The first steps of dioxygen activation in naphthalene 1,2-dioxygenase have been investigated by means of hybrid density functional theory. Reduction of molecular oxygen by this Rieske dioxygenase occurs in the catalytic domain accommodating a mononuclear non-heme iron(II) complex, and it requires two external electrons ultimately delivered by a Rieske [2Fe-2S] cluster hosted in the neighboring domain. Theoretical tools have been applied to gain insight into the O-2-binding step and into the first one-electron-transfer process involving the mononuclear and the Rieske centers, and yielding an iron(II)-superoxo intennediate. The reaction, which is mimicked with a model including both metal sites, is found to be a reversible equilibrium. Although the entropic loss associated with the binding of O-2 to iron(II) is not canceled by the corresponding enthalpic binding energy, it is, however, balanced by the exothermicity of the electron transfer process from the Rieske cluster to the dioxygen-bound iron(II) complex. The rationalization for the calculated energetics is related to the values of the ionization potential (IP) of the. Rieske cluster and the electron affinity (EA) of the mononuclear iron complex: the latter is computed to be higher than the former, when dioxygen is bound to the metal. The possibility that a second external electron is delivered to the mononuclear site before dioxygenation of the substrate has also been examined. It is shown that, if the second electron is available in the Rieske domain, the electron transfer process is energetically favored. The results acquired with the large model comprising the two metal centers are compared to the corresponding information collected from the study of smaller models, where either the mononuclear iron complex or the Rieske cluster is included.