Influence of chemical bond length changes on the crystal field strength and "ligand-metal" charge transfer transitions in Cs₂GeF₆ doped with Mn⁴⁺ and Os⁴⁺ 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.