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The local structure of the trigonal Ti3+ center in LiF crystal is theoretically investigated by using the perturbation formulas of the anisotropic g factors g(parallel to) and gi(perpendicular to) for a 3d(1) ion in trigonally distorted octahedra based on the cluster approach. From the studies on the basis of various possible structure models, the local structure of the trigonal Ti3+ center may be characterized as [TiF3O3](6-) cluster (or model 1). In this model, the impurity Ti3+ is expected to substitute for the host Li+ ion and shift away from its regular lattice site along the [1 1 1] (or C-3) axis bit about 0.19 Angstrom due to the strong electrostatic attraction of the O-2(-) triangle replacing the original F- triangle. The magnitude of the above displacement obtained in this work is comparable with that (approximate to0.2-0.3 Angstrom) given by ENDOR experiment. Moreover, the cubic field parameter Dq (approximate to1497 cm(-1)) based on the above structure model is also in agreement with that (approximate to1500 cm(-1)) obtained from the experimental optical spectra of the studied system. The theoretical investigations of the local structure in this work may be useful to understand optical properties of Ti-doped LiF. (C) 2003 Elsevier B.V. All rights reserved.