A theoretical method for studying the inter-relation between electronic and molecular structure has been proposed based on the complete energy matrices for a d 3 configuration ion in a tetragonal ligand-field. By means of this method, the local structure for Cr 3+ ion doped in oxides TiO 2 (anatase) and MgO has been determined. The calculated results indicate that the local structure of the (CrO 6 ) 9− cluster in TiO 2 :Cr 3+ and MgO:Cr 3+ systems exists as a compressed distortion relative to the regular octahedron. Meanwhile, the dependence of the EPR zero-field splitting parameter D on the local structure parameter ΔR (ΔR=R 1 −R 2 ) has been revealed. In addition, the relation between the EPR g-factors (g∥,g⊥,Δg) and the orbit reduction factor k has been discussed for the two systems, suggesting that the orbit reduction factor k is very important to understand the EPR g-factors.