Physical Chemistry , 1st ed.

Example 16.8

In an ESR experiment where the microwave radiation was fixed at 10.0 GHz,

the MI,z^12 absorption of an ESR spectrum of the methyl radical appears

at a magnetic field strength of 0.3376 T, and the MI,z^12 absorption ap-

pears at 0.3353 T. Calculate the hyperfine coupling constant aand predict the

position of the other two absorptions expected for the MI,z^32 and the

MI,z^32 absorptions.

Solution

The following two equations, based on equation 16.17, need to be satisfied:

0.3376 T Bmag field a^12 

0.3353 T Bmag field a^12 

There are two equations and two unknowns. They can be solved simultane-

ously using simple linear algebra techniques (that is, substitution). Upon do-

ing so, one finds a value ofa0.0023 T 23 G, as well as a Bmag fieldof

0.3366 T. Using equation 16.17, we can predict the absorptions for MI,z^32 

and MI,z^32 as

0.3366 T (0.0023 T)( ^32 ) 0.3401 T for MI,z^32 

0.3366 T (0.0023 T)(^32 ) 0.3332 T for MI,z^32 

Four equally spaced lines are expected.

Nonequivalent nuclei make a different contribution to the hyperfine split-

ting. If a nucleus having spin Iand a different nucleus having spin Jare in a

molecule, then one can expect up to (2I 1)(2J 1) separate absorptions in

the ESR spectrum. In some cases, lines lie practically on top of each other and

are unresolved, so that fewer lines than expected are seen. ESR spectra can get

complicated. Figure 16.12 shows an example of an ESR spectrum of a relatively

simple compound.

In many organic molecules, the gfactor of the electron is about 2. However,

unpaired electrons are also present in many metal compounds, especially metal

compounds having atoms of transition metal or lanthanide or actinide ele-

ments. These unpaired electrons are from dor forbitals, and the molecules are

not considered free radicals. However, the unpaired electrons do give rise to

signals via a resonance phenomenon. Metals having unpaired electrons in dor

forbitals are paramagnetic, so when the magnetic resonance technique is ap-

plied to such compounds, it is called electron paramagnetic resonance,or EPR.

Although the general ideas behind the technique are similar, the gvalues are

different, up to about 4 in some transition metal complexes. Different mi-

crowave regions are used, depending on the gfactor, magnetic field strength

available, resolution, and other factors. Microwave frequencies at about

9.5 GHz, 24 GHz, and 35 GHz are common. Magnetic field strengths must be

consistent with equation 16.11 in order for resonance to occur.

16.5 Nuclear Magnetic Resonance

We considered electron spin resonance spectroscopy before nuclear magnetic

resonance spectroscopy because ESR deals primarily with the subatomic

16.5 Nuclear Magnetic Resonance 571

75 G

Figure 16.12 The ESR spectrum of the CF 3
radical, showing the complexity due to hyperfine
coupling. The cluster of tiny signals in the center
is an impurity.Source:M. T. Rogers and L. D.
Kispert,J. Chem. Phys.,1967, 46: 3193.