Theoretical studies of the spin Hamiltonian parameters for the two tetragonal Cu$^{2+}$ centers in the calcined catalysts CuO-ZnO

TL;DR

This paper theoretically investigates the spin Hamiltonian parameters of two Cu$^{2+}$ centers in calcined CuO-ZnO catalysts, revealing their local tetragonal distortions and Jahn-Teller effects through perturbation formulas and superposition modeling.

Contribution

It introduces a theoretical approach to determine local structural distortions of Cu$^{2+}$ centers in catalysts using high order perturbation formulas and superposition model analysis.

Findings

Relative elongation ratios of 5% and 3% for the two centers.

Theoretical parameters agree well with observed data.

Larger elongation linked to greater Jahn-Teller distortion.

Abstract

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.