Rutile, anatase, brookite and titania thin film from Hubbard corrected and hybrid DFT

Abstract

As a benchmark, the structural, electronic and optical properties of the three main phases of TiO _2 crystals have been calculated using Hubbard U correction and hybrid functional methods in density-functional theory. These calculations are compared concerning the available experimental observations on pristine TiO _2 crystals. Modified hybrid functionals, particularly the PBE0 functional with 11.4% fraction of exact exchange, are shown to provide highly accurate atomic structures and also accurate electronic structure data, including optical excitation energies. With DFT + U, accurate optical spectra are also possible, but only if the Hubbard U is applied on the O 2p electrons exclusively. Furthermore, both methods, the 11.4%-PBE0 hybrid functional and the DFT + U _p scheme have been used to study TiO _2 amorphous ultra-thin films, confirming the agreement of the two methods even with respect to small details of the optical spectra. Our results show that the proposed DFT + U _p methodology is computationally efficient, but still accurate. It can be applied to well-ordered TiO _2 polymorphs as well as to amorphous TiO _2 and will allow for the calculations of complex titania-based structures.

Keywords

• density functional theory
• hubbard correction
• hybrid functionals
• amorphous thin film
• titanium dioxide
• semiconductor