The interplay between the fictitious spin S' = 1/2 and the effective spin S̃=3/2 for Co²⁺(3d⁷) ions is considered. The available experimental data on the Ze g_{i}' factors for the two Co²⁺ complexes in PbMoO₄ obtained using the fictitious "spin" S'=1/2 description serve for determination of the Zeeman g_{i} factors corresponding to the effective spin S̃ =3/2. The second-rank zero-field splitting parameters D and E (S̃ = 3/2) are also indirectly determined from the experimental EMR data by employing the formulas arising from projection of the g_{i}(S̃=3/2) factors onto the g_{i}'(S' = 1/2) factors. The so-determined second-rank zero-field splitting parameters and g_{i}(S̃ = 3/2) factors will enable comparison with the respective quantities obtained in a subsequent paper using a combined modeling approach.
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