The fluorine superhyperfine (shf) tensor measured in BaFCl:La2+ has been found to be practically isotropic, a result which is certainly anomalous when compared to that for d9 centers with one unpaired electron in a x2−y2 orbital. This puzzling fact has been explored by means of density functional calculations. Obtained results confirm that in the C4v equilibrium geometry the unpaired electron lies in a b1(~x2−y2) orbital which overlaps with the 2s orbitals of four F− ligands. For explaining the origin of the near isotropy, which is well reproduced by the present calculations, the simple D4h and C4v LaF42−, YF42−, and AgF42− centers have also been investigated. Although the obtained results stress the high dependence of the isotropic shf constant As on the metal-ligand distance R, a near isotropy of the shf tensor is only reached for LaF42− (but not for YF42−) under C4v symmetry which corresponds to the actual symmetry of the La2+ center in the BaFCl lattice. The origin of this peculiar situation is shown to come from the mixing between 5d and 4f orbitals of La2+ allowed in C4v symmetry thus stressing the role played by 4f orbitals in bonding properties. Writing As=CR−ns it is shown that for the D4h LaF42− and YF42− complexes the exponent ns is around 20, while it is only equal to 4 for AgF42−. This huge difference is shown to stem from the quite distinct slope of the radial d wave function at the equilibrium distance for the two d1 centers and the d9 AgF42− unit. Finally, the present calculations strongly support that the intense band peaked at 17 890 cm−1 Recorded in the optical absorption spectrum of BaFCl:La2+ is indeed a 5d4f transition.