The zero-field splitting and local structure for V2+ ions in CsMgX3 $(X = Cl, Br, I)$ crystals are theoretically investigated using complete diagonalization method (CDM) for a $3d^{3}$ ion in trigonal symmetry. Spin–spin (SS) and spin–other-orbit (SOO) interactions are taken into account in addition to the general spin–orbit (SO) interaction. On this basis, using ligand ion displacement model, we find that the ligand ions move away from $C_{3}$-axis, and therefore the local angles in the $V^{2+}$ centres are larger than the angles in the hosts. The results show good agreement with the observed values.
