Compounds Containing Tetragonal Cu2⁺ Complexes: Is the d_x^2–_y²–d_3z²–r² Gap a Direct Reflection of the Distortion?

It is widely assumed that the gap, Δ, between d_x²–_y² and d_3z²–_r² orbitals in fluorides and oxides containing tetragonal Cu²⁺ or Ag²⁺ complexes directly reflects the tetragonal distortion in the MX₆ complex (M = d⁹ ion; X = F^–, O^2–). This assumption on that relevant quantity is shown to be not correct through the study of pure K₂CuF_4-, KCuF_3-, and Cu²⁺-doped KZnF₃ and K₂ZnF₄ model compounds. Indeed, ab initio calculations prove that Δ in these insulating materials also depends on the internal electric field created by the rest of lattice ions on active electrons confined in a given CuF₆^4– complex. This internal field, especially important for layered compounds, is shown to explain all puzzling experimental facts on the d–d transitions of the studied systems and is of interest in the search of new Cu²⁺ and Ag²⁺ superconducting materials where a strong correlation between Δ and the transition temperature, Tc, has been conjectured.