Simulation of multi-frequency EPR spectra for a distribution of the zero-field splitting.

We present a numerical procedure called 'grid-of-errors' to extract the distribution of magnetic interactions from continuous-wave electron-paramagnetic-resonance (EPR) spectra at multiple microwave frequencies. The approach is based on the analysis of the lineshape of the spectra and explicitly worked out for high-spin systems for which the lineshape is determined by a distribution of the zero-field splitting. Initial principal values of the zero-field splitting tensor are obtained from the EPR spectrum at a microwave frequency in the high-field limit, and the initial distribution is taken Gaussian. Subsequently, the grid-of-errors procedure optimizes this distribution, without any restriction to its shape, taking into account spectra at various microwave frequencies. The numerical procedure is illustrated for the Fe(III)-EDTA complex. An optimized distribution of the zero-field splitting is obtained, which provides a proper description of the EPR spectra at 9.5, 34, 94, and 275 GHz. The proposed approach can be used as well for distributions of magnetic interactions other than the zero-field splitting.