NMR Spectroscopy

Spin Systems of Multiple Nuclei

¹H NMR is the most common application of NMR spectroscopy. The rate of precession of a particular proton depends upon the magnitude of the local magnetic field ( B₀ ) experienced by the proton.

The vast majority of B₀ is attributable to the large, powerful magnetic field ( B ) in which the sample is placed. However, there are additional contributions to B₀ arising from the magnetic moments of other nuclei (including other ¹H) as well as electrons. These chemical contributions to B₀ are generally only a few parts-per-million of B, but the effects of these chemical contributions are measurable.

The result is that a sample containing ¹H usually contains protons in multiple chemical environments. The Larmor frequency depends upon the local magnetic field each proton experiences, so each type of proton precesses at its characteristic frequency.

The bulk magnetization for the sample is the sum of the bulk magnetization contributions from each type of proton. Because protons in different chemical environments precess at different frequencies, the FID shows multiple frequency components. Processing the FID with the Fast Fourier Transform produces a spectrum showing multiple peaks, one for each type of ¹H.

NMR spectroscopy is thus a powerful tool for identifying the number of different types of chemical environments for protons. Additionally, the chemical shift of each signal provides information on the nature of the chemical environment. The area under each peak in the ¹H spectrum is a measure of the number of protons in each chemical environment.

Experiment

The spin system in this simulation contains multiple nuclei with different Larmor frequencies. The bulk magnetization attributable to each type of nuclei is shown in the animation by arrows of different colors. The length of each arrow is proportional to the total number of nuclei of that type.

The vector sum of the bulk magnetizations attributable to each type of nucleus produces the bulk magnetization of the sample, which is measured by the x and y detectors. For simplicity, only the signal from the x detector is shown in the graph of the FID.

In this spin system, none of nuclei interact with other types of nuclei. Therefore, each type of nuclei appears in the spectrum as simple peak (a singlet). The area under each peak is proportional to the number of nuclei of that type. In NMR spectroscopy, one "integrates" a peak by graphing a cumulative integration of the signal passing from left to right across a peak. The resulting integration signal is loosely a step where the height of the step is proportional to the area under the peak.

The instrument is a 100 MHz spectrometer. In addition to sample peaks, the spectrum also contain a peak for TMS, which is the most upfield (lowest frequency) peak.

Run the simulation and answer the following questions.

• Other than TMS, how many different types of nuclei are present in the sample?
• What are the chemical shifts of the various nuclei?
  (You can disregard TMS, which is a 0 ppm by definition.)
• What is the relative number of nuclei of each type?
• In what ways does the FID look similar to a spectrum for a single type of nuclei?
  In what ways does it have different features? Explain the differences.
• Why do the various peaks have different widths?
• Why do the various peaks have different heights?
  Identify two factors that affect the relative heights.