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Complete diagonalization of the energy matrix and high order perturbation formulae of spin-Hamiltonian (SH) parameters possessing D(4h) symmetry for the 4d(9) ion based on the crystal- and ligand-field theory in tetragonal symmetry are expressed and applied to the study of local distortion structure of the KCl:Ag(2+) crystal. The calculated results agree well with experimental findings. Both complete diagonalization of energy matrix and high order perturbation approach are appropriate for the investigations of SH parameters of 4d9 ions in tetragonal crystals. Tetragonal distortion due to the Jahn-Teller effect for the tetragonal Ag(2+) center at the K(+) site of KCl crystal is also acquired from the calculations. (C) 2010 Elsevier B.V. All rights reserved.