  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.
