Angular Distortion around $Cr^{3+}$ Ions Doped Diammonium Hexaaqua Magnesium Sulphate Single Crystal

The aim of the present study is to explain the local distortion around $Cr^{3+}$ ions doped in the title crystal using the latest experimental data regarding optical and EPR spectra. We calculated $g_ǁ$, $g_⊥$, and D spin-Hamiltonian parameter as function of angle between the $C_3$ axis and metal-ligand chemical bond in local distorted octahedral cluster $[CrO_6]^{9-}$ formed after doped crystal. The method is based on the single spin-orbit coupling parameter model, in the cluster approach using Macfarlane high order perturbation formulae. The results compared with experimental data give a reasonable agreement.