Theoretical studies of the EPR parameters and local structures for the two Cu²⁺ centers in Cd(HCOO)₂ ·2H₂ O

Based on the studies of the electron paramagnetic resonance parameters for two types of the Cu²⁺ centers in Cd(HCOO)₂ ·2H₂ O by using the high-order perturbation formulas for a 3d⁹ ion in a rhombically elongated octahedron, local structure of the doped copper ion is determined. Research suggests that the impurity Cu²⁺ replaces the host Cd²⁺ and undergoes the local rhombic elongation distortion, characterized by the axial elongation ratios of 4.1%, and 3.8% along the z-axis and the planar bond length variation ratios of 3.8%, and 3.1% along the x-axis and y-axis, for Cu²⁺ Centers, I and II, respectively. The above slightly different axial elongation ratios and planar bond length variation ratios may suitably account for the slightly dissimilar axial g anisotropies Δg (≈0.351 and 0.339) and perpendicular g anisotropies δg (≈0.028 and 0.022) of the two centers, respectively.