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The reaction mechanism for nitrous oxide (${N}_{2}O$) direct decomposition into molecular nitrogen and oxygen was studied on binuclear iron sites in Fe-ZSM-5 zeolite using the density functional theory (DFT). Starting from the hydroxylated bi-iron complex ${\left}^{+}$, a reductive dehydroxylation pathway was proposed to justify the formation of the active site ${\left<{Fe}^{II}\left(\mu -O \right)\left(\mu -OH \right){Fe}^{II} \right>}^{+}$. The latter contains two FeII ions linked via oxo and hydroxo bridges, ${{Z}^{-}\left<{Fe}^{II}\left(\mu -O \right)\left(\mu -OH \right){Fe}^{II} \right>}^{+}$, and for the first time was considered to catalyze the ${N}_{2}O$ ecomposition. The DFT results show the activity of ${\left<{Fe}^{II}\left(\mu -O \right)\left(\mu -OH \right){Fe}^{II} \right>}^{+}$ complex for the ${N}_{2}O$ decomposition. The first step of the catalytic reaction corresponds to a spontaneous adsorption of ${N}_{2}O$ over FeII sites, followed by the surface atomic oxygen loading and the release of molecular nitrogen. The formation of molecular ${O}_{2}$ occurs through the migration of the atomic oxygen from one iron site to another one followed by the recombination of two oxygen atoms and the desorption of molecular oxygen. The computed reactivity over the binuclear iron core complex ${\left<{Fe}^{II}\left(\mu -O \right)\left(\mu -OH \right){Fe}^{II} \right>}^{+}$ is consistent with experimental data reported in the literature. Although the dissociation steps of the ${N}_{2}O$ molecules, calculated with respect to adsorbed ${N}_{2}O$ intermediates, are highly energetic, the energy barrier associated with the atomic oxygen migration is the highest one. Up to 700 K, the oxygen migration step has the highest free energy barrier, suggesting that it is the te-limiting step of the overall kinetics. This result explains the absence of ${O}_{2}$ formation in experimental study of ${N}_{2}O$ decomposition at temperatures below 623 K.