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Analysing Low-Spin Ferric Complexes Using Pulse EPR Techniques: A Structure
Determination of Iron(III)tetraphenylporphyrin (bis 4-methylimidazole)
E. Vinck and S. Van Doorslaer
CW-EPR spectra and simulations.
In figure A the simulation of the CW-EPR spectrum of Fe(III)TPP(4-MeIm)2, using the g
values reported in the article, is shown.
1
0.5
0
-0.5
-1
-1.5
100
150
200
250
300
350
400
Magnetic Field (mT)
450
500
550
600
Figure A: CW-EPR spectrum of Fe(III)TPP(4-MeIm)2 taken at 20 K (upper curve) and
simulation of this spectrum, using the g-values reported in the article (lower curve).
Simulations of the nitrogen HYSCORE spectra – detailed spectra
Figure B (a-e) Observer position g=gx, experimental spectrum (blue) + simulations (red)
using different spin-system sets as marked under each simulation.
Note that the cross-peak at (4.24, 0.8) MHz in the (+,+) quadrant is only generated by the
S=1/2, Np1, Np3 combination (Figure Bb). Since also the signals from the very weakly
coupled remote nitrogens are expected to arise in the [0,5;0,5] MHz region, it is crucial to
check all combinations. Mark also that the S=1/2, Np1, Np3 combination is the only one
that generates the (-dqp, 2dqp) and (-2dqp, 2dqp) combination peaks (Figure Bb).
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Figure Ba: Simulation using three-spin system (S=1/2, Np1, Np2).
Figure Bb: Simulation using three-spin system (S=1/2, Np1, Np3).
Figure Bc: Simulation using three-spin system (S=1/2, Np2, Np4).
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Figure Bd: Simulation using two-spin system (S=1/2, Nim).
Figure Be: Simulation using four-spin system (S=1/2, Np1, Np2, Nim).
Figure C(a-c). Observer position g=gy, experimental spectrum (blue) + simulations (red)
using different spin-system sets as marked under each simulation.
Figure Ca: Simulation using three-spin system (S=1/2, Np1, Np2).
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Figure Cb: Simulation using two-spin system (S=1/2, Nim).
Figure Cc: Simulation using four-spin system (S=1/2, Np1, Np2, Nim).
Figure D(a-c). Observer position g=gz, experimental spectrum (blue) + simulations (red)
using different spin-system sets as marked under each simulation.
Figure Da: Simulation using three-spin system (S=1/2, Np1, Np2).
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Figure Db: Simulation using two-spin system (S=1/2, Nim).
Figure Dc: Simulation using four-spin system (S=1/2, Np1, Np2, Nim).
Simulation of the nitrogen HYSCORE spectra – sensitivity to the in-plane rotation
of the hyperfine and nuclear quadrupole tensors with respect to the g tensor.
Figure E (a-c)Observer position g=gy, experimental spectrum (blue) + simulations (red).
The simulation were done using the three-spin system S=1/2, Np1, Np2 and for different
values of the Euler angle  of the nuclear quadrupole and hyperfine tensor, as marked
under each simulation. For values of  larger than 25 (for Np1) and 115 (for Np2), the
simulations display features that differ largely from the experimental spectra (see Figure
Ec). Therefore, it can be concluded that the maximum deviation of the g axes from the
Fe-N bond amounts 25.
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1 [MHz]
Figure Ea: Simulation using an Euler angle  of 0 for Np1 and 90 for Np2.
1 [MHz]
Figure Eb: Simulation using an Euler angle  of 20 for Np1 and 110 for Np2.
1 [MHz]
Figure Ec: Simulation using an Euler angle  of 30 for Np1 and 120 for Np2.
Simulation of 1D-Combination Peak experiments.
The 1D-Combination Peak spectra display peaks arising from couplings with the nearest
protons (NP) of the imidazole ring. From the magnetic field dependence of the shift of
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this NP peak from twice the proton Larmor frequency, one can determine the distance
between the iron and the nearest proton, the isotropic Fermi contact interaction and the
orientation of the Fe-H axis. In the following this procedure will be explained.14
The nuclear transition frequencies να and νβ, corresponding with electron spin manifold α
and β respectively, for a S=1/2, I=1/2 system (e.g. the Fe-H system) are given by 14:
gA
( g~A)
 m  n~ (mS
  I 1)( mS
  I 1)n
(1)
g
g
Where n=(n1, n2, n3)=(cos sinθ, sin sinθ, cos) is the unit vector that describes the
orientation of the magnetic field vector in the molecular frame, g and A are the g-tensor
and the hyperfine tensor respectively and I is the proton Larmor frequency. This
expression can be rewritten as:
m
(2)
 mS  ( ( S ( g j A ji n j )   I ni ) 2 )
g j
i
S
with
Aij  Aiso ij 
0  e gn  n
g i (3ni n j   ij )
4hR 3
(3)
Here Aiso is the isotropic Fermi contact interaction and R is the distance between the
unpaired electron spin and the nucleus (e.g. between Fe and the nearest proton). From
these expressions it can be seen that the shift of the nearest proton peak (+=+) from
twice the proton Larmor frequency (2I) depends on the distance between the iron and
the nearest proton, the isotropic Fermi contact interaction and the orientation of the Fe-H
axis (given by the angle  between the gz and the Fe-H axis and the angle  between the
projection of the Fe-H axis in the (gx, gy) plane and the gx axis). 1D-CP experiments were
performed at different magnetic field positions between 240 mT and 275 mT and the
maximal shift of the NP peak from twice the Larmor frequency was determined for each
position.
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Figure F. Schematic representation of the relation between the HYSCORE and 1D-CP
information.
In order to fascilitate the determination of the maximum shift, proton HYSCORE spectra
were used. Figure F shows schematically the relation between the 1D-CP experiments
and the HYSCORE spectra. In the 1D-CP experiments the exact determination of the
maximum shift of the combination peak is sometimes masked by the presence of
contributions of different orientations, where these are cleary separated in the HYSCORE
spectra. The 1D-CP experiments have however the advantage that they can be recorded
quite fast, even if they are recorded for several  values at each magnetic-field setting.
The measurement of HYSCORE spectra at different  values is far more time consuming,
especially if the echo is weak as in the example under study. In order to combine the
advantages of both techniques, 1D-CP measurements were done at a large number of
magnetic-field settings and correlated with HYSCORE data at some selected positions.
The data on the field dependence of the maximal shift of the combination frequency is
shown in Figure 5b (see article text) together with the best fit for R = 0.315 nm ( 0.002
nm), Aiso = -0.3 MHz (0.5 MHz),  = 35 ( 5) and  = 10o (10). Using these
parameters the proton HYSCORE spectra could be satisfyingly simulated (see figure G).
The principal hyperfine values and Euler angles mentioned in the figure caption of Figure
G were obtained from the diagonalization of the square of the asymmetric matrix A in
equation (3). At observer position g=gx only a weak proton signal could be detected, even
when matching pulsed were used. This is not unexpected due to the high magnetic-field
setting (and subsequent high nuclear Zeeman frequency) and the significant g strain (and
thus reduction of the echo intensity) at this position. We therefore refrained from
interpretations of the proton HYSCORE spectrum at this position.
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Figure G: Experimental (black) and simulated (red) proton HYSCORE spectra (a)
position gz (245 mT), (b) position gy (304 mT). The simulation parameters used are
A3=5.8 MHz, A2= -2.6 MHz, A1=-3.2 MHz and α=14, β=40, γ=10.