We investigate how nanospaces surrounded by a 10-membered ring of ZSM-5 zeolite affect the reaction intermediates formed during dioxygen activation by enclosed dicopper cations. Two types of dioxygen intermediates are considered: one is an O(2)...Cu(2) complex, where dioxygen binds to the two Cu cations, and the other is a bis(mu-oxo)dicopper complex converted from an O(2)...Cu(2) complex by the cleavage of the O-O bond. We employ large-scale density functional theory (DFT) calculations with the B3LYP functional to examine the energetics of the two dioxygen intermediates inside a 10-membered ring of ZSM-5 with double Si --> Al substitutions at variable locations. The properties of the O(2)...Cu(2) complexes, such as the dioxygen bridging modes and dioxygen activation, are strongly affected by the locations of the two Al atoms within the 10-membered ring. In particular, the O(2)...Cu(2) complexes have either end-on or side-on bridging modes depending on the substituted Al positions. On the other hand, the steric hindrances of a ZSM-5 cavity play crucial roles in determining the properties of the bis(mu-oxo)dicopper complexes containing a diamond Cu(2)O(2) core. By restricting its Cu(2)O(2) core to a 10-membered ring of ZSM-5 in which the two Al atoms are second-nearest neighbors, each Cu cation is tetrahedral four-coordinate. On the other hand, the Cu cations have almost square planar coordination inside a ZSM-5 where the Al atoms are fourth-nearest neighbors. The different Cu coordination environments are responsible for the different levels of stability; the planar diamond Cu(2)O(2) core is 30.7 kcal/mol more stable relative to the tetrahedral case. Since the ZSM-5 nanospaces directly influence the stability of the bis(mu-oxo)dicopper complexes by changing the Cu coordination environments, zeolite confinement effects on the bis(mu-oxo)dicopper complexes are more noticeable than those in the O(2)...Cu(2) cases. The DFT findings are important in terms of catalytic functions, because the spatial constraint from the ZSM-5 should significantly contribute to the stability of the reaction intermediates formed during the dioxygen activation.