Catalytic Reaction Mechanism of NO–CO on the ZrO2 (110) and (111) Surfaces

Due to the large population of vehicles, significant amounts of carbon monoxide (CO), nitrogen oxides (NOx), and unburned hydrocarbons (HC) are emitted into the atmosphere, causing serious pollution to the environment. The use of catalysis prevents the exhaust from entering the atmosphere. To better understand the catalytic mechanism, it is necessary to establish a detailed chemical reaction mechanism. In this study, the adsorption behaviors of CO and NO, the reaction of NO reduction with CO on the ZrO2 (110) and (111) surfaces was performed through periodic density functional theory (DFT) calculations. The detailed mechanism for CO2 and N2 formation mainly involved two intermediates N2O complexes and NCO species. Moreover, the existence of oxygen vacancies was crucial for NO reduction reactions. From the calculated energy, it was found that the pathway involving NCO intermediate interaction occurring on the ZrO2 (110) surface was most favorable. Gas phase N2O formation and dissociation were also considered in this study. The results indicated the role of reaction intermediates NCO and N2O in catalytic reactions, which could solve the key scientific problems and disputes existing in the current experiments.


Introduction
Heterogeneous catalysis always be used to decrease the emission of automobile exhausts (CO, NO x and HC), such as the Rhodium catalytic system to convert toxic gas NO to inactive product N 2 [1,2]. However, the rare and expensive characteristics of noble metal Rh limit its widespread use. Thus, quantities of investigations have been conducted to develop effective and economical catalyst systems.
As zirconium dioxide (ZrO 2 ) has high thermal stability, excellent redox properties and an acid-basic site on its surface, it is a good catalyst and support material for various reactions, such as CO 2 methanation [3,4], water-gas shift [5,6], NH 3 selective catalytic reduction [7,8], and hydrodeoxygenation [9,10]. Especially, the transition metal oxide dispersed onto the surface of ZrO 2 exhibits powerful activity for NO reduction. Okamoto et al. [11] found that Cu/ZrO 2 catalysts showed high NO conversion to N 2 at low temperature through a nitrous oxide (N 2 O) intermediate for a NO-CO reaction. As the supporter, ZrO 2 has better performance than CeO 2 in reducing the energy barrier of NO dissociation [12]. Besides, ZrO 2 also provides abundant NO x adsorption sites [13][14][15], which is beneficial for NO reduction. Koga et al. discovered that c-ZrO 2 (110) ultrathin film covering a Cu surface exhibited high NO x reduction activity [16].
NO reduction by CO may simultaneously eliminate two kinds of pollutants and convert them into harmless CO 2 and inactive N 2 , via the stoichiometric reaction 2CO + 2NO → 2CO 2 + N 2 . Dramatically, Int. J. Mol. Sci. 2019, 20, 6129 2 of 14 isocyanate (NCO) species and gas phase N 2 O were detected via experimental equipment during the reaction of NO with CO [17,18]. NO-CO reaction mechanisms involving NCO and N 2 O as intermediate complex have been considered on Co 3 O 4 (110)-B [19], Pd/γ-Al 2 O 3 (110) [20], and Cu-doped SrTiO 3 (100) [21] catalyst surfaces. It is widely believed that CO abstracts lattice oxygen of catalyst to produce CO 2 and oxygen vacancy through the Mars-van Krevelen mechanism [22], and then NO reduction occur on the defective catalyst surface via NCO or N 2 O intermediate species to form N 2 . Although previous studies have provided significant insight on NO-CO catalytic reaction mechanism, the catalytic cycle paths of NO reduction by CO on ZrO 2 surfaces remain elusive.
Surface formation energies of three low-index c-ZrO 2 (100), (110) and (111) were computed, as shown in Table S1. In this study, we adopted the most stable surface (111) and a relatively reactive surface (110) as the exposed surfaces. The adsorption behaviors of CO and NO on ZrO 2 (110) and (111) surfaces and possible reaction pathways for CO 2 and N 2 formation with corresponding energy evolution were carefully discussed based on DFT calculations. Through in-depth analysis and research, the role of reaction intermediates NCO and N 2 O in catalytic reactions will be clarified, which can solve the key scientific problems and disputes existing in the current experiments.

CO and NO Adsorption on ZrO 2 (110) Surface
The structure models of ZrO 2 (110) surface, as shown in Figure 1a, exposes threefold coordinated O (O 3c ) and sixfold coordinated Zr (Zr 6c ) atoms. In the surface, the Zr-Zr bond distance is 3.710 Å and the Zr-O bond distance is 2.247 Å. The lattice constant of ZrO 2 bulk is 5.115 Å, which is in good agreement with experimental result of 5.090 Å [23].
Three adsorption sites were considered (  Table 1 lists all the value of E ads . 2 NO reduction by CO may simultaneously eliminate two kinds of pollutants and convert them into harmless CO2 and inactive N2, via the stoichiometric reaction 2CO + 2NO → 2CO2 + N2. Dramatically, isocyanate (NCO) species and gas phase N2O were detected via experimental equipment during the reaction of NO with CO [17,18]. NO-CO reaction mechanisms involving NCO and N2O as intermediate complex have been considered on Co3O4 (110)-B [19], Pd/γ-Al2O3 (110) [20], and Cu-doped SrTiO3 (100) [21] catalyst surfaces. It is widely believed that CO abstracts lattice oxygen of catalyst to produce CO2 and oxygen vacancy through the Mars-van Krevelen mechanism [22], and then NO reduction occur on the defective catalyst surface via NCO or N2O intermediate species to form N2. Although previous studies have provided significant insight on NO-CO catalytic reaction mechanism, the catalytic cycle paths of NO reduction by CO on ZrO2 surfaces remain elusive.
Surface formation energies of three low-index c-ZrO2 (100), (110) and (111) were computed, as shown in Table S1. In this study, we adopted the most stable surface (111) and a relatively reactive surface (110) as the exposed surfaces. The adsorption behaviors of CO and NO on ZrO2 (110) and (111) surfaces and possible reaction pathways for CO2 and N2 formation with corresponding energy evolution were carefully discussed based on DFT calculations. Through in-depth analysis and research, the role of reaction intermediates NCO and N2O in catalytic reactions will be clarified, which can solve the key scientific problems and disputes existing in the current experiments.

CO and NO Adsorption on ZrO2 (110) Surface
The structure models of ZrO2 (110) surface, as shown in Figure 1a, exposes threefold coordinated O (O3c) and sixfold coordinated Zr (Zr6c) atoms. In the surface, the Zr-Zr bond distance is 3.710 Å and the Zr-O bond distance is 2.247 Å . The lattice constant of ZrO2 bulk is 5.115 Å , which is in good agreement with experimental result of 5.090 Å [23].
Three adsorption sites were considered (

Gas Molecule
Adsorption Site E ads (eV) Figure   CO C-end As shown in Figure 1, after fully structural optimization, CO (C-end and O-end) and NO (N-end and O-end) gas molecules preferred to adsorb on Zr T site of ZrO 2 (110) surface. As for CO molecule adsorption, E ads of CO (C-end and O-end) adsorbed on Zr T site was −0.676 eV and −0.360 eV, respectively, indicating the C-end adsorption was more energetically favorable than O-end. In the same way NO N-end adsorption was more stable than NO O-end adsorption on ZrO 2 (110) surfaces. Coordinates for all the optimized structures were presented in Table S3.

Path 1
The Mars−van Krevelen (MvK) mechanism is a universal reaction step for CO oxidation [24] and NO-CO reaction [19] on metal oxide surfaces. As shown in Figure 2, the NO-CO catalytic cycle reaction started when the first CO gas molecule adsorbed on Zr T site (state ii) with an adsorption energy of −0.676 eV, and with the change of lattice O-C distance to 3.098 Å. After adsorption, CO extracted surface oxygen atom to form CO 2 and a surface oxygen vacancy (state iii) through the MvK mechanism. In the corresponding transition state (TS1), the lattice O-CO bond decreased to 1.568 Å and the lattice O-C-O angle changed to 116.105 • . Moreover, the energy barrier for this process was 1.948 eV, the result clearly shows that CO oxidation reaction can happen smoothly on ZrO 2 (110) surface by using exhaust temperature. We calculated two cycle reaction mechanisms (path 1 and path 2) and N 2 O formation mechanism all share common steps to form oxygen vacancies on ZrO 2 (110) surface.
In the next step, CO 2 desorption into the gas phase (state iv) costs energy of 0.283 eV, then O V was occupied by the first NO gas molecule forming a O V -NO complex structure (state v), and the energy of 2.310 eV is released. Subsequently, the next CO weakly adsorbed to adjacent O atom of the NO (state vi) with an adsorption energy of −0.510 eV. In TS2, the N-O bond broke and O atom moved toward CO to form OC-O bond by overcoming an energy barrier of 2.263 eV, and the OC-O bond length was changed from 2.683 Å at state vi to 1.637 Å. After TS2, the second CO 2 molecule formation occurs (state vii). The reaction was exothermic by 1.246 eV. The similar reaction steps have been explored for Pd/γ-Al 2 O 3 (110), the second CO abstracted lattice O atom from N-loaded Pd/γ-Al 2 O 3 (110) surface with an energy barrier of 1.88 eV [20].
3 mechanism. In the corresponding transition state (TS1), the lattice O-CO bond decreased to 1.568 Å and the lattice O-C-O angle changed to 116.105°. Moreover, the energy barrier for this process was 1.948 eV, the result clearly shows that CO oxidation reaction can happen smoothly on ZrO2 (110) surface by using exhaust temperature. We calculated two cycle reaction mechanisms (path 1 and path 2) and N2O formation mechanism all share common steps to form oxygen vacancies on ZrO2 (110) surface. Then, the second CO 2 desorbed into the gas phase leaving a N-doped surface (state vii), in which N atom embedded at surface oxygen vacancy site. The desorption energy of CO 2 is approximately 0.3 eV, the interaction of ZrO 2 surface with CO 2 was much weaker than that with NO (E ads ≈ 0.7 eV), which have been reported by Luo et al. [13]. After the second CO 2 desorption, the second NO gas molecule located at N-doped ZrO 2 (110) surface (state ix) with the binding energy of −0.068 eV. Once NO interacted with the embedded N atom, formation of a relatively stable intermediate complex bent N 2 O (state x) was very easy. As we can see from the energy profile ( Figure 2), the process could facilely occur without energy barrier and release 3.286 eV energy. The energy barrier for N 2 O dissociation was extremely low only 0.002 eV. After TS3, N-O bond and N-Zr bond dissociated to produce N 2 (state xi), then N 2 desorption into gas phase cost 0.458 eV, O atom successively diffused to oxygen vacancy site via an obvious barrierless process with releasing energy of 0.510 eV, the integrated ZrO 2 (110) surface was recovered eventually.
Accordingly, from calculated energy profile (Figure 2), the overall catalytic cycle is strongly exothermic. However, the second CO oxidation has greater activation energy of 2.263 eV, determining the rate of catalytic cycle. We proposed the other catalytic cycle path to produce CO 2 and N 2 via NCO species.

Path 2
As presented in Figure 3, the reaction mechanism of O V surface formation is shared with path 1. Subsequently, NO adsorbed on O V site, the value of NO O-end adsorption was −1.605 eV, which bound weaker than that of NO N-end. Then, the second CO directly combined with N atom to generate the NCO intermediate (−1.614 eV, state vi). The second NO adsorbed on Zr T site adjacent to NCO complex (−0.208 eV, state vii). In the co-adsorption configuration, NCO and NO moved toward each other via TS2 to form a NNCO 2 four-membered ring intermediate (state viii) with an energy barrier of 0.355 eV. The subsequent step was NNCO 2 intermediate dissociation to produce N 2 and CO 2 (state ix) with a barrier of only 0.141 eV. With N 2 and CO 2 desorption by costing 0.563 eV energy, the catalytic surface was recovered. As we can see from the energy profile (Figure 3), the rate-determining step is the CO oxidation by the lattice oxygen, indicting ZrO2 (110) surface exhibits weakly catalytic activity for low-temperature oxidation of CO. Liang et al. observed that c-ZrO2 ultrafine powder showed relatively high activity for CO oxidation with light-off temperature at ~280 °C (50% conversion) and ~550 °C (100% conversion) [25,26]. As reported in the literature, metal doping was particularly effective for the formation of oxygen vacancy [21,27]. As for NO reduction reaction, the formation of oxygen vacancy is crucial for NO adsorption and reduction reaction [28][29][30]. On defective ZrO2 (110) surface, NO decomposition and N2 formation are occur easily as a result of a very small barrier of 0.355 eV via path 2. Although for the defective Co3O4 (110)-B surface [19], the most favorable NO reduction processes are energetically less competitive with a higher barrier of 1.48 eV, i.e., the ZrO2 (110) surface is remarkable for NO reduction.

N2O formation.
Beginning with the oxygen vacancy surface (state iv, Figure 4) the first gas NO molecule located at OV site (state v, Figure 4) by releasing 1.605 eV energy, the second incoming NO molecule N-end bound with surface N atom (state vi, Figure 4) with strong exothermicity of 2.872 eV. Subsequently, the ONN-O bond broke into N2O via TS2 (Figure 4). After TS2, the gas-phase N2O (state vii, Figure 4) formation, the barrier for the process was 0.987 eV, the reaction was exothermic by 1.345 eV. Eventually, N2O desorption into the gas phase (state viii, Figure 4) cost 0.456 eV and ZrO2 (110) surface recovered. As we can see from the energy profile (Figure 3), the rate-determining step is the CO oxidation by the lattice oxygen, indicting ZrO 2 (110) surface exhibits weakly catalytic activity for low-temperature oxidation of CO. Liang et al. observed that c-ZrO 2 ultrafine powder showed relatively high activity for CO oxidation with light-off temperature at~280 • C (50% conversion) and~550 • C (100% conversion) [25,26]. As reported in the literature, metal doping was particularly effective for the formation of oxygen vacancy [21,27]. As for NO reduction reaction, the formation of oxygen vacancy is crucial for NO adsorption and reduction reaction [28][29][30]. On defective ZrO 2 (110) surface, NO decomposition and N 2 formation are occur easily as a result of a very small barrier of 0.355 eV via path 2. Although for the defective Co 3 O 4 (110)-B surface [19], the most favorable NO reduction processes are energetically less competitive with a higher barrier of 1.48 eV, i.e., the ZrO 2 (110) surface is remarkable for NO reduction.

N 2 O formation.
Beginning with the oxygen vacancy surface (state iv, Figure 4) the first gas NO molecule located at O V site (state v, Figure 4) by releasing 1.605 eV energy, the second incoming NO molecule N-end bound with surface N atom (state vi, Figure 4) with strong exothermicity of 2.872 eV. Subsequently, the ONN-O bond broke into N 2 O via TS2 (Figure 4). After TS2, the gas-phase N 2 O (state vii, Figure 4) formation, the barrier for the process was 0.987 eV, the reaction was exothermic by 1.345 eV. Eventually, N 2 O desorption into the gas phase (state viii, Figure 4) cost 0.456 eV and ZrO 2 (110) surface recovered. In cold start engines or lean-burn conditions N2O is the main by-product of NO reduction [31], and the formation of N2O on ZrO2 surface has been observed through NO temperature-programmed desorption experiment [13]. N2O is one of the six greenhouse gases specified in the Kyoto Protocol, the greenhouse activity is 310 times of CO2 [32]. Catalytic systems for N2O decomposition should be employed in catalytic converters.
Three reaction pathways have been calculated on the ZrO2 (110) surface: the gas phase N2O was observed via experimental equipment and in [18] it was also formed by theoretical calculation; our work provides the mechanism of N2O formation. Path 1 involving bent N2O intermediate was proposed to produce harmless CO2 and inactive N2, this cycle had a relatively high barrier than path 2 involving surface NCO intermediate, indicting CO2 and N2 formation mainly through path 2. Besides, the activation barriers for N2O and N2 formation on OV-ZrO2 (110) surface were 0.987 eV and 0.355 eV, respectively. The results imply that NO is selectively converted to N2 versus N2O under mild conditions.
In Figure 5   In cold start engines or lean-burn conditions N 2 O is the main by-product of NO reduction [31], and the formation of N 2 O on ZrO 2 surface has been observed through NO temperature-programmed desorption experiment [13]. N 2 O is one of the six greenhouse gases specified in the Kyoto Protocol, the greenhouse activity is 310 times of CO 2 [32]. Catalytic systems for N 2 O decomposition should be employed in catalytic converters.
Three reaction pathways have been calculated on the ZrO 2 (110) surface: the gas phase N 2 O was observed via experimental equipment and in [18] it was also formed by theoretical calculation; our work provides the mechanism of N 2 O formation. Path 1 involving bent N 2 O intermediate was proposed to produce harmless CO 2 and inactive N 2 , this cycle had a relatively high barrier than path 2 involving surface NCO intermediate, indicting CO 2 and N 2 formation mainly through path 2. Besides, the activation barriers for N 2 O and N 2 formation on O V -ZrO 2 (110) surface were 0.987 eV and 0.355 eV, respectively. The results imply that NO is selectively converted to N 2 versus N 2 O under mild conditions.

Path 1'
Based on the lowest energy structures of CO and NO on ZrO2 (111) surface, the first step was gas-phase CO interaction with surface Zr atom (−0.410 eV, state ii), as shown in Figure 6, CO may incorporate lattice O via TS1 where the distance between CO molecule and O atoms was decreased from 2.787 Å to1.246 Å . After TS1, a gas phase CO2 molecule (state iii) formed. The energy barrier was equivalent to 2.949 eV. Next, CO2 overcame 0.130 eV binding energy desorption into gas-phase. Specifically, the following path 1' and N2O formation mechanisms share as common steps as discussed above.  For the adsorption behavior of CO (C-end and O-end) and NO (N-end and O-end) on ZrO 2 (111) surface, we again researched that the Zr T site was the most favorable adsorption site; the CO C-end adsorbed on Zr T site had maximum adsorption energy −0.788 eV, which suggested that CO C-end adsorption was slightly preferred on ZrO 2 (111) surface. Moreover, NO O-end adsorption was thermodynamically impossible, because of the positive E ads .

Path 1'
Based on the lowest energy structures of CO and NO on ZrO 2 (111) surface, the first step was gas-phase CO interaction with surface Zr atom (−0.410 eV, state ii), as shown in Figure 6, CO may incorporate lattice O via TS1 where the distance between CO molecule and O atoms was decreased from 2.787 Å to1.246 Å. After TS1, a gas phase CO 2 molecule (state iii) formed. The energy barrier was equivalent to 2.949 eV. Next, CO 2 overcame 0.130 eV binding energy desorption into gas-phase. Specifically, the following path 1' and N 2 O formation mechanisms share as common steps as discussed above.  Note that the energy barrier corresponding to TS1 (2.949 eV, Figure 6) is evidently high and oxygen vacancy formation on ZrO 2 (111) surface is difficult at low-temperature. Once oxygen vacancy formation on ZrO 2 (111) surface, NO adsorption and reduction are facile.
In state v, the NO molecule N-end was located at O V site with a strong exothermicity of 2.923 eV.

2.4.3.Mechanism involving N2O
The formation process of N2O was same as the case found on ZrO2 (110) surface. The second NO bonded with N atom of first adsorbed NO. With the N-O and N-Zr bond dissociation, N2O formation. The energy profile and corresponding structure models of reactant, transition state and product were illustrated in Figure 8.  . Energy profile (a) and structure models (b) of reactants, transition states, and products for N2O formation on ZrO2 (111) surface. The energy profile is placed above, and structure models are placed below.
As N2O is a hazardous by-product, its decomposition processes have been conducted on transition metal surfaces [33,34]. Following with the decomposition mechanism of N2O on Pd-OV/γ-Al2O3 (110) surface proposed by Gao [20]. We calculated N2O decomposition process on OV-ZrO2 (111) surface, as shown in Figure 9. The binding energy of N2O adsorption was equivalent to −0.166 eV, in the corresponding transition state the N-O bond length increased from 1.195 Å to 1.288 Å . By breaking the already activated N-O bond, the desired product N2 was formed and the dissociated O atom filled the OV. The reaction barrier for N2O decomposition is 0.288 eV, and the N2 desorption from the ZrO2 (111) surface requires 0.128 eV. As N 2 O is a hazardous by-product, its decomposition processes have been conducted on transition metal surfaces [33,34]. Following with the decomposition mechanism of N 2 O on Pd-O V /γ-Al 2 O 3 (110) surface proposed by Gao [20]. We calculated N 2 O decomposition process on O V -ZrO 2 (111) surface, as shown in Figure 9. The binding energy of N 2 O adsorption was equivalent to −0.166 eV, in the corresponding transition state the N-O bond length increased from 1.195 Å to 1.288 Å. By breaking the already activated N-O bond, the desired product N 2 was formed and the dissociated O atom filled the O V . The reaction barrier for N 2 O decomposition is 0.288 eV, and the N 2 desorption from the ZrO 2 (111) surface requires 0.128 eV.
From calculated energy barriers, we found that CO oxidation by surface lattice oxygen was the rate-determining step during the process of NO reduction with CO, the reaction barriers were 1.948 eV and 2.949 eV on ZrO 2 (110) and (111) surfaces, respectively. The results indicated that compared with ZrO 2 (111) surface, ZrO 2 (110) surface had more remarkable ability to catalyze NO reduction with CO because of the lower activation barrier. From the calculated adsorption energies, CO and NO all preferred to adsorb on ZrO 2 (110) surface, which is consistent with the results of surface formation energies for (110) surface was relatively reactive than (111) surface. For the reaction mechanism of NO reduction by CO, similar reaction processes were found on ZrO 2 (110) and (111) surfaces. Intermediate complex bent N 2 O was produced during path 1, path 1' and → NCO intermediate was produced during path 2, path 2', hazardous N 2 O gas molecule was formed both on ZrO 2 (110) and (111) surfaces. Figure 9. Energy profile (a) and structure models (b) of reactants, transition states and products for N2O adsorb on oxygen vacancy ZrO2 (111) surface to generate N2 (g). The energy profile is placed above, and structure models are placed below.
From calculated energy barriers, we found that CO oxidation by surface lattice oxygen was the rate-determining step during the process of NO reduction with CO, the reaction barriers were 1.948 eV and 2.949 eV on ZrO2 (110) and (111) surfaces, respectively. The results indicated that compared with ZrO2 (111) surface, ZrO2 (110) surface had more remarkable ability to catalyze NO reduction with CO because of the lower activation barrier. From the calculated adsorption energies, CO and NO all preferred to adsorb on ZrO2 (110) surface, which is consistent with the results of surface formation energies for (110) surface was relatively reactive than (111) surface. For the reaction mechanism of NO reduction by CO, similar reaction processes were found on ZrO2 (110) and (111) surfaces. Intermediate complex bent N2O was produced during path 1, path 1' and NCO intermediate was produced during path 2, path 2', hazardous N2O gas molecule was formed both on ZrO2 (110) and (111) surfaces.

Materials and Methods
Periodic DFT calculations were executed using DMol 3 module of Material Studio software package [35,36]. The exchange-correlation functional was treated by generalized gradient approximation with the Perdew-Wang 91 (GGA-PW91) [37]. The double numerical plus d-functions (DND) basis set was used to optimize all spin unrestricted structures. SCF tolerance was employed to 1.0 × 10 −5 , the convergence tolerance of maximum energy change, maximum force, and maximum displacement were set as 2.0 × 10 −5 Ha, 0.004 Ha/Å , and 0.005 Å , respectively. The transition states (TS) were calculated with linear synchronous transit (LST) and quadratic synchronous transit (QST) method [38,39] and vibrational analysis was performed to identify TS have only one imaginary frequency.
The slab models of ZrO2 (110) and (111) surfaces were built with a 15-20 Å vacuum thickness to avoid interaction between neighboring slabs. The ZrO2 (110) surface consisting of four atomic layers with the lowest two layers being kept fixed in their bulk positions, whereas the others were allowed to relax with adsorbed molecules. The Brillouin zone was sampled with a (1 × 2 × 1) Monkhorst-Pack k-point grid [40]. The ZrO2 (111) surface consisting of six atomic layers with the bottom four layers were kept fixed and the top two layers were relaxed. A (2 × 2 × 1) Monkost-Pack grid [40] for the Figure 9. Energy profile (a) and structure models (b) of reactants, transition states and products for N 2 O adsorb on oxygen vacancy ZrO 2 (111) surface to generate N 2 (g). The energy profile is placed above, and structure models are placed below.

Materials and Methods
Periodic DFT calculations were executed using DMol 3 module of Material Studio software package [35,36].
The exchange-correlation functional was treated by generalized gradient approximation with the Perdew-Wang 91 (GGA-PW91) [37]. The double numerical plus d-functions (DND) basis set was used to optimize all spin unrestricted structures. SCF tolerance was employed to 1.0 × 10 −5 , the convergence tolerance of maximum energy change, maximum force, and maximum displacement were set as 2.0 × 10 −5 Ha, 0.004 Ha/Å, and 0.005 Å, respectively. The transition states (TS) were calculated with linear synchronous transit (LST) and quadratic synchronous transit (QST) method [38,39] and vibrational analysis was performed to identify TS have only one imaginary frequency.
The slab models of ZrO 2 (110) and (111) surfaces were built with a 15-20 Å vacuum thickness to avoid interaction between neighboring slabs. The ZrO 2 (110) surface consisting of four atomic layers with the lowest two layers being kept fixed in their bulk positions, whereas the others were allowed to relax with adsorbed molecules. The Brillouin zone was sampled with a (1 × 2 × 1) Monkhorst-Pack k-point grid [40]. The ZrO 2 (111) surface consisting of six atomic layers with the bottom four layers were kept fixed and the top two layers were relaxed. A (2 × 2 × 1) Monkost-Pack grid [40] for the ZrO 2 (111) surface geometry optimization. In all cases, an orbital cutoff of 5.0 Å was used to improve the computational performance and a 2 × 2 supercell was applied.
The adsorption energies (E ads ) of CO and NO gas molecules on ZrO 2 (110) and (111) surfaces were calculated by the following formula, E ads = E (surface + gas molecules) − E (surface) − E (gas molecules) (1) where E (surface + gas molecules) is the total energy of the system involving the ZrO 2 (110) or (111) catalyst with the adsorbed CO or NO gas molecule, E (surface) is the total energy of isolated ZrO 2 (110) or (111) surface, and E (gas molecules) is the total energy of a single CO or NO gas molecule.
To validate the methods, we calculated the energy of NO, CO, N 2 and CO 2 molecules in a large unit cell of 10 Å × 10 Å × 10 Å, and compared the bond distances with the values calculated at the B3LYP/6-31G(d) level [41]. We listed all the values in Table S2, the calculated bond distances were within 1% of ones.

Conclusions
In summary, DFT calculations were performed to investigate NO reduction with CO on ZrO 2 (110) and (111) surfaces. For the ZrO 2 (110) surface, two cycle reaction pathways (paths 1 and 2) for CO 2 and N 2 formation were presented, and the path 2 involving the process of the NCO intermediate interaction with NO was energetically favorable. The similar cycle reaction pathways (paths 1' and 2') were found on ZrO 2 (111) surface, but CO oxidation by lattice O had a significantly higher energy barrier of 2.949 eV. The results indicated that compared with ZrO 2 (111) surface, ZrO 2 (110) surface had more remarkable ability to catalyze NO reduction with CO. Our calculations also clearly showed that the existence of oxygen vacancies on ZrO 2 (110) and (111) surfaces were crucial for NO adsorption and reduction reaction. NO healing O V was a strongly exothermic process (2.0-3.0 eV) and successive reactions all exhibited lower energy barriers, especially path 2 (0.355 eV) and path 1' (0.405eV). The mechanism involving N 2 O also was explored, and the activation barriers for N 2 O formation on O V -ZrO 2 (110) and (111) were 0.987 eV and 0.515 eV, respectively. The relatively higher barriers imply that NO is selectively converted to N 2 versus N 2 O under mild conditions. Supplementary Materials: Supplementary materials can be found at http://www.mdpi.com/1422-0067/20/24/ 6129/s1. Author Contributions: Conceptualization, C.Z. and X.S.; methodology, X.C. and Z.W.; software, X.C. and Z.W.; validation, X.S.; formal analysis, X.C. and Z.W.; investigation, C.Z. and X.S.; resources, X.S.; data curation, X.C.; writing-original draft preparation, X.C.; writing-review and editing, C.Z. and X.S.; supervision, X.S.; project administration, C.Z. and X.S.; funding acquisition, C.Z. and X.S.