This paper describes a novel application of a ligand field model in the study of the local molecular structure of the (CrF 6) (3-) coordination complex. Based on the ligand field model, the complete energy matrix which contains the electron-electron repulsion interaction, the ligand field interaction, the spin-orbit coupling interaction, and the Zeeman interaction, has been constructed for a d (3) configuration ion in a tetragonal ligand field. In order to study the relation between the EPR, the optical spectra, and the local lattice structures around the centers with tetragonal symmetry in AMF 3 codoped with Cr (3+) and Li (+) ions, a three-layer-ligand model is proposed. By diagonalizing the complete energy matrix and employing the three-layer-ligand model, the variational ranges of the local structural parameters around the Cr (3+) ions are determined, respectively. The results show that the local lattice structures around the Cr (3+) ions in AMF 3 exhibit a compressed distortion, and the magnitude of distorted parameter Delta R 1 of the Cr (3+)-V M center is different from that of the Cr (3+)-Li (+) center in AMF 3. The compressed distortion is ascribed to the fact that the radius of the Cr (3+) ion is smaller than those of M (2+) (M = Cd, Mg, Zn). Moreover, a linear correlation between the difference in the magnitude of distortion parameterDelta R for two different defect centers and the difference in the corresponding values of the zero-field-splitting parameter Delta D are found first.