An alternate approach to the n electron many-body problem is known to be the density functional theory which projects the 3n dimensional problem onto 3D space with an effective energy density functional. There are however two practical problems: a systematic derivation of suitable density functionals does not exist yet, and relativity has to be included. In previous work we have presented a highly accurate 2-spinor fully relativistic solution of the two-center Coulomb problem utilizing the finite-element Method (FEM), and furthermore developed a relativistic minimax 2-spinor LCAO. Here we will present Dirac-Fock-Slater (DFS-) density functional calculations for two-atomic molecules up to super heavy systems using 2-spinor (minimax) FEM and the minimax LCAO in a linearized approximation (LARM). The FEM gives highly accurate benchmark results for the DFS functional. Especially considering dimers of the group Ib (or 11) and the very asymmetric oxides of group IIb (or 12) with up to super heavy atoms like UubO and Rg_2, we found that LCAO fails to give the correct systematic trends. The accurate FEM results shed a new light on the quality of the DFS-density functional and exhibit surprising properties of the Morse potential approximation to molecular binding energy curves.