Abstract
Periodic boundary condition (PBC) calculations using the Heyd-Scuseria-Ernzerhof screened Coulomb hybrid functional (HSE03) have been carried out to investigate the electronic structure of the anatase and rutile TiO2 bulk solids. As a comparison, we have performed the investigation using local density approximation (LDA), generalized gradient approximation (GGA), and conventional hybrid functionals. It is proved that the truncation of the Hartree-Fock (HF) exchange terms, whose evaluation is the bottleneck of the PBC calculations, is much accelerated in the HSE03 model when compared to the conventional hybrid model. Cohesive energies for anatase and rutile calculated by HSE03, as well as the GGA and conventional hybrid functionals, are shown to be in a good agreement with the experimental values. As is well known, band gaps obtained by LDA and GGA are underestimated by 40 % in comparison with the experimental values. Usage of a hybrid functional significantly improved the evaluation of the band gaps. Actually, the absolute errors calculated with HSE03 are about 0.3 eV for both anatase and rutile. Geometric parameters obtained by HSE03, which are between LDA and GGA values, reasonably agree with experiment. As for bulk moduli, HSE03 gives values close to LDA rather than GGA. As a consequence, the present study confirms that the new type of hybrid functional HSE03 brings about reasonable computational cost and achieves high accuracy comparable with or superior to the conventional hybrid functionals.
