Non-orthogonal tight-binding model for tellurium and selenium

The twofold coordinated heavier group-VI elements tellurium and selenium with the trigonal crystal structure have unshared electron pairs (lone pairs) which control the interplay of the intra- and inter-chain interactions and their sensitivity on pressure and temperature. We have developed tight-binding (TB) parameters for the helical structures of tellurium and selenium using the Naval Research Laboratory Tight-Binding (NRL-TB) method. The TB parameters were derived by fitting to the band structures and total energies of density functional theory (DFT) calculations. We have applied the TB parameters to study the phase stabilities of different structures under hydrostatic pressure. We have predicted (without fitting) the volume dependence of the rhombohedral and diamond structures, the bcc to rhombohedral and rhombohedral to simple cubic phase transitions and the elastic constants of the trigonal structures, all in agreement with ab initio and experimental results. While the results for the unrelaxed vacancy formation energies and surface energies are in good agreement with the DFT values, we find large discrepancies for the relaxed values indicating that the present set of TB parameters cannot accurately capture the inter-chain interactions.