Zn substitutional lithium ( Li Zn ) and sodium ( Na Zn ) acceptors and their complexes with common donor impurities ( Al Zn , Hi, and HO) in ZnO have been studied using hybrid functional calculations. The results show that the complexes are not exclusively charge neutral, but rather exhibit a thermodynamic ( + / 0 ) transition level close to the valence band maximum. The positive charge states are associated with a polaronic defect state, similar to those of the well-studied charge-neutral isolated acceptors. This incomplete passivation has profound consequences for the optical properties of the complexes. Indeed, electron transitions from the conduction band minimum to the ( + / 0 ) transition level of the complexes result in broad luminescence bands that are blueshifted with respect to those originating from the isolated acceptors. Such complexes are proposed as a potential defect origin of the green luminescence observed at the high-energy side of the orange luminescence band (caused by Li Zn ) in hydrothermally grown ZnO. This prediction is supported by experimental photoluminescence and secondary ion mass spectrometry data on a hydrothermally grown ZnO sample. We have also explored how the parameters controlling the fraction and screening of exchange in the Heyd-Scuseria-Ernzerhof (HSE) hybrid functional influence the results by comparing two parametrization approaches: (i) the conventional one where the exchange fraction is adjusted to reproduce the experimental band gap, and (ii) tuning both parameters in order to also comply with the generalized Koopmans theorem (gKT). Interestingly, these approaches were found to yield similar results.