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The optical band positions and spin-Hamiltonian parameters (g factors g(parallel to) g(perpendicular to) and zero-field splitting D) for the trigonal Cr3+ centers in Y2Ti2O7 crystal are calculated from the complete diagonalization (of energy matrix) method based on the two-spin-orbit-parameter model. In the calculations, the contributions to spectral data from both the spin-orbit parameter of central d(n) ion and that of ligand ion are considered and the crystal field parameters used are estimated from the superposition model. The calculated results are in reasonable agreement with the experimental values. The defect structures of Cr3+ center is suggested. (C) 2012 Elsevier B.V. All rights reserved.