Optical spectrum and Jahn-Teller splitting of ${\mathrm{Cu}}^{2+}$ sites in ${\mathrm{K}}_2$${\mathrm{CuF}}_4$ based on ab initio studies of (${\mathrm{CuF}}_6$${)}^{4\mathrm{-}}$ clusters

Using a (${\mathrm{CuF}}_6$${)}^{4\mathrm{-}}$ cluster plus up to 30 counterions to model the ${\mathrm{Cu}}^{2+}$ site in ${\mathrm{K}}_2$${\mathrm{CuF}}_4$, we carried out Hartree-Fock and configuration-interaction (CI) calculations for all five states corresponding to the $d^9$ configuration of ${\mathrm{Cu}}^{2+}$. We find that electron correlation CI leads to an increased importance of charge transfer states and a 20% increase in ligand field separations. The CI calculation gives good agreement with experimental ligand field spectra and confirms one of the two previous assignments. We also examined various distortions of the (${\mathrm{CuF}}_6$${)}^{4\mathrm{-}}$ cluster and extracted the Jahn-Teller (JT) coupling constants. These results support a previous analysis (based on semiempirical calculations) of the cooperative Jahn-Teller ordering observed in ${\mathrm{KCuF}}_3$ and ${\mathrm{K}}_2$${\mathrm{CuF}}_4$; however, the present results find that this ordering distortion is dominated by the anharmonic term of the potential energy associated with fluorine $e_g$ displacements (second-order JT interactions account only for 10% of the effect).