BIOINORGANIC CHEMISTRY A Short Course Second Edition

ELECTRON PARAMAGNETIC RESONANCE 123

μβ=−g S (3.34)

E=⋅μB (3.35)

(^) ΔEh=ν (3.36)
Replacing μ by its equivalent operator from equation 3.34 and E by H , the
Hamiltonian, equation 3.35 becomes
Hg=⋅βSB (3.37)
or by replacing the dot product by ms , the projection of S onto B and multiply-
ing by the magnitude ofB , equation 3.38 is written as
Egg=βsB (3.38)
Giving ms its two values, ± 1/2, one fi nds equation 3.39 :
ΔEgB=−[]EE 12 //− 12 β (3.39)
If one then defi nes the resonance condition, BR (alternately written as B 0 or
asBL when referring to the laboratory fi eld associated with a particular EPR
instrument system), as the magnetic fi eld at which the energy of the transition
comes into resonance with the fi eld, one fi nds equation 3.40 or, more usefully,
equation 3.41.
ΔEgB==hνβR (3.40)
g
h
BR

=

ν

β

(3.41)

From the knowledge of the spectrometer ’ s operating frequency (held constant)
and the magnetic fi eld intensity at which maximum EPR absorption occurs as
one varies the magnetic fi eld, one easily calculates g from equation 3.41.

Figure 3.19 Removal of degeneracy of the α and β electron spin states by a magnetic
fi eld. (Adapted with permission of John Wiley & Sons, Inc. from Figure 2.16 of refer-
ence 3. Copyright 1997 Wiley - VCH.)

Energy, E

ms = +1/2

ms = -1/2

Field Strength

α β

ΔE = hν = gβB

E = + (1/2) gβB

E = - (1/2) gβB

B