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The high-order perturbation formulas of electron paramagnetic resonance (EPR) parameters (g factors g(parallel to), g(perpendicular to) and zero-field splitting D) for 3d(8) ions in trigonal octahedral clusters are established. These formulas contain the contributions not only from the crystal-field (CF) mechanism, but also from the charge-transfer (CT) mechanism (which is not considered in the widely used CF theory). From these formulas, the EPR parameters and the impurity-induced defect structures for Ni(2+) ions in CdX(2) (X = Cl, Br) crystals are studied. The calculated EPR parameters are coincident with the experimental values, and the defect structure of Ni(2+) impurity center obtained from the calculation is different from the corresponding structure in the host crystal. The sign of Q(CT) (Q = Delta g(parallel to), Delta g(perpendicular to), or D) due to CT mechanism agrees with that of the corresponding Q(CF) due to CF mechanism and the relative importance of CT mechanism (characterized by Q(CT)/Q(CF)) increases with increasing covalence of 3d(8) clusters and hence with raising atomic number of ligand X. So, in the explanations of the EPR parameters of 3d(8) (or other 3d(n)) ions in crystals with the heavy-element ligand ion (e. g., Br(-)), the calculated formulas based on the two-mechanism (CF and CT mechanisms) model are preferable to those based on only the CF mechanism in the CF theory. (C) 2008 Elsevier B. V. All rights reserved.