98 INSTRUMENTAL METHODS
3.4 Nuclear Magnetic Resonance,
3.4.1 Theoretical Aspects,
While chemists are usually concerned with the behavior of electrons orbiting
the nucleus, the instrumental method called nuclear magnetic resonance
(NMR) is a technique based on the properties of the atom ’ s nucleus. Interac-
tion of the atom ’ s electrons with the nucleus yields important structural and
chemical information that can be gathered using NMR techniques. Nuclear
magnetic resonance spectroscopy can provide information on structure,
dynamics, kinetics, binding processes, electronic structure, and magnetic prop-
erties of bioinorganic molecules in solution. Basic information about the NMR
technique as summarized here is taken from reference 21.
Nuclei of natural isotopes (atoms of chemical elements differing in the
number of neutrons in their nuclei) may possess angular momentum or spin
and therefore magnetic moments. One defi nes spin by the following equation:
spin=+[(II 1 )]^12 / (3.12)
where =h/2π and I = nuclear angular momentum = 0, 1/2, 1, 3/2,....
The nuclear angular momentum, I , is quantized with magnitude m , where
m = I , I − 1 , I − 2 ,... , − I , yielding 2 I + 1 equally spaced spin states with angular
quantum numbersI. Additionally, a nucleus with spin has a magnetic moment,
μ. Components of μ having different spin states μ m / I yield 2 I + 1 components
for μ. Application of an external magnetic fi eld splits spin states into different
potential energy states, accounting for the origin of the nuclear magnetic reso-
nance phenomenon.
The angular momentum and magnetic moment of nuclei act as parallel or
antiparallel vectors, and the ratio between these is known as the magnetogyric
ratio, γ. The magnetogyric ratio is given in terms of equation 3.13 :
γ
πμ μ
==2
hI I(3.13)
For I > 1/2, nuclei also possess an electric quadrupole moment, Q. Quadrupolar
nuclei exchange energy with electric fi elds in the rest of the molecule in which
they are located causing profound effects on NMR spectra. Table 1.1 of refer-
ence 21 lists the nuclear properties of some elements. One property of nuclei,
receptivity, or natural signal strength, depends on the intrinsic sensitivity of
the nucleus weighted by its natural abundance. Usually the receptivity of a
nucleus is high if the magnetic moment, μ , is high. Usually, the^13 C nucleus,
which has a fairly weak signal and natural abundance of 1.108%, is arbitrarily
given a receptivity of 1.00 with the receptivity of all other nuclei calculated
relative to it. The resonant frequency in a particular magnetic fi eld (2.348 T in
reference 21 , Table 1.1 ) is proportional to the magnetogyric ratio and will vary
slightly according to the chemical and electronic environment in which the
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