ABSTRACT
Nuclear magnetic resonance (NMR) spectroscopy has many similarities with the
molecular spectroscopic techniques involving transitions between electron
energy levels. However, NMR stands apart in many details, which will be
briefly discussed in this introduction section. The obvious distinction is that
NMR involves transitions between nuclear energy levels. In the absence of exter-
nal magnetic or electric fields, the energy levels of the ground state of an isolated
nucleus are degenerate. It is the external magnetic field that brings the distinction
between the nuclear energy levels. If we apply external magnetic field B0 on a
sample containing nuclei with nonzero spin angular momentum I (i.e., magneti-
cally active spins), the 2Iþ 1 nuclear energy levels will be E ¼ gIzB0 (1)
in which the proportionality factor, referred to as gyromagnetic ratio, g is the characteristic constant for a given isotope. Because the values of angular momen-
tum are quantized with the magnetic quantum number m (IZ ¼ h m, where h is the Planck’s constant), so are the nuclear energy levels known as Zeeman
levels. Following the selection rule governing any magnetic dipole transitions
(Dm ¼+1), the differences between the Zeeman energy levels are DE ¼ h gB0 ¼ h v0 (2)
where v0 is the frequency (in units of radian per second) of the electromagnetic radiation, corresponding to the difference between the spin energy levels,
known as Larmor frequency. Equation (2) also predicts linear dependence of
the energy level difference on the external magnetic field B0. For the currently
available magnetic fields, the energy difference falls into the radio frequency
(rf) portion of the electromagnetic radiation. When the system is at thermal
equilibrium, the population of the given energy level is given by the Boltzmann
distribution
Ni ¼ exp Ei kBT
(3)
where Ni is the number of nuclei occupying energy level Ei, kB is the Boltzmann
constant, and T is the absolute temperature. In contrast to the electronic tran-
sitions, at temperatures close to the room temperature, the product of kBT is
several orders of magnitude larger than the difference between the Zeeman
levels DE. Consequently, even random thermal fluctuations can very efficiently induce the nuclear spin transitions, nearly equalizing the number of nuclei occu-
pying each Zeeman energy level. Being directly proportional to the population
difference, the NMR signal strength is significantly weaker compared with other
atomic or molecular spectroscopies involving electron levels transitions. Out of
200,000 1H spins placed into the external magnetic field of 11.7 T (500 MHz 1H
frequency), approximately 100,001 spins will occupy the lower energy level
and 99,999 the higher one. Effectively, only 1/200,000 of the sample gives rise to the observable NMR signal. When compared with other spectroscopies,
NMR is a relatively insensitive technique.
