Department of Chemistry, University of Wisconsin-Milwaukee
Milwaukee, WI 53201,
USA A program simulating anisotropic 1/2 spin
system has been created, its parameters being: gxx, gyy, gzz, and relevant
line-width Wx, Wy and Wz. The line shape can be set to Lorenztian or Gaussian
shapes along with experimental conditions, such as frequency and scan range.
By using this program, different anisotropic 1/2 system can be simulated,
any EPR detected species with S=1/2 system can be analyzed. Different conditions
with different gxx, gyy, gzz and different Wx, Wy, Wz values are considered
here and their simulated EPR spectra are presented. Electron paramagnetic resonance (EPR)--- also
called electron spin resonance (ESR)---has assumed an increasingly prominent
position in various fields, especially in biophysical chemistry during the
past two decades. The phenomenon is based on the magnetic moment of an unpaired,
spining free electron. In a magnetic field, the unpaired electron---which
has a spin quantun number S=1/2 (ms = +-1/2) --- precesses about the field
axis (z axis) with a component of its spin angular momentum either parallel
(ms = +1/2) or antiparallel (ms = -1/2) to the z axis. An oscillating magnetic
field at right angles to the field axis induces transitions between the two
spin states when the frequency of the field is at or near the Larmor frequency
of the precessing electron. There are mainly the following frequency at which
the EPR spectrometers working:
1-2 GHz (L-band) and 2-4 GHz (S-band), 8-10 GHz (X-band), 35 GHz (Q-band)
and 95 GHz (W-band). Here, only X-band are considered for EPR simulation.
Computer simulation is based on the spin Hamiltonian
in the following equation (assuming no hyperfine interaction):
If it were possible to orient all defects along the Z axis, the spectrum
would consist of only a single line. If the line position is ascertained
for the field, respectively, along the X, Y, Z directions, the position are
described by gxx, gyy, gzz. For such systems of axial symmetry, then gxx=gyy.
The program for simulation of EPR spectrum of S=1/2 system is also derived
from the program to simulate high spin systems (S = 3/2,
5/2, 7/2, 9/2). In this poster, different conditions will be considered
(gxx # gyy # gzz, gxx = gyy > gzz, gzz > gxx = gyy, gxx = gyy = gzz,
here the symbol "#" means not equal), linewidth Wx, Wy, Wz along X,
Y, Z directions respectively are also can be changed if needed. Part of the
simulated EPR spectra will be presented here.
Figure 1 shows the simulated EPR spectra with
different gxx, gyy, gzz values (for simple, g values selected as 2.1,2.0,1.9),
and the g values in Figure 2 are from the reference elsewhere, actually,
any given gxx, gyy, gzz values, the simulated EPR spectrum can be obtained.
Figure 3 shows that the linewidth (Wx, Wy, Wz) also affect the shape of the
signal, but the theta and phi steps do not much change the shape of the simulated
EPR spectra (see Figure 4).
Author also studies the angular dependent
EPR simulation, from Figure 5, it is clearly to see that at different set
of the Phi degree, the signal at gzz does not change. When Phi is 0 degree,
the signal at gxx is appeared; when Phi is 90 degree, the signal at
gyy is appeared; when Phi is 45 degree, the signal at ~ (gxx+gyy)/2 is appeared.
From Figure 6, it is known that when theta is 0 degree, almost no signal
appeared; when theta is 45 degree, the signals of ~ gyy, gzz appeared; when
theta is 90 degree, the signals of ~ gxx, gyy appeared.
The same regularity is obtained when different
range of Theta and Phi are set (see Figure 7): when the Phi range is set
between 0 degree and 30 degree (Phi step is one degree, the same for other
Phi ranges), the signal at ~ gxx is appeared; when the Phi range is set between
60 degree and 90 degree, the signal at gyy is appeared; when the Phi range
is set between 30 degree and 60 degree, the signals at ~ (gxx+gyy)/2 are
appeared. The siganl at gzz is independent of the change of Phi. When the
Theta range is set between 0 degree and 30 degree (Theta step is one degree,
the same for other Theta ranges), the siganl at ~ gzz is appeared; when the
Theta range is set between 30 degree and 60 degree, the siganls at ~ (gyy+gzz)/2
are appeared; when the Theta range is set between 60 degree and 90 degree,
both siganls at gxx and gyy are appeared (see Figure 8).
The lineshape (mixture of gaussian
and lorentzian, gaussian, and lorentzian) is also affect the shape of the
simulated EPR spectra (see Figure 9). If the gxx, gyy, gzz values are given
(for instance gxx=2.03, gyy=2.02, gzz=2.00), different Wx, Wy, Wz values
selected are also affect the shape of simulated EPR spectra (see Figure
10,11,12), particular to the simulated EPR spectra by using of Gaussian and
its mixture with Lorentzian lineshapes(Figure 10 and Figure 11).
1. Data
Input and
Data
Output
2. Part
of the program and the subroutines used
1. J. R. Pilbrow, Lineshapes in Frequency-Swept and Field-Swept EPR for
Spin 1/2, Journal Magnetic Resonance, 58, 186-213(1984).
2. John E. Wertz and James R. Bolton, Electron Spin Resonance, Elementary
Theory and Practical Applications, published 1986 by Chapman and Hall.
3. Louis J. Libertini and O. Hayes Griffith, Orientation Dependence of
the Electron Spin Resonance Spectrum of Di-t-butyl Nitroxide, Journal of
Chemical Physics, 53, 1359-1367(1970).
4. Hanqing Wu, EPR Spectra Simulation of Spin 3/2,
5/2, 7/2, 9/2 Systems, WATOC96, E-Posters
#2 at
http://www.ch.ic.ac.uk/watoc/abstracts/.
Return to main WATOC
Poster page
Figure 1. EPR spectra of S=1/2 with different gxx, gyy, gzz values
at Wx = Wy =Wz = 10 G
Figure 2. EPR spectra of S=1/2 with different gxx, gyy,
gzz values at Wx = Wy =Wz = 10 G (g values from references)
Figure 3. EPR spectra of S=1/2 with different g = 2.06, 1.93,
1.86 at different linewidth of W values
Figure 4. EPR spectra of S=1/2 with different g = 2.06, 1.93,
1.86 at different different theta, phi steps.
Figure 5. Simulated EPR spectra of S=1/2 with g = 2.06, 1.93,
1.86 at different Phi degree
Figure 6. Simulated EPR spectra of S=1/2 with g = 2.06, 1.93,
1.86 at different Theta degree
Figure 7. Simulated EPR spectra of S=1/2 with g = 2.06, 1.93,
1.86 at different range of Phi degree
Figure 8. Simulated EPR spectra of S=1/2 with g = 2.06, 1.93,
1.86 at different range of Theta degree
Figure 9. Simulated EPR spectra of S=1/2 with g = 2.06, 1.93,
1.86 by using different lineshape (mixture(1), gaussian(2), lorentzian(3))
at W=10 G.
Figure 10. Simulated EPR spectra of S=1/2 with g = 2.03, 2.02,2.00 by
using lineshape of mixture of gaussian and lorentzian (W436 means Wx=4
G, Wy=3G,Wz=6 G respectively).
Figure 11. Simulated EPR spectra of S=1/2 with g = 2.03, 2.02,2.00 by
using lineshape of gaussian (W436 means Wx=4 G, Wy=3G,Wz=6 G respectively).
Figure 12. Simulated EPR spectra of S=1/2 with g = 2.03, 2.02,2.00 by
using lineshape of lorentzian (W436 means Wx=4 G, Wy=3G,Wz=6 G respectively).
1. Different g values and the line-width (W) of each signal (gxx,
gyy, gzz) of spin S=1/2 system can be "effectively" simulated. The lineshape
of the signals can also be selected.
2. The angular dependent EPR spectra simulations show that
the EPR spectra of orientated samples can also be analyzed.
APPENDIX
REFERENCES