Simulation of EPR spectra with automatic fitting of the spectroscopic parameters and of the reorientational correlation time

Abstract

The simulation of EPR spectra is often necessary for the accurate determination of the principal values of the electronic Zeeman and hyperfine tensors. The automatic adjustment of these principal values and of linewidths enables us rapidly to achieve a satisfactory agreement between the observed and the calculated spectra. The usual criterion of least squares may be applied to the deviations to perform this adjustment. In two or more dimensions, a minimization algorithm derived from that of Levenberg–Marquardt is applied. In one dimension, the algorithm of the Fibonacci series has been used.

This approach lends itself to the determination of parameters, such as the reorientational correlation time, which may not be deduced by a casual inspection of spectra. It is illustrated by the example of a poly(4-vinylpyridine) gel, crosslinked by vanadyl ions. Whereas the gel is rigid at low temperatures, the motion of the paramagnetic probe modifies the spectral shapes for this gel above 260 K.

The first stage involves only the spectral parameters which are fitted from the low-temperature spectrum, using second-order perturbation formulae. The second stage requires a model of reorientation; simulations have clearly shown that a Brownian diffusion model must be preferred to a random-jump model. By keeping the spectral parameters as constants, the reorientational correlation time, as well as linewidths, can be determined at several temperatures by the above minimization.