Calculation of the zero-field splitting D and g(perp)parameters in EPR for d3 spin systems in strong and moderate axial fields

TL;DR

This paper compares numerical and analytical methods for calculating zero-field splitting and g-perp parameters in d3 spin systems in strong and moderate axial fields, providing guidelines for experimental conditions and the applicability of perturbation theory.

Contribution

It introduces criteria for when third-order perturbation theory is accurate versus when exact numerical calculations are necessary for d3 spin systems in EPR.

Findings

Single-frequency EPR at a magic angle yields accurate third-order perturbation results.

For dual-frequency experiments, the ratio hν/|2D| must be below 0.25 for perturbation accuracy.

Measurements at specific angles with respect to the axial field are unreliable for third-order perturbation theory.

Abstract

Numerical and analytical methods are used to investigate the calculation of the zero field splitting |2D| and g(perp) parameters in EPR for octahedrally surrounded d3 spin systems (S = 3/2) in strong and moderate axial crystal fields (|D|>=h{\nu}). Exact numerical computer calculations are compared with analytical results obtained from third-order perturbation theory. From the analyses we conclude that EPR measurements performed at a single frequency with the magnetic field H at a magic angle {\alpha}_M, where 62deg < {\alpha}_M < 63deg, with respect to the axial crystal field of the d3 spin system, yields an almost exact solution in third-order perturbation theory. For dual frequency experiments, i.e. X-K, X-Q and K-Q band experiments, performed with the magnetic field H at an angle of {\alpha} = 90deg with respect to the axial crystal field, the ratio h\u{psion}/|2D| has to be smaller than 0.25 in order to use third order perturbation calculations within an error limit of 0.020% in the g(perp) values. For values of h\u{psion}/|2D| >= 0.25 one has to proceed with exact numerical computer calculations. Finally, we conclude that measurements performed at a single EPR frequency experiment with the magnetic field H directed along two specific angles with respect to the axial crystal field of the octahedrally surrounded d3 centre, i.e. {\alpha} = 90deg and {\alpha} = 35deg16 respectively, third-order perturbation theory gives non-reliable results for the |D| and g(perp)-values.