Comparative first-principles structural and vibrational properties of rutile and anatase TiO₂

The structural and vibrational properties of two polymorphs of TiO₂, rutile and anatase, have been investigated by first-principles methods at different levels of exchange-correlational (XC) energy functionals in density functional theory (DFT). Reports in the literature to date are contradictory regarding the stability of the rutile phase using DFT XC-functionals more sophisticated than simple local-density approximation. Here the PBEsol generalized gradient approximation (GGA), TPSS meta-GGA, and HSE06 hybrid functionals have been employed to demonstrate the XC-functional effects on the calculated structural, phonon and thermodynamic properties of rutile and anatase TiO₂. Lattice and elastic parameters correctly calculated with these XC-functionals show good agreement with the experimental values. Calculated phonon frequencies generated stable phonon dispersion relations for both rutile and anatase TiO₂when correctly converged, in agreement with the experimental observations. The phonon frequencies along high symmetry Brillouin zone paths and their corresponding phonon density of states showed sensitivity to different levels of XC-functional employed in phonon dispersion prediction. Nevertheless, the thermodynamic properties of rutile and anatase TiO₂estimated by harmonic approximations are in excellent experimental agreement and are effectively invariant to the level of theory employed in the DFT XC-functional.