In ESR experiment of impurity paramagnetic ions, static magnetic field is applied along the axis. So, parallel g-factor has been measured. I need to calculate perpendicular g-factor. We calculated LS coupling constant, and octahedral crystal field splitting.
It is not possible to do so based only on the octahedral ligand field and spin-orbit coupling. You need the low-symmetry ligand field splittings. The perturbation expressions are set out in e.g. Chapter 6f in "Introduction to Ligand Field Theory" by C. J. Ballhausen, where you can see that for the tetragonally elongated octahedron you need knowledge of at least two of the three energy orbital energy differences allowed in this symmetry.
Alternatively, if possible, take the experimental approach: Measure also an orientaion averaged spectrum (powder sample) and both g-values should be directly accessible.
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