Mark P. Griffin, Centre for Magnetic Resonance, University of Queensland, 4072, Brisbane, AUSTRALIA; Kevin E. Gates, Department of Mathematics, University of Queensland, 4072, Brisbane, AUSTRALIA; Graeme R. Hanson, Centre for Magnetic Resonance, University of Queensland, 4072, Brisbane, AUSTRALIA; Chris Noble, Centre for Magnetic Resonance, University of Queensland, 4072, Brisbane, AUSTRALIA; Kevin Burrage, Centre for Magnetic Resonance, University of Queensland, 4072, Brisbane, AUSTRALIA

The experimentalist in electron paramagnetic resonance measures the absorbation of microwave radiation by a paramagnetic material within a known magnetic field. The result of an EPR experiment is a spectra of magnetic field vs intensity of the reflected radiation. From the analysis of this spectra, parameters of a spin Hamiltonian and thus the physical properties of the subject material can be determined.

For complex spectra the determination of the spin Hamiltonian parameters is not straight forward and the parameters are determined through the simulation of the experiment with each set of parameters. The simulation procedure is an integration over the angular orientation of the magnetic field. The integration is a function of the Hamiltonian matrix and the microwave frequency. The function gives rise to considerable computational complexity - in order to find the appropriate transitions the eigenvalues must be known for the Hamiltonian for all values of the magnetic field strength and orientations of the magnetic field strength to the molecule. Once the integration has been performed for the initial set of Hamiltonian parameters, an optimisation procedure is then followed in order to refine the parameters and match the simulated and observed experimental spectrum. We are concerned with this simulation and optimisation process.

Traditional methods for this computer simulation use matrix diagonalisation to evaluate the eigenvalues and eigenvectors of the Spin Hamiltonian matrix. One approach, the eigenfield method considers each orientation in the angular grid independently. The magnetic field range is divided into a number of intervals, and Matrix diagonalisation is performed in each interval[1]. Second order perturbation is then used to locate the resonant field positions. Unfortunately, matrix diagonalisation is a time-consuming process (each diagonalisation requires 8 to 10 n^3 operations, where n is the size of the Spin Hamiltonian matrix) and is not feasible to simulate EPR spectra from complex spin systems. An alternative approach is Homotopy which traces the eigenvalues and eigenvectors from one Hamiltonian to another (which is adjacent with respect to magnetic field and angle). This results in reduced computational times (each iteration requires 2/3 n^3 operations)[2]. Results of this method suggest that the simulation time of this approach may be less than half that of the eigenfield approach.

1. Belford et al., J. Magn. Reson., 1973, 11, 251. 2. Gates et al., J. Magn. Reson., 1998, 135, 104.

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