Empirical tight-binding model for titanium phase transformations

For a previously published study of the titanium hexagonal close packed (α) to omega (ω) transformation, a tight-binding model was developed for titanium that accurately reproduces the structural energies and electron eigenvalues from all-electron density-functional calculations. We use a fitting method that matches the correctly symmetrized wave functions of the tight-binding model to those of the density-functional calculations at high symmetry points. The structural energies, elastic constants, phonon spectra, and point-defect energies predicted by our tight-binding model agree with density-functional calculations and experiment. In addition, a modification to the functional form is implemented to overcome the "collapse problem" of tight binding, necessary for phase transformation studies and molecular dynamics simulations. The accuracy, transferability, and efficiency of the model makes it particularly well suited to understanding structural transformations in titanium.