Based on the equilibrium geometries of [Cu2(dbdmed)2O2]2+ and [Cu2(en)2O2]2+ obtained within density-functional theory, we investigate their molecular electronic structure and optical response. Thereby results from occupation-constrained as well as time-dependent DFT (ΔSCF and TDDFT) are compared with Green's function-based approaches within many-body perturbation theory such as the GW approximation (GWA) to the quasiparticle energies and the Bethe-Salpeter equation (BSE) approach to the optical absorption. Concerning the ground-state energies and geometries, no clear trend with respect to the amount of exact exchange in the DFT calculations is found, and a strong dependence on the basis sets is to be noted. They affect the energy difference between bis-μ-oxo and μ-η2:η2-peroxo complexes by as much as 0.8 eV (18 kcal/mol). Even stronger, up to 5 eV is the influence of the exchange-correlation functional on the gap values obtained from the Kohn-Sham eigenvalues. Not only the value itself but also the trends observed upon the bis-μ-oxo to μ-η2:η2-peroxo transition are affected. In contrast, excitation energies obtained from ΔSCF and TDDFT are comparatively robust with respect to the details of the calculations. Noteworthy, in particular, is the near quantitative agreement between TDDFT and GWA+BSE for the optical spectra of [Cu2(en)2O2]2+. © 2013 Wiley Periodicals, Inc.