Energy isosbestic points in third-row transition metal alloys

The total electronic energies of the six electrons per atom (e^- per atom) alloys W, TaRe, HfOs, and YIr and the seven electrons per atom alloys Re, WOs, TaIr, HfPt, and YAu have been calculated in the local density approximation of density functional theory. When one considers common alloy structures such as atomically ordered variants of the body-centered cubic, face-centered cubic, or hexagonally closest packed structures and plots the total electronic energy as a function of the unit cell parameter, one finds for both the six and seven electrons per atom series energetic isosbestic points. An energetic isosbestic point corresponds to a critical value of the size parameter for which all members of the 6 or 7 e^- per atom series of compounds have nearly identical total electronic energy. Just as in spectroscopy, where the existence of such isosbestic points is the hallmark of two compounds present in the mixture, an energy isosbestic point^[1.2] implies there are just two separate energy curves. For both series it is found that the total electronic energy can be viewed as the weighted sum of a purely covalent term and a purely ionic term. Two semi-quantitative models are proposed to account for these two separate energies, In the first model the total energy is viewed as the sum of the elemental structural energy plus an ionic energy based on the Born-Mayer ionic model, In the second model one considers within the confines of μ₂-Hückel theory the evolution of the total electronic energy as the Coulombic H_ii integrals change in value.