Determination of Electron Spin Resonance Static and Dynamic Parameters by Automated Fitting of the Spectra

(Received 19 June 1995, accepted 22 September 1995)

Abstract
When measurements on single crystals are not feasible, approximate values of the static spin Hamiltonian parameters are in many cases obtained from the ESR spectra of randomly oriented paramagnetic species. The accuracy of such determinations is considerably improved by optimizing these parameters by means of automated simulation programs resorting to the nonlinear least squares fit of experimental spectra. The principles of the simplex method of Nelder and Mead and of the method of Levenberg-Marquardt, generally used for that purpose, are reported. Examples are given of the applications of the latter, which has the advantage of converging rapidly, to S = 1/2 paramagnetic species in rigid matrices. Optimization procedures based on the Levenberg-Marquardt algorithm, are extended to the determination of dynamic parameters of nitroxide spin-probes, namely their tumbling correlation times in fluid and viscous isotropic media as well as in liquid crystalline phases or their exchange rates between inequivalent sites. Lastly, it is shown on the example of a nitroxide biradical, that similar methods can be applied to the study of the dynamics of multiple conformational changes in a paramagnetic flexible molecule.