A b i n i t i o model potential study of local distortions around Cr+ and Cr3+ defects in fluorite

Abstract

In this paper we present the results of a theoretical study of the local geometry distortions produced by Cr⁺ and Cr³⁺ ions in fluorite, by means of the ab initio environment model potential method [J. Chem. Phys. 8 9, 5739 (1988)]. The valence energy and wave function of the (CrF₈)^q−(q=7,5) clusters embedded in the CaF₂ lattice represented by 118 ab initio model potential ions plus 750 point‐charge ions are calculated using a short CI, which includes all states related to the dⁿ ionic configuration. A geometry optimization is performed for CaF₂: (CrF₈)⁷⁻ within the cubic point symmetry and for CaF₂: (CrF₈)⁵⁻ within the D_3d point symmetry; the conclusions of analyses of the multimode Jahn–Teller coupling T₁⊗(ε+τ₂+τ^’₂) are used to address the geometry optimization, which is completed by a final unrestricted search. In an attempt to study all the structures proposed along previous experimental studies, the D_3d structure corresponding to an octahedral cluster plus two axially displaced fluorines (octahedron+2) is investigated. Taking the ground state energy of the perfect cube as a reference, the results show that the most stable D_3d distortion corresponds to an elongated cube in a ⁴A_2g ground state, with an energy of about −1700 cm⁻¹, while the compressed cube and the octahedron+2 structure energies are found to be −780 and +40 000 cm⁻¹, respectively. A joint analysis of the available experimental data and the results of our calculations are presented.