Automatic fitting procedures for EPR spectra of disordered systems: Matrix diagonalization and perturbation methods applied to fluorocarbon radicals

Two types of automatic fitting procedures for EPR spectra of disordered systems have been developed, one based on matrix diagonalization of a general spin Hamiltonian, the other on 2nd order perturbation theory. The first program is based on a previous Fortran code complemented with a newly written interface in Java to provide user-friendly in and output. The second is intended for the special case of free radicals with several relatively weakly interacting nuclei, in which case the general method becomes slow. A least squares' fitting procedure utilizing analytical or numerical derivatives of the theoretically calculated spectrum with respect to the g- and hyperfine structure (hfs) tensors was used to refine those parameters in both cases. 'Rigid limit' ESR spectra from radicals in organic matrices and in polymers, previously studied experimentally at low temperature, were analyzed by both methods. Fluorocarbon anion radicals could be simulated, quite accurately with the exact method, whereas automatic fitting on, e.g. the c-C4F8− anion radical is only feasible with the 2nd order approximative treatment. Initial values for the 19F hfs tensors estimated by DFT calculations were quite close to the final. For neutral radicals of the type XCF2CF2 the refinement of the hfs tensors by the exact method worked better than the approximate. The reasons are discussed. The ability of the fitting procedures to recover the correct magnetic parameters of disordered systems was investigated by fittings to synthetic spectra with known hfs tensors. The exact and the approximate methods are concluded to be complementary, one being general, but limited to relatively small systems, the other being a special treatment, suited for S = 1/2 systems with several moderately large hfs.