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The high-order perturbation formulas of spin-Hamiltonian (SH) parameters (g factors g(||),g(perpendicular to) and zero-field splitting D) for 3d(x) ions in trigonal octahedral sites of crystals are derived considering not only the crystal-field (CF) mechanism, but also the charge-transfer (CT) mechanism (which is neglected in the extensively used CF theory). From these formulas and by considering the suitable impurity-induced local lattice relaxation. the SH parameters of CsCdX(3):Ni(2+) (X = Cl, Br) crystals are calculated. The results are in reasonable agreement with the experimental values. The sign of Q(CT) (Q = Delta g(||). Delta g(perpendicular to) or D. where the g-shift Delta g(i) = g(i) - g(c). g(c) approximate to 2.0023 is the free-electron value) due to CT mechanism is the same as that of the corresponding Q(CF) due to CIF mechanism. The relative importance of CT mechanism (characterized by Q(CT)/Q(CF)) increases with the, increasing atomic number of ligand X. So. for 3d(n) ion clusters in crystals with heavy element ligand ion (e.g., Br(-)), the reasonable explanations of SH parameters should contain the contributions from both CF and CT mechanisms. (C) 2008 Elsevier B.V. All rights reserved.