Can undoped calcium tetraborides exist? An answer from the comparison of its density functional theory electronic structure with that of rare-earth metal tetraboride

Periodic density functional theory calculations are used to discuss the existence of metal tetraborides M(B)4 with divalent metals. Tetraborides which contain metal atoms inserted in a three-dimensional boron network made of B-6 octahedra and B-2 dumbbells exhibit a pseudo energy gap for a count of 60 valence electrons per M-4(B-6)(2)(B-2)(2) formula unit. Such a count satisfies the stability electron requirement for B-6(2-) (20 electrons) octahedra and B-2(2-)(8 electrons) units and allows the filling of two supplementary low-lying bands deriving from the valence metallic d atomic orbitals. This favored electron count is not reached for CaB4 which is then formally deficient by one electron per metal atom, This indicates that CaB4 is unlikely to exist without n-doping.