Abstract: This work attempts to unveil the similarities and differences between Jahn-Teller (JT) and non-JT systems involving CuF6 4- units. For achieving this goal, we firstly explore Na2CuF4 and NaF:Cu2+ systems through first principles calculations and pay particular attention to the links between JT and non-JT systems looking at the electronic density of the hole. The results on Na2CuF4 in the monoclinic P21/c space group and also in the parent Pbam structure reveal that the local geometry can be understood as an initial tetragonally compressed CuF6 4- unit, followed by an additional orthorhombic instability that excludes the JT effect as the origin. Although the present results on NaF:Cu2+ underpin an elongated equilibrium geometry such as that measured for Cu2+ ions in the cubic perovskite KZnF3, the force constant for NaF:Cu2+ is half that for KZnF3:Cu2+. This crucial fact is direct proof of the elastic decoupling of CuF6 4- from the NaF lattice leading to a JT energy, EJT, which is twice that found for KZnF3:Cu2+. However, both systems have practically the same linear electron-vibration coupling constant, V1e, a relevant fact whose origin is discussed. The final aim of this work concerns the influence of tetragonal and orthorhombic distortions as well as the internal electric field on the A1g-B1g energy gap, ?, of a variety of systems with CuF6 4- complexes. Interestingly, it is shown that compounds with orthorhombic instability and an internal electric field can have a ? value comparable to the JT system NaF:Cu2+. Accordingly, explanations for optical spectra of transition metal compounds based on simple parameterized models can be meaningless. The present study shows that properties displayed by d9 compounds in low symmetry lattices can hardly stem from a static JT effect.

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