BioPHYSICAL chemistry

Hyperfine structure

The gvalue will be different in protein environments, due
to differences in the local magnetic field compared to the
applied field. In EPR, one of the primary effects is the con-
tribution of the proton spins and their associated dipole
moments on the field. In the presence of a nuclear spin, I,
the local magnetic field, is:

Bloc=B+amI where mI=±1/2 for a proton (16.19)

where a is called the hyperfine coupling constant. For an
interaction with a proton (mIof +1/2 and −1/2) each of the
two energy levels splits, resulting in four levels. Since mImust
be constant during the experiment, two of the transitions
are possible in an EPR experiment at magnetic fields of:

(16.20)

The presence of one line is then split equally into two lines (Figure 16.19).
If the nuclear spin is larger, the splittings will accordingly become more
complex with 2I+1 hyperfine lines being present, although not all of
the lines may be resolved (See Chapter 20).

Electron nuclear double resonance

We can now consider a double-resonance condition as we did for NMR.
The microwave frequency is fixed at resonance and a radiofrequency wave
is applied. When the radiofrequency is at resonance for a nuclear spin
nearby the electron spin, then the radiofrequency will flip the nuclear
spin and be sensed by the electron (Figure 16.20). Writing the total energy
of the system as:

(16.21)

leads to the transitions occurring at

(16.22)

Thus, the EPR signal changes when the radiofrequency is resonant with
a nearby nuclear spin. The EPR effectively becomes a means to obtain the

ννRF νμN N

A

=± hgB=

2 00

where

E

gB ha g BeB N N

=± ±

μμ

24 2

5

B

h

g

B

h

BBg

=− =+

ν

μ

ν

μ

1

2

1

2

and

CHAPTER 16 MAGNETIC RESONANCE 365

mI  –^12

mS  –^12

mS  –^12

B  0 B increasing mI  – 21

mI  –^12

mI  –^12

Figure 16.19The

interaction between

an unpaired electron

spin and a nuclear

spin results in four

energy levels and

the splitting of the

EPR signal.