Effect of Water Molecule on Photo-Assisted Nitrous Oxide Decomposition over Oxotitanium Porphyrin: A Theoretical Study

Abstract

Water vapor has generally been recognized as an inhibitor of catalysts in nitrous oxide (N₂O) decomposition because it limits the lifetime of catalytic reactors. Oxygen produced in reactions also deactivates the catalytic performance of bulk surface catalysts. Herein, we propose a potential catalyst that is tolerant of water and oxygen in the process of N₂O decomposition. By applying density functional theory calculations, we investigated the reaction mechanism of N₂O decomposition into N₂ and O₂ catalyzed by oxotitanium(IV) porphyrin (TiO-por) with interfacially bonded water. The activation energies of reaction Path A and B are compared under thermal and photo-assisted conditions. The obtained calculation results show that the photo-assisted reaction in Path B is highly exothermic and proceeds smoothly with the low activation barrier of 27.57 kcal/mol at the rate determining step. The produced O₂ is easily desorbed from the surface of the catalyst, requiring only 4.96 kcal/mol, indicating the suppression of catalyst deactivation. Therefore, TiO-por is theoretically proved to have the potential to be a desirable catalyst for N₂O decomposition with photo-irradiation because of its low activation barrier, water resistance, and ease of regeneration.

1. Introduction

Nitrous oxide (N₂O) is an anthropogenic gas reported as the largest contribution to the ozone depleting gas emissions [1]. Once it is transported to the stratosphere, it destroys the ozone and causes the greenhouse effect. At present, the development of technologies for the abatement of N₂O mainly focuses on (i) nonselective catalytic reduction, (ii) selective catalytic reduction, and (iii) direct catalytic decomposition. Among the up-to-date technologies, the direct decomposition of N₂O (deN₂O) has attracted much attention because of its efficiency and cost effectiveness [2,3,4,5]. Researches in the field of N₂O catalytic decomposition mainly focus on low-temperature deN₂O catalysts that can be applied to N₂O abatement in medical operating rooms, nitric acid plants, three-way catalytic converters, etc. For example, N₂O is used as an anesthetic gas in hospitals and it can lead to miscarriages in gestation, liver disorder, kidney trouble, and so on. Doi et al. [6,7] worked on the deN₂O of the air contaminated with N₂O in operating rooms by varying the alumina-supported metals (Pt, Pd, or Rh), and found that the Rh/Al₂O₃ is the most suitable catalyst for deN₂O in operating rooms which could reach 100% decomposition at 773K.

The catalytic deN₂O has been studied to a greater extent than selective catalytic reduction (SCR) over a large variety of catalysts, including noble metals [4,8,9,10,11], perovskites [12,13,14], metal oxides [15,16,17,18], and zeolites [19,20,21,22]. It is also important to note that in deN₂O processes, tolerance to various substances coexisting in the exhaust gases (e.g. NO_x, SO₂, O₂, and H₂O) should be simultaneously accomplished without sacrificing low-temperature activity. For example, the effect of SO₂ and/or H₂O on the NO_x and N₂O reduction was examined over the In/Al₂O₃-Ru/Al₂O₃ dual-bed reactor. Their transient experiments showed that the N₂O conversion dropped to zero in the presence of SO₂ and H₂O [23,24]. In addition, there have been reports of various catalysts which show that their catalytic performance of deN₂O is decreased due to the active site poisoned with water vapor or oxygen molecules produced during the reaction [25,26,27,28]. Regarding to water inhibition, it was studied, theoretically, by Heyden et al. [27] who concluded that water impurity (<100 ppm) may strongly affect the kinetics of N₂O decomposition, leading to an increase in apparent activation energy for 26 kcal/mol approximately. It is, obviously, important to take into account both the reaction mechanism and activation energy. In addition, those who are working on development of new catalysts for deN₂O should consider the effect of water at the active sites as well as the catalytic site regeneration by oxygen desorption, which is key to the reaction.

Besides thermal deN₂O, photo-assisted direct decomposition is another alternative method for N₂O removal [29,30,31]. This method applies light as the energy source for initiating the reaction, and the catalysis is active even at low gas concentration and low temperature. Therefore, with a suitable catalyst, a photocatalytic under the UV and near UV lights with wavelength 200–400 nm can be applied to decompose N₂O. In general, N₂O is decomposed into N₂ and O₂ under a photocatalytic reaction [32] by

$${\mathrm{N}}_2\mathrm{O} \stackrel{hv, catalyst}{\to } {\mathrm{N}}_2+ \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.{ \mathrm{O}}_2$$

(1)

The well-accepted photo-catalyst for N₂O decomposition is TiO₂ loaded with various noble metals [33,34,35,36]. However, noble metals are expensive for practical uses. Thus, a search for low-cost and effective catalysts for photocatalytic N₂O decomposition has been of great interest.

Porphyrin is a potential compound because it possesses two axial coordination sites which are suitable for anchoring to a solid substrate, such as in the metal-porphyrin assembly that features in several useful applications, including photovoltaic materials, field-responsive materials, and catalytic materials [37,38,39,40]. In our previous theoretical work [41], we proposed that low-valent titanium(II)-porphyrin (Ti-por) is a good catalyst for deN₂O under thermal conditions; the activation energies in the energy profiles are comparable to other potential catalysts. However, this low-valent Ti-por can be easily oxidized to form a more stable structure, reducing its suitability. The high-valent oxotitanium(IV)-porphyrin (TiO-por) is a better choice and has been reported as a potential catalyst for chemical and biological reactions [42,43,44]. Because of the structural combination of TiO and the electron-rich porphyrin ligand, it is of interest to extend the theoretical study to the photo-assisted deN₂O. In this work, we theoretically investigated the reaction mechanism of deN₂O with the TiO-por catalyst by using density functional theory (DFT), and included a water molecule at the active site, and studied O₂ desorption as well.

2. Results and Discussion

The presence of water in the system might provide some steric hindrance around the active site and increase the activation energy barriers of the reaction. Hence, the effect of water was intensively studied in this work. Considering water molecule at the TiO site (Figure 1), we divided the N₂O decomposition over the TiO-por into four elementary steps as follows.

Step 1: Water-complex formation on TiO-por

TiO-por + H₂O → Ti(OH)₂-por

(2)

Step 2: First N₂O decomposition

Ti(OH)₂-por + 1st N₂O → TiO(OH)₂-por + N₂

(3)

Step 3-A: Second N₂O decomposition followed by water desorption (Path A)

TiO(OH)₂-por + 2nd N₂O → Ti(OOH)₂-por + N

(4)

Ti(OOH)₂-por → TiO₃-por + H₂O

(5)

Step 3-B: Water desorption followed by second N₂O decomposition (Path B)

TiO(OH)₂-por → TiO₂-por + H₂O

(6)

TiO₂-por + 2nd N₂O → TiO₃-por + N₂

(7)

Step 4: Catalyst regeneration; oxygen formation and desorption

TiO₃-por → TiO-por + O₂

(8)

As mentioned earlier, the thermal and photo-assisted reactions were simulated by using the DFT calculations of singlet and triplet states, respectively. The calculated activation energies of all steps in the singlet and triplet states are listed in

Table 1. Activation energy (kcal/mol) for N₂O direct decomposition including the water molecule on singlet and triplet states of TiOH-por catalysts.

Reaction Step	Activation Energy (kcal/mol)
	1TiOH-por	3TiOH-por
1st N2O decomposition Ti(OH)2-por + N2O → TiO(OH)2-por + N2	63.57	27.57
Path A 2nd N2O decomposition and water desorption TiO(OH)2-por + N2O → Ti(OOH)2-por + N2	67.87	29.01
Path B water desorption and 2nd N2O decomposition TiO2-por + N2O → TiO3-por + N2	68.41	12.36
Oxygen formation TiO3-por → TiO-por + O2	5.12	barrierless

. Based on the pairwise comparison, it can be clearly seen that in the overall reaction processes of N₂O direct decomposition in the photo-assisted condition, TiO-por (³TiO-por) catalyst gives a more favorable reaction route with lower activation barriers. Therefore, the details of each reaction step in the photo-assisted condition will be further discussed. For the photo-absorption of the system, the absorption spectra of TiO-por and N₂O are compared in Figure S1. The first absorption band of TiO-por appears in the range of 300–400 nm which is assigned as the transition among the Gouterman’s four orbitals (Figure S2). On the other hand, the absorption of N₂O appears at around 100–150 nm, in FUV region. Thus, the UV light irradiation selectively promotes TiO-por to the excited state which leads to the N₂O decomposition reaction. The spin density plot of the ³TiO-por (Figure S3) also shows that the UV absorption is characterized as π–π* transition, with the spin density predominantly localized at meso-nitrogen positions.

2.1. Water Dissociation over the TiO-por

The energy profile of water dissociation over the TiO-por is shown in Figure 2 with optimized structures. First, a water molecule approaches the TiO site, in which Ti is slightly above the porphyrin plane and this water molecule undergoes adsorption with the TiO-por (AD1), resulting in an energy change of −7.57 kcal/mol. The optimized AD1 structure shows that a weak hydrogen bond is generated with a distance of 2.00 Å; the structural parameters of the adsorbed water are not significantly changed.

The first step of the reaction is the concerted hydrogen transfer and Ti–O bond formation, which was preceded by the O2–H1 bond breaking and O1–H1 bond formation, as seen in the structure of TS1. The activation energy barrier of this step is 19.61 kcal/mol. The H1 of the water molecule forms a bond with the O1 with a distance of 1.13 Å and an <O1–H1–O2 angle of 138.5°. Because of this O–H bond formation, the Ti–O1 bond is elongated to 1.75 Å at an angle to the porphyrin plane. This structure results in the O2 atom of the water molecule being closer to the Ti atom. The imaginary frequency at TS1 is 1284i cm⁻¹. The O1–H1 bond formation follows, with the O1–H1 bond distance of 0.96 Å. In addition, the Ti–O2 bond forms with a bond distance of 1.89 Å (IN1). Therefore, the new active site is generated as Ti(OH)₂ (IN1), from the water associated TiO-por catalyst. The relative energy of IN1 is −3.00 kcal/mol, which is slightly exothermic, but endothermic when being relative to AD1.

2.2. First N₂O Decomposition

After water dissociation and formation of Ti(OH)₂ (IN1), the first N₂O decomposition proceeds. The reaction profile consists of four stationary points: N₂O adsorption, first transition state, N₂ production, and N₂ desorption, as displayed in Figure 3. The molecule weakly interacts with the OH via a hydrogen bond with an adsorption energy of −4.94 kcal/mol (AD2). Then, it forms a Ti–O3 bond (2.28 Å) at the transition state (TS2), in which the N₂O molecule shows a bent structure with an <O3–N1–N2 of 150°. The O3–N2 bond is elongated from 1.18 Å to 1.46 Å, indicating that the O3–N2 bond is activated. Because of this insertion, the Ti–O1 bond is elongated from 1.85 Å to 2.03 Å. This transition state has an activation energy barrier of 27.57 kcal/mol, with an imaginary frequency of 439i cm⁻¹. The N–O bond breaks at the next intermediate (IN2), and a Ti–O3 bond is formed with a distance of 1.93 Å. Because of this Ti–O3 bond formation, the Ti–O1 bond becomes weak and the O1 approaches the O3 atom with a distance of 1.45 Å. The product N₂ molecule is generated in this step. It requires 3.11 kcal/mol to desorb the N₂ molecule from the catalyst intermediate (IN2-1). Consequently, in the first N₂O decomposition step, the N₂O molecule weakly adsorbs over the hydroxyl-oxotitanium porphyrin (Ti(OH)₂-por) and the N₂O decomposition needs an activation energy of 27.57 kcal/mol to generate the N₂ molecule.

2.3. Second N₂O Decomposition

Two possible routes, Path A and Path B, were examined for the second N₂O decomposition. Path A is the case where the second N₂O is decomposed before water desorption. Alternatively, a water molecule is desorbed before the second N₂O decomposition in Path B.

Path A: The second N₂O decomposition (Figure 4) starts from the IN2-1 (TiO(OH)₂-por) whose active site is coordinated by three oxygen atoms. All the steps of this decomposition proceed similarly to the first N₂O reaction. First, the AD3A intermediate is formed when a second N₂O is adsorbed on top of the IN2-1; the terminal O atom of N₂O interacts with the OH on the Ti center. The calculated adsorption energy is −3.77 kcal/mol. Through the transition state (TS3_A) at an imaginary frequency of 608i cm⁻¹, N–O bond dissociation occurs to form the intermediate IN3_A and a weakly interacting N₂ molecule. The activation energy barrier of this step is 29.01 kcal/mol, which is the same energy as the first N₂O decomposition. The produced N₂ desorbs from the active site, which requires 3.29 kcal/mol, and leaves the IN3-1_A intermediate, which consists of two OH groups coordinated at the Ti center. The resultant H₂O has a nearly linear structure with the <H1–O1–H2 angle being 171°. As a result, the H₂O molecule is formed easily (IN4_A) in an exothermic process, −20.34 kcal/mol relating to the IN3-1_A intermediate. Finally, the water molecule is generated and desorbed with energy of 9.61 kcal/mol (IN4-1_A).

For Path B, when considering the structure of IN2-1 (Figure 5) and the alternative pathway is also possible, namely, the H₂O molecule is released at the beginning, since the O1 has a hydrogen bond with the H2 atom and the distance is 2.25 Å with ∠H1–O1–H2 of about 171°. Thus, Path B starts from H₂O molecule desorption, which produces the intermediate IN3_B. The formation of the water molecule is an exothermic step with a relative energy of −11.59 kcal/mol. After the water desorption (IN3-1_B), the active site becomes the TiO₂-por intermediate. Then, the second N₂O interacts with the TiO₂-por intermediate with an energy change of −5.10 kcal/mol (AD4_B); this coordination is slightly stronger than the N₂O adsorption in Path A. To decompose the N₂O molecule over the TiO₂-por through the transition state (TS4_B) requires an activation energy of 12.37 kcal/mol, which is much lower than the case of Path A (TS3_A). This TS4_B has an imaginary frequency of 648i cm⁻¹, and the N₂O molecule has a bent structure with an ∠O3–N1–N2 angle of 126°. The O3 forms a Ti–O bond and the N1–O3 bond dissociates to give intermediate IN4_B. Finally, the N₂ molecule desorbs from IN4_B, which generates TiO₃-porphyrin (IN4-1_B). The calculated desorption energy of the N₂ molecule is 4.45 kcal/mol.

In general, the rate-determining step of N₂O direct decomposition is desorption of the produced O₂ from the catalysts. The O₂ desorption from the active site usually requires high energy, which could prohibit reaction when the active site is deactivated [20,26,27,45,46]. However, our present work found that the O₂ is formed over the TiO₃ intermediate of IN4-1_A and IN4-1_B in both Path A and Path B, as shown in the last step of Figure 4 and Figure 5, respectively. It is worth noting that O₂ molecule (IN5 intermediate) is easily formed with activation energy of 6.45 kcal/mol and barrierless for Path A and Path B, respectively. Furthermore, this O₂ formation step is an extremely exothermic process. Therefore, it is shown that the TiO₃-por catalyst intermediate easily regenerates the active TiO-por catalyst, which is an advantage of this catalyst, compared with the related zeolite catalysts for N₂O decomposition [45,46].

2.4. Overall Energetics of Photo-Assisted N₂O Decomposition over Hydroxyl-Oxotitanium Porphyrin Catalysts

The overall reaction energy profile of the water dissociation followed by N₂O decomposition on the TiO-por is summarized in Figure 6. Initially, the water molecule is adsorbed on the TiO-por catalyst at −7.57 kcal/mol (AD1), and the active site becomes Ti(OH)₂ (IN1). As regarding to the first N₂O decomposition, the N₂O molecule is slightly adsorbed on Ti(OH)₂-por active site (AD2), requiring 27.57 kcal/mol (TS2) for the N–O dissociation to produce the N₂ molecule. The active site then becomes the TiO(OH)₂-por (IN2-1). Two pathways are possible starting from the IN2-1 intermediate. In Path A, H₂O formation follows the second N₂O adsorption. The activation energy in this pathway is 29.01 kcal/mol (TS3_A). In Path B, the water molecule releases prior to N₂O decomposition. In Path B, the second N₂O decomposition occurs with an energy barrier of 12.37 kcal/mol (TS4_B). Therefore, the second N₂O decomposition over the TiO₂-por in Path B is expected to be more preferable than over the TiO(OH)₂-por of Path A, as summarized in Scheme 1. The final step is catalyst regeneration by oxygen molecule formation, and the calculated activation energy is barrierless to form the extremely exothermic intermediate, and the oxygen molecule easily desorbs from the surface of catalyst with only 4.96 kcal/mol. In the overall reaction, the N–O dissociation of the first N₂O molecule in Step 2 is the rate-determining step, which correlates well with the N₂O decomposition over Cu-ZSM5 [47]. It is worth to note that this present N₂O direct decomposition reaction has total reaction energy approximately at −52.58 kcal/mol.

2.5. Effect of Water Molecule on the N₂O Decomposition Barriers

On the pairwise comparison of the theoretical reaction mechanism for N₂O decomposition with and without introducing H₂O, only a few works have addressed this issue [26,27]. It is well known that Fe-ZSM5 zeolite is one of the potential catalysts for N₂O direct decomposition and more importantly, theoretical analysis addressed the issue of activation barriers for the first and second N₂O decompositions and oxygen molecule formation. Thus, the present oxotitanium porphyrin catalyst for deN₂O with/without water molecule can be compared with the Fe-ZSM5 zeolite [27] to elucidate the catalytic potential and the effect of water. In

Table 2. Activation energy (kcal/mol) of the first and second N₂O decompositions and oxygen formation over the Fe-ZSM5 and oxotitanium(IV) porphyrin.

Process	Activation Energy (kcal/mol)
	Z−[FeO]+ a	Z−[Fe(OH)2] + a	3TiO-por b	3Ti(OH)2-por
1st N2O	30.4	42.8	29.9	27.6
2nd N2O	20.1	61.7	11.5	12.4
O2 formation	8.0	16.0	0.6	barrier less

^a Ref [27], ^b Ref [41].

, a comparison has been made between the Fe-ZSM5 zeolite catalysts with and without water in the N₂O decomposition, and these are represented by Z⁻[FeO]⁺ and Z⁻[Fe(OH)₂]⁺ active sites, respectively. It is clear that the Z⁻[Fe(OH)₂]⁺ active sites result in higher activation barriers to decompose the N₂O and form oxygen. Comparing oxotitanium porphyrin with and without water molecule represented by ³Ti(OH)₂-por and ³TiO-por, [41] respectively, the N₂O decomposition over the ³Ti(OH)₂-por results in similar activation barriers as the ³TiO-por active site [41]. In addition, these trends are also seen in the singlet state of oxotitanium porphyrin in this work. These results imply that the hydroxyl site of oxotitanium porphyrin produced by water dissociation does not increase the activation energy barrier for deN₂O, whereas the Z⁻[Fe(OH)₂]⁺ catalyst shows a significant increase in the activation energy barriers for the first and second N₂O decompositions and the desorption energy of the oxygen molecule.

For the photo-assisted reaction, which is the main target in this work, the presence of water molecule on the active site of oxotitanium porphyrin has been intensively examined, to get a thorough view of the catalytic activity for N₂O decomposition, as displayed the overall reaction pathway in Scheme 1. In the absence of water [41], the first N₂O directly decomposes into N₂ product and ³TiO₂-por intermediate forms. The first N₂O adsorption on the TiO-por active site is −5.71 kcal/mol with activation energy barrier of 35.37 kcal/mol, it is worth mentioning that these energies do not include the zero-point energy (ZPE) correction [41]. In this reaction with presence of water, water molecule adsorption on the ³TiO-por site (−7.57 kcal/mol) is stronger than the N₂O molecule. The water molecule more favorably covers the catalyst surface and generates the hydroxyl active site ³Ti(OH)₂-por. Over ³Ti(OH)₂-por active sites, the N₂O adsorption energy is −4.94 kcal/mol and the calculated energy barrier to decompose the N₂O is 27.57 kcal/mol. These results mean that the N₂O decomposition is not inhibited by the presence of water at the active site ³Ti(OH)₂-por. On the other hand, water molecules seem to act as an assisting reagent in the N₂O decomposition, as it can easily desorb after the N₂O decomposition process. Therefore, the TiO-por is proposed as a candidate catalyst for photo-assisted N₂O decomposition even under aqueous condition.

3. Computational Details

Nitrous oxide decomposition on the TiO-por model system was considered in the ground and excited states. The reaction pathways were calculated with the DFT method using the M06-L functional [48,49], in which full geometry optimization was performed without any geometrical restriction. To simulate the lowest lying excited state potential energy surface which represents the reaction under photo-irradiation, we adopted the unrestricted DFT (UM06L) method for triplet state calculation. The unrestricted DFT method is occasionally used for the calculations of photo-catalytic reactions [41,50,51]. The M06L functional has been examined with some variants of the coupled clusters [52,53] and other DFT functionals for systems including metals [52,53,54]. Although the energy barrier is sometimes underestimated, it works well in comparison with other global hybrid functionals. A basis set of double zeta plus polarization, i.e., 6-31G(d,p) was adopted for C, O, N, and H atoms, and the relativistic effective core potential of Hay–Wadt (LANL2DZ) was used for the Ti atom. All calculations were carried out with the Gaussian09 suite of programs Rev. B01 [55].

For the deNO_x simulation, H₂O and N₂O gases were used as the reactants. We considered both singlet and triplet spin states to simulate the reactions under thermal and photo-assisted conditions, respectively, the latter of which is assumed to be continuous photo-excitation with a considerable lifetime in the excited state without radiative or nonradiative decay. A vibrational analysis was done at each stationary point; all the intermediates were confirmed as true local minima and the transition states were first-order saddle points with only one imaginary frequency. The reaction energy profiles in terms of electronic with ZPE correction were calculated. The energy profile at each step was presented in the relative energy, which is defined as

$$\Delta E=E_{complex}-\left(E_{catalyst}+E_{adsorbate}\right)$$

(9)

where $E_{complex}$, $E_{catalyst}$, and $E_{adsorbate}$ are the total energies of the catalyst-adsorbate complex, the starting TiO-por complex at each step, and the isolated reactant molecules, respectively. The negative (positive) value indicates the stable (unstable) adsorption complex relative to the isolated systems.

4. Conclusions

The elementary reactions of N₂O decomposition over the oxotitanium porphyrin under thermal and photo-assisted conditions in the presence of water have been examined using DFT method with the unrestricted M06L/6-31G(d, p) level of theory. The potential energy profiles show that the entire reaction is an exothermic process. The reaction steps of N₂O decomposition over hydroxyl-oxotitanium porphyrin can be summarized as follows. For the first N₂O decomposition, the N–O bond dissociation over the Ti(OH)₂-por intermediate is the rate-determining step and requires an activation energy of 27.57 kcal/mol. Then, a spontaneous process of releasing the H₂O from the TiO(OH)₂-por catalyst intermediates is the preferable route, as examined in Path B, and the second N₂O decomposition over the TiO₂-por requires a lower activation energy of 12.37 kcal/mol than the first one. In the last step of catalyst regeneration, the O₂ formation from the TiO₃-por intermediate is a spontaneous process with a barrierless activation energy and a desorption energy of oxygen molecule only 4.96 kcal/mol, which is an advantage of this kind of catalyst.

Therefore, from this theoretical investigation, it is worth noting that the presence of water does not inhibit the N₂O decomposition on the catalyst surface. As a final note, the exhaust gas contains various compounds such as H₂O, O₂, N_xO_y, CO₂, and therefore, a theoretical study on the N₂O decomposition reaction needs to consider the effect of other gases in the reaction mechanism as well. The comprehensive study of overall reaction mechanism, which involves all effects, will be useful to guide experimental catalyst development for deN₂O applications.