Here is an example NMR spectra of 1-1-2 trichloral ethane. We'll cover the delta scale in parts per million, the units of the x-axis later. For now, think of it as being related to the law and more procession frequency. What you should focus on now is that there are two peaks, a peak called HA, at about 4 parts per million, and a peak called HB, at about 5.75 parts per million. Even though this spectra is coming from the protons, and they all have the same total intrinsic spin, the proton labeled HA have different larmor procession frequencies than those of HB. Recall how we quantified the larmor procession frequency, and that it was equal to the gyromagnetic ratio times the magnetic field divided by 2 pi. Since the gyromagnetic ratio is the same for all the protons, then the magnetic field must be different for protons labeled HA and HB, which will explain the two peaks. Recall that moving charges induce magnetic fields. So the observed shifts in the peaks, called chemical shifts, is due to the applied magnetic field inducing a circulation of electrons in a molecule. The circulation of electrons gives rise to an additional magnetic field that either adds or subtracts to the externally applied one. Therefore, the local magnetic field seen by a given nuclei is equal to the applied magnetic field B0, plus the induced magnetic field B induced. And this can alternatively be expressed as 1-sigma times B0, where the shielding constant sigma takes into account effects of the local magnetic field from the atoms electrons, the atoms neighbors, as well as the solvent. Here is a schematic which illustrates the effect of the shielding constant. The red arrow represents the direction and magnitude of the applied magnetic field. A given nucleus is shielded from the applied field by the movement of electrons near it. The induced magnetic field is then illustrated by the blue arrow. This results in an effective magnetic field which is actually experienced by the nucleus, illustrated by the green arrow. The chemical ships we saw before reported on a delta scale in parts per million. This is calculated by finding the LARMOR procession frequency of a given nuclei and finding it relative difference from a reference LARMOR procession frequency and multiplying that by a million. So, delta is equal to new minus nu knot divided by nu knot times 1 times 10 to the power of 6. The typical reference used for proton NMR is that from tetra methylsilane or TMS, which is illustrated on the right. The LARMOR procession frequency for the nuclei and the reference is calculated by using an updated version of the previously defined equation, now taking into account the shielding constant sigma. It is now nu is equal to the gyromagnetic ratio times 1 minus sigma times the applied magnetic field divided by 2 pi. The ranges of typical chemical shifts measured in parts per million are illustrated in the figure. Again, these shifts are determined relative to TMS. So, back to our sample NMR spectra of 112 tri-chloroethane. We can see that the protons listed as HA are in a different bonding environment than the one identified as HB. The HA protons have two protons bound to the central carbon atom with one chlorine, while the HB proton has only one proton bound to the central carbon atom with two chlorines. This difference in bonding leads to different shielding constants, which modifies the local magnetic field experienced by HA and HB. Finally, this difference in the local magnetic field modifies the LARMOR procession frequency, meaning that HA will have a different chemical shift than HB. This is how NMR can be such a powerful and sensitive technique, as it can detect differences in the local environment around each proton, and these differences can result in identifying molecule structure to a high degree of accuracy. Now that we have rationalized why there are different peaks possible for the same type of nuclei, let's zoom in on the two peaks HA and HB. We can see that the peak assigned to HA is actually two peaks, and the peak for HB is actually three peaks. We will now examine why this is. First, we will define the term chemical equivalence. Nuclear and the same bonding environment are generally considered to be chemically equivalent. For example, in glycine, which is illustrated on the far left, has two types of chemically equivalent protons, HA, which are both bound to the nitrogen and HB, which are both bound to the central carbon. The same goes for a seed aldehyde, illustrated in the center, where HA represents the three protons bound to one of the carbons and HB for the single hydrogen bound to the other carbon. Parasylene on the right is a little larger with 10 hydrogens, but it is only two types of chemically equivalent hydrogens. This final example really illustrates the idea of chemical equivalence. The hydrogens labeled HA on either methyl carbon exist in the same bonding arrangement and as a result are chemically equivalent. Additionally, the hydrogens labeled as HB on the central ring also exist in the same bonding arrangement. Therefore, they are also chemically equivalent. To see how chemically inequivalent nuclei that are adjacent to each other affect one another, let's return to the spectra from 112 tri-chloroethane. Let's focus on the signal from HA. There is only one hydrogen which is chemically inequivalent to the HA hydrogens, and it is labeled as HB. It can have a spin that points with the applied magnetic field or against the magnetic field. There are many 112 tri-chloroethane molecules in the sample, which is equally likely for the HB proton to be parallel or antiparallel to the applied magnetic field. The reason why this matters is that chemically inequivalent hydrogens can either enhance or shield the local magnetic field experienced by the adjacent inequivalent nuclei. Therefore, the one HB hydrogen, depending upon the direction of the spin of its nucleus, enhances or shields the applied magnetic field experienced by the HA hydrogens. This results in a slight splitting of the signal into two, since there are only two possibilities for the spin of HB. This effect is called spin-spin coupling. Let's now look at the spin-spin coupling effect for HB. The signal for HB is split into three, because there are more possibilities for the spin combinations of the HA nuclei. So again, starting with the signal for the HB nuclei, it experiences a local magnetic field that is modified by the chemically inequivalent hydrogens, the HAs. Since there are two of them, there are four combinations for their intrinsic spin, both being parallel, both antiparallel, and the two mixed states. The two parallel states enhance the local magnetic field experienced by HB. The two antiparallel cases shield the HB proton from the applied magnetic field, and the two mixed states cause no change at all since their effect is canceled. This is why there are three peaks. The relative magnitude of each of the three peaks is determined by the number of ways that peak is produced, and so since there are twice as many ways to have HA cause no change to the local magnetic field at HB, then its signal is twice as large. This spin-spin coupling has some limitations. First, chemically equivalent hydrogens do not split each other's signals. So in 112 trichloroethane, the two HAs do not split each other's signals. Second, there is a limit in how far away chemically inequivalent nuclei can be before splitting no longer occurs. For example, in ethyl acetate, there are three groups of chemically equivalent hydrogens. Since there are roughly five bond lengths between the HA nuclei and the nearest chemically equivalent nuclei, in this case being HB, then HA does not experience any splitting due to spin-spin coupling. N equivalent spin one-half nuclei split the signal of a nearby chemically inequivalent group of nuclei into N plus one lines, with an intensity distribution given by something called Pascal's triangle, which is illustrated here. So using 112 trichloroethane again as an example, there is one HB, so it splits the signal from the HAs into one plus one or two signals. Additionally, there are two HAs, so the signal from HB will be split into two plus one or three signals. To use Pascal's triangle, we first find the row with as many entries as we do peaks in the signal. The numbers indicate how large each peak will be. So for HA, since there are two peaks, we look at the second row, which says the peak heights are the same. And for HAB, since there are three peaks, we choose the third row, which says that the middle peak will be twice as large as the outer two peaks. Pascal's triangle is meant to be an easy way to predict the relative peak intensity for any NMR spectra due to spin-spin coupling. In this lecture, we qualitatively examine NMR spectroscopy. The spectra from this type of spectroscopy is dependent upon how nuclei have spins and those spins are affected by magnetic fields, by measuring how the magnetic moments of these nuclei within intrinsic angular momentum relax when perturbed can show the chemical makeup of a sample. This is NMR spectroscopy. Peak shifts relative to a reference are based on the local magnetic field at each nuclei. This local magnetic field is affected by the local bonding arrangement, as well as the spin-spin coupling of nearby chemically inequivalent nuclei. Music