Cu²⁺ in Layered Compounds: Origin of the Compressed Geometry in the Model System K₂ZnF₄:Cu²⁺

Many relevant properties (including superconductivity and colossal magnetoresistance) of layered materials containing Cu²⁺, Ag²⁺, or Mn³⁺ ions are commonly related to the Jahn–Teller instability. Along this line, the properties of the CuF₆^4– complex in the K₂ZnF₄ layered perovskite have recently been analyzed using a parametrized Jahn–Teller model with an imposed strain [Reinen, D. Inorg. Chem.2012, 51, 4458]. Here, we present results of ab initio periodic supercell and cluster calculations on K₂ZnF₄:Cu²⁺, showing unequivocally that the actual origin of the unusual compressed geometry of the CuF₆^4– complex along the crystal c axis in that tetragonal lattice is due to the presence of an electric field due to the crystal surrounding the impurity. Our calculations closely reproduce the experimental optical spectrum. The calculated values of the equilibrium equatorial and axial Cu²⁺–F^– distances are, respectively, R_ax = 193 pm and R_eq = 204 pm, and so the calculated distortion R_ax – R_eq = 11 pm is three times smaller than the estimated through the parametrized Jahn–Teller model. As a salient feature, we find that if the CuF₆^4– complex would assume a perfect octahedral geometry (R_ax = R_eq = 203 pm) the antibonding a_1g*(∼3z2 – r2) orbital is placed above b1g*(∼x2 – y2) with a transition energy E(²A_1g → ²B_1g) = 0.34 eV. This surprising fact stresses that about half the experimental value E(²A_1g → ²B_1g) = 0.70 eV is not due to the small shortening of the axial Cu²⁺–F^– distance, but it comes from the electric field, E_R(r), created by the rest of the lattice ions on the CuF₆^4– complex. This internal field, displaying tetragonal symmetry, is thus responsible for the compressed geometry in K₂ZnF₄:Cu²⁺ and the lack of symmetry breaking behind the ligand relaxation. Moreover, we show that the electronic energy gain in this process comes from bonding orbitals and not from antibonding ones. The present results underline the key role played by ab initio calculations for unveiling all the complexity behind the properties of the model system K₂ZnF₄:Cu²⁺, opening at the same time a window for improving our knowledge on d⁹, d⁷, or d⁴ ions in other layered compounds.