First-principles simulation of the intracage oxidation of nitrite to nitrate sodalite First-principles simulation of the intracage oxidation of nitrite to nitrate sodalite

We study the oxidation of NO (cid:255) 2 to NO (cid:255) 3 by dioxygen in the cages of sodalite, by using the combined blue moon ensemble (BME) and Car Parrinello approaches. Our results indicate the active participation of the zeolite framework in the reaction via peroxy-like defects. Moreover, a molecular level explanation of the experimentally found ﬁrst-order kinetics is given. A spin-unpolarized density functional approach has been adopted. However, our results suggest that interactions in the zeolite cage may reduce the O 2 triplet–singlet energy gap, therefore, justifying the adopted approximation. (cid:211) 2000 Elsevier Science B.V. We study the oxidation of NO2− to NO3− by dioxygen in the cages of sodalite, by using the combined blue moon ensemble (BME) and Car Parrinello approaches. Our results indicate the active participation of the zeolite framework in the reaction via peroxy-like defects. Moreover, a molecular level explanation of the experimentally found first-order kinetics is given. A spin-unpolarized density functional approach has been adopted. However, our results suggest that interactions in the zeolite cage may reduce the O2 triplet–singlet energy gap, therefore, justifying the adopted approximation. ABSTRACT


Introduction
We present a simulation on an oxidative reaction, NO À 2 1 2 O 2 3 NO À 3 , inside sodalite cages. This intracage reaction has been experimentally studied in the temperature range 900±1000 K [1±3]: the oxidizing agent is molecular oxygen, and the reaction, ®rst-order with respect to NO À 3 is completed in 30 h. The reported experiments do not allow a microscopic analysis of the reaction mechanism.
We have studied the intracage oxidation by using the constrained molecular dynamics (blue moon ensemble, BME) method [4,5] together with the ab initio molecular dynamics approach [6]. These two combined techniques have been applied to both liquid phase reactions [7,8] and heterogeneous catalysis [9,10].
We have adopted perfect spin-pairing in our calculations, therefore, one of the reactants, molecular oxygen, is in the singlet excited state, which is about 100 kJ mol À1 above the triplet ground state in the gas phase.
The reaction occurs in air at high temperature: molecular oxygen diuses inside sodalite causing an expansion of the crystals and then oxidizing of the nitrate. As the dissociation energy of O 2 is 493.7 kJ mol À1 [12], a homolytic event is improbable. Moreover, due to the ionic character of the 13 intracage reduction. This choice makes the BME easier to apply. It consists of performing a series of constrained simulations, in which a degree of freedom is kept constant and the constraint force is averaged over each simulation. The degree of freedom is constrained to dierent values from an initial to a ®nal state. The integral of the constraint forces corresponds to minus the dierence in free energy.
In the nitrate sodalite ( Fig. 1) the constrained degree of freedom is one of the NO bonds of NO À 3 in one cage. We performed a series of simulations with dierent values of such distance, constrained by using the RATTLE algorithm [13], starting from the equilibrium value of such a distance. Moreover, we performed other`unconstrained' simulations as well: the nitrite sodalite, the nitrate sodalite, and the nitrite sodalite with one oxygen molecule. All simulations were performed with the Car±Parrinello method at a constant temperature of 1000 K [14]. Norm-conserving pseudopotentials [15,16] were used, the Becke±Perdew functional was chosen [17,18]. A plane waves cuto of 60 Ry at the C point was used. Unconstrained systems were studied for about 4.5 ps, while constrained simulations were continued till convergence in the constraint force was reached, 3±5 ps depending on the value of the constraint.
The gas phase ground state of oxygen is a 3 R À g triplet and the ®rst excited state is a singlet 94.3 kJ mol À1 higher [19]. With the DFT used here, such a dierence amounts to 156 kJ mol À1 and to 241 kJ mol À1 by using the Hartree±Fock approximation, with a triple-zeta + polarization basis set. The dissociation energy of O 2 is 554 kJ mol À1 for the triplet and 398 kJ mol À1 for the singlet with the DFT approximation (the experimental value is 493.7 kJ mol À1 ). The calculated gas phase DE for the reaction 2NO À 2 O 2 NO 3 is À402X2 kJ mol À1 using a spin-unpolarized functional and À246X2 kJ mol À1 when a spin-polarized (triplet) functional is used. However, interactions may contribute to reduce the triplet±singlet gap. Test calculations have been carried out, and are discussed below. The nitrite sodalite system was modeled by one cell (lattice parameter 8.923 # A). The nitrite sodalite + O 2 system was simulated by using the cell parameter of nitrate sodalite (8.996 # A) [3].

Results
The unconstrained simulation of nitrite sodalite, in agreement with experimental data, indicates that the NO À 2 anions in the b-cages present dynamical disorder, with the NO À 2 rotating inside the cavity [20].
The NO À 3 anions, in the unconstrained simulation, rotate as well. However, due to the larger size of NO À 3 with respect to NO À 2 , the motion is more hindered. Experiments suggest orientational disorder for NO À 3 [1] as well. The unconstrained simulation of nitrite sodalite + O 2 suggested a possible mechanism for the intracage oxidation. The O 2 molecule left its starting position (midway between adjacent NO À 2 ), and diused towards one of the two NO À 2 , forming a labile complex, NO 2 Á Á Á O 2 À in equilibrium with the NO À 2 and O 2 species (Fig. 2). This simulation  provides an indication about the structure of thè ®nal state' of the reverse reaction studied by BME. The motion of the nitrate anions in the b-cages is a`frictioned' rotational motion, as only two rotations of NO À 3 occurred in the simulation. This behavior is dierent from the one found in nitrite sodalite, where NO À 2 rotates on a time scale of about 100 fs. Therefore, our`®nal' NO À 2 should behave in a similar fashion, rotating faster than thè initial' NO À 3 . The calculated constraint forces are reported in Table 1. The calculated free energy (Fig. 3) shows that the nitrite sodalite + O 2 system is less stable than nitrate sodalite, as in experiments. The activation free energy for the oxidative process was calculated to be 30 kJ mol À1 and the reaction free energy to be about À75 kJ mol À1 .
In the ®rst three simulations, constrained at 1.5, 1.75 and 2.0 # A respectively, the constrained NO À 3 behaved quite normally, as it slowly rotated like a nitrate anion. Now the oxygen atom should still be bonded to N. At a value of the constraint of 2.5 # A, the situation changed. There was a change in sign of the constraint force. This indicates that the forces exerted by the whole system have changed sign along the N±O distance, suggesting that the constrained oxygen and nitrogen were no longer chemically bonded. Now the NO À 2 fraction of the constrained nitrate rotates faster than a typical nitrate, and more similar to a`free' NO À 2 in nitrite sodalite.
Now the constrained oxygen atom should be quite reactive, and as it is still far away from the other NO À 3 , it interacts with the zeolite framework. Indeed the constrained oxygen is now approximately midway between two b-cages and close to the oxygen atom forming the ring shared by two cavities. Actually the constrained oxygen`links' to Table 1 Calculated values of the constraint force f for each constrained distance r. Distances in # A, forces in a.u.   the framework and forms various kinds of defects easily interchanging from one to another. Fig. 4 shows some characteristic structures (with the constraint at 2.5 # A). The ®rst one is a peroxy-defect (Fig. 4a), where the constrained O is linked to a framework oxygen. This structure then evolves, and the constrained oxygen`enters' the sodalite framework. In Fig. 4b, a peroxy-bridge defect is shown, where a O 2 species is placed between an Al and a Si, each oxygen of the defect being linked to only one of the tetrahedral cations (Si or Al). Fig. 4c shows another defect, namely an O 2 species shared between two tetrahedral cations, with each oxygen linked to both Al and Si. We have monitored the total charge of the constrained NO À 3 anion in order to see whether the initial negative charge on the nitrate is conserved in the NO À 2 product: we found that the oxygen`leaving' the nitrate is neutral, and the O 2 defect can be a real peroxy-species O À2 2 , considering an O 2À anion the framework oxygen.
Recently, the energetics and geometries of defect centers in zeolites in oxidative conditions have been reported [21]. Such investigation proves that peroxy-like defects in aluminosilicate structures may have a formation energy in the range 40±150 kJ mol À1 . Moreover, their presence is supported by several experimental studies [22±25].
In the other constrained simulations (constraint, respectively, at 2.75, 3.0, 3.5, 3.75, 3.9 # A) the formation of this kind of defect is observed in the whole simulation times, and defects transform each other in a very short time ($100 fs). However for such values of the constraint, the reactive O atom was still bound to the framework. Only when the constraint was set to an NO distance of 4.0 # A the reactive events occurred. After a few fs, the oxygen trapped in the framework defects left the four ring region and diused in the adjacent cage colliding with the second NO À 3 . The collision ®rst led to the transient species NO 2 Á Á Á O 2 À , that appeared in the unconstrained nitrite sodalite O 2 simulation. Such species reached rapid equilibrium with the separated NO À 2 and O 2 compounds. The ®nding that the ®nal state of the inverse reduction reaction is similar to the one found in the unconstrained simulation of nitrite sodalite + O 2 strongly supports the idea that the NO 2 Á Á Á O 2 À complex is the ®rst step in the direct reaction (after the O 2 diusion inside the cavities). Such a complex may activate the molecular oxygen and actually when the O 2 was complexed to the NO À 2 , its bond length increased and its oscillation became wider, showing a weaker O±O bond (see Fig. 5). Once the O±O bond is weakened one of the oxygen atoms of O 2 can interact with the frame-  work forming the defects described above. Then, the reactive oxygen gets into the adjacent cage where there is still a NO À 2 , reacting to form a second NO À 3 . This proposed mechanism ®ts the ®rst-order kinetics with respect to NO À 3 described in the literature: the formation of the ®rst NO À 3 is the slow step, namely the transformation of the NO 2 Á Á Á O 2 À complex in a NO À 3 and an oxygen atom linked to the frame should be the rate determining step.
The results presented so far were obtained by using spin-unpolarized DFT, implying that the O 2 is in the excited singlet state. Were the gas phase energy gap transferable to condensed phases, the presented results could be biased by the adopted approximation. However, in a highly ionic system, isolated system data may not be pertinent. We have calculated the triplet±singlet energy dierence for the isolated NO 2 Á Á Á O 2 À complex, by using the same scheme as for bulk calculations, for a series of geometries taken from the zeolite trajectories. The dierences in energy for such a system reduce to 1±10 kJ mol À1 , always favoring the triplet state. For a few con®gurations of the bulk nitrite sodalite + O 2 , we have calculated the same energy gap: the triplet±singlet DE's reduce to a few kJ mol À1 , however, this time favoring the singlet state. Such results indicate a stabilization of singlet oxygen in the nitrite sodalite system.

Conclusions
We have studied the intracage oxidation NO À 2 1 2 O 2 3 NO À 3 in sodalite by means of the blue moon ensemble and Car Parrinello MD combined methods. The reaction was simulated by following the inverse reduction process. Such an approach has allowed us an easier application of the BME sampling and could be of general scope.
We have found a free energy for the oxidation at 1000 K of the order of À75 kJ mol À1 and an activation free energy of about 30 kJ mol À1 . A mechanism for this chemical reaction that may explain at microscopic level the experimentally found ®rst-order kinetics with respect to NO À 3 was proposed. Furthermore, our simulations predict that the sodalite framework is directly involved in the reaction via the formation of defect centers after reacting with the dioxygen.
Beyond the relevance in this particular study, the peroxy-like defects can be reaction intermediates in other zeolites-based oxidations in industrial applications. On the basis of our results, it can be supposed that more eective oxidizing media can be obtained by modifying zeolites and mesoporous aluminosilicates in order to allow an easier formation of peroxy-like structures. In this respect, the presented data may suggest a possible activation of the inert triplet state of dioxygen in the cavities of nitrite sodalite to the more reactive singlet O 2 [26].