Optical excitations and coupling constants in FeO42− and CrO44− complexes in oxides: Density functional study

Abstract

The experimental crystal field (CF) and charge transfer (CT) spectra due to Fe6+-doped K2XO4 (X=S, Se, Cr) and Cr4+ in oxides have been investigated by density functional (DF) calculations on FeO42− and CrO44− complexes at different values of the metal–ligand distance, R. To this aim the coupling constants, Aα and Aε, with the A1 and the Jahn–Teller E modes have also been calculated. The present results explain reasonably the transition energies and coupling constants observed for Fe6+ and Cr4+ in oxides and account for the following experimental features: (i) The different nature of the first CF and CT excitations observed on passing from Fe6+ to Cr4+ in oxides. (ii) Why for Fe6+ in oxides the dominant coupling is with the E mode for the CF states while with the A1 mode for CT states. (iii) Why on going from Cr4+ to Fe6+ in oxides the coupling constant Aα of CT states decreases while the opposite is found for CF ones. The role played by the covalency on these questions is explained on simple grounds, stressing that it drastically decreases the Aα value for CT states. This fact together with the value να=820 cm−1 accounts for the low value of the Huang–Rhys factor Sα=2.5 in the assigned 1t1↓→4t2↓ CT excitation of K2SeO4:Fe6+. As a salient feature the R dependence of 10Dq (which determines Aα for the T23 CF state) is found to be greatly sensitive to the small admixture (≈0.5%) of 2s(O) orbitals in the antibonding 2e level. The electronic relaxation decreases the energy of the first CT transition of FeO42− by 19 000 cm−1, the charge distribution being however the same as that of the ground state. The important role played by the trigonal distortion for reducing the Jahn–Teller effect in the first excited state of Cr4+ in oxides is analyzed through a phenomenological model. Though no further neighbors of the host lattice are included, the calculated equilibrium distances for FeO42− and CrO44− are only 3% and 8% higher than experimental values found for Cr4+ to Fe6+ in oxides. Moreover the calculated value of the να frequency at the right equilibrium distance essentially coincides with experimental findings indicating that force constants between oxygen and further neighbors likely play a minor role. In comparison with recent ab initio plus configuration interaction results on FeO42− the DF scheme offers a simpler description of ground and CT states.