A rigorous evaluation of spin-Hamiltonian parameters and linewidth from a polycrystalline EPR spectrum

Details are given of a procedure to evaluate the spin-Hamiltonian (SH) para meters and the linewidth from a polycrystalline EPR spectrum by using a lea st-squares fitting (LSF) technique in conjunction with numerical diagonaliz ation of the SH matrix. The required resonance line positions are computed rather quickly using a homotopy technique, in which the position at an exte rnal magnetic field (B) orientation (theta, phi) is used as the initial val ue in a LSF procedure to estimate the position at an infinitesimally close B-orientation, (theta + delta theta, phi + delta phi). The resonance line p ositions are calculated successively in this procedure for all orientations of B over a grid of (theta, phi) values for the unit sphere. The eigenvect ors of the SH matrix are used to calculate the intensities of the EPR lines exactly for each orientation of B. Details are given of how to compute rig orously the first and second derivatives of the chi(2)-function with respec t to the SH parameters and the linewidth using the eigenvalues and eigenvec tors of the spin-Hamiltonian matrix for a polycrystalline spectrum required in the LSF procedure. It is explained how this technique is generalized to include two or more magnetically inequivalent paramagnetic species, as wel l as how it is used for the simulation of other EPR-related spectra, The pr ocedure is illustrated by evaluation of the Mn2+ SH parameters and Lorentzi an linewidth from the 249.9-GHz EPR spectrum of Mn(gamma-picoline)(4)I-2. ( C) 1999 Academic Press.