ESR of spin 5/2 systems with axial symmetry and moderately large zero-field splittings. Application of line-shape calculations to the interpretation of randomly oriented microcrystallite spectra

Abstract

Magnetic resonance line positions and intensities are calculated for the simplified spin‐Hamiltonian H =D[S z 2 −S(S+1)/3]+g μ B H · S with S=5/2 . The resonance line positions and intensities are found by direct diagonalization of the matrix of ℋ and are plotted versus the axial angle θ and the magnetic fieldH. The region 1/2≲|D|/h ν ≲ 2 is explored, where v=the microwave frequency, and line shapes integrated over all orientations are calculated using a Gaussian line shape with isotropic linewidth. The results are compared with the experimental EPR spectra of two crystallographically isomorphic high‐spin trisdithio‐oxalato‐Fe(III) salts, one having |D|=0.26 GHz (treated by perturbation theory, including quartic spin operators), and the other |D|=6.8 GHz . Single crystal measurements were made for the former case, but only powder measurements of the latter system were possible. Calculation of the powderline shape for the |D|=6.8 GHz spectrum for both X‐band and K a ‐band EPR spectra gives good agreement with experiment and explains the increased multiplicity of lines in these and similar experimental spectra as due to strong mixing of all S = 5/2 basis states under the influence of the DS z 2 operator. This gives rise to an unexpectedly large number of anomolous transitions, for which only a line shape properly averaged by integration over the unit sphere can give a reasonably accurate simulation of the experimental spectrum. The results also show that several previously published tables for the line positions of Fe(III) salts for the general axial or orthorhombic case must be used with care when interpreting powder or glass spectra, and spin‐Hamiltonian parameter values inferred from them ought to be confirmed by some independent method. The results of this study are important for the interpretation of the EPR of biological and metal‐ligand compounds which are difficult or impossible to obtain in crystalline form.