Nuclear Magnetic Resonance Spectroscopy

Consider the magnetic properties of an atomic nucleus. The nucleus of an atom spins and as a consequence, if the charge is not symmetrically placed on the nucleus, the spinning charge will constitute a circular current and will produce an associated magnetic field similar to a small bar magnet. Not all nuclei possess an asymmetric charge but among those that do are the hydrogen and the ¹³C nuclei, which are the nuclei of major importance for NMR spectroscopy. However, most elements or one of their isotopes have their charge asymmetrically placed and, thus, exhibit magnetic properties.

If the spinning nucleus is placed in a strong external magnetic field, the nucleus can adopt a small number of possible orientations. The hydrogen nucleus is permitted just two orientations, which can be in the direction of the magnetic field or opposite to the direction of the field. This situation is depicted in figure 1.

Figure 1. The Energy Levels of a Hydrogen Nucleus Situated in a Magnetic Field.

Now if the nucleus is exposed to radiation of frequency (ν) and this causes the nucleus to ‘flip’ (see figure 1) then the energy involved (ΔE) will be given by.

ΔE = hν (1)

where (h) is Plank’s Constant

This is the basis of Magnetic Resonance Spectrometry

When a hydrogen nucleus is placed in a magnetic field the external field will act upon the spinning nucleus to try to change its spinning axis to be in line with the magnetic field.

Now when a force acts upon a spinning body to change its axis of rotation then, to conserve the angular momentum, the spinning body will precess.

The Precessing nucleus is depicted diagramatically in Figure 2.

Figure 2. A Precessing Nucleus.

From quantum rules, the Precessing nucleus has only two possible orientations. Consequently, if energy is supplied to the spinning nucleus, employing electromagnetic radiation of the necessary frequency, energy will be absorbed and the Precessing nucleus will be displaced from one orientation to the other.

The magnetic quantum number for the proton is ± 1/2 and consequently, the frequency (ν) at which this transition can occur can be calculated from the equation:

₍₂₎

where (μ)	is the nuclear magnet moment,
(H)	is the external magnetic field strength,
and (h)	is planks constant

Now the nuclear magnet moment for the proton is 2.793 Bohr magnetrons (1 magnetron = 5.093 x 10^-24 erg/gauss) and thus, if it is situated in a field of 15,000 Gauss, the frequency required to make the transition is given by,

Employing the same equation and taking a range of transition frequencies, the different field strengths can be calculated for different frequencies and different nuclei. The results of such calculations are shown in Table 1.

Table 1. NMR Field Strengths and Frequencies for Some Different Nuclei

Consider a sample containing different protons, is situated in a strong magnetic field and irradiated at the transition frequency. Assume the sample is then scanned by a second, low intensity magnetic field, When the transition of a proton actually occurs, energy will be absorbed and that energy can be electronically detected.

Figure 3. A Low-Resolution NMR Spectrum of Ethyl Alcohol

The Spectrum obtained for alcohol is shown in figure 4. The device has been examined on a low-resolution spectrometer. The sample has been irradiated with electromagnetic waves of the calculated frequency and the intensity of the magnetic field was then scanned over a narrow range close to that where the absorption of energy was expected to take place. The energy of absorption, which is sensed electronically, is shown plotted against field strength to provide the NMR Spectrum. There are several points of interest arising from the resulting simple Spectrum shown in figure 3. First, it can be shown that the three peaks have areas in the proportions of 1:2:3 which would indicate that they arise from the proton associated with the oxygen atom, the methylene protons and the methyl protons.

Thus, the spectrum discloses the relative number of protons associated with each peak from the relative peak areas.

Second, the proton peaks appear at different values of the scanned magnetic field. This is because, due to their specific environment, they experience shielding from the electron clouds from neighbouring atoms. As a consequence, although all the protons absorb energy at the same frequency (because the frequency in this experiment is fixed) the applied field must be different for each type of proton, to compensate for their dissimilar magnetic environments.

Now,

and H_C = α(H_F+H_S) (3)

Where (α) is the shielding effect of the electron environment of the proton.

Thus, H = H_F+H_S -α(H_F+H_S)

or, H= (H_F+H_S)(1-α) (4)

In fact it is the chemical environment of the proton that will affect the diamagnetic shielding constant (α). Consequently, the relative positions of the absorption peaks, called the ‘chemical shift’ will be determined by the magnitude of (α) and will disclose the nature of the chemical environment and contribute information with regard to the overall structure of the molecule.

Thus, the position of the peaks, the chemical shift, discloses the nature of the chemical environment of the proton and consequently, contributes to the elucidation of the chemical structure.

If the resolution of the NMR machine is increased (which, in practice, will mean that the widths of the peaks are reduced relative to their movement apart, viz. chemical shift) then the proton peaks will show a well-defined and predictable fine structure. An example of the Spectrum of ethyl alcohol that would be obtained on a NMR spectrometer having greater resolution is shown in figure 4

Figure 4. A High Resolution NMR Spectrum of Ethyl Alcohol

The Spectrum shows that the magnetic field affecting the environment of a given proton is also influenced by protons on the adjacent carbon atoms. For example, the methylene protons can contribute magnetic influence at three different levels to the field experienced by the methyl protons. The magnetic fields due to the each methylene proton can act in opposite directions or both in one direction or the other. Thus, as there are three different contributions, the methyl protons will display three peaks. Furthermore, as the probability of both protons acting in the same direction is half that of them acting in opposition, the centre peak will be twice the height of the side peaks.

In a similar way, the three protons of the methyl group can contribute fields at four different levels to the methylene protons. There are two possibilities for them all to act in one direction and two possibilities where two are acting in one direction and the other in opposition. Thus the methylene protons will display four peaks. As the probability of the two protons acting in one direction and the other in opposition is twice as great as all the protons acting in one direction or the other, the two centre peaks will be twice the height of the outside peaks.

As already stated the position of the peaks (the chemical shift) indicates the chemical nature of the neighbouring groups. The fine structure of the proton peaks provides information on the degree of the proton saturation of the neighbouring atoms. In addition, the area of the peaks provides quantitative information on the distribution of the protons throughout the molecule. Even with this brief and somewhat superficial treatment of NMR spectroscopy, the value of the technique to the analyst for substance identification and for structure elucidation becomes quite obvious.

For those requiring more information on NMR, the books by P.J. Hore (1) and Paudler (2) are strongly recommended.