Tight-binding description of the electronic structure and total energy of tin

The Naval Research Laboratory (NRL) tight-binding (TB) method was applied to tin, a material which is known to exist in the diamond structure (α-Sn) at zero temperature and low pressures. A small change in the pressure drives tin to the β-Sn structure, which is stable up to 9.5 GPa at room temperature. In this paper we present the NRL-TB parameterization for tin, applying it to the study of the bulk properties of both α-Sn and β-Sn. The parameters were determined by fitting to a database of first-principles band structures and total energies, generated using the general potential linearized augmented plane-wave method for the fcc, bcc, sc and diamond structures, with limited information from calculations of the β-Sn phase. We report the success of this method in predicting the two stable structures α-Sn and β-Sn in the correct order, even though these structures have a small energy difference. We also discuss the NRL-TB method's ability to calculate electronic band structures and density of states. We confirm the semimetallic and metallic character for the α-Sn and bcc phases respectively. We also calculate the elastic constants of α-Sn and β-Sn, as well as high-symmetry point phonon frequencies of α-Sn and compare our results with experiment. Finally, TB molecular dynamics calculations are used to explore the behaviour of tin at finite temperatures. We compute the temperature dependence of the Debye-Waller B factor, finding it to be consistent with experiment up to room temperature.