Theoretical introduction to Nuclear Magnetic Resonance

This is a brief description about spectroscopy by Nuclear Magnetic Resonance or NMR. NMR is a powerful and harmless tool used for biophysical characterization of molecules with atomic resolution.

Nuclear magnetic resonance (NMR) spectroscopy is a technique that takes advantage of the quantum mechanical properties of the atomic nucleus known as spin. Nuclei with spin quantum numbers different to zero behave with a finite charge distribution, thus having a magnetic moment proportional and parallel to the nuclear spin. These nuclei act like tiny magnets (dipoles) and can be, in principle, detected by NMR. 

When a sample is placed in a stationary magnetic field (B0), its NMR active nuclei tend to align parallel or antiparallel with that external field. The dipoles oriented against the B0 are in a less stable state and are present at a lower population. The sum of all nuclear magnetic dipoles gives rise to the net magnetization (M). When the sample is irradiated with photons with a determined amount of energy (a radiofrequency pulse), the net magnetization will change from its equilibrium state to a less stable one, afterwards, when the system goes back to its initial state, a signal is emitted and recorded. NMR spectroscopy measures the energy absorbed during this process within the radiofrequency (RF) spectrum.

The energy difference (ΔE) between the less and more stable spin levels is proportional to the magnetic field (B0) and the nucleus associated dipole moment (μ). Simultaneously, μ values depend on the gyromagnetic ratio (g) and the nuclear spin (I) values, which are characteristic of each isotope.

When a system at an equilibrium within the presence the an external magnetic field B0, the application of a determined radiofrequency pulse will tilt the net magnetization from the z axis. The resonance phenomenon occurs when this applied radiofrequency pulse matches the energy difference (ΔE) between the nuclear spins levels. The energy of the absorbed photon (E = hv0, being h the Planck’s constant and v the frequency) depends on the resonance radiofrequency that has to be matched. The tilted net magnetization evolves as a time-dependent manner in order to recover its equilibrium; in other words, the nuclei return from a higher energy state (beta) to their initial lower energy state (alpha), releasing energy during this process, and this decay renders the FID (free induction decay).

The FID is recorded during a specific time range and given that in this time domain the signal is not fully interpretable (the signal obtained from each nuclei is mixed), the Fourier transform is applied to convert the time-dependent signal into a frequency domain. The individual contributions of the different spins to the FID are separated by means of their resonance frequency.

When a radiofrequency pulse is applied, all spins may experience the same effect; however, if the time length of the pulse applied is very long (in a so-called soft pulse), the range of frequencies excited is narrow. This soft pulse can be used to selectively excite determined ranges of frequencies, and in solution NMR is widely used to saturate the water signals without altering the rest of the frequencies. 

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