Department of Chemistry, University of Wisconsin-Milwaukee
Milwaukee, WI 53201, USA
A program simulating anisotropic 1/2 spin system has been edited, parameters of gxx, gyy, gzz, and relevant line-width Wx, Wy, Wz and line shape(Lorentzian and Gaussian shapes) can be set along with the experiment condition, such as frequency, scan range. By using this program, various of 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 betwwen 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 given the gxx, gyy, gzz values (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).
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