Understanding the formation mechanism of the [Cu_2O]^(2+) active site in Cu-ZSM-5 is important for the design of efficient catalysts to selectively convert methane to methanol and related value-added chemicals and for N_2O decomposition. Spectroscopically validated DFT calculations are used here to evaluate the thermodynamic and kinetic requirements for formation of [Cu_2O](2+) active sites from the reaction between binuclear Cu(I) sites and N_2O in the 10-membered rings Cu-ZSM-5. Thermodynamically, the most stable Cu^I center prefers bidentate coordination with a close to linear bite angle. This binuclear Cu^I site reacts with N_2O to generate the experimentally observed [Cu_2O]^(2+) site. Kinetically, the reaction coordinate was evaluated for two representative binuclear Cu^I sites. When the Cu-Cu distance is sufficiently short (5.0 Å), N_2O binds in a "terminal" η^1-O fashion to a single Cu^I site of the dimer and the resulting E_a for N_2O activation is significantly higher (16 kcal/mol). Therefore, bridging N_2O between two Cu^I centers is necessary for its efficient two-electron activation in [Cu_2O]^(2+) active site formation. In nature, this N_2O reduction reaction is catalyzed by a tetranuclear Cu_Z cluster that has a higher E_a. The lower E_a for Cu-ZSM-5 is attributed to the larger thermodynamic driving force resulting from formation of strong Cu^(II)-oxo bonds in the ZSM-5 framework
