Molecular Cluster Modeling of Chromium Complexes in Elpasolite Crystals.

The ^4A_{2g} and ^4T_{2g} states of chromium-doped K_2NaGaF_6, K_2NaScF_6 and Cs _2NaYCl_6 were modeled by embedded cluster calculations at both ambient and elevated pressures. Ab initio molecular-cluster calculations were performed on a twenty-one atom cluster by utilizing the MELD program. Effective core potentials were employed in conjunction with double -zeta quality basis sets on chromium and chloride ions. All fluorine orbitals were explicitly included while sodium, potassium, and cesium ions were represented by bare effective core potentials. The external interactions of the embedded cluster were represented by Buckingham pair potentials, and its relaxed configuration was determined as a function of pressure in each electronic state by the HADESR modification of the HADES III lattice-statics code. Optical emission energies were calculated as functions of pressure in good agreement with experiment. Predicted linear-coupling parameters for a_{1g }, e_{g}, and t_{2g} symmetry-adapted displacements of nearest-neighbor halogen ions (corresponding to the Huang-Rhys factor S_0 and the Jahn-Teller stabilization energies E_ {JT}) yielded Stokes shifts in satisfactory agreement with experiment. The pressure dependence of approximate vibration frequencies was predicted correctly, but the calculated values are about 15% too high; this systematic discrepancy is attributed to neglect of electron correlation. A new method which was developed for optical lineshape simulation by direct diagonalization of the vibrational Hamiltonian was applied to the calculation of radiationless transition rates between the two electronic states. Radiationless transition rates predicted for the fluoride compounds were lower by two orders of magnitude than the values inferred from experiment, while those for the chloride compound were too small by ten orders of magnitude. This discrepancy is essentially due to the lack of anticipated quadratic coupling to the t_{2g} mode. However, the pressure dependence of the transition rate was predicted correctly. Inclusion of a_ {1g} anharmonicity worsened the agreement in all three compounds. The t_{2g} adiabatic potential energy curves for the chloride compound were recalculated with limited configuration interaction. A substantial improvement was observed in the transition rate due to enhanced quadratic coupling, but t _{2g} anharmonicity made a negative contribution.