A first-principles study of the dielectric properties of TiO₂ polymorphs.

We present an analysis of the dielectric properties of the three polymorphs of TiO₂ (rutile, anatase and brookite phases), using ab initio time-dependent density functional perturbation theory based on the Vignale-Kohn functional. We implement this functional, which incorporates many-body effects, using the periodic program BAND. The improved result for the density of states spectra for brookite is suggestive of increased titanium ion Jahn-Teller effects for this phase. The imaginary and real components of the frequency-dependent dielectric functions show notable dielectric anisotropies, with implications for excitonic interactions, for all three common phases of TiO₂. Comparison of the electron energy-loss spectrum for undoped and doped rutile and anatase reveals the critical role of collective charge excitations in photocatalytic mechanisms. The correlation between plasmon peaks present at lower energies and decreased photocatalytic activity due to substitutional aluminum doping in combination with oxygen vacancies in rutile and anatase is highlighted. Moreover, there is clear correlation between dielectric properties and the microstructure of the TiO₂ polymorphs as suggested via the framework of the Born effective charge and Hirshfeld charge distribution schemes.