Electron paramagnetic resonance: Nonlinear least-squares fitting of the Hamiltonian parameters from powder spectra with the Levenberg-Marquardt algorithm

Abstract

In many instances, the deduction of spectroscopic parameters from electron paramagnetic resonance spectra depends on spectrum simulation and parameter optimization. We have developed two software packages based on the approximate formulae of Iwasaki for the calculation of line positions and on the Levenberg-Marquardt algorithm for nonlinear least-squares optimization. Our software applies to systems having an anisotropicg-tensor and an arbitrary number of hyperfine interactions with nuclei. They are written in the FORTRAN 77 programming language. At present, neither the nuclear quadrupolar interaction nor the nuclear Zeeman interaction terms are handled. The programs CRISAJU and EPRPOWDERFIT apply to the cases of single crystals and powders, respectively. For use in the latter, thanks to the software ODYSSEE which implements automatic differentiation of algorithms, an ancillary subroutine, which contributes to the performance of the optimization, was created automatically

Single-crystal EPR study and DFT structure of the [Mo(CO)5PPh3]+· radical cation

“…The angular variation of the EPR signals was measured in steps of 101 in the three reference planes. The g and hyperfine tensors were determined using a second-order perturbation treatment and the results were optimized with a least-squares minimization program [18].…”

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

“…The first method, first developed by Misra [7] in seminal work is general but limited to relatively small systems; it was used e.g to analyse the zero-field splitting of a Mn 2+ complex from its 249 GHz powder spectrum by the least squares method. A recently published treatment [9] employing perturbation theory, is better suited for systems with hyperfine couplings due to several nuclei or with a moderately large zero-field splitting in case S>½. In both methods analytical expressions for the derivatives of the fitted spectrum with respect to the spin Hamiltonian parameters were employed.…”

“…This method is employed also here in the Xfit programme. Analytic derivatives were generated automatically in the programme by Soulié and Berclaz [9] based on perturbation theory. In both cases the extra computational load to obtain the derivatives together with the spectrum (1) appears to the relatively low, compared to that for numeric differentiation.…”

“…It provides a possibility of obtaining analytical derivatives of the energy differences E p -E q used to calculate the resonance field, and consequently of the coupling tensors. An alternative method to obtain analytical derivatives when the resonance fields B pq were obtained by perturbation theory was recently published [9].…”

[M(CO)4PPh3]− radicals (M=Cr, Mo, W): DFT and single crystal EPR investigations

“…The EPR reference axes were oriented with respect to the crystallographic axes: for Cr(CO) 5 EPR spectra were recorded on a Bruker 300 spectrometer and crystals were irradiated with a Philips X-ray tube equipped with a tungsten anticathode. The EPR tensors were obtained by using an optimization program which adjusts the terms of the spin Hamiltonian in order to obtain the best fitting with the experimental angular variation of the signals in three perpendicular planes [11].…”