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) parameters and the linewidth from a polycrystalline EPR spectrum by using a least-squares fitting (LSF) technique in conjunction with numerical diagonalization of the SH matrix. The required resonance line positions are computed rather quickly using a homotopy technique, in which the position at an external magnetic field (B) orientation (theta, phi) is used as the initial value in a LSF procedure to estimate the position at an infinitesimally close B-orientation, (theta + deltatheta, phi + deltaphi). The resonance line positions are calculated successively in this procedure for all orientations of B over a grid of (theta, phi) values for the unit sphere. The eigenvectors 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 rigorously the first and second derivatives of the chi(2)-function with respect to the SH parameters and the linewidth using the eigenvalues and eigenvectors 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 well as how it is used for the simulation of other EPR-related spectra. The procedure is illustrated by evaluation of the Mn(2+) SH parameters and Lorentzian linewidth from the 249.9-GHz EPR spectrum of Mn(gamma-picoline)(4)I(2).