Determination of the high c/a ratio of hexagonal metals with a semi-empirical tight-binding method

A semi-empirical tight-binding potential is developed to reproduce the high c/a ratio of zinc and cadmium. In this scheme, we show that the calculation of the electronic energy by the standard recursion method with the Harrison model for the hopping integrals and their radius dependence is not able to predict c/a values higher than the ideal one γ0=8/3=1.633. Only, the recursion method limited to first neighbours has permitted to get the right c/a ratio of zinc and cadmium. The calculated energies of different structures (2H, 4H, 6H and 3C) show that the hexagonal compact structure (2H) is always most stable.