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

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.


Introduction
Nitrous oxide (N 2 O) 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 N 2 O 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 N 2 O (deN 2 O) has attracted much attention because of its efficiency and cost effectiveness [2][3][4][5]. Researches in the field of N 2 O catalytic decomposition mainly focus on low-temperature deN 2 O catalysts that can be applied to N 2 O abatement in medical operating rooms, nitric acid plants, three-way catalytic converters, etc. For example, N 2 O 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 deN 2 O of the air contaminated with N 2 O in operating rooms by varying the alumina-supported metals (Pt, Pd, or Rh), and found that the Rh/Al 2 O 3 is the most suitable catalyst for deN 2 O in operating rooms which could reach 100% decomposition at 773K.
Their transient experiments showed that the N 2 O conversion dropped to zero in the presence of SO 2 and H 2 O [23,24]. In addition, there have been reports of various catalysts which show that their catalytic performance of deN 2 O 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 N 2 O 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 deN 2 O 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 deN 2 O, photo-assisted direct decomposition is another alternative method for N 2 O 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 N 2 O. In general, N 2 O is decomposed into N 2 and O 2 under a photocatalytic reaction [32] by The well-accepted photo-catalyst for N 2 O decomposition is TiO 2 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 N 2 O 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 deN 2 O 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 deN 2 O. In this work, we theoretically investigated the reaction mechanism of deN 2 O with the TiO-por catalyst by using density functional theory (DFT), and included a water molecule at the active site, and studied O 2 desorption as well.

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 N 2 O decomposition over the TiO-por into four elementary steps as follows.
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. 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 ( 3 TiO-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 3 TiO-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.

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. Step 1: Water-complex formation on TiO-por Step 2: First N 2 O decomposition Step 3-A: Second N 2 O decomposition followed by water desorption (Path A) Step Step 4: Catalyst regeneration; oxygen formation and desorption TiO 3 -por → TiO-por + O 2 (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. Based on the pairwise comparison, it can be clearly seen that in the overall reaction processes of N 2 O direct decomposition in the photo-assisted condition, TiO-por ( 3 TiO-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 N 2 O 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 N 2 O 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 N 2 O decomposition reaction. The spin density plot of the 3 TiO-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.

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.

barrierless
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.  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.

First N 2 O Decomposition
After water dissociation and formation of Ti(OH) 2 (IN1), the first N 2 O decomposition proceeds. The reaction profile consists of four stationary points: N 2 O adsorption, first transition state, N 2 production, and N 2 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

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.

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

Second N 2 O Decomposition
Two possible routes, Path A and Path B, were examined for the second N 2 O decomposition. Path A is the case where the second N 2 O is decomposed before water desorption. Alternatively, a water molecule is desorbed before the second N 2 O decomposition in Path B.
Path   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.   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 IN4-1A and IN4-1B in both Path A and Path B, as shown in the last step of Figures 4 and 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].

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 (TS3A). 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 (TS4B). 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. In general, the rate-determining step of N 2 O direct decomposition is desorption of the produced O 2 from the catalysts. The O 2 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 O 2 is formed over the TiO 3

intermediate of IN4-1 A and IN4-1 B in both Path A and Path B, as shown in the last step of Figures 4 and 5, respectively. It is worth noting that O 2 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 O 2 formation step is an extremely exothermic process. Therefore, it is shown that the TiO 3 -por catalyst intermediate easily regenerates the active TiO-por catalyst, which is an advantage of this catalyst, compared with the related zeolite catalysts for N 2 O decomposition [45,46].

Overall Energetics of Photo-Assisted N 2 O Decomposition over Hydroxyl-Oxotitanium Porphyrin Catalysts
The overall reaction energy profile of the water dissociation followed by N 2 O 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 N 2 O decomposition, the N 2 O 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 N 2 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, H 2 O formation follows the second N 2 O adsorption. The activation energy in this pathway is 29.01 kcal/mol (TS3 A ). In Path B, the water molecule releases prior to N 2 O decomposition. In Path B, the second N 2 O decomposition occurs with an energy barrier of 12.37 kcal/mol (TS4 B ). Therefore, the second N 2 O decomposition over the TiO 2 -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 N 2 O molecule in Step 2 is the rate-determining step, which correlates well with the N 2 O decomposition over Cu-ZSM5 [47]. It is worth to note that this present N 2 O direct decomposition reaction has total reaction energy approximately at −52.58 kcal/mol.

Scheme 1.
Overall reaction pathways of the photo-assisted N2O decomposition with/without a water molecule (the energy is in kcal/mol).

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, 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 3 Ti(OH)2-por and 3 TiO-

Scheme 1.
Overall reaction pathways of the photo-assisted N2O decomposition with/without a water molecule (the energy is in kcal/mol).

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, 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 3 Ti(OH)2-por and 3 TiO-Scheme 1. Overall reaction pathways of the photo-assisted N 2 O decomposition with/without a water molecule (the energy is in kcal/mol).

Effect of Water Molecule on the N 2 O Decomposition Barriers
On the pairwise comparison of the theoretical reaction mechanism for N 2 O decomposition with and without introducing H 2 O, 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 N 2 O direct decomposition and more importantly, theoretical analysis addressed the issue of activation barriers for the first and second N 2 O decompositions and oxygen molecule formation. Thus, the present oxotitanium porphyrin catalyst for deN 2 O 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, a comparison has been made between the Fe-ZSM5 zeolite catalysts with and without water in the N 2 O 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 N 2 O and form oxygen. Comparing oxotitanium porphyrin with and without water molecule represented by 3 Ti(OH) 2 -por and 3 TiO-por, [41] respectively, the N 2 O decomposition over the 3 Ti(OH) 2 -por results in similar activation barriers as the 3 TiO-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 deN 2 O, whereas the Z − [Fe(OH) 2 ] + catalyst shows a significant increase in the activation energy barriers for the first and second N 2 O 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 N 2 O decomposition, as displayed the overall reaction pathway in Scheme 1. In the absence of water [41], the first N 2 O directly decomposes into N 2 product and 3 TiO 2 -por intermediate forms. The first N 2 O 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 3 TiO-por site (−7.57 kcal/mol) is stronger than the N 2 O molecule. The water molecule more favorably covers the catalyst surface and generates the hydroxyl active site 3 Ti(OH) 2 -por. Over 3 Ti(OH) 2 -por active sites, the N 2 O adsorption energy is −4.94 kcal/mol and the calculated energy barrier to decompose the N 2 O is 27.57 kcal/mol. These results mean that the N 2 O decomposition is not inhibited by the presence of water at the active site 3 Ti(OH) 2 -por. On the other hand, water molecules seem to act as an assisting reagent in the N 2 O decomposition, as it can easily desorb after the N 2 O decomposition process. Therefore, the TiO-por is proposed as a candidate catalyst for photo-assisted N 2 O decomposition even under aqueous condition.

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, H 2 O and N 2 O 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 ∆E = E complex − E catalyst + E adsorbate (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.

Conclusions
The elementary reactions of N 2 O 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 N 2 O decomposition over hydroxyl-oxotitanium porphyrin can be summarized as follows. For the first N 2 O 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 H 2 O from the TiO(OH) 2 -por catalyst intermediates is the preferable route, as examined in Path B, and the second N 2 O decomposition over the TiO 2 -por requires a lower activation energy of 12.37 kcal/mol than the first one. In the last step of catalyst regeneration, the O 2 formation from the TiO 3 -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 N 2 O decomposition on the catalyst surface. As a final note, the exhaust gas contains various compounds such as H 2 O, O 2 , N x O y , CO 2 , and therefore, a theoretical study on the N 2 O 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 deN 2 O applications.