Geometry of the $\text{}^4T_{2g}$ Excited State in $Cs_2SiF_6:Mn^{4+}$

The aim of this paper is to calculate the equilibrium displacements of the $\text{}^4T_{2g}$ potential surface minimum from the ground state along the $a_{1g}$ and $e_g$ Jahn-Teller active modes for the octahedral $[MnF_6]^{2-}$ cluster obtained by doping $Mn^{4+}$ ions in $Cs_2SiF_6$ host crystal. The equilibrium displacements in normal and Cartesian coordinates were estimated from force constants of $[MnF_6]^{2-}$ cluster and Huang-Rhys factors associated with the Jahn-Teller stabilization energy. A net equatorial expansion and an axial stretching of the geometry of the $[MnF_6]_{2-}$ cluster in first $\text{}^4T_{2g}$ excited state, as combined effect of the $a_{1g}$ and $e_g$ displacements, were demonstrated.