The bonding in hexagonal Ba2/3Pt3B2 and CeCo3B2 type ternary metal borides

Tight-binding calculations with an extended Hückel Hamiltonian were performed on Ba_2/3Pt₃B₂ and LuOs₃B₂. Hypothetical linear metal boride chains present in these materials are analyzed with a three-dimensional model that contains a trigonal bipyramidal T₃B₂ (T = transition metal) building unit for the compounds. The geometrical structure for the T₃B₂ trigonal bipyramids depends on the number of electrons. For systems that have greater than 36 electrons in its trigonal bipyramidal building unit, a structural distortion is expected. Electron back donation from the electron-rich M₃ fragment to the empty e′ set on B₂ creates boron–boron interaction along the z-axis. Boron–boron pairing then participates as an electron sink and causes a trigonal distortion of the platinum Kagome net. On the other hand, a system with <35 electrons should have an undistorted, CeCo₃B₂ type structure. The electronic factors that create the breathing motion are discussed and analyzed with the aid of molecular and solid-state models. The metal–metal bonding associated with the structural properties also has been examined.