  The Heyd-Scuseria-Ernzerhof (HSE) hybrid functional has become a widely used
tool for theoretical calculations of point defects in semiconductors. It
generally offers a satisfactory qualitative description of defect properties,
including the donor/acceptor nature of defects, lowest energy charge states,
thermodynamic and optical transition levels, Franck-Condon shifts,
photoluminescence (PL) band shapes, and carrier capture cross sections.
However, there are noticeable quantitative discrepancies in these properties
when compared to experimental results. Some of these discrepancies arise from
the presence of self-interaction in various parametrizations of the HSE. Other
errors are due to the use of the periodic boundary conditions. In this study,
we demonstrate that the error corrections scheme based on extrapolation to the
dilute limit effectively eliminates the errors due to artificial electrostatic
interactions of periodic images and interactions due to the defect state
delocalization. This yields parametrizations of HSE that satisfy the
generalized Koopmans' condition, essentially eliminating self-interaction from
defect state orbitals. We apply this HSE Koopmans tuning individually to a
range of cation site acceptors in GaN (Be\textsubscript{Ga},
Mg\textsubscript{Ga}, Zn\textsubscript{Ga}, Ca\textsubscript{Ga},
Cd\textsubscript{Ga}, and Hg\textsubscript{Ga}) and compare the HSE results
with experimental data from PL spectra. The Koopmans-compliant HSE calculations
show a significantly improved quantitative agreement with the experiment.
