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

The metal-ligand equilibrium distance, R-e, vibrational frequencies, crysta l-field (CF) and charge transfer (CT) transition energies, Huang-Rhys facto rs, 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 latti ce have been used. In the CrF6K8K611+ cluster the computed equilibrium dist ance using a generalized gradient approximation functional is R-e = 1.88 An gstrom and an overall agreement with experimental spectroscopic parameters is achieved. As salient feature it is pointed out that 6% errors in R-e can lead to errors of similar to 40% and similar to 25%, respectively, in the calculated vibrational frequencies and the 10 Dq parameter. Moreover the fo rce constant, k(T), involved in the A(1g) symmetrical mode at the equilibri um 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 k(T). The ca lculated oscillator strengths confirm that the transitions involving the li gand t(1u) orbital and the antibonding e(g)*up arrow and e(g)*down arrow on es should be the most intense among the nine allowed CT transitions. Moreov er, CT transitions connecting two orbitals which do not have the same sigma or pi character are found to display an oscillator strength much smaller t han for the rest of the cases. This idea is shown to be also valid for othe r transition-metal complexes. The computed Huang-Rhys factor associated wit h the A(1g) mode, S-A, for the lowest CT transition is shown to be about te n times higher than that corresponding to the T-4(2g) CF state and explains the experimental bandwidth. The origin of this important difference is dis cussed. Finally, the electronic relaxation in the first T-4(2g) CF state is shown to induce an important decrement (similar to 40%) of the (4)A(2g) -- > T-4(2u) transition energy and an increase of the total charge on the cent ral ion of only 0.2 e. (C) 1999 American Institute of Physics. [S0021-9606( 99)30602-4].