ELECTRON PARAMAGNETIC RESONANCE 127
at low fi eld (from gx and gy , g⊥ or g perpendicular). The spectrum is also
said to be axial. It will appear as shown below in Figure 3.22C.- gx ≠ gy ≠ gz. The spectrum is said to be rhombic. Three different EPR
values are recorded. Figure 3.22D shows this behavior.
When there is more than one unpaired electron in the paramagnetic center,
zero - fi eld splitting (zfs) will occur. Zero - fi eld splitting is the separation in
energy of the variousms states in the absence of an applied magnetic fi eld. It
is the result of interelectronic interactions and ligand fi elds of low symmetry.
The hamiltonian for zfs is written as equation 3.42 , where D is the axial zfs
parameter andE/D indicates the degree of rhombic distortion in the electronic
environment. The zfs is applied as a correction to the energies of the individual
spin states arising from spin – orbit coupling.
HDS S
E
D
zfs=−+ −⎡ zxySS
⎣⎢⎤
⎦⎥
221 22
3
() (3.42)
The case of high - spin Fe(III) ( S = 5/2) is important because it is found in high -
spin heme systems of hemoglobin and myoglobin (see Section 7.2 ). The param-
eterD is a directed quantity; that is, it characterizes the magnitude and direction
of axial distortion. In the high - spin Fe(III) heme case, the direction is normal
to the heme plane. Actually, three cases are of interest for the S = 5/2 system.
When D = 0 there is no zfs, the separation between all levels is the same, and
eachms level converges to a common origin at zero fi eld. Therefore each level
comes into resonance at the same value ofBL , and a single EPR line is seen.
This simple behavior has never been observed in a biological system. When
0 < D < hν , the levels are split in zero fi eld because the paramagnet experiences
a small asymmetry in its environment which separates thems values. The levels
converge to different origins. When the zero - fi eld separation is small, the levels
can come into resonance withBL and fi ve separate resonances are observed.
In the third case, D >> hν , the zero - fi eld splitting is very large. The separation
betweenms ± 3/2 and ± 5/2 is too large for the transitions to be observed. Only
transitions within thems = ± 1/2 levels are observed, and these are very sensitive
to the orientation of the paramagnet with respect to the applied fi eld. The EPR
spectrum would look like that of Figure 3.22C with greater separation of g||
fromg⊥ and a lower relative intensity for g||. It can be calculated that the
ms = ± 1/2 transitions correspond to a g|| value of 2.0 and g⊥ values of 6.0 (2 S + 1
withS = 5/2). This is the circumstance found for hemes where the square - planar
array of four porphyrin nitrogen ligands gives rise to largeD values. A more
complete discussion is found on pages 145 – 152 of reference 29 ; Figures 11 and
14 are particularly instructive, and the interested reader is referred there.
3.5.2 Hyperfi ne and Superhyperfi ne Interactions, CONTENTS ix
Hyperfi ne interactions in EPR spectra arise when the paramagnet fi nds itself
in the vicinity of a nucleus having a nuclear spin and consequently a nuclear