Hybrid density functional theory is used to study reasonably realistic models of the oxygen-evolving manganese complex in photosystem II. Since there is not yet any X-ray structure of the complex, other types of experimental and theoretical information are used to construct the model complexes. In these complexes, three manganese centers are predicted to be closely coupled by mu-oxo bonds in a triangular orientation. Using these models, the previously suggested oxygen radical mechanism for O2 formation is reinvestigated. It is found that the oxygen radical in the S3 state now appears in a bridging position between two manganese atoms. It is still suggested that only one manganese atom is redox-active. Instead, a number of surprisingly large trans-effects are found, which motivate the existence and define the function of the other manganese atoms in the Mn4 cluster. Calcium has a strong chelating effect which helps in the creation of the necessary oxygen radical. In the present model the chemistry preceding the actual O-O bond formation occurs in an incomplete cube with a missing corner and with two manganese and one calcium in three of the corners. The external water providing the second oxygen of O2 enters in the missing corner of the cube. The present findings are in most cases in good agreement with experimental results as given in particular by EXAFS.