An Introduction to NMR Spectroscopy
Shelby Feinberg and Steven Zumdahl
Nuclear magnetic resonance spectroscopy (NMR) has risen to the same level of importance as electronic and vibrational spectroscopy as a tool for studying molecular properties, particularly structural properties. Although the following discussion of nmr specifically deals with hydrogen atom nuclei in organic molecules, the principles described here apply to other types of molecules as well. Many other types of nuclei (13C, 19F, 31P, etc.) have nuclear spins and thus can be studied using NMR techniques.
Certain nuclei, such as the hydrogen nucleus (but not carbon-12 or oxygen-16), have a nuclear spin. The spinning nucleus generates a small magnetic field, called "". When placed in a strong external magnetic field, called Ho, the nucleus can exist in two distinct spin states: a low energy state A, in which is aligned with the external magnetic field, Ho, and a high energy state B, in which is opposed to the external magnetic field, Ho (figure 1). Alignment of with Ho is the more stable and lower energy state.
Figure 1
In NMR, transitions from the more stable alignment, A, (with the field) to the less stable alignment, B, (against the field) occur when the nucleus absorbs electromagnetic energy that is exactly equal to the energy separation between the states (E). This amount of energy is usually found in the radiofrequency range. The condition for absorption of energy is called the condition of resonance. It can be calculated as the following:
h = Planck’s constant
H = the strength of the applied magnetic field, Ho, at the nucleus
= the gyromagnetic ratio (a constant that is characteristic of a particular nucleus)
= the frequency of the electromagnetic energy absorbed that causes the change in
spin states
There are three features of NMR spectra that we will focus on: the number and size of signals, the chemical shift, and spin-spin coupling.
Number and Size of Signals
Let’s consider how the NMR spectrometer can distinguish between hydrogen nuclei and produce multiple signals. Magnetically equivalent hydrogen nuclei produce one signal. These hydrogen nuclei experience the same local environment. For example, in a molecule such as diethyl ether (Figure 2), there are two sets of magnetically equivalent hydrogens. The hydrogens labeled a are six magnetically equivalent methyl hydrogens, while the hydrogens labeled b are four magnetically equivalent methylene hydrogens. Notice that the methyl (a) hydrogens are all located adjacent to a carbon containing two hydrogen atoms. Additionally, the methylene (b) hydrogens are all located adjacent to an oxygen atom and a carbon atom containing three hydrogen atoms.
Figure 2
Because of rapid rotations about sigma bonds and molecular symmetry, the six methyl hydrogens (a) and the four methylene hydrogens (b) comprise two individual magnetically equivalent groups of hydrogens. The methyl hydrogens (a) experience a different total magnetic field than the methylene hydrogens (b), because of different local magnetic fields. As a result, the resonance energy, E, corresponding to the frequency of absorption, , will be different for these two groups of hydrogen nuclei. Thus, the NMR spectrometer can distinguish between groups of hydrogen nuclei which experience different local magnetic fields. Different frequencies are required for the two different groups of hydrogens, thereby producing two distinct signals.
The areas of the signals are directly proportional to the number of hydrogens. So, in the case of diethyl ether, the two peaks have an area ratio of 3:2 (or 6:4), because there are six methyl hydrogens (a) and four methylene hydrogens (b). We will look at an actual spectrum presently.
The Chemical Shift
When an organic molecule is placed in an external magnetic field, Ho, each hydrogen nucleus experiences a total field that is the sum of Ho and two other local magnetic fields: one produced by bonding and non-bonding electrons, He, and the other produced by neighboring protons which possess a nuclear spin, Hh. Thus, the applied magnetic field (Ho) is constant, while the magnetic fields produced as He and Hh are not constant. The magnetic field produced by the neighboring electrons (He) determines the position (relative frequency) of an nmr peak (called the chemical shift). The magnetic fields produced by neighboring nuclei (Hh) are smaller than He and cause splitting of an NMR peak (called spin-spin coupling). This will be discussed later.
For the moment, let’s assume that Hh is zero. There is no spin-spin coupling. Under these conditions, the total magnetic field, H, experienced by a particular nucleus is given by Ho + He. That is, we are assuming that the resonance energy is only dependent on the sum of the external magnetic field and the magnetic field produced by neighboring electrons. A mathematical representation of the value of this resonance energy is the following:
If we vary the frequency () of the electromagnetic energy until h = E, absorption will cause a transition in spin states, and a signal will be recorded by the NMR spectrometer.
The position of an NMR signal is recorded relative to the position of the signal of an internal standard. This standard is commonly tetramethyl silane (TMS), (CH3)4Si. If TMS absorbs at frequency s, and the hydrogen nucleus of interest absorbs at , the spectrometer will record a signal at , where o is the spectrometer frequency (commonly 60 megacycles per second). is called the position of absorption, or the chemical shift, expressed as parts per million (ppm) on a scale of 0-10 ppm. TMS absorbs at 0.0 ppm, while most nuclei absorb downfield towards 10 ppm. The value of is independent of Ho, but it DOES depend on He. Figure 3 gives a few examples of how neighboring atoms affect the chemical shifts of hydrogen atoms.
Figure 3
Hydrogen nuclei which absorb at large are said to be deshielded from the external magnetic field. These signals appear downfield (towards 10 ppm) from TMS because the frequency at which they absorb differs greatly from the frequency of the TMS hydrogens. As a result, the value of s is large. Deshielding is caused by adjacent atoms which are strongly electronegative (e.g. oxygen, nitrogen, halogen) or groups of atoms which possess -electron clouds (e.g. C=O, C=C, aromatics).
Let’s now look at the nmr spectrum of benzyl acetate (Figure 4).
Figure 4
Note that there are three absorptions corresponding to the three sets of magnetically equivalent hydrogens. Compare the chemical shifts with those given in Figure 3. The relative area of the peaks corresponds to the number of hydrogens in each set (3:2:5).
Spin-Spin Coupling
We have discussed how the position of an NMR absorption is affected by the magnetic field produced by neighboring electrons (He). Now, let’s examine how the magnetic field produced by neighboring protons (Hh) affects the splitting of the NMR absorption. The peaks can appear as singlets, doublets, triplets, etc… Let’s first consider the absorption of a hydrogen atom (Hx) with only one neighboring hydrogen atom (Hy) (Figure 5).
Figure 5
If we assume that Hx is aligned with Ho, then the neighboring hydrogen nucleus will have approximately equal probability of existing in either the low energy state, A, or the high energy state, B. Refer to Figure 1 for a clear picture of these energy states. For those molecules in which the neighboring hydrogen nucleus exists in the low energy state, its magnetic field (Hh) will add to the magnetic field (Ho + He) and for those molecules in which the neighboring hydrogen nucleus exists in the high energy state, its magnetic field (Hh) will subtract from the magnetic field (Ho + He). As a result, two different peaks are observed. A higher frequency is required for the low energy state, while a lower frequency is required for the high energy state. This two line pattern is called a doublet, and we say that the neighboring hydrogen nucleus (Hy) splits the absorption of Hx into a doublet. The intensity of the two lines will be equal, because the probability of the neighboring hydrogen nucleus (Hy) existing in either spin state A or B is approximately equal.
When there are two magnetically equivalent adjacent hydrogen nuclei, three possibilities exist for their combined magnetic fields (Figure 6).
Figure 6
Note that both can have spin state A, one can have spin state A and the other have spin state B, or both can have spin state B. These three possibilities have a probability ratio of 1:2:1, which correspond to three different absorption frequencies. The appearance of the resulting NMR signal is a three line pattern, called a triplet, with intensities 1:2:1.
When there are three magnetically equivalent neighboring hydrogen nuclei (Figure 7), the absorption splits into a quartet with intensity pattern 1:3:3:1 for similar reasons to those aforementioned.
Figure 7
In general, N magnetically equivalent neighboring hydrogen nuclei will split the absorption into N + 1 lines. The intensity ratios are equal to the coefficients of the expansion (a + b)N, or Pascal’s triangle.
The spacing between the lines of a doublet, triplet, or quartet is dependent on the coupling constant. It is given the symbol J, and it is measured in units of cycles per second. Coupling constants range in magnitude from 0 to 20 cps. Observable coupling will generally occur between hydrogen nuclei which are separated by no more than three sigma bonds. For example, in the molecule 2-butanone (Figure 8), hydrogens from groups aand b split one another because they are only separated by three bonds. However, hydrogens from group c are not split by any other hydrogens because they are separated from other hydrogens by more than three sigma bonds.
Figure 8/
Examples of typical coupling constants are given in Figure 9.
Figure 9
Note that coupling is never observed between magnetically equivalent hydrogen atoms.
Let’s now consider the coupling of hydroxylic protons (OH). Hydroxylic protons do not split other protons, nor are they split by other protons. These protons undergo exchange between two molecules of alcohol. This exchange is so fast that these protons sample molecules with all possible spin states, giving rise to a singlet in the NMR spectrum at a position which is the average for all the spin states of the other hydrogens.
For example, ethanol gives an NMR spectrum consisting of a triplet, quartet, and a singlet, as seen in the idealized spectrum in Figure 10. Even though the hydroxylic proton is separated from a methylene hydrogen by three bonds, the signal given by the hydroxylic proton is not split by the methylene protons, nor are the methylene hydrogens split by the hydroxylic proton because of proton exchange.
Figure 10