The big off-center displacement along <001> directions observed for Ni+ in CaF2 is explored through density functional theory (DFT) calculations on a NiF8Ca1217+ cluster, placing the Ni+ ion at different (0,0,z) points. For supporting the results additional calculations on clusters with a total of 51, 99, and 107 atoms have also been carried out. In a first step calculations have been performed for the (xy)(5/3)(xz)(5/3)(yz)(5/3) configuration where the three xy,xz, and yz antibonding crystal-field levels (degenerated in cubal geometry) are forced to have the same electronic occupancy. While the energy minimum for this configuration of NiF8Ca1217+ appears at z=0, it is found, however, at z(0)=1.07 Angstrom when the unpaired electron is fully located on the b(2) orbital transforming like xy. The z(0) values obtained for clusters with 51 (z(0)=1.13 Angstrom), 99 (z(0)=1.17 Angstrom) and 107 (z(0)=1.17 Angstrom) atoms outline the small dependence of the phenomenon on cluster size. This big off-center motion, which concurs with electron paramagnetic resonance data, is shown to arise mainly from a delicate balance between an electrostatic barrier, avoiding the impurity displacement and the energy gained through bonding on passing from eightfold to fourfold coordination. Following this analysis an increase of the lattice parameter and a diminution of ligand electronegativity both favor the off-center motion of d(9) ions in lattices with fluorite structure. First DFT calculations by means of a 21-atom cluster lead in fact to an off-center motion for Ag2+ and Cu2+ in SrCl2, while both ions would be on center in CaF2, these results being in agreement with experimental findings. At variance with the normal situation for on-center 3d impurities the energy minimum for the crystal-field excited state corresponding to the xy-->x(2)-y(2) transition is found at z=0, thus involving a huge displacement with respect to the ground state. To our knowledge this DFT study is the first one on off-center d(9) ions in CaF2-type lattices. The present results stress that the phenomenon though subtle can be understood with a modest computational effort.
