DFT calculations give insight into the formation of peroxo intermediates 1-8 from a series of Cu(I) complexes bearing N-hexadentated macrocyclic dinucleating ligands, suffering an oxidation by their interaction with molecular oxygen. The discussion is thus based on the side-on peroxo cores, omitting the case of complex 8 for which the most favored structure is the trans-peroxo due to para Substitution and the steric encumbrance produced by the methylation of the aminic N atoms. The frontier molecular orbital theory explains deeply the O-2 binding to the Cu(I) complexes, giving key relationships between the energy of particular orbitals of the copper complex before the O-2 binding and the corresponding ones for the free O-2. On the other hand, tools,Such as the energy decomposition analysis and Mayer bond orders reveal the slight differences due to the different types of ligands.