The third- and fourth-order perturbation formulas based on the dominant spin-orbit coupling mechanism for the zero-field splitting D of 3d 5 ion in tetragonal symmetry have been established from the strong-field scheme. From the formulas, the spin-lattice coupling coefficient G 1 1 (which is related to the zero-field splitting D due to the slight tetragonal distortion under stress) of MgO:Mn 2 + and the zero-field splitting D of the tetragonal Mn 2 + -V O center in SrTiO 3 are calculated. The results suggest that in the cases of 3d 5 clusters with small tetragonal distortion, the lowest (third)-order perturbation formula is applicable; however, in the cases of large tetragonal distortion, the higher (fourth)-order contribution is comparable with the third-order one and should be taken into account. The displacement of Mn 2 + in the Mn 2 + -V O center and hence the microstructures of this centre in SrTiO 3 are also obtained. The relaxation pattern is consistent with that of the isoelectronic Fe 3 + -V O center in KNbO 3 crystal obtained from both the shell-model simulations and the embedded-cluster calculations.