Using a reliable lattice relaxation model, the ionic positions of the orthorhombic Gd³⁺–M⁺ complexes (M≡Li, Na, K, Rb, Cs) in CaF₂ are calculated. These results are then employed to analyse the spin parameters of the ground state 4f⁷ ⁸S7/2 splitting of the rare earth ion Gd³⁺ derived from the wealthy set of electron paramagnetic resonance data available in the literature. Useful results, namely the fitted values of the intrinsic parameters of the superposition model, are then obtained and it is found that these intrinsic parameters follow a parabolic dependence on the ligand distances. This distance dependence could be further applied to study similar Gd³⁺–M⁺ centres in other fluorite lattices such as SrF₂ and BaF₂. Copyright © 1993 Elsevier Sequoia. All rights reserved.