18.7 Nuclear Magnetic Resonance Spectroscopy (NMR)

Nuclear magnetic resonance (NMR) spectroscopy, also known as magnetic resonance spectroscopy (MRS), is a powerful analytical technique used to determine the structure of molecules. It relies on the interaction between atomic nuclei with non-zero nuclear spins and an external magnetic field. When these nuclei absorb electromagnetic radiation in the radio frequency range (approximately 4 to 900 MHz), they re-orient themselves within the magnetic field.

The exact frequency at which a nucleus resonates is highly dependent on its specific chemical environment. This sensitivity allows NMR spectra to provide detailed information about:

• Individual functional groups within a molecule.
• The connectivity and spatial relationship between nearby atoms.

Because NMR spectra are unique and characteristic for individual compounds, it is one of the most important methods for identifying molecular structures, especially for organic compounds. Similar to IR Spectroscopy→, NMR is a non-destructive technique.

18.7.1 Principle of NMR

The fundamental principle of NMR involves the magnetic properties of atomic nuclei.

1. Nuclear Spin: Certain atomic nuclei possess a quantum mechanical property called spin. Since nuclei are charged, this spinning motion generates a small magnetic field, causing the nucleus to act like a tiny bar magnet (a magnetic dipole).

2. Random Orientation: In the absence of an external magnetic field, the magnetic dipoles of these nuclei are oriented randomly.

3. Applying an External Magnetic Field ($B^{\circ }$): When a sample is placed in a strong external magnetic field ($B^{\circ }$), the nuclei align themselves in one of two possible spin states:

• Low Energy State: Aligned with the applied magnetic field (parallel).
• High Energy State: Aligned against the applied magnetic field (anti-parallel).

4. Resonance: The energy difference between these two states corresponds to a specific frequency in the radio wave portion of the electromagnetic spectrum. When the sample is irradiated with radio waves of this exact frequency, the nuclei in the low energy state can absorb the energy and "flip" to the high energy state. This absorption of energy is called resonance.

5. Signal Detection: When the nucleus returns to its lower energy ground state, it emits the absorbed energy at the same radio frequency. This emitted signal is detected and processed to generate the NMR spectrum for the compound.

18.7.2 NMR Active Nuclei

Not all nuclei can be studied by NMR. A nucleus must be "NMR-active" to produce a signal.

• Condition for Activity: To be NMR-active, a nucleus must have a non-zero nuclear spin quantum number ($I\ne 0$). This property is what allows the nucleus to interact with an external magnetic field.

• Determining Nuclear Spin: The value of the nuclear spin quantum number ($I$) depends on the number of protons and neutrons in the nucleus. Nuclei with an odd number of protons, an odd number of neutrons, or both, will have a non-zero spin. These typically have half-integer spin values ($I=\frac{1}{2},\frac{3}{2},\frac{5}{2},\dots$).

• Common NMR-Active Nuclei:

  • Hydrogen-1 (${}^1\mathrm{H}$)
  • Carbon-13 (${}^{13}\mathrm{C}$)
  • Fluorine-19 (${}^{19}\mathrm{F}$)
  • Phosphorus-31 (${}^{31}\mathrm{P}$)

For organic chemists, the most important and commonly used nuclei are ${}^1\mathrm{H}$ and ${}^{13}\mathrm{C}$.

18.7.3 Chemical Shift and Reference Standards

In NMR, the position of a signal is measured relative to a reference standard, most commonly Tetramethylsilane (TMS), $(C{H}_3{)}_{4}Si$. TMS is chosen because it is chemically inert, volatile, and its 12 protons are equivalent and highly shielded, giving a single sharp peak at a lower frequency than most organic protons.

The difference between the resonance frequency of the nucleus and the reference (TMS) is called the Chemical Shift ($\delta$), expressed in parts per million (ppm).

• Shielding: Electrons around a nucleus create a local magnetic field that opposes the external field.
• Deshielding: Electronegative atoms (like O, N, or halogens) pull electron density away from protons, "deshielding" them and causing them to resonate at higher frequencies (downfield).

18.7.4 Interpreting NMR Spectra

An NMR spectrum provides three main types of information:

1. Number of Signals: Indicates how many different sets of equivalent protons are in the molecule.
2. Position of Signals (Chemical Shift): Indicates the chemical environment of the protons.
3. Integration (Area under peaks): The area is proportional to the number of protons contributing to that signal.