Chemistry Reference
In-Depth Information
The integral in Equation 9.31 converges if
n
is set to ~100,000 or larger. We also note that we
approximated the value of sin
x/x
to 1 for |
x
|
10
−10
.
The simulations can be made to reproduce the initial ratio of i ts in Equation 9.27 using the mea-
sured
T
1
(
≤
s) and i tting the distance
r
(nm), which is the only adjustable parameter. For canthaxan-
thin and BI the experimental i ts and the integrated values showed the best match in a very narrow
temperature range (±10 K) in the vicinity of the maximum enhancement in the relaxation rate. The
distances obtained from the curve i ts were similar to those determined from 1/
T
M
- 1/
T
M0
differ-
ence, namely, 13.0
μ
2.0 Å for BI. It was found for canthaxanthin,
which shows no prominent peak in the relaxation rate, that the distance does not depend on 1/
T
M
-
1/
T
M0
. Using the ratio of curve i ts, we can estimate the value of
r
for canthaxanthin as 9. 0
±
2.0 Å for canthaxanthin and 10.0
±
±
3.0 Å
in TiMCM-41 in the temperature range of 110-130 K.
9.16 EFFECT OF DISTANT METALS ON
g
-TENSOR
When an organic radical is located near a high-spin metal ion, the
g
-tensor of the radical depends
on the exchange interaction between the radical and the metal ion.
Multifrequency HF-EPR permits precise determination of the
g
-values of the exchange-coupled
organic radical metal ion species, provides parameters for accurate simulation of the EPR spectra,
and allows determination of detailed information about the radicals themselves and their environ-
ment (Gerfen et al. 1993, Un et al. 1995, Bar et al. 2001, Ivancich et al. 2001).
For instance, the Hamiltonian that describes the interacting system of an oxoferryl spin
S
=
1
(
S
Fe
) with a radical spin
S
=
½ (
S
rad
) is given in equation
H
(9.34)
rad
rad
Fe
Fe
Fe
Fe
rad
Fe
=β
Sg
⋅
⋅
B
+β
Sg
⋅
⋅
B
+
SDS
⋅
⋅
−
J
⋅
SS
⋅
where
β
is the Bohr magneton
B
is the applied magnetic i eld
g
rad
and
g
Fe
are the
g
-tensors of the radical and the iron species
D
is the ZFS tensor for iron
J
is an isotropic exchange coupling
S
rad
and
S
Fe
are the vector spin operators
The
g
-tensor of the radical and the distance between the exchange-coupled radical and oxofer-
ryl species can be obtained from spectral simulations at different frequencies. The
g
-values for the
oxoferryl moiety and the ZFS tensor of the iron species were i xed in the simulations. The adjustable
parameters in the i tting procedure were the exchange coupling,
J
, and the three
g
-values of the radi-
cal. The lower frequency EPR spectra of the radical can be well-simulated by using the parameters
determined from the highest frequency spectrum. It should be emphasized that if exchange interac-
tion (
D
and
J
parameters) is left out from the simulations, the lower frequency spectra cannot be
well-i tted by use of the
g
-values obtained from the higher frequency spectrum.
9.17 DIMERS DETECTED BY
g
-TENSOR ANISOTROPY VARIATION
The
g
-tensor principal values of radical cations were shown to be sensitive to the presence or absence
of dimer- and multimer-stacked structures (Petrenko et al. 2005). If face-to-face dimer structures
occur (see Scheme 9.7), then a large change occurs in the
g
yy
component compared to the monomer
structure. DFT calculations coni rm this behavior and permitted an interpretation of the EPR mea-
surements of the principal
g
-tensor components of the chlorophyll dimers with stacked structures like
the P
700
special dimer pair cation radical and the P
700
special dimer pair triplet radical in photosystem
I. Thus dimers that occur for radical cations can be deduced by monitoring the
g
yy
component.
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