Structural and electronic properties of neutral and anionic CuO2 molecules are investigated within density functional theory. The lowest energy structures are the bent CuOO and the linear OCuO-. Consideration of temperature effects via first-principles molecular dynamics simulations allows to conclude that two CuO2- isomers (bent CuOO- and CuO2- side-on) coexist at very close energies in the measured photoelectron spectrum, for different spin states. Among the isomers of CuO2, bonding is the most covalent in the linear OCuO molecule.