PRINCIPLE OF NMR SPECTROSCOPY

Nuclear Magnetic Resonance (NMR) spectroscopy is a powerful technique employed for various analytical purposes, especially structural characterization of organic compounds.

NMR deals with the behavior of nucleus under the influence of a strong magnetic field and absorption of radiofrequency. Not all nuclei can be studied in NMR. Nuclei having some spin can be observed with NMR spectroscopy. Spin is associated with nuclei having an odd atomic number or mass number or both, for example ¹³C has an odd mass number and even atomic number (6), ²H has an even mass number and odd atomic number, while ¹H has both the values odd. All of these nuclei are NMR active. On the other hand ¹²C, ¹⁶O have even mass number and atomic number and thus cannot be studied in NMR. Nuclei with spin have an angular momentum and magnetic moment lending them paramagnetism, thus acting as tiny small magnets. The ratio of the two quantities is known as the gyromagnetic ratio (g), which is a characteristic property of every different type of nucleus.

Spin States

Nuclei can have several spin states depending upon their spin quantum number. The number of possible spin states can be calculated from the formula, 2I + 1.

For example: Proton (¹H) has a spin quantum number ½. The number of possible spin states are 2 (+1/2 and -1/2).

                        2(1/2) + 1 = 2

            Deuterium (²H) has spin = 1, so it can 3 spin states.

            2 (1) + 1 = 3

The nuclei are arranged randomly in the absence of an external magnetic field. When placed in a magnetic field, spin active nuclei arrange themselves in all possible state and start precessing. Precession is the movement of nuclei just like a top just before it falls.

The frequency at which a nucleus precesses is known as the precessional frequency or Larmor frequency (w), which is directly proportional to the strength of the applied magnetic field (B_o)

w = gB_o

Population of Spin states

When the nuclei are placed in a magnetic field they align themselves in all possible spin states. For a proton nucleus, only two states are possible. Thus a proton nucleus will either align against the direction of the applied magnetic field or in the direction of the field. In fact both the states are populated, but there always will be a slight excess of population in the lower energy spin state (a). This excess is known as the Boltzmann’s excess and can be calculated from the Boltzmann distribution law.

This slight excess of population in the alpha state is the basis of the NMR signal. Saturation is a situation in which the population of both the states become equal and no signal is observed.

The magnetization of the nuclei in both the states cancel the effect of each other, but because there is a small excess in the lower energy state, we observe a net magnetization from the combined effect of the excess nuclei aligned in the direction of the applied magnetic field, shown by a net magnetization vector (Mo). Mo is by default shown at z-axis, its equilibrium state, pointing in the direction of Bo.

Radiofrequency pulse (Absorption of Energy)

We already know that nuclei (proton) or the net magnetization for that matter is precessing with a particular frequency, called the larmor frequency. When a strong pulse of radiofrequency is applied, the frequency that matches the larmor frequency of proton is absorbed and the nuclei flip. In other words when the radiofrequency is absorbed, the nuclei jump from lower energy to higher energy state. The radiation thus needs to have energy equal to the energy gap between the two states.

NMR Signal

The nuclei need to relax back to their equilibrium state (z-axis). This relaxation is detected by the detector and signals are sent to the recorder which then plots the transitions in the form of NMR signal.