  The spin Hamiltonian parameters for the two Cu$^{2+}$ centers $A1$ and $A2$
in the calcined catalysts CuO-ZnO are theoretically investigated using the high
order perturbation formulas of these parameters for a $3d^{9}$ ion in
tetragonally elongated octahedra. In the above formulas, the tetragonal field
parameters $Ds$ and $Dt$ are determined from the superposition model, by
considering the relative axial elongation of the oxygen octahedron around the
Cu$^{2+}$ due to the Jahn-Teller effect. Based on the calculations, the
relative elongation ratios of about 5% and 3% are obtained for the tetragonal
Cu$^{2+}$ centers $A1$ and $A2$, respectively. The theoretical spin Hamiltonian
parameters are in good agreement with the observed values for both systems. The
larger axial elongation in center $A1$ is ascribed to the more significant low
symmetrical (tetragonal) distortion of the Jahn-Teller effect. The local
structures characterized by the above axial elongations are discussed.
