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

As a benchmark, the structural, electronic and optical properties of the three main phases of TiO$\rm{_2}$ 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$\rm{_2}$ 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 $\rm{DFT+U}$, accurate optical spectra are also possible, but only if the Hubbard U is applied on the O $\rm2p$ electrons exclusively. Furthermore, both methods, the 11.4%-PBE0 hybrid functional and the $\rm{DFT+U_p}$ scheme have been used to study TiO$\rm{_2}$ 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 $\rm{DFT+U_p}$ methodology is computationally efficient, but still accurate. It can be applied to well-ordered TiO$\rm{_2}$ polymorphs as well as to amorphous TiO$\rm{_2}$ and will allow for the calculations of complex titania-based structures.