This paper describes a novel application of a ligand field model in the study of the local molecular structure of the (CrF6)(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 Cr3+ 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 Cr3+ ions are determined, respectively. The results show that the local lattice structures around the Cr3+ ions in AMF3 exhibit a compressed distortion, and the magnitude of distorted parameter Delta R-1, of the Cr3+-V-M center is different from that of the Cr3+-Li+ center in AMF3. The,compressed distortion is ascribed to the fact that the radius of the Cr3+ ion is smaller than those of M2+ (M = Cd, Mg, Zn). Moreover, a linear correlation between the difference in the magnitude of distortion parameter Delta R for two different defect centers and the difference in the corresponding values of the zero-field-splitting parameter AD are found first.