The complete diagonalized Hamiitonian matrixes of 3d2/3d8 ion configuration with trigonal symmetry have been established by irreducible representation method. The spectral hyper-fine structure and the constants of crystal structure and zero-field splitting parameters of CsNiCl3 crystal, as well as the Jahn-Teller effect and the influence of the spin singlet on the ground levels of Ni2+ ion have been studied. The results agree with the experimental facts. Besides, taking into account the influence of the spin-spin (SS) coupling interactions and the Trees correction which were neglected in previous publications, we find that the zero-field splitting parameters arise from four mechanisms, namely: (1) Spin-orbit coupling mechanism; (2) Spin-spin coupling mechanism; (3) Spin-orbit and spin-spin combined coupling mechanism; (4) Spin-orbit and Trees correction combined coupling mechanism. The spin-orbit coupling mechanism is the most important one and the other three mechanisms can not be neglected.