 Okay, so NMR, as we've discussed it so far, doesn't actually appear to be all that useful a technique for a chemist. What we understand about NMR at the moment is the difference in energy between two nuclear spin states is proportional to the magnetic field, even with this extra complication that the shielding due to the electrons that surround a nucleus tend to reduce that magnetic field as experienced at the nucleus, but still when we increase the magnetic field, that increases the energy difference and that increases the frequency at which we should see absorption causing a nucleus to change its spin state and go from the lower state to the upper state. With just that understanding, if we apply a particular magnetic field which is shielded to produce some lower magnetic field at the nucleus, we can predict what frequency to look for absorption or resonance of these hydrogen nuclei, and if the system absorbs electromagnetic radiation at that frequency, we know there's protons there or hydrogen atoms. If it doesn't, then we know there's no hydrogen atoms there. But just detecting hydrogen atoms is not all that useful. What is useful, however, is the fact that this absorption takes place at a slightly different frequency or a slightly different shielding strength for every different type of hydrogen atom and different types of molecules. So what we mean by that is, remember, if we have an H atom surrounded by a proton surrounded by a single electron that we call a hydrogen atom, those electrons are responsible for this shielding. If we have a molecule like H2, that is a neutral molecule, the two hydrogen atoms are equally electronegative, so those electrons are equally shared between the two hydrogen atoms. But if we compare that to an example like, let's say, hydrogen chloride, where the chlorine is more electronegative than the hydrogen, then the electron that belongs to the hydrogen will be somewhat depleted on the hydrogen side. It's kind of a net positive charge here and net negative charge on the chlorine. So the chlorine, of course, has more electrons than the hydrogen to begin with, more valence electrons, and in addition, it pulls some of the electrons away from the hydrogen because of its electronegativity. Key point being there's less electron density surrounding this hydrogen in HCl than there is around either one of the hydrogens in H2. So on the proton anyway, the H2 molecule has higher electron density. The proton, the hydrogen in the HCl molecule, the proton is surrounded by a lower electron density. Higher electron density leads to stronger shielding effect. There's more electron density around the hydrogen, so that does a better job of shielding, so that means the value of this constant sigma, the shielding constant, is larger in H2 than it would be in HCl. If sigma is larger, that reduces this quantity. I'm subtracting sigma from one here, so this quantity is reduced. So that means when the shielding is large, you could think of that as saying the frequency at which the molecule absorbs is also, I'm sorry, going to be the opposite of large. It's going to be decreased. When I increase sigma, that decreases the frequency, or another way to think about it is, if I ask what magnetic strength, what magnetic field strength do I need in order to generate a particular frequency, if this quantity is reduced by large shielding, the B0, the external magnetic field, would need to increase. So that's an important feature of shielding, and these magnetic resonance measurements is that when the shielding is stronger, when there's more electron density and more shielding, the external magnetic field strength needs to be larger. So that same phenomenon happens in every proton in every different molecule. The chemical environment, the amount of electron density surrounding every proton in a molecule is different, and it gets a little bit more complicated for more complicated organic molecules like, for example, if I put up on the screen here a picture of the NMR spectrum for a somewhat complicated molecule like this ethyl acetate molecule. So let me just make sure all the protons are visible. So this carbon right here is a methylene carbon with two protons, two hydrogens on it. So we've got three hydrogens here, which are all identical to each other, two hydrogens on this methylene group, three hydrogens on this methyl group at the other end of the molecule. The chemical environment of each of these protons is different from all the others. The shielding is going to be different in each one of these molecules. So what that means is the magnetic field strength and or the frequency at which they absorb are also all going to be different from one another. And that's what's shown in this NMR spectrum for this molecule is what's plotted here is not the frequency directly, not the magnetic field strength directly, but something called the chemical shift. And that's this idea that the magnetic field strength, the external magnetic field strength is a little different for every proton. Zero on this scale is not zero field strength or zero frequency. That's where resonance takes place for a reference substance. In particular, in most cases, when we do proton NMR, that's a molecule called tetramethylsilane. Details of that molecule are not terribly important other than that's a neutral molecule. The protons in tetramethylsilane are not surrounded by any particularly electronegative atoms. So the electron density around the hydrogens in that molecule is about as high as we can get in many different compounds. So this compound has the most shielding of most hydrogen atoms in typical organic molecules. So this is our reference state all the way at the right end of this spectrum. And then progressively, the more electronegative a nearby atom is in a molecule, the more electrons get withdrawn from the hydrogen, the less shielding is taking place. So the lower the external magnetic field strength. So the way to interpret an NMR spectrum, as we move in this direction, we can interpret the peaks over on this side of the spectrum as having more shielding and consequently higher external strength. So usually we call the chemical shift upfield. The magnetic field is larger, so we call that an upfield shift. And the opposite is true in this direction. Peaks that appear over at the left side of the spectrum with larger values of this chemical shift, those are hydrogens that are experiencing less shielding usually because they're near some electronegative atom that's withdrawing some of the electron density. Lower amount of shielding results in what we call a downfield shift in the chemical shift. So let's take a look at this molecule and see if we can identify which of these peaks should belong to which protons in this particular molecule. And remembering that let's take this set of peaks, for example, these are the ones with the strongest downfield chemical shift. So that's the least amount of shielding. That's going to be the hydrogens with the smallest amount of electron density around them because that electron density has been withdrawn to some nearby electronegative group in the molecule. And in fact, this oxygen in this ester group is fairly electronegative. It will have withdrawn some of the electrons from the methylene group in this ethoxy side chain of the ester. So let's see if I label that group, that methylene group, as A. Those are the protons with the lowest amount of electron density around them in this molecule and they're going to absorb with the strongest downfield shift. On the other hand, these methyl protons in the methyl group of this ethoxy side chain of the ester, those methyl protons, I'll call that side group B, or those protons B, those are farther away from the electronegative ester group and it turns out that those protons appear in at a much lower chemical shift, further upfield, less downfield. And in between, we have this methyl group alpha to the carbonyl, if I call that those protons C, label them C, those are sort of intermediate. They're not as reduced in electron density as the methylene hydrogens over here but they are next door to a carbonyl group so there's still a substantial amount of withdrawal of electrons from that methyl group toward the electronegative carbonyl. So what that means is this large peak in the middle here, that's responsible, the methyl group that's alpha to the carbonyl is responsible for this peak here at about a chemical shift of about two parts per million. So that also brings up the fact that the units of chemical shift, typically those units are given in parts per million, it's worth understanding what that means. The chemical shift that we denote by delta, that is a measure of the frequency at which a molecule absorbs, a particular proton absorbs relative to the frequency for this reference molecule, tetramethylsilane in this case. So a molecule with a downfield shift and less shielding is going to have the opposite of this situation so if it's got less shielding it's going to have a smaller external field that's the downfield shift and it's going to have a larger frequency. So the frequency of these hydrogens is larger than the frequency of the reference hydrogen, that difference is taken relative to the frequency of the external magnetic field. So if there were no shielding at all, the frequency that would be needed to excite the nuclear spin excitations in a bare external electric field, that's this nu not value. But the point is it's just a shift, a chemical shift, the amount of change in the frequency relative to some reference molecule taken normalized relative to the external electric field. So when we say the chemical shift is four parts per million or two parts per million or one part per million, what that means is the frequency and or the magnetic field experienced at the nucleus is different from the value for this reference molecule by four parts in a million, four times 10 to the minus six. So it's a relatively small shift, the shielding values are pretty small but they're certainly large enough to measure and the fact that we can measure different values for a methyl group on one side of the molecule and the other side of the molecule, sorry methyl group and methyl group and the methylene group helps us to use NMR to identify different functional groups in a molecule. There's other things to interpret about this NMR spectrum as well such as why we have four peaks here and only a single peak here and three peaks here. So there's definitely more features of an NMR spectrum to examine that require a little more quantum mechanics to understand. But this basic idea of a chemical shift telling us something about the chemical environment of each of the protons in this molecule is one of the powerful features of NMR.