Which hybrid GGA DFT is suitable for Cu2O2 systems if the spin contamination error is removed?

Several hybrid density functional sets with a broken-symmetry (BS) method: UB3LYP, UB3PW91, UPBE0, UB(38HF)P86, and UBHandHLYP are examined on the geometry of the Cu2O2 core of the active site of oxyhemocyanin (oxyHc). In order to make a nature of each functional set clear, a spin contamination error involved in the BS singlet (S = 0) state is removed from an energy gradient by an approximately spin-projected geometry optimization (AP-opt) method. After the AP-opt correction, both UB3LYP and UBHandHLYP give more accurate results for the distance between the center of mass of O-O and that of Cu-Cu that is often represented as a reaction coordinate R. In the viewpoint of structural and physicochemical properties, reliabilities of these functional sets are in the order of UBHandHLYP > UB3LYP ≫ UB3PW91 > UB(38HF)P86 > UPBE0.