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

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.