Theoretical Studies of the Spin Hamiltonian Parameters and Local Structures for the Two Tetragonal $Cu^{2+}$ Centers in $Ca(OH)_2$

The spin Hamiltonian parameters (g factors $g_{∥ },$ $g_{⊥}$ and the hyperfine structure constants $A_{∥ },$ $A_{⊥}$) and the local structures for the two tetragonal $Cu^{2+}$ centers I and II in $Ca(OH)_2$ are theoretically studied from the perturbation formulae of these parameters for a $3d^9$ ion under tetragonally elongated octahedra. The $[Cu(OH)_6]^{4-}$ clusters on the substitutional $Ca^{2+}$ site are found to suffer the relative elongations by about 0.083 Å and 0.065 Å for centers I and II, respectively, along the $C_4$ axis due to the Jahn-Teller effect. The above tetragonal elongations may entirely depress the original trigonal distortion of the host $Ca^{2+}$ site in $Ca(OH)_2$. The calculated spin Hamiltonian parameters based on the above Jahn-Teller elongations show good agreement with the experimental results. The EPR spectra and the local structures for the two centers are compared with one another.