Department of Chemistry, University of Wisconsin-Milwaukee
Milwaukee, WI 53201,
USA
ABSTRACT
The field-swept absorption spectrum of a powder distribution of spins is simulated by numerical integration and by the use of matrix diagonalization. The spin Hamiltonian for high-spin (S = n/2, n=3,5,7,9) systems is given by this equation:
where D and E are the axial and rhombic zero-field splitting parameters, respectively. There are n(n+1)/2 possible transitions between i and j levels (i, j = 1 to (n+1), i not equal j). It is necessary to set the i and j values, but not all of the transitions are necessary to simulate. Figure A, and Figure B show the simulated EPR spectra of S=3/2, 5/2, 7/2, 9/2 systems with D=1 cm-1, E=0, and the transition between 1 and 2. Different conditions with different spin systems and different D and E values can also be simulated.
Electron paramagnetic resonance (EPR), also known as electron spin resonance (ESR) and electron magnetic resonance (EMR), is the name given to the process of resonant absorption of microwave radiation by paramagnetic ions or molecules, with at least one unpaired electron spin, and in the presence of a static magnetic field (see "What is EPR"). It has a wide range of applications in chemistry, physics, biology, and medicine: it may be used to probe the "static" structure of solid and liquid systems, and is also very useful in investigating dynamic processes.
Computer simulation is based on the spin Hamiltonian
in the following equation:
where all zero-field splitting terms higher than second order are neglected.
D and E are axial and rhombic zero-field splitting parameters. Part of the
simulated EPR spectra will be presented here.
Figure 1 shows the comparison among different
spin systems (S=3/2, 5/2, 7/2, 9/2) when D= 1 cm-1 and E/D=0.0, only 1 to
2 levels transition can be obtained, other transitions ( from i to j, i and
j equal 1 to 2S+1, i not equal j) are not much contributed to the absorption
(or dabsorption/dH). When E/D varies, the absorption position is shifted
and other transitions (like 3 to 4 levels) are also contributed to the
absorption.
Figure 2 shows the comparison of simulated
EPR spectra of different E/D values at S=3/2, D=1.0 cm-1 condition for 1
to 2 transition (the lowest Kramers doublet transition), we can see the signal
(positions) or the effective g values are very sensitive to the E/D values
(see another figure).
The EPR spectrum of the nitric oxide complex of ferrous rPAH formed by exposure
of the pterin-reduced enzyme to ascorbate/nitrite under anaerobic conditions
(see the original paper by T. Joseph Kappock et al) has g = 4.12 and
g = 3.88, which is essentially identical to those reported for the NO adducts
of isopenicillin N-synthase (g = 4.09, g = 3.95), the non-heme iron site
of photosystem II (g = 4.09, g = 3.95), protocatechuate 4,5-dioxygenase (g
= 4.09, g = 3.91), catechol 2,3-dioxygenase (g = 4.16, g = 3.83), soybean
lipoxygenase, and the model complex [Fe(EDTA)(NO)] (g = 4.10, g = 3.90).
The EPR spectrum with E/D = 0.02 in Figure 2 is the right one for these Fe-NO
complexes.
Figure 3 and Figure 4 show the absorption of
1 to 2 transition and 3 to 4 transition respectively, and the intensity or
strength of 3 to 4 transition is about 10% of that of 1 to 2
transition. The signals are E/D dependent.
The D value set as 1 cm-1 has same result as
D > 1 cm-1 for X-band EPR simulation. If the rhombic parameter E supposed
to be zero, the value of the zero-field splitting parameter D can be evaluated
from the intensity dependence of the transitions, according to the Boltzmann
distribution of the two Kramers' level, (+-1/2) and (+-3/2) associated with
the ground spin state S=3/2.
Figure 5 is an example of EPR
simulation for S=5/2, D=1.0 cm-1, E/D=0.03 condition, different transitions
(1 to 2, and 3 to 4 are marked on the figure). Only the 1 to 2 transition
largely contribute the whole simulated EPR spectra (marked as "sum" in Figure
5), transition 5 to 6 is almost negligible (not ploted in Figure 5). Many
heme or non-heme proteins
have high-spin (S=5/2) electron paramagenetic resonance (EPR) signals composed
of at least one component. If the D and E/D values are given for S=5/2 species,
the simulated EPR spectra can be obtained.
When E/D value increase,
the intensity or strength of 3 to 4 transition will also increase. After
E/D > 0.1, the 3 to 4 transition becomes largely contribution to the
absorption.The effective g value is much sensitive to the E/D value, see
Figure 6 in the following (the relationships between g values and E/D value
can be see from another figure published elsewhere).
By using the created program,
different linewidths and lineshapes (Lorentzian and Gaussian shapes) can
be selected. Figure 7 is an example of EPR spectra at different selection
of linewidth.
Figure 8 shows that when the D values
is large than the frequency, the absorption is almost the same, when the
D value close to the frequency, the absorption position is shifted. When
E/D=0.33, the intensity of transition from 1 to 2 is negligible(see
another figure).
Spin S=7/2 system may be obtained in mutiple
metal systems. Figure 9 is an example of EPR simulation for S=7/2 with D=1.00
cm-1 and E/D=0.1, we can see the intensity of transition from 3 to 4 is largely
contribute to the simulated EPR spectra ("sum" in Figure 9), other transition
is negligible for contribution to the simulated EPR spectra.
The same results can obtained, when E/D changes,
the absorption position and strength or intensity are also changed (see Figure
10 below). The g~5 signal can be seen from Figure 10.
S=9/2 system may be obtained from the
coupling between S=5/2 and S=2. Different conditions for simulation of S=9/2
system can also be selected as above (see another
figure for relationships between g values and E/D value). Figure 11 still
shows the sensitivty of E/D values affect the simulated EPR spectra, and
Figure 12 shows one of many simulated EPR spectra at particular condition
(D=1.0 cm-1, E/D=0.1). The signal at g~7 is appeared on the simulated EPR
spectra
2. When E/D increases from 0 upto 1/3, other transitions
(like transition from 3 to 4) are also seen, when E/D is close to 1/3, the
transition from 1 to 2 is negligible. The simulated EPR spectra is very sensitive
to the E/D value for all the spin systems.
3. Super spin systems (S=7/2,9/2) can also contribute to the absorption
of g value between 5 and 7, in which the S=5/2 system with large D value
(larger than the frequency) and small value of E/D is normally appears. The
S=3/2 system with a large D value and a small value of E/D produces EPR signals
between 3 and 5.
1. Data
Input and
Data
Output
2. Part
of the program and the subroutines used
1. G. Van Veen, Simulation and Analysis of EPR Spectra of Paramagnetic
Ions in Powders, Journal of Magnetic Resonance, 30, 91-109(1978).
2. Hagen, W. R., D. O. Hearshen, R. H. Sands, and W. R. Dunham, A Statistical
Theory for Powder EPR in Distributed Systems, J. Magn. Res., 61, 220-232(1985).
3. D. M. Wang and J. R. Pilbrow, Symmetry Relationships for the Four Energy
Levels and the Angular Property of the EPR Spectra for a Spin-3/2 System,
Journal of Magnetic Resonance, 77, 411-423(1988).
4. An-Suei Yang and Betty J. Gaffney, Determination of Relative Spin
Concentration in Some High-Spin Ferric Proteins Using E/D-Distribution in
Electron Paramagnetic Resonance Simulations, Biophysical Journal, 51,
55-67(1987).
5. T.J. Kappock, P.C. Harkins, S. Friedenberg & J.P. Caradonna,
Spectroscopic and Kinetic Properties of Unphosphorylated Rat Hepatic
Phenylalanine Hydroxylase Expressed in Escherichia coli: Comparison
of resting and activated states", J. Biol. Chem. 270,
30532-30544 (1995).
Abstract
Full
Text
[Medline]
6. Mark J. Nelson, The Nitric Oxide Complex of Ferrous Soybeans
Liopxygenase-1, J. Biol. Chem. 262, 12137-12142(1987).
7. Hanqing Wu, EPR Spectra Simulation of Anisotropic
Spin 1/2 System, WATOC96, E-Posters
#1 at
http://www.ch.ic.ac.uk/watoc/abstracts/.
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WATOC Poster page
Figure 1. EPR spectra of Spin 3/2, 5/2, 7/2, 9/2 system when
D=1 cm-1, E/D=0.0, 1 to 2 transition.
1. S=3/2 system
Figure 2. Simulated EPR spectra of S=3/2 within small range of
E/D ( from 0.01 to 0.03) at D=1.0 cm-1 for 1 to 2 transition
Figure 3. Simulated EPR spectra of S=3/2 with different E/D values
at D=1.0 cm-1 for 1 to 2 transition.
Figure 4. Simulated EPR spectra of S=3/2 with different E/D values
at D=1.0 cm-1 for 3 to 4 transition.
2. S=5/2 system
Figure 5. Simulated EPR spectra of S=5/2 with D=1.0
cm-1 and E/D=0.03
Figure 6. Simulated EPR spectra of S=5/2 within narrow
range of E/D at D=1.0 cm-1 for transition from 3 to 4.
Figure 7. Simulated EPR spectra of S=5/2
with different linewidth (W values, here set Wx = Wy = Wz = W) at D=1.0
cm-1 and E/D=0.15 for transition from 3 to 4.
Figure 8. Simulated EPR spectra of S=5/2 with different
D values at E/D=0.33 for transition from 3 to 4.
3. S=7/2 system
Figure 9. Simulated EPR spectra of S=7/2 with
D=1.0 cm-1 and E/D=0.1
Figure 10. Simulated EPR spectra of S=7/2 with
different E/D values at D=1.0 cm-1
4. S=9/2 system
Figure 11. Simulated EPR spectra of S=9/2 with different E/D values
at D= 1.0 cm-1
Figure 12. Simulated EPR spectra of S=9/2 with E/D=0.1 at D=1.0
cm-1
1. When E/D=0.0, D > frequency (considered X-band here), only
the transition from 1 to 2 can be seen with EPR simulation, with the g value
at 2S+1 (for instance S=5/2, the g value is 6). When E/D=1/3, g=4.3 signal
can be seen for S=5/2 system.
REFERENCES