The electron paramagnetic resonance (EPR) parameters ( g factor g i , and hyperfine structure constants A i , with i = x , y , z ) and local structures for Cu 2+ centers in M 2 Zn(SO 4 ) 2 ·6H 2 O (M = NH 4 and Rb) are theoretically investigated using the high order perturbation formulas of these EPR parameters for a 3 d 9 ion under orthorhombically elongated octahedra. In the calculations, contribution to these EPR parameters due to the admixture of d -orbitals in the ground state wave function of the Cu 2+ ion are taken into account based on the cluster approach, and the required crystal-field parameters are estimated from the superposition model which enables correlation of the crystal-field parameters and hence the studied EPR parameters with the local structures of the Cu 2+ centers. Based on the calculations, the Cu–H 2 O bonds are found to suffer the axial elongation ratio δ of about 3 and 2.9% along the z -axis, meanwhile, the planar bond lengths may experience variation ratio τ (≈3.8 and 1%) along x - and y -axis for Cu 2+ center in (NH 4 ) 2 Zn(SO 4 ) 2 ·6H 2 O and Rb 2 Zn(SO 4 ) 2 ·6H 2 O, respectively. The theoretical results show good agreement with the observed values.

中文翻译：

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M2Zn（SO4）2·6H2O（M = NH4和Rb）晶体中Cu2 +中心的局部结构研究

M 2 Zn（SO 4）2·6H 2 O中Cu 2+中心的电子顺磁共振（EPR）参数（g因子gi和超精细结构常数A i，i = x，y，z）和局部结构（M = NH 4和Rb）理论上是使用这些EPR参数的高阶扰动公式针对正交正交伸长的八面体下的3 d 9离子进行研究的。在计算中，基于聚类方法，考虑了由于Cu 2+离子的基态波函数中d轨道的混合而对这些EPR参数的贡献，并根据计算得出了所需的晶体场参数。叠加模型，使晶体场参数以及因此研究的EPR参数与Cu 2+中心的局部结构相关。根据计算，发现Cu–H 2 O键沿z轴的轴向伸长率δ约为3和2.9％，同时，平面键长度沿x-的方向可能有变化率τ（≈3.8和1％）。分别在（NH 4）2 Zn（SO 4）2·6H 2 O和Rb 2 Zn（SO 4）2·6H 2 O中Cu 2+中心的y轴。理论结果与实测值吻合良好。