  Results from hybrid density functional theory calculations on the
thermodynamic stability and optical properties of the Zn vacancy
($V_{\text{Zn}}$) complexed with common donor impurities in ZnO are reported.
Complexing $V_{\text{Zn}}$ with donors successively removes its charge-state
transition levels in the band gap, starting from the most negative one.
Interestingly, the presence of a donor leads only to modest shifts in the
positions of the $V_{\text{Zn}}$ charge-state transition levels, the sign and
magnitude of which can be interpreted from a polaron energetics model by taking
hole-donor repulsion into account. By employing a one-dimensional configuration
coordinate model, luminescence lineshapes and positions were calculated. Due to
the aforementioned effects, the isolated $V_{\text{Zn}}$ gradually changes from
a mainly non-radiative defect with transitions in the infrared region in
\textit{n}-type material, to a radiative one with broad emission in the visible
range when complexed with shallow donors.
