so that they go down to here. That’s called a 90° pulse, and they’ll rotate down like that.

And now forget the rotating frame. They’ll look like they’re just pointing out toward us in the rotating frame. But if we go back to the real frame, the laboratory frame, what we see is this whole bunch precessing around the field. And now as they precess around the field in the laboratory frame, there will be a net horizontal field that they’re generating, a magnetic field. And that will be the antenna that broadcasts a signal that we can hear.

And what will determine the frequency of that signal that’s going to be coming out from going back and forth, and back and forth or around? What will its frequency be? How rapidly are they precessing? It says 100 MHz. And what determined the 100 MHz? The strength of this big magnetic field. Remember, the more you twist on something, the faster it precesses. So we could make it 100 MHz. If we had half as big a big field, it’d be 50 MHz. Or twice the field, it would be 200 MHz, and so on.

So we get a signal that’s 100 MHz radio frequency in the laboratory frame, that we could detect with an antenna. But in time it will relax. This is a non-equilibrium situation when we put the energy in to make it go down. And in time it’ll come back to equilibrium. And that process is called relaxation. And there are various things that control how fast that happens. But it will reestablish equilibrium, and it will be very important later in the lecture about this relaxation, and you’ll see why.

So a 90° pulse makes the spinning nuclei, protons, or C-13s, broadcast a frequency that tells what their local magnetic field is. The higher the field, the faster they precess, the higher the frequency. Now let’s first look at this as it arises in magnetic resonance imaging, where the purpose is to locate protons within the body using a non-uniform magnetic field. Now, the idea of tomography is important here. I’ve taken this from a Colorado Physics-2000 page.

So this is a slice through somebody’s body, show their rib cage, spine, and so on, and they’re wearing some sort of jacket that’s opaque to X-rays. And we’re interested in finding what it looks like inside, where these things are. So what we do is we take X-rays, and send an X-ray beam straight through and see how much gets through. And we scan the X-ray from top to bottom, and see how much gets through at every different x-coordinate.

So we do a scan, and it starts at the top, but oops, there’s something there. And there’s even more there. And lots, then a little bit more. And for when we hit the spine, there’s going to be quite a bit, and so on. But that’s just a one-dimensional picture of the density. Now what we’re going to do is take that same picture and just smear it out to the right. So that’s the profile, top to bottom, or stomach to back, of this particular slice through the body of bones or whatever it is.

Now the neat trick is that you rotate that, rotate it by 15°. And now do the same thing again, and superimpose the new one on the old one. And now rotate another 15° and do the same trick, scan top to bottom and add it up. And do it again, and again, and again, and again, and again, again, again, and again. And see what you got now? When you superimpose all those, you get what it looked like, the two-dimensional slice through the thing. So that’s called tomography. If you can get a one-dimensional projection, and do it in lots of different directions and add them together, you can get the two-dimensional, or in fact, a three-dimensional picture of what’s going on inside.

So that’s the trick that’s used, except you want to do it for protons, not for bone. So we want to find protons in the body. For example, let’s find where there’s fluid water in the body. So there’s a body, and we put it inside this cylinder and wrap the cylinder with special wire, that if we cool it to liquid helium temperature is superconducting. So essentially, we’ve made a big solenoid magnet that goes along the body’s axis.

Now, what will happen? Well, suppose that field is 1.5 Tesla, which means 15,000 Gauss. A Gauss, you remember, is about the size of the earth’s magnetic field more or less, so 15,000 times as strong as the earth’s magnetic field. So what will happen to the protons in there? Well, they’re going to precess. And in that field, at 15,000 Gauss or 1.5 Tesla, they’ll precess at 63 MHz. So if we put an antenna in there and give a 90° pulse, we’re going to hear a signal at 63 MHz. Our radio will pick that up. So we know there are protons in the body. Surprised? No.

The question is, where are the protons in the body? Now here’s an analogy to figure this out. Suppose we had a cricket in this room, and wondered where it was. But I’m blind. I can hear, but with only one ear, so I can’t hear… I don’t have spatial resolution with my ear. How can I find out where the cricket is in this room? Anybody got an idea?

Well, I have one bit of control over the room. I can make a temperature gradient in the room, make it cold in front and warm behind. Suppose I can do that. Now how can I find the cricket? What? Derek?

Student: Crickets chirp at different speeds at different temperatures.

Professor J. Michael McBride: You hear it chirping. You count how many there are in 13 seconds and add 40. You establish a temperature gradient and you listen with a stopwatch. And if you go to Snopes, you can see that this is not an urban legend or a rural legend. It’s true that you can do that. And they actually show this picture of Doctor LeMone from Boulder, Colorado, who actually did this with crickets, and showed that it gives a very good measure of the temperature. So if I could establish a temperature gradient from front to back, and count for 13 seconds and add 40, and knew what the temperature was, I’d know how far from front to back. What would I do next if I want to find the cricket?

I’d fiddle with the air conditioning controls and make a temperature gradient from left to right. I could even make one from top to bottom, and then I’d know what its x-, and its y-, and its z-coordinates are. So I could find the cricket that way. So we’re going to do the same thing with the protons in the water in the body. So back to the body here. What I need is not a uniform field, where all the protons are going at 63 MHz. I want to make them faster in some regions than others. So what I do is I put two coils around this solenoid.

And in the one near the head, I make the current go that way, which reinforces the field. And in the one near the feet I make it go that way, which subtracts from the field. So now I’ve generated a gradient along the body. And it turns out to be that what’s actually used is about 40 microtesla per millimeter. So if I went, like, 25 millimeters, about an inch, that would be 1000 microtesla, that is a millitesla. So it’d be about one part in 15,000. Or, pardon me, one part– it’s a millitesla out of a 1.5 tesla, so about a part per 1000 difference.

So that means if I slice the body there or there, on the first slice– remember, there’s is a gradient from foot to head– so there we have the average. 63 MHz is going to be a signal coming out from protons that are in that first slice. But in the second slice they’re going to be at 63.05, about a part per 1000, because there’s a higher field near the head. And if I did another slice another inch or so along, it’d be 63.1 MHz.

So if I had an antenna and could hear all these different frequencies and how strong the signal was, I’d get a profile of the proton distribution from foot to head. So just like we did with the X-rays scanning down. I now know how much water there is at different places along the height of the body, or the length of the body. What do we want to do next? Matt?

Student: You do it in a different direction–

Professor J. Michael McBride: So we want to make a gradient in a different direction, so I stop the current in those green coils and put on yellow coils with current going that way, which adds to the big field on the right. And then I put other coils over here, which the current goes that way and subtracts from the current– from the field on the left. And when I do that, I get a gradient from right to left. So then I can do a slice and find out how water is oriented that way. And then I can put coils on the top and bottom, analogous to these, and get a vertical gradient, and get it that way.

And in fact, by putting a certain amount of current in all these coils at the same time, different amounts in different coils, I can make a slice that goes in any direction I want to, and find out how much is there. So now in three dimensions I can do one of these tomographic reconstructions, and get where the water is in the body.

Now, much more interesting than that, which is itself very powerful, is functional NMR, or MRI, magnetic resonance imaging. Where you locate protons whose signal strength is being fiddled with. So for example, we talked about relaxation, how fast the signal goes away. If you measured this for the different signals you were getting, how fast they went away, then you’d know something about a difference from one part of the body to the other, that the protons in this part, their signal is going away rapidly, whereas here they’re not. So you could get something about how the protons are behaving, not just what their local field is.

So for example, blood oxygen level dependent or B-O-L-D, BOLD imaging, you can do this. And you get a spatial resolution of about one millimeter, and a temporal resolution of about two seconds.

So every two seconds, you can get where oxygen is in the body, unusual amounts of oxygen, Now, how is that relevant? Because if you have cell activity, it increases the blood oxygen supply, and that speeds the relaxation, how fast the signal goes away.

So now, these are very weak signals. So the way you tell something about them, is to take a difference. Where did we see a difference map before? Do you remember? Remember when we look for bonds in X-ray, we look at the observed electron density minus what you’d have for the atoms. That difference signal, tells you how it shifted for bonds. Well, you do a similar kind of thing here. You get a difference map. Now, this is a bunch of different slices through the brain. And what’s lit up is where there’s relaxation. That is, where there’s oxygen, where the brain cells are active under one circumstance, minus how active they are under some other circumstance. It’s a difference.

So the brain is working harder when it’s in one state than the other. Now, what are the two states? It’s the subject being shown donuts minus the signal when the subject is being shown car keys. So these are places where the brain lights up when it sees donuts, but doesn’t light up when it sees car keys. Now, this particular subject had recently been fed. And they did it also for someone who had not been fed, who was fasting. And their brain really lit up when they saw donuts versus car keys. So you can imagine that this is very, very popular with psychologists and so on, people interested in brain and all sorts of things, where you can use this trick of differences to see where something’s happening in one case versus another.

Chapter 2. The Development of NMR Spectroscopy [00:16:16]

So that’s MRI, and, of course, it’s not fundamentally our business here to talk about MRI. Except, we want to see things happening in molecules. Now, why can’t we do exactly the same trick with molecules to find out where protons are in a molecule? How do we know that something is here, rather than here, rather than here in the brain? We establish a magnetic gradient so that you get a different field here and here, and you get different frequencies. And you can distinguish where it is in the brain.

What’s the problem with doing that for a molecule, and looking at different protons in molecules? What’s the difference between my brain and a molecule? There are lots of differences, but one of them is, that I hope my brain is an awful lot bigger than a molecule. So you can’t establish a gradient big enough across the small dimensions of a molecule, so that protons in different regions will have different frequencies. Within any one molecule it should all be the same field for practical purposes. So we can’t do this trick, or can we?

So we want to locate protons within molecules. And now we want to have, not a gradient, we want to have a uniform field. If we could make the gradient big enough, maybe that would be useful, but we can’t make it big enough. So let’s go the other direction and make it absolutely the same everywhere, a uniform field. Now, and then what we’re going to do is listen until we hear– and put up one of these pulses in– and hear the frequency with which these protons– if there are protons there in the sample, we’ll hear them.

Of course, most organic substances have protons in them. So it doesn’t surprise you that as I scan the magnetic field– increasing the magnetic field, which changes the precession frequency– while listening with a radio that’s tuned to just one frequency, as I go along, at someplace I’m going to have the right frequency. And the protons are going to give me a signal.

Of course, if I had different nuclei in there that were different magnetic strengths, then I’d get signals at different places. But I’m going to only look at– only listen for protons. OK, so there it is. Bingo! Protons. Whoop! Protons again. Protons again. There are different signals for protons. Not all protons are equivalent.

Now, the difference here, between this signal and this signal, and how big the magnetic field is, is very, very small. It differs by only that fraction, 2.48 parts in a million. They’re almost exactly the same. But they’re a little bit different, just parts per million different.

Now, when this was discovered it was an annoyance for the physicists who were mostly interested in things like measuring how strong the magnetic moment was, how fast the precession was for protons. But they put something in there that has protons and they find out there are different protons. Which one is the real proton? So they called this the chemical shift, because these differences had something to do with a chemical environment.

But this was a gold mine for chemists, because since the beginning people have been– since 1850, at least– people have been interested in chemical structure. But the only way they could do it was convert one molecule to another, count isomers– as we discussed last semester with Koerner, and so on– and try to use logic to figure out what structure would be consistent for these various transformations, chemical transformations. And, of course, then there was X-ray, which really did show where atoms were. But here’s something that could work in liquids. Not everything can be a crystal. So this looked really, really promising.

Now, this sample was ethanol. Now, what do you think the three different signals are in ethanol? Well, one must be the OH. One must be the H’s of the CH₂, and one must be the H’s of the CH₃. Now, doing such an experiment requires that the field be very, very uniform, because if, as you go from one part of your sample to another, the field changes by a couple parts per million, then the methyl protons in this part of the sample will appear the same place that the CH₂ protons appear in this part of the sample, or the OH does in this part of the sample, even if the gradient across the sample is only a part per million or so, a couple parts per million. And that’s one of the reasons these peaks are not infinitely sharp. One of the reasons they’re broad is that the field isn’t perfectly uniform. But it’s very good. It’s within a fraction of a part per million.

Now, in the late 1950s, as it says here, chemistry departments began buying commercial NMR spectrometers. This one was called the Varian A-60, and it’s the one I learned to operate. And they had to have fields that were homogeneous enough to determine molecular structure. So they had to have fields that were different, that didn’t vary by more than a small part of a part per million, so that you could tell things about chemical shifts and spin-spin splittings, which we’re going to be talking about in the rest of this lecture.

But, of course, these things were expensive and many different people were using them, so it was a challenge to keep the field homogeneous to obtain sharp lines. Now, there were knobs in there that you could turn the current to coils, to cancel a gradient in one direction or another, or another, or another. And most of them were hidden behind that door, and the door said on it, “Do Not Open.” Because someone who knew what he was doing came in at the beginning of the day and turned all those knobs just right, so the field was very uniform. And if anybody else came in and twiddled them, then the next guy to come in was really up a creek. So do not touch these gradient knobs. In fact, there was one there, the y-gradient, which would have its own special sign, “Do not touch this.”

Now, this was fine, but across New Haven… or across the Long Island Sound here, you see the smokestacks of Port Jefferson and the medical building at State University in New York at Stony Brook. And there was a physical chemist at Stony Brook who fiddled with them. His name was Paul Lauterbur. And in 1972 he would take over this machine every night, and he’d just wreck the field homogeneity. And, of course, late at night before he left, or early morning, he would turn all the knobs back, because he was really an expert at NMR.

But the reason he did this was to establish gradients in different directions so that he could locate– he had a sample tube, and he filled it with D₂O, not protons. And in it he put two capillary tubes that had water in them. So he did exactly the kind of experiment we were talking about.

And in Nature in 1973, he published this, where he scanned vertically and got this, scanned horizontally and got this, scanned at 45° or –45° and got those, and could find out where these water samples were inside D₂O. And he called that zeugmatography, but the name didn’t catch on. But the good news was that 30 years later he got the Nobel Prize in Physiology or Medicine, for inventing MRI. And that’s what he worked on the rest of his life. So it was a chemist who invented MRI.

So there are lots and lots of magnetic resonance spectrometers. And I already showed you some X-ray diffractomers around, which have put classical structure proof by chemical transformation, the kind of thing that we talked about Koerner doing, and even IR, mostly out of business, although there are still things for which IR is as good or even better than NMR.

And, in fact, there was a Yale– before I came here, there was a organic chemistry professor who was in the field called natural products, where the job was to take something that came from nature and figure out what its structure was. And the way to do it, in those days, was to do these chemical transformations and try to make it from something or make it into something whose structure you knew. So these were great puzzles, and it was really a big operation. But when NMR came along, he abandoned organic chemistry and took up fundamental research on quantum theory. And in fact, later he became a professional studio photographer. He was just wiped out by NMR coming along, which is the way people know structures now. We haven’t really talked about that much, about how people knew– we’ve talked about different structures, but not really how people figured them out, except when they used X-ray. But this is an even more common way of determining structures routinely, is spectroscopy. And in particular, nowadays, magnetic resonance spectroscopy.

So a couple of years ago I took a tour through the department and took photographs of magnetic resonance spectrometers to show you here. So across from your lab you may have noticed this door which says Chemical Instrumentation Center, and it says warning over here, about magnetic fields, so if you have a pacemaker, be careful. And you go inside there, and some of these have now been moved since I took the pictures, but you see these things sticking up like here, and here. And if you go around, you see these big cans, WARNING: strong magnetic field. Here’s another one. Here’s another one. That’s a 500 MHz spectrometer. Here’s a 500 MHz spectrometer. Here’s a 600 MHz spectrometer. Here’s another 600 MHz spectrometer.

And out in the courtyard, behind your lab, there’s this special little building that was constructed specially for a big magnet. And it has this one, which is an 800 MHz spectrometer, which turns out to be 8³ power. That is 512 times as sensitive as a 100 MHz spectrometer, not to mention other advantages that we’re going to talk about below.

Now, why is it 8³? It’s because of the Boltzmann factor. Remember, this signal comes because there are more that point with the field than against the field. We only see the difference between those two. And if you have a bigger energy difference, you’ll get a bigger population difference. So you get an eightfold factor from that. But the energy quantum that you’re dealing with, in going from one level to another, becomes eight times as big. That’s an advantage in your signal. And the sensitivity of the electronics, when it’s eight times bigger, is also better. So all these things go together to make it 500 times better, and even more than 500 times better when you consider what we’ll talk about soon, the chemical shift advantage. So that’s why one pays the big bucks to have a machine like that.

Here are just some others that I took around. And now by the cross hall there, next to your lab, when you walk down there on this side of it, there’s a room that has electron paramagnetic resonance spectrometers. So this is a much smaller magnet, not one of these big liquid-helium-cooled things. And the reason is that this is to study free radicals, which have magnetic electrons. Mostly electrons come in pairs, and their magnetisms cancel. But in certain molecules, free radicals, there’s an odd electron, whose magnetism is detectable. So this is to study free radicals. And the electron magnet is 660 times stronger than the proton. So you don’t need such a big field to make it precess. So you can use just 0.3 Tesla instead of several Tesla for electron paramagnetic resonance. So there are two of those spectrometers.

And in fact, we don’t have one of these, but there’s now commercially available a 1000 MHz spectrometer, which is 23.5 Tesla. And at the Florida State University National High Field Magnet Lab, there’s a field that’s pulsed that goes to 45 Tesla. And it’s a national lab. You don’t pay to use it. But you have to have a great experiment to be assigned time to do things there.

So there are lots of these things around.

Chapter 3. Counting Protons by Integration [00:29:16]

Now let’s go back and see why it’s so good. OK, we have these three signals, and as we said, we’re interested in which peak is which set of protons. Now, how do we know which is which? Can anybody see a way of figuring out which is the CH₃, which is the CH₂, and which is the OH? Any guesses? Yeah.

Student: The size of the peaks.

Professor J. Michael McBride: Ah! If you have twice as many protons, there should be twice as strong a signal. You measure the strength of the signal by how much area is under it, by integrating it. So if we measure the integrals, we see they’re in the ratio of 1:2:3, so it’s clear that that’s the 1, that’s the 2, and that’s the 3. Now, we couldn’t do this in IR, because we had these normal modes, and had, for example, C=O. And remember, as the C=O vibrated, something else vibrated at the same time, and other things, and they could cancel or reinforce. So the signal intensities were very, very different for different groups.

But here the protons are all essentially exactly the same. They differ only by a part per million, or a few parts per million, so the intensities are proportional to the number of protons, because the difference is so subtle. So you can count protons by the area under these peaks. That’s what it says here. The number is proportional to the number protons because they’re so similar, not like IR peaks.

 Now, how can you use this? Here was one of the very first uses of a subtle organic chemistry question. This was an advertisement by the Varian Corporation in 1955, who were trying to sell those machines I showed you, that the guy over at– Paul Lauterbur messed up the field on every night.

So this was example number 20, the “use of integrated intensities in structural analysis.” So there’s a question of the structure of C₇H₈, whether it’s this or this. And notice that those two are related to one another, because if we shifted the electrons like that, one would go to the other. So you could imagine them going back and forth by an electrocyclic reaction. And the question is, which is it really?

Well, you could try to figure out by chemical transformation, and people did that. So which is it? Well, let’s try ozonolysis. Now, do you remember what happens with ozonolysis and then oxidation? You cleave C=C double bonds and make carbonyl groups there, an acid, make a carboxylic acid group when you add the H₂O₂. So these would give different products. Notice that on the left, you would cleave three bonds, on the right, you’d cleave only two double bonds. So on the left, you would get that diacid. On the right, you’d get the diacid that has two more carbons.

Now, in fact, that acid on the right was known. It’s called cis-caronic acid, and that’s what you got. So what’s the conclusion? The conclusion is that the structure must be B, not A. So that’s a classical structure proof by chemical transformation.

But here’s a completely different way of going about it. Take the NMR spectrum and count the protons. So the group on the left there are protons that are attached to double bonded carbons, and on the right, to single bonded carbons. And now, notice that the compound B has four of each kind. But compound A has six of one kind and two of the other. And if you integrate, you find that those ratios are 2.9:1, 3:1. So which is it? It must be A that you’re taking the spectrum of. That’s the one that’s 3:1. So it must be that that’s the structure, but then how do you explain this misleading chemical transformation? It must be that there’s an equilibrium between these two things that lies to the left, so when you take the spectrum that’s the stuff you see, that’s most of the material. But it’s not as reactive with ozone as the stuff on the right. So that little bit of stuff on the right is what reacts with ozone and gives the product.

So the chemical transformation was misleading. And this is the kind of thing that made this Yale natural products organic chemistry professor pull out his hair and become a quantum chemist, and then a studio photographer, that you couldn’t do what he was trained to do anymore. So spectroscopy took over in determining structure, and we’re going to talk a little bit about how you do this.

Now, Chemistry 220 website has a bunch of NMR problems. There are 40 problems there, and I took this from one of them and fiddled with it a little bit. And in fact, let me just see, I think I left an extra– well, I’ll go through here and– there’s going to be an extra slide in here.

So we can integrate. And see that there are 2 and 3, and 3. So we know that the 2 must be that CH₂, but there are two CH₃ groups, one is one and one is the other. That’s at low resolution, where the field isn’t so uniform. But if you make the field really, really uniform, if you tweak those knobs just right, so that the peaks don’t get broadened by having different fields in different parts of the sample, and in fact, spin the sample, so that a given molecule actually is going around and sampling different parts to average the field, to make it even more uniform, then you see this thing with sharp peaks. So it’s the same 3, 3, 2, but they look a little different here.

So the peak width is about three parts per billion, and that’s just, as you see, a single peak there. But this next one is a little different. That’s a triplet, 1:2:1. So that’s one of those CH₃ groups, but which CH₃ group? Oh, pardon me, I got it backwards. This was a CH₃ group, and it turns out to be this one. This CH₃ group is split into three, and it’s that one. Now, why is it not a single peak? What’s different? OK, well, that splitting is 0.029 parts per million. I obviously blew it up in order to be able to see it clearly here.

And this is a 250 MHz spectrum. So it means that splitting, the difference in frequency, of protons in one environment or the other, is 7.3 Hz. And it’s exactly the same there, 7.3 Hz. Now, if you look here, that’s a quartet. And those are 7.3 Hz as well.

Now, what’s that last signal, this little tiny one down here? Well, notice that the solvent is CDCl₃. Now, why would they pay the bucks, the big bucks, to get deuterium rather than just using normal chloroform, CHCl₃, for a solvent. What would it look like if the solvent were CHCl₃? You’d have an enormous peak from the solvent, that hydrogen of the solvent. It would wash out the other things. So you make it deuterium. But it’s not 100% deuterium. There’s a tiny, tiny amount of protium in there. So that tiny signal comes from a little bit of CH₃ [correction: CHCl₃] in the solvent.

Chapter 4. Local Magnetic Fields and the Chemical Shift [00:37:33]

So the 90° pulse makes the spinning nuclei broadcast a frequency that tells their local magnetic field, in a uniform field. Now, there’s the big uniform field. But what the nucleus sees is an effective local magnetic field, which is, of course, the big field– that’s mostly it– but little, little tiny differences due to the chemical environment. And let’s see how we do it.

OK, just to back up at first, you could make the applied field inhomogeneous, as an MRI. And then the field can be, for example, 2 Tesla, 30,000 Gauss, with a gradient of 4 Gauss per centimeter for human samples. And if you have a tiny thing, you could make a bigger gradient. So for small animals you can get 50 Gauss per centimeter and do the imaging that we talked about.

But in chemistry it’s different. In chemistry, you make it really homogeneous, so the only differences come not from where the proton is in the sample, but from where it is in a molecule. And now we’re interested in a molecular field that’s added to or subtracted from the big field. And mostly it’s subtracted from, as you’ll see. So these molecular fields then tell you about the molecular environment, these tiny shifts.

So there are two sources of these local magnetic fields, besides the enormous big field that you put on. One is electrons orbiting. Now, the electrons come in pairs that tend to orbit in opposite directions, so they tend to cancel. But there’s a little bit of excess, for reasons we don’t need to go on to, of one orbiting over the other. So you get effects from electron orbiting. And the magnitude of this shift is about 12 parts per million for protons, or 200 ppm for carbon, the range of values you can get from that.

Which is – so this is grossly exaggerated. It should be only parts per million of this, not, you know, like a 20th or something like that, or a 10th. OK, so one thing about the environment is how many electrons are around doing this orbiting? The other thing is there are other magnetic nuclei nearby who have fields, too. So if you’re this proton, or listening for this proton, its field is not only going to be the big field, not only what’s coming from the electrons orbiting, but also what’s coming from other nuclei that are in the vicinity, being oriented either this way or this way.

OK, and those we measure in Hz, and you’ll see why we measure one in ppm, and the other in Hertz very soon. So anyhow, when you add all those things together, you get an effective field. And that’s what determines the frequency of the signal you’re going to hear.

So first we’re going to talk about the chemical shift, what happens from orbiting. So electron orbiting gives this little red B, but the reason the electrons orbit is because of the applied field. And the bigger the applied field, the bigger the orbiting. So that says the red field is proportional to the blue field. If you spent the money to get a bigger magnet, you’d get twice as much orbiting, so the red would be the same [correction: twice as big]. So that says that what you measure then is a fractional thing, because it’s not a standard difference. It depends on how big your magnet is. If you make your magnet twice as big, the shift is twice as big, the red field is twice as big. So it’s a fraction of the big one. So you measure it in parts per million, in a fractional unit rather than in an absolute unit, like an energy unit, like Hertz.

OK, so here’s a scale of parts per million. Let’s see what different values we have. Now, the standard that’s used it’s called TMS, tetramethylsilane. Now, why use such a weird molecule as your standard? Well, it’s a small molecule and it’s volatile. So you can add a drop to your sample, but you can easily get it out again if you want to recover your sample, because it evaporates easily.

Now, it has four CH₃ groups, but they’re all identically situated, so it will just give one peak rather than a more complicated molecule, so that’s good. But the thing that’s really special is that the silicon is, being a metal, is partially plus, and the methyl is largely minus, which means there are more electrons around the protons, which means there’s a bigger shielding. This B is bigger than it would be if there were fewer electrons around. So it shifted all the way to one end of the spectrum, so it doesn’t overlap other things that you might have in your sample. So you have a standard, then, that you can use, with high electron density around the protons, which defines 0.

And now, you get another peak from your sample, and see where it is compared to this. For example, if you have a carboxylic acid, the H on a carboxylic acid is way what’s called downfield. Why? Why is it very different from the hydrogen in TMS? Anybody see why the COOH hydrogen might be different? The environment of it? The OH is electron withdrawing, especially with the carbonyl group on it. So the electrons get sucked away from the hydrogen. You don’t have as much of that red shielding effect, so it’s shifted way down to the other end.

So on the right, it’s said to be shielded. That is, the electrons around the proton cancel the big field, but only a teeny bit of it, only a few parts per million. And it’s called upfield, and it’s also a place where there’s high electron density. And it’s called a low chemical shift. This scale is the chemical shift numbers, and that’s defined as zero, so it’s a very low number. And it’s also low frequency, because we have lots of electrons, relatively big value here. There is very small, relatively small, magnet effective field, relatively small. So a low precession frequency, not such a big field.

By contrast, the OH is called deshielded, downfield, low electron density, high chemical shift, and high frequency.

Now, if you have a proton that’s attached to a normal carbon, not one that’s attached to silicon, which is giving electrons away, then it comes around 1, or between 1/2 and 2. And these were found just by putting different known samples in and seeing where the peaks came. But if you have oxygen, halogen, or nitrogen attached to the carbon, in the same way that silicon donated electrons to carbon, these electronegative atoms take electrons from the carbon, which take electrons from the hydrogen, which make B smaller, which shift it downfield. So in that region, between 2.5 and 4.5.

If the carbon, to which the hydrogen is attached, is itself attached to a carbon, not to one of these electronegative elements, but that carbon has oxygen on it, then the oxygen is sucking electrons from carbon, from carbon, from hydrogen, so it’s shifted down a little bit. So a hydrogen on a carbon attached to a carbonyl is in between there.

If you have a carbon attached to a double bond, it’s shifted down still further. Now, why should a hydrogen attached to a double bond be different from a carbon with a double bond, be different from a hydrogen attached to a carbon with only single bonds? What difference? Mimi?

Student: The π bond?

Professor J. Michael McBride: It’s not the– well, actually, to tell you the truth, it probably is the π bond, but that’s not the explanation that people usually give. What other difference? What difference is there in the sigma system? Liang?

Student: Hybridization?

Professor J. Michael McBride: Pardon me.

Student: Hybridization.

Professor J. Michael McBride: The hybridization, right? This is an sp², more s, more electron withdrawing. Whereas these carbons are sp³, so as you pull electrons to the carbon, away from the hydrogen, you shift down. That makes sense. In fact, this, you might expect, would be the same. It’s shifted even a little further down. All these things were discovered empirically, just by putting known samples in and finding out where they come. And then an aldehyde is, you won’t be surprised to hear, is still further down, because it has the oxygen– it’s not only double bonded, it has an oxygen pulling away.

So all these things more or less make sense, in terms of electron withdrawal, or donation to the hydrogen. But in fact, it’s a little more subtle than that.

Now ROH is funny, because it can come at lots of different positions, depending on concentration, and depending on temperature. Why would concentration have anything to do with it? Why would it have come at a different place if you had more ROH? Lauren?

Student: The hydrogen bonding between molecules

Professor J. Michael McBride: If you have hydrogen bonding and that affects the chemical shift, the higher concentration, more hydrogen bonding, higher temperature, less hydrogen bonding. So OH comes at lots of different positions depending on those factors.

But you can already see from this, that if you take a spectrum and see peaks in different positions, you can try to say, aha! This looks like it has hydrogens that are just attached to carbons that are all single bonded. It has hydrogens on double bonded carbons, blah, blah. You measure the integral and see how many of each kind there are, and you can then do puzzles, like the ones in that web page that I mentioned, to try to figure out what structures are.

Now, let’s see if you’ve learned from this. Where should you expect the hydrogen that is attached to the carbon of an acetylene? Where would you expect it to come? What’s special? Noelle, you got any idea on this? What’s special about it?

Student: The triple bond.

Professor J. Michael McBride: Can’t hear.

Student: The triple bond.

Professor J. Michael McBride: The triple bond. So now, how is the triple bond going to affect things?

Student: Hybridization.

Professor J. Michael McBride: It will affect the hybridization, in what way?

Student: Will it be deshielding?

Professor J. Michael McBride: It’ll be sp. It’ll be an sp hybrid, which is more electron withdrawing, than sp², than sp³. So it should be pulling electrons away, deshielding, as you say, because the electrons are shielding, so it should shift to the left, compared to the double bond ones, right? Wrong. It actually comes up there.

So there’s more to it than what we’re saying. Now, what is this more to it? Unfortunately, the clock has run, so you’re going to have to wait for tomorrow to find that out. But the good news is that when you hear it, you’re going to be able to impress your roommate, because this is due to diamagnetic anisotropy. So you can explain diamagnetic anisotropy to your roommate.  It’s worth waiting for.

[end of transcript]

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