relatively evenly spaced. It is easy to define a hyperfine coupling constant a,hav-
ing units of T (tesla), such that
Blocal environmentBmag field aMI,z (16.17)
The local environment magnetic field Bis thus slightly different than the im-
posed magnetic field Bby some quantized multiple of the hyperfine coupling
constant. Hyperfine coupling constants are typically on the order of millitesla,
but they are large enough to detect in modern ESR spectroscopy. Figure 16.11
shows an ESR spectrum with a well-defined hyperfine coupling constant. The
hyperfine coupling constant is useful in that the ESR spectrum can indicate
what atom or atoms (since atoms have specific nuclear spins) the unpaired
electron is “on.”Example 16.7
How many ESR peaks would be present due to a single unpaired electron on
each of the following? (Use the fact that the nuclear spins of H, N, and P are,
respectively,^12 , 1, and ^12 .)
a.A hydrogen atom
b.An NH 3 radical
c.A PH 3 radicalSolution
a.A single hydrogen atom has two possible MIvalues: ^12 and ^12 .It will
therefore have two different local magnetic fields (depending on the value of
MI), and so will have two ESR absorptions due to hyperfine coupling.
b.The combination of the single N atom’s spin of 1 and the three hydrogen
atoms’ spins of^12 means a value ofMI,molof^52 . Therefore, the zcomponent of
the combined nuclear spins,MI,z, can range from ^52 to ^52 . There are six pos-
sible MI,zvalues and so six ESR absorptions.
c.Similar to part b, the possible total z-component nuclear spins range from
2 to 2 in integral steps, for a total of five possible MI,zvalues. This indi-
cates five possible values for the local magnetic field, yielding five ESR ab-
sorptions.The number of first-derivative peaks seen in an ESR spectrum can provide
a lot of information about a molecule’s structure, because in a molecule any
atom that has a nuclear magnetic moment contributes to the hyperfine cou-
pling. Consider the methyl radical, CH 3 . The carbon nucleus has I0 and so
does not contribute to the ESR hyperfine splitting. The three hydrogen atoms
each have I^12 , and the possible combinations of the nuclear spins MI,z
are ^32 (all three nuclear spins in the ^12 direction), ^12 ,^12 , and ^32 (all
three nuclear spins in the ^12 direction). Therefore, four lines are expected
in the ESR spectrum of the methyl radical, and that is what is seen experi-
mentally. Similarly, for the benzene radical anion there are seven distinct lines
in the ESR spectrum due to the six protons. Nonequivalent nuclei contribute
differently to the hyperfine coupling. Therefore, ESR spectra for polyatomic
molecules can quickly get complicated, but extracting the proper information
from them provides quite a bit of detail about the structure of the ESR-active
species.570 CHAPTER 16 Introduction to Magnetic Spectroscopy
(b)a a(a)Figure 16.11 (a) An unpaired electron on an
atom having a nuclear spin of zero shows a single
absorption in an ESR spectrum. However, (b) an
electron on an atom having a nonzero nuclear
spin shows multiple absorptions due to the inter-
action of the electron spin and the nuclear spin.
This interaction is called hyperfine coupling. The
amount of coupling is measured by the hyperfine
coupling constant,a. Here, the electron is on an
atom having I1.