By adopting the intermediate-field scheme, the microscopic origins of the spin-Hamiltanian (SH) parameters for 3d2ion at trigonal (C3v, D3, D3d) symmetry, taking into account the spinspin(SS) and spin-other-orbit(SOO) coupling interactions omitted in previous publications, have been investigated on the basis of complete diagonalization method(CDM). We find that the SH parameters arise from four microscopic mechanisms, i.e. (1) Spin-orbit(SO) coupling mechanism; (2) SS coupling mechanism; (3) SOO coupling mechanism; (4) SO-SS-SOO combined coupling mechanism. The SO coupling mechanism in the four coupling mechanisms is the most important one, but the contributions to zero-field splitting parameter D from other three coupling mechanisms cannot be omitted.