Defects influence the electronic and optical properties of crystals, so their  identification is crucial to develop device technology for materials of micro/opto-electronics and photovoltaics. The identification requires the accurate calculation of the electronic transitions and the paramagnetic properties of defects. The achievable accuracy is strongly limited in case of the (semi)local approximations to density functional theory, because of the underestimation of the gap and of the degree of localization. 
In the past two decades, hybrid functionals, mixing semi-local and nonlocal exchange semi-empirically, have emerged as an alternative. Very often, however, the parameters of such hybrids have to be tuned from material to material. I will describe the theoretical foundations for the proper tuning and show that if the relative position of the band edge states are well reproduced, and the generalized Koopmans’ theorem is fulfilled by the given parametrization, the calculated defect levels and localizations can be very accurate. I will demonstrated this with the two-parameter Heydt-Scuseria-Ernzerhof hybrid, HSE(α,μ) for Group-IV and  Gallium-based semiconductors. 
The transferability of the optimal parameters of HSE(α,μ)  are limited, which causes problems, e.g., in studying defects in alloys. As an alternative, I will describe a new screened exact-exchange functional, with one tunable parameter, which does not change upon substitution of the anion or cation. This functional is now patched to VASP.

Peter Deák is a retired professor of the University of Bremen. He graduated as a physicist at the University Budapest in 1976. He holds the “Doctor of the Physical Science” title of the Hungarian Academy of Science. After postdoc positions at SUNY@Albany and at MPI-Stuttgart, he was appointed as full professor at the Technical University Budapest in 1993. In 2004 he left Hungary and took up position as substitute professor at the U. Paderborn. Since 2006 he has been working at the BCCMS. 
His research is directed to solving practically relevant problems of materials science by using atomistic quantum mechanical simulations, in close cooperation with experiments.