5 Comprehensive DFT study of the nitrous oxide decomposition over Fe-ZSM- .93
5.4 Computational results and discussion
5.4.2 Catalytic cycle on Z - [FeO] +
As shown in the last section Z-[FeO]+ sites are catalytically active. Parts of the catalytic cycle on Z-[FeO]+ were discussed above and will not be repeated. As noted above, one reaction pathway for the N2O dissociation leads to Z-[FeO2]+, whereas another leads to dioxo Z-[OFeO]+ species. The transition state for the reaction of Z-[FeO]+(ON2) to form Z-[OFeO]+ and N2 is characterized by a bending of the N2O molecule from 180° in the adsorbed state to 140.5° (MS = 4) or 143.6° (MS = 6) in the transition state, whereas the
length of the N´-O´´ bond of the N2O molecule increases from 1.20 Å to 1.44 Å (MS = 4) or 1.54 Å (MS = 6). The activation barrier for the decomposition is E‡(MS = 4) = 27.5 kcal/mol or E‡(MS = 6) = 30.7 kcal/mol. The imaginary frequency associated with the transition state mode is 810i cm-1 (MS = 4) or 892i cm-1 (MS = 6). Both the transition state structures and the energetics are very similar for the reaction pathways leading to Z-[FeO2]+ and Z-[OFeO]+. Figure 5.10 illustrates the transition state structures on both PESs. The zero-point corrected energy of Z-[OFeO]+ on the quartet PES is approximately 2 kcal/mol higher than on the sextet PES. The surface O-atoms are located 1.59 Å (MS = 4) or 1.68 Å (MS = 6) from the Fe atom. The O-O bond length is 2.71 Å (MS = 4) or 2.32 Å (MS = 6). There is no chemical bond between the two oxygen atoms. The surface oxygen atoms are much closer to the iron atom in the Z-[OFeO]+ structure than in the Z-[FeO2]+ structure and, therefore, much more similar to Z-[FeO]+, for which the Fe-O bond length is 1.68 Å (MS = 4) or 1.66 Å (MS = 6). The calculated vibrational modes associated with the Fe-O stretch in Z-[OFeO]+ are 955 cm-1 and 1012 cm-1 on the quartet PES and 643 cm-1 and 868 cm-1 on the sextet PES. Figures 5.6 and 5.7 illustrate that the Z-[OFeO]+ species is 8.3 kcal/mol higher in energy than the Z-[FeO2]+ species. A reaction pathway connecting Z-[OFeO]+ and Z-[FeO2]+ was
Figure 5.10: Transition state structures for N2O decomposition on Z-[FeO]+. On the left MS = 4, on the right MS = 6
Both Z-[OFeO]+ and Z-[FeO2]+ sites are catalytically active for the N2O dissociation.
N2O adsorbs through the N-end with an enthalpy of adsorption of ∆Hads(MS = 4) = 4.5 kcal/mol or ∆Hads(MS = 6) = -3.2 kcal/mol on Z-[OFeO]+, and with an enthalpy of adsorption of ∆Hads(MS = 4) = 0.3 kcal/mol or ∆Hads(MS = 6) = -2.3 kcal/mol on Z-[FeO2]+. N2O adsorption through the O-end is as weak as through the N-end:
∆Hads(MS = 4) = 4.5 kcal/mol or ∆Hads(MS = 6) = -3.0 kcal/mol on Z-[OFeO]+ and
∆Hads(MS = 4) = 0.7 kcal/mol or ∆Hads(MS = 6) = -1.2 kcal/mol on Z-[FeO2]+. Taking into account the loss of entropy associated with the adsorption process, it follows that N2O does not adsorb on the quartet PES and only weakly on the sextet PES.
One reaction pathway was found for N2O dissociation from Z-[OFeO]+(ON2) and one for Z-[FeO2]+(ON2), yielding Z-[O2FeO]+. The transition state for the reaction leading from Z-[OFeO]+(ON2) to Z-[O2FeO]+ is characterized by a bending of the N2O molecule from 180° in the adsorbed state to 149.7° (MS = 4) or 139.7° (MS = 6) in the transition state. In addition, the N´-O´´ bond length of the N2O molecule increases from 1.20 Å to 1.68 Å (MS = 4) or 1.42 Å (MS = 6) in the transition state. The activation barrier for the decomposition is E‡(MS = 4) = 42.9 kcal/mol and E‡(MS = 6) = 16.5 kcal/mol. The imaginary frequency associated with the transition state mode is 790i cm-1 (MS = 4) and 716i cm-1 (MS = 6). On the sextet PES the transition state involves first the formation of a superoxide species on top of the iron atom. From the activation barriers it follows that the quartet PES is non-reactive while the sextet PES is very reactive. Figure 5.11 illustrates the transition state structures on both PES. From the heats of reaction,
∆HR(MS = 4) = -28.8 kcal/mol or ∆HR(MS = 6) = -18.3 kcal/mol, it can be concluded that the reverse reaction is very slow and that decomposition is essentially irreversible.
The transition state for the reaction leading from Z-[FeO2]+(ON2) to Z-[O2FeO]+ is characterized by a bending of the N2O molecule from 180° in the adsorbed state to 140.8° (MS = 4) or 139.9° (MS = 6) in the transition state. In addition, the N´-O´´ bond length of the N2O molecule is increased from 1.20 Å to 1.44 Å (MS = 4) or 1.42 Å (MS = 6) in the transition state. The activation barrier for decomposition is
O
before N2O decomposition; on the quartet PES after N2O decomposition.E‡(MS = 4) = 24.0 kcal/mol or E‡(MS = 6) = 20.1 kcal/mol. The imaginary frequency associated with the transition-state mode is 732i cm-1 (MS = 4) and 717i cm-1 (MS = 6).
Figure 5.12 illustrates the transition state structures on both PESs. Taking into account the enthalpy of reaction, ∆HR(MS = 4) = -16.8 kcal/mol or ∆HR(MS = 6) = -12.0 kcal/mol and transition-state energy, it can be concluded that the reverse reaction is slow and that decomposition is again essentially irreversible. It is important to note that the activation barrier with respect to the gas phase for N2O decomposition on Z-[FeO2]+ and on Z-[OFeO]+, 17.3 kcal/mol or 12 kcal/mol (both MS = 6), is lower than the activation barrier for N2O decomposition on Z-[FeO]+, 24.0 or 24.3 kcal/mol (both MS = 6). This relationship is in opposition to conclusions drawn from experimental studies (Kiwi-Minsker, 2003; Wood et al., 2004; Bulushev et al., 2004) and calculations reported by Ryder et al. (2002). Nevertheless, it will be shown in chapter 6 that this result does not contradict experimental data.
Z-[O2FeO]+ consists of a superoxide O2- anion and a O- or O2- anion on top of a Fe2+ or Fe3+ cation. The O-O bond length of the superoxide O2- anion is 1.29 Å (MS = 4) or 1.31 Å (MS = 6). The Fe-O bond distance of the superoxide anion to the iron cation is 1.89 Å and 2.20 Å on the quartet PES and 1.91 Å and 2.06 Å on the sextet PES. Based on the O-O bond distance and the associated vibrational frequency, 1227 cm-1 (MS = 4)
O
Figure 5.12 Transition state structures for N2O decomposition on Z-[FeO2]+. On the left MS = 4, on the right MS = 6.
or 1191 cm-1 (MS = 6), the diatomic oxygen can be best described as a superoxide anion.
The third O-anion bonded to the iron cation has a Fe-O distance of 1.63 Å (MS = 4) or 1.62 Å (MS = 6) and a vibrational mode associated with Fe-O stretches of 913 cm-1 (MS = 4) or 923 cm-1 (MS = 6). It is interesting to note that for Z-[O2FeO]+ the quartet PES is again preferred to the sextet PES by 1.5 kcal/mol.
Oxygen can desorb from Z-[O2FeO]+. As mentioned above, the ground state of the oxygen molecule is a triplet 3Σg– state with two unpaired electrons so that O2 desorption is accompanied by a spin change of the zeolite cluster. If the cluster representations of both reactant and product states lie on the sextet PES, the spin-change barrier is calculated to be 8.0 kcal/mol (sextet/octet PES) for the desorption reaction. By contrast, if the reactant state is on the sextet PES and the product state is on the quartet PES no spin change occurs and the transition state for the O2 desorption can be determined. In this case, the activation barrier is E‡ = 6.9 kcal/mol. The imaginary frequency associated with the transition state mode is 83i cm-1 (MS = 6). Finally, for the case where the reactant and product states are on the quartet PES the calculated spin-surface crossing barrier (quartet/sextet PES) is 21.6 kcal/mol. It is important to note that the enthalpy of O2 desorption is very small: ∆HR(MS = 4) = 4.2 kcal/mol, ∆HR(MS = 6) = -0.6 kcal/mol, ∆HR(MS = 6/4) = 3.0 kcal/mol. Therefore, O2 desorption Z-[O2FeO]+ from the more reactive sextet PES should be very fast. The low enthalpy of desorption
is consistent with the absence of O2 inhibition on the rate of N2O decomposition on Fe-ZSM-5 (Fu et al. 1981; Leglise et al., 1984; Panov et al., 1990; Kapteijn et al., 1997).
The adsorption process is entropically very unfavorable, so that a significant enthalpy of adsorption is required to poison Z-[FeO]+sites by O2. The fast O2 desorption process on the other hand is a contradiction to experimental results from Wood et al. (2004) and Bulushev et al. (2004) who claim that the desorption process is the rate-limiting step in the N2O decomposition cycle.