Compounds Containing Tetragonal Cu²⁺ Complexes: Is the d_{x²–y²}–d_{3z²–r²} Gap a Direct Reflection of the Distortion?

It is widely assumed that the gap, Δ, between d x 2 – y 2 and d 3 z 2 – r 2 orbitals in fluorides and oxides containing tetragonal Cu 2+ or Ag 2+ complexes directly reflects the tetragonal distortion in the MX 6 complex (M = d 9 ion; X = F –, O 2– ). This assumption on that relevant quantity is shown to be not correct through the study of pure K 2 CuF 4 -, KCuF 3 -, and Cu 2+ -doped KZnF 3 and K 2 ZnF 4 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 CuF 6 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 Cu 2+ and Ag 2+ superconducting materials where a strong correlation between Δ and the transition temperature, T c, has been conjectured.