The DFT (U)PBE0 method was used to calculate the structural parameters of the C₅H₅Yb·, C₅H₅Lu, C₈H₈Lu·, C₈H₈Yb, (C₅H₅)₂Yb, (C₅H₅)₃Yb, C₅H₅YbC₈H₈, C₅H₅Ce·C₈H₈, C₅H₅LuC₈H₈, (C₈H₈)₂Lu, (C₈H₈)Ce*, (C₈H₈)₂Ce, (C₈H₈LuC₈H₈)₂Yb, and (C₈H₈Ce·C₈H₈)₂Yb molecules. In the (C₈H₈)₂Ce molecule, the oxidation state of the lanthanide is higher than in the quadruple-decker (C₈H₈LnC₈H₈)₂Yb complexes, in the C₅H₅LnC₈H₈ molecules, and in the free radicals (C₈H₈)₂Ce* and (C₈H₈)₂Lu. Oxidation of (C₅H₅)₂Yb with cyclooctatetraene and the binding of the (C₈H₈)₂Ln molecules by ytterbium(II) are exothermic reactions. The atomic charges and the dipole and quadrupole moments are indicative of incomplete transfer of the lanthanide valence electrons to the ligands, i.e., of a significant covalent component of the η⁵ and η⁸ bonds. Lutetium interacts with cyclooctatetraene as a lanthanide, without showing the properties of transition metals.