Influence of chemical bond length changes on the crystal field strength and “ligand-metal” charge transfer transitions in Cs2GeF6 doped with Mn and Os ions

Detailed study of dependence of the crystal field strength 10Dq and lowest charge transfer (CT) energies for different interionic distances in Cs₂GeF₆:Mn⁴⁺ and Cs₂GeF₆:Os⁴⁺crystals is presented. The calculations were performed using the first-principles discrete-variational Dirac-Slater (DV-DS) method. As a result, the functional dependencies of 10Dq and lowest CT energy on the metal-ligand distance R were obtained without any fitting or semiempirical parameters. It was shown that 10Dq depends on R as 1/Rⁿ, with n=4.0612 and 4.3874 for Cs₂GeF₆:Mn⁴⁺ and Cs₂GeF₆:Os⁴⁺, respectively. Two approximations (linear and quadratic) are obtained for the dependence of the lowest CT energy on R; CT energy decreases when R increases with dE(CT)/dR=−638 and −1080 cm⁻¹/pm for Cs₂GeF₆:Mn⁴⁺ and Cs₂GeF₆:Os⁴⁺, respectively, if the linear approximation is used. These values can be used for estimations of the lowest CT energies for Mn⁴⁺ and Os⁴⁺ ions in other hosts with fluorine ligands. Estimations of the electron-vibrational interaction (EVI) constants, Huang-Rhys parameters, and Stokes shifts for all the above-mentioned crystals were performed using the obtained 10Dq and E(CT) functions.