Crystal-field and charge transfer transitions due to Cr3+ ions in fluorides

Abstract

The metal-ligand equilibrium distance, Re, vibrational frequencies, crystal-field (CF) and charge transfer (CT) transition energies, Huang–Rhys factors, Stokes shift, as well as oscillator strengths of allowed CT transitions due to Cr3+ in fluorides, have been investigated using density functional theory. CrF63− and CrF6K8K611+ clusters simulating Cr3+ in the K3CrF6 lattice have been used. In the CrF6K8K611+ cluster the computed equilibrium distance using a generalized gradient approximation functional is Re=1.88 Å and an overall agreement with experimental spectroscopic parameters is achieved. As salient feature it is pointed out that 6% errors in Re can lead to errors of ∼40% and ∼25%, respectively, in the calculated vibrational frequencies and the 10 Dq parameter. Moreover the force constant, kT, involved in the A1g symmetrical mode at the equilibrium distance is shown to be mainly determined by the interaction between the central ion and the ligands while the interaction between the latter ones and K+ neighbors leads to a contribution which is about 25% of kT. The calculated oscillator strengths confirm that the transitions involving the ligand t1u orbital and the antibonding eg*↑ and eg*↓ ones should be the most intense among the nine allowed CT transitions. Moreover, CT transitions connecting two orbitals which do not have the same σ or π character are found to display an oscillator strength much smaller than for the rest of the cases. This idea is shown to be also valid for other transition-metal complexes. The computed Huang–Rhys factor associated with the A1g mode, SA, for the lowest CT transition is shown to be about ten times higher than that corresponding to the T2g4 CF state and explains the experimental bandwidth. The origin of this important difference is discussed. Finally, the electronic relaxation in the first T2u4 CT state is shown to induce an important decrement (∼40%) of the A2g4→A2u4 transition energy and an increase of the total charge on the central ion of only 0.2 e.