We studied the energetics of dioxygen binding and the core isomerization between the Cu-2(mu-eta(2):eta(2)-O-2) and Cu-2(mu-O)(2) core structures of {[LCu](2)O-2}(2+), L = 1,4,7-triazacyclononane (1) and L = hydrotris(pyrazolyl)borate (2), by gradient-corrected density functional methods. N-Substituted derivatives of 1 and 2 are synthetic inorganic mimics of oxyhemocyanin with similar physical and spectroscopic properties but different chemical behavior. The calculated dioxygen binding energies of 1 and 2 are -60 and -184 kJ/mol, respectively, in line with the observation that 1 binds oxygen reversibly and 2 does so irreversibly. Bond energy decomposition-showed that orbital interactions contribute equally to the binding energy of 1 and 2, which explains the similarities in their spectral properties. Electrostatic interactions due to the negatively charged ligand are responsible for stronger binding in 2. The core isomerization energies for isomerization from the Cu-2(mu-eta(2):eta(2)-O-2) to the Cu-2(mu-O)(2) isomers of 1 and 2 are +1 and +12 kJ/mol, respectively. The barrier heights of the core isomerizations of 1 and 2 relative to the Cu-2(mu-eta(2):eta(2)-O-2) isomer are 33 and 37 kJ/mol, respectively. The results on 1 are in line with the experimentally observed fast and reversible interconversion between the two isomers while these data on 2 suggest that the observation of 2 in the (mu-O)(2) isomer was only prevented by its thermal instability. We also considered a purely theoretical model compound, {[(NH3)(3)Cu](2)O-2}(2+) (3). Calculations on 3 show that this model is clearly inadequate even for qualitative energetic modeling of dioxygen binding while it is successful in describing spectral, structural, and magnetic properties. Calculations show that the isomerization of 3 is endoergic by 49 kJ/mol, and there is essentially no energy barrier relative to the higher energy (mu-O)(2) isomer. The dioxygen binding energy of 3 is endoergic by 160 kJ/mol as opposed to the exoergic binding in both 1 and 2.