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The KTiOPO 4 (KTP) band structure and dielectric function are calculated on various levels of theory starting from density-functional calculations. Within the independent-particle approximation an electronic transport gap of 2.97 eV is obtained that widens to about 5.23 eV when quasiparticle effects are included using the GW approximation. The optical response is shown to be strongly anisotropic due to (i) the slight asymmetry of the TiO 6 octahedra in the (001) plane and (ii) their anisotropic distribution along the [001] and [100] directions. In addition, excitonic effects are very important: The solution of the Bethe-Salpeter equation indicates exciton binding energies of the order of 1.5 eV. Calculations that include both quasiparticle and excitonic effects are in good agreement with the measured reflectivity.

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 $\rm{2p}$ 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.

The atomic geometry and energetics of oxygen and potassium vacancies in potassium titanyl phosphate (KTP) as well as their electronic and optical properties are studied within density-functional theory in dependence of their charge state. Oxygen vacancies formed between Ti and P are characterized by a negative-U behavior. Their neutral charge state is favored for Fermi levels near the conduction band and gives rise to a defect level in the band gap, which leads to an additional optical absorption peak. In contrast, the two-fold positive charge state, stable for low and intermediate values of the Fermi level, modifies the KTP optical response only slightly. Oxygen vacancies formed between two Ti atoms are two-fold positively charged, while potassium vacancies are negatively charged irrespective of the Fermi level position. In both these cases, the KTP optical response is essentially not affected.

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