Ab initio calculations of the impurity centers R3+ (R = La - Lu) in CaF2 were carried out. The calculations were performed by using hybrid functional which takes into account both local and nonlocal (at the Hartree - Fock formalism) exchange. The crystal structure of impurity centers was investigated. The distance “rare-earth ion - ligand”, the radial and angular coordinates of the ions at several coordination spheres near to the impurity ion are determined. Calculations were carried out in the program CRYSTAL17, designed to simulate periodic structures within the MO LCAO approach.