Basic theory of NMR Spectroscopy

The property of a nucleus known as its spin is the basis of nuclear magnetic resonance spectroscopy. The nucleus has a magnetic moment, μ and an angular momentum, P and these two vector quantities are related through the expression:

μ = γP

γ is the magnetogyric ratio which is a unique constant for a particular nucleus. γ can either be positive (e.g. ¹H, ¹³C) or negative (e.g. ¹⁵N, ¹⁹Si).
The sensitivity of a nucleus in the NMR experiment depends on γ. Nuclei with a very large γ are said to be sensitive (i.e. easy to observe) while those with a small γ are said to be insensitive.
For every isotope of the element, there is a nuclear spin quantum number, I, which has a value n/2, where n is an integer.  For a nuclei with I = ½, there are two energy values in the magnetic field. m = +½ is the lower energy, more stable spin state (α) and m = -½ is the higher energy state (β).
The Boltzmann Distribution Law states that in the presence of a magnetic field, the nuclear spins will distribute themselves between the two energy levels. Due to its lower energy, the α state will be preferentially occupied.
Irradiating this state with a radiofrequency excitation stimulates a transition to a state of higher energy. However transitions will only arise when the energy gap between the states is matched exactly with the incoming radiofrequency so that the two are in resonance.
In an NMR experiment, transitions are induced between energy levels by irradiating the nuclei in the magnetic field with electromagnetic waves of the appropriate frequency. Transition from the lower to the upper energy level corresponds to an absorption of energy, whilst transitions in the reverse direction correspond to an emission of energy.
Thus this absorption is observed as a signal, the so-called resonance signal in the NMR spectrum.

The Chemical Shift

The exact position of each peak in an NMR spectrum is its chemical shift and it is a useful parameter for structure determination. Chemical shifts are due to the effects of electrons setting up tiny local magnetic fields that shield a nearby nucleus from the field and therefore cause different nuclei to come to resonance at different places.
By correlating chemical shifts with environment, we can learn about the chemical nature of each nucleus. Table 14.2 of the Physical Chemistry book shows the chemical shifts for some common functional groups found in molecules.

Spin-spin Coupling

Spin-spin coupling is brought about by small magnetic interactions that occur between nuclei of neighbouring atoms which are mediated through the intervening electrons.
As a consequence of this, the NMR spectral lines appear as a multiplet, instead of a singlet resonance. The separation between two lines in a spectrum is called the spin-spin coupling constant and is given the symbol J and it is measured in hertz.
The multiplicity of a signal in an NMR spectra is given by (n+1), where n is the number of coupling nuclei in the neighbouring groups. For example, if a nucleus H_A has two chemically different neighbouring nuclei H_B and H_C, the signal for H_A would be split into a doublet of doublets.
The relative intensities within a multiplet are given by Pascal’s triangle (binomial coefficients) as illustrated in Table 14.3 of the Physical Chemistry book.

Spin-spin Decoupling

The simplification of complicated NMR spectra involves the elimination of scalar spin-spin coupling. The technique used for this purpose is known as the spin-spin decoupling experiment (also known as double resonance).
Spin-spin decoupling involves irradiation of a nucleus at its resonance frequency using a second radiofrequency oscillator. The ‘extra’ energy given to a particular nucleus results in a rapid inter-conversion between its nuclear spin states. Now an adjacent nucleus experiences only an average of the nuclear spin states of the irradiated nucleus. Therefore the splitting (coupling) pattern disappears.