Density functional calculations are performed to study the CuO3 species in the neutral, cationic and anionic charge states. Three stable isomers OCuO2 (C-2v), Cu(O-3) (C-2v) and OCuOO (C-s) are obtained. The most stable geometries of the CuO3 species are found to depend strongly on the charge states. For the neutral, the ground state is the OCuO2 quartet, while it is the Cu(O-3)(+) singlet for the cation. For the anion, the OCuO2-singlet and OCuOO- triplet are found to be quasi-isoenergetic and both are lower in energy than the Cu(O-3)(-) singlet. The equilibrium bondlengths, vibrational frequencies and electronic configurations are obtained. A theoretical assignment for the features in the photoelectronic spectrum (PES) is given at the local spin density approximation level. Our results compare well with the available experimental results and show that the anionic OCuO2 (C-2v) and OCuOO (C-s) isomers coexist in the PES experiment.