Insight into the Mechanism of CO Oxidation on WO3(001) Surfaces for Gas Sensing: A DFT Study

The mechanism of CO oxidation on the WO3(001) surface for gas sensing performance has been systematically investigated by means of first principles density functional theory (DFT) calculations. Our results show that the oxidation of CO molecule on the perfect WO3(001) surface induces the formation of surface oxygen vacancies, which results in an increase of the surface conductance. This defective WO3(001) surface can be re-oxidized by the O2 molecules in the atmosphere. During this step, the active O2− species is generated, accompanied with the obvious charge transfer from the surface to O2 molecule, and correspondingly, the surface conductivity is reduced. The O2− species tends to take part in the subsequent reaction with the CO molecule, and after releasing CO2 molecule, the perfect WO3(001) surface is finally reproduced. The activation energy barriers and the reaction energies associated with above surface reactions are determined, and from the kinetics viewpoint, the oxidation of CO molecule on the perfect WO3(001) surface is the rate-limiting step with an activation barrier of about 0.91 eV.


Introduction
Metal oxides are widely used as gas sensitive materials due to their reproducibility and typical surface properties which are suitable for gas detection. Tungsten trioxide (WO 3 ) is one of the most promising gas sensor candidates. Up to now, most studies have focused on the application of WO 3 in NO x sensors [1][2][3][4][5], while little attention has been paid to its use in sensors for other gases. Carbon monoxide (CO) is a toxic and environmentally-hazardous gas. More than 80% of the CO in the atmosphere comes from the imperfect combustion of carbonaceous materials and vehicle exhaust. With the development of the urban environment and increased auto use, it is necessary to detect the amount of CO to control the air quality, and the development of CO sensing materials has become an important subject of current research [6][7][8][9][10][11][12]. Owing to their advantages of wide detection range, good stability, long lifetime and rapid response, metal oxides are absolutely competitive candidate materials for CO detection [13][14][15]. However, the microscopic mechanism of the surface reactions underlying the sensing properties toward CO are still far from being understood, especially for the WO 3 -based sensor materials.
Before 2006, Azad et al. [16] reported that WO 3 has the sensitivity towards CO gas. Then Wu et al. [17] prepared a CoOOH-WO 3 type CO sensor. Their experimental results showed that such a composite sensing material produces a better CO response at 25 • C. A mechanism of CO sensing on this nanocomposite surface has been supposed based on the adsorption and desorption of CO molecules, as well as the surface oxidation reactions between adsorbed CO and adsorbed oxygen atoms. Hübner [18] and co-workers examined the sensing of CO with WO 3 -based gas sensors as a function of the oxygen background conditions, which attracted our great interest and attention. They recorded CO 2 formation when CO was exposed to the WO 3 surface in spite of a very low oxygen partial pressure. This phenomenon indicates that the CO oxidation by the metal oxide material, that is to say, the direct reduction of the WO 3 surface is the most possible cause for the decrease of surface resistivity, which is much different from the sensing mechanism observed in SnO 2 sensor materials. Moreover, they observed the defective surface was re-oxidized and the surface resistance increased when the oxygen partial pressure increased due to the fact that the O 2 molecules react with oxygen vacancies. Thus the magnitude of WO 3 sensor signal depends on the equilibrium between the generation of oxygen vacancies and their cancellation. Ahsan and co-workers [19] synthesized Fe-doped WO 3 thin films with good response to CO gas at 150 • C by a thermal evaporation method. Similarly to the findings above, the CO molecule is oxidized to CO 2 on this nanostructure surface, resulting in a drop in film resistance, and the active species for CO oxidization is assumed to be O 2 − .
Recently, a new-style WO 3 -based nanowire was successfully fabricated by Zappa's group as a CO detector [20]. They deduced the change of surface resistance on account of the balance between the adsorbed active oxygen species (O 2 − , O − or O 2− ) and their vanishing due to the chemical reaction with CO. Generally speaking, the resistivity change of the sensors is associated with the oxidation-reduction reaction of gas adsorbed on the sensor surface, so understanding the oxidation reaction of CO on the surface is a key to improve the sensing performance of the sensor material, and carrying out corresponding theoretical research at the molecular level is very necessary. However, compared with the experimental reports, theoretical publications in regard to CO sensing with WO 3 gas sensor are lacking so far. Most present theoretical works mainly focus on the adsorption behavior of CO at WO 3 surfaces [21], while few studies refer to the CO oxidation on the WO 3 surface for sensing. Oison et al. [22] investigated the CO adsorption condition on WO 3 film with and without redox reaction via ab initio calculations. On the basis of their calculations, the former is much more important for the sensing mechanism than the latter. The number of oxygen vacancies (V * O ) and surface conductivity increase when CO is oxidized to CO 2 on the WO 3 surface, which is in accordance with previous experimental results [18]. In recent studies, a series of first principle calculations have been performed by Tian's group [23,24]. Their results further confirm the significance of CO oxidation process for WO 3 sensing mechanism, and suggest that the existence of the oxygen vacancies decreased the sensitivity of WO 3 surface towards CO to some extent.
As a surface-controlled type semiconductor, WO 3 surface has many active sites. When the reduced CO gases approaches to the WO 3 sensor surface, they can be oxidized by the surface oxygen species, but perhaps also by the lattice oxygen atoms of WO 3 surface or the oxygen species from the chemisorbed oxygen molecules in the atmosphere. Meanwhile, the chemical reactions between CO and WO 3 surface are involved in the change of the oxygen vacancy concentration, which is directly related to the surface resistivity of the sensor material. It should be noted that although pure WO 3 needs to be modified (doping, noble metal deposition, or modification of the morphology), or used at a specific temperature to improve its sensing performance, the study of CO sensing progress on a clean WO 3 surface is still of great importance, as it could provide theoretical guidance for the development of better WO 3 -based sensors. Based on the above, in this work we have systematically discussed the oxidation reactions of CO molecule on the WO 3 (001) surfaces for gas sensing. Particularly, we reveal the role of oxygen vacancies and active oxygen species on the sensing performance of WO 3 -based materials.

Computational Details
First-principle calculations based on DFT were carried out utilizing the Vienna ab initio simulation package (VASP) [25][26][27][28], and the ultrasoft pseudopotentials [29,30] were used to describe the interaction between the ion cores and valence electrons. The generalized Perdew-Wang gradient approximation (PW91) [31] exchange-correlation functional was employed, and the kinetic cutoff energy for the planewave expansion was set to 400 eV. In the calculations, the convergence energy threshold for self-consistent iteration was set at 10 −4 eV, and the residual atomic forces were smaller than 0.03 eV/Å. The effects of spin polarization were considered, and the dipole correction in the direction of the surface normal was applied.
As in our previous study [32], a five-layer periodic slab model were adopted to simulated the WO 3 (001) surface with γ-monoclinic phase (Figure 1a), and in the calculations, half of the terminal oxygen atoms on the top layer were transferred to the bottom to avoid residual charges on the surface. During the structural optimization, the atoms on the top three layers were fully relaxed in all directions while the others were fixed to bulk. The vacuum gap was set to 10 Å for the investigation on the adsorption and oxidation of CO molecule. During the geometry optimization and energy calculations of free CO or O 2 , the molecule was placed in a 15 Å × 15 Å × 15 Å cubic box in order to avoid the interaction between the adjacent molecules. The optimized bond lengths of C-O and O-O bond are 1.144 Å and 1.237 Å, which are in good agreement with the experimental values and other theoretical results [22]. threshold for self-consistent iteration was set at 10 −4 eV, and the residual atomic forces were smaller than 0.03 eV/Å. The effects of spin polarization were considered, and the dipole correction in the direction of the surface normal was applied. As in our previous study [32], a five-layer periodic slab model were adopted to simulated the WO3(001) surface with γ-monoclinic phase (Figure 1a), and in the calculations, half of the terminal oxygen atoms on the top layer were transferred to the bottom to avoid residual charges on the surface. During the structural optimization, the atoms on the top three layers were fully relaxed in all directions while the others were fixed to bulk. The vacuum gap was set to 10 Å for the investigation on the adsorption and oxidation of CO molecule. During the geometry optimization and energy calculations of free CO or O2, the molecule was placed in a 15 Å × 15 Å × 15 Å cubic box in order to avoid the interaction between the adjacent molecules. The optimized bond lengths of C-O and O-O bond are 1.144 Å and 1.237 Å, which are in good agreement with the experimental values and other theoretical results [22]. The adsorption energy (Eads) of CO or O2 molecule on the WO3(001) surface is described as: where Etotal is the total energy for the slabs with the adsorption of CO or O2, Eslab is the total energy of the WO3(001) surface, and Emolecule stands for the energies of free CO or O2. For the O2 molecule, the ground state is triplet state. The positive value of Eads indicates the adsorption is thermodynamically favorable.
Since the oxygen vacancy is also considered, the formation energy of oxygen vacancy (Evac) on the WO3(001) can be calculated according to the following formula [22]: The adsorption energy (E ads ) of CO or O 2 molecule on the WO 3 (001) surface is described as: where E total is the total energy for the slabs with the adsorption of CO or O 2 , E slab is the total energy of the WO 3 (001) surface, and E molecule stands for the energies of free CO or O 2 . For the O 2 molecule, the ground state is triplet state. The positive value of E ads indicates the adsorption is thermodynamically favorable.
Since the oxygen vacancy is also considered, the formation energy of oxygen vacancy (E vac ) on the WO 3 (001) can be calculated according to the following formula [22]: (2) in which E def , E perf are the total energies of the WO 3 (001) surface with and without oxygen vacancy, respectively. E O 2 is the total energy of free O 2 molecule. n represents the number of oxygen atom removed from the surface. The negative value indicates the formation of oxygen vacancy is thermodynamically feasible.
Concerning the CO oxidation reactions on the WO 3 (001) surface, the climbing image nudged elastic band (CINEB) method [33,34] was used to determine the minimum energy path (MEP). The energy barrier of the CO oxidation reaction is defined by the energy difference between the transition state (TS) and reactant. The vibrational frequency analysis was also performed to ensure that the predicted TS corresponded to the first-order saddle point in the reaction path. The values of frequencies were calculated from the diagonalization of the mass-weighted Hessian matrix constructed by the finite-difference process.

Surface Oxygen Species on WO 3 (001) Surface
One of the first problems to solve is the possible oxygen species for CO oxidation, which is significant in sensing. Therefore before exploring the mechanism of CO oxidization on the WO 3 (001) surfaces, we have examined the adsorption behavior of O 2 on the sensor surface, including the perfect and defective WO 3 (001) surfaces, and the most stable optimized configurations are displayed in Figure 2a Figure S1). Among them, the most stable adsorption structure is that the O 2 molecule occupies the site just above the tungsten atom that the top oxygen atom is removed (namely W v for clarity), and the O-O bond is parallel to the surface (see Figure 2b). The adsorption energy of this configuration is about 1. and such active group will play an important role in the CO oxidation. We have further investigated the reaction path for the adsorption of O 2 molecule on the defective WO 3 (001) surface by using the CINEB method, and the results indicate that no energy barrier is obtained for this process. Therefore, it seems that when the defective WO 3 (001) surface is exposed to air, the O 2 molecule can be easily adsorbed on the surface.

Adsorption of CO on WO3(001) Surfaces
In this section, we will discuss the adsorptions of CO molecules on the perfect, defective and O2 pre-adsorbed WO3(001) surface, respectively. Figure 3a displays the optimized structure for the adsorption of CO on the perfect WO3(001) surface. It can be seen that the C-W bond length is 2.510 Å and the distance between C and O atom (namely Oc) in CO is nearly the same as that of the free CO molecule (1.139 Å vs. 1.144 Å), indicating a weak interaction between the CO molecule and surface. In addition, a slight shrink of the C-O bond demonstrates that the CO molecule acts as an electron donor when it interacts with the perfect WO3(001) surface, and this conclusion is in accordance with the electron affinity (EA) result obtained by Oison et al. [22]. As shown in Figure 3a, the adsorption of CO has a small effect on the surface structure, so it can be expected that the electronic structure of the perfect WO3(001) surface is maintained after CO adsorption, implying that the variation of the electric resistance of the system caused by CO adsorption is small. The result of adsorption energy (Eads) also shows that the CO molecule is physically adsorbed on the perfect WO3(001) surface with a small Eads of 0.44 eV. This result is also in good agreement with the value (Eads = 0.37 eV) reported in a recent work by Oison et al. [22].
Similar to the perfect WO3(001) surface, the CO molecule also prefers to interact with the Wv atom just under the oxygen vacancy on the defective WO3(001) surface through its C ending. The adsorption energy of this configuration is calculated to be about 0.34 eV, which is slightly smaller than the value of perfect surface. Although the optimized Wv-C bond length (2.401 Å) is about 0.1 Å shorter than that on the perfect surface, the interaction between CO and defective surface is still weak. Correspondingly, the adsorption of CO molecule also has little influence on the properties of the substrate, including the surface resistance.
For the defective WO3(001) surface that is modified by the pre-adsorbed O2 molecule, the most favorable adsorption configuration is quite different from above two cases. As presented in Figure   −

Adsorption of CO on WO 3 (001) Surfaces
In this section, we will discuss the adsorptions of CO molecules on the perfect, defective and O 2 pre-adsorbed WO 3 (001) surface, respectively. Figure 3a displays the optimized structure for the adsorption of CO on the perfect WO 3 (001) surface. It can be seen that the C-W bond length is 2.510 Å and the distance between C and O atom (namely O c ) in CO is nearly the same as that of the free CO molecule (1.139 Å vs. 1.144 Å), indicating a weak interaction between the CO molecule and surface. In addition, a slight shrink of the C-O bond demonstrates that the CO molecule acts as an electron donor when it interacts with the perfect WO 3 (001) surface, and this conclusion is in accordance with the electron affinity (EA) result obtained by Oison et al. [22]. As shown in Figure 3a, the adsorption of CO has a small effect on the surface structure, so it can be expected that the electronic structure of the perfect WO 3 (001) surface is maintained after CO adsorption, implying that the variation of the electric resistance of the system caused by CO adsorption is small. The result of adsorption energy (E ads ) also shows that the CO molecule is physically adsorbed on the perfect WO 3 (001) surface with a small E ads of 0.44 eV. This result is also in good agreement with the value (E ads = 0.37 eV) reported in a recent work by Oison et al. [22].
Similar to the perfect WO 3 (001) surface, the CO molecule also prefers to interact with the W v atom just under the oxygen vacancy on the defective WO 3 (001) surface through its C ending. The adsorption energy of this configuration is calculated to be about 0.34 eV, which is slightly smaller than the value of perfect surface. Although the optimized W v -C bond length (2.401 Å) is about 0.1 Å shorter than that on the perfect surface, the interaction between CO and defective surface is still weak. Correspondingly, the adsorption of CO molecule also has little influence on the properties of the substrate, including the surface resistance.
For the defective WO 3 (001) surface that is modified by the pre-adsorbed O 2 molecule, the most favorable adsorption configuration is quite different from above two cases. As presented in Figure 3c except that the C-Om bond is somewhat longer. After the adsorption of CO molecule, the Wv-Om bonds elongate from about 1.9 Å to 2.0 Å. The formation of this adsorption structure is quite exothermic with an adsorption energy of 3.07 eV, and therefore, the strongly thermodynamic driving force for the formation of this configuration can be expected.

Oxidation of CO on WO3(001) Surfaces
On the basis of the previous discussion, the lattice oxygen and oxygen species O2 − are the main active sites for the redox reactions between CO gas and the WO3 sensor surface. When CO attacks the perfect WO3(001) surface, a top oxygen (Ot) transfers to the molecule, and a CO2 product is produced. From Figure 4a, the lengths of C-Ot and C-Oc bond lengths are 1.179 Å and 1.167 Å, respectively, very close to the length of C-O bond in the free CO2 molecule (1.16 Å). The newly formed CO2 molecule is weakly adsorbed on the surface with the distance between O and surface W atoms longer than 2.7 Å. It is noted that, accompanying the generation of CO2 molecules, the perfect WO3(001) surface becomes defective, and such oxygen vacancy leads to significant changes of the surface structure (see Figure 4a). Comparing the band structures between the perfect and defective WO3(001) surfaces given in Figure 5, a great influence for the electronic property can be observed when the oxygen vacancy is formed. It is clear that the semiconductor property of WO3 bulk is preserved for the perfect surface although the band gap is small due to the well-known shortcoming of pure DFT method. The removing of the top oxygen atom leads to several partly occupied energy bands appeared at the Fermi level, resulting in the metallic character of the defective WO3(001) surface. Therefore, it can be expected that the conductivity of the WO3(001) surface is enhanced after oxidation of CO molecule.
The oxidation reaction of CO on the perfect WO3(001) surface can be described as: leading to the formation of oxygen vacancy ( O V  ) and releasing of electron. Accompanying the increase of the oxygen vacancy concentration, a sharp change in the electronic conductivity is achieved. The corresponding reaction energy of CO oxidation that is defined as the energy difference between before and after CO oxidation is about 1.50 eV, indicating that such a process is exothermic.

Oxidation of CO on WO 3 (001) Surfaces
On the basis of the previous discussion, the lattice oxygen and oxygen species O 2 − are the main active sites for the redox reactions between CO gas and the WO 3 sensor surface. When CO attacks the perfect WO 3 (001) surface, a top oxygen (O t ) transfers to the molecule, and a CO 2 product is produced. From Figure 4a, the lengths of C-O t and C-O c bond lengths are 1.179 Å and 1.167 Å, respectively, very close to the length of C-O bond in the free CO 2 molecule (1.16 Å). The newly formed CO 2 molecule is weakly adsorbed on the surface with the distance between O and surface W atoms longer than 2.7 Å. It is noted that, accompanying the generation of CO 2 molecules, the perfect WO 3 (001) surface becomes defective, and such oxygen vacancy leads to significant changes of the surface structure (see Figure 4a). Comparing the band structures between the perfect and defective WO 3 (001) surfaces given in Figure 5, a great influence for the electronic property can be observed when the oxygen vacancy is formed. It is clear that the semiconductor property of WO 3 bulk is preserved for the perfect surface although the band gap is small due to the well-known shortcoming of pure DFT method. The removing of the top oxygen atom leads to several partly occupied energy bands appeared at the Fermi level, resulting in the metallic character of the defective WO 3 (001) surface. Therefore, it can be expected that the conductivity of the WO 3 (001) surface is enhanced after oxidation of CO molecule. The oxidation reaction of CO on the perfect WO 3 (001) surface can be described as: leading to the formation of oxygen vacancy (V O ·) and releasing of electron. Accompanying the increase of the oxygen vacancy concentration, a sharp change in the electronic conductivity is achieved. The corresponding reaction energy of CO oxidation that is defined as the energy difference between before and after CO oxidation is about 1.50 eV, indicating that such a process is exothermic.  In the case of CO oxidation on the WO3(001) surface which is modified by pre-adsorbed oxygen, both oxygen species on this surface, namely the top oxygen and the oxygens belonging to the O2 − group may react with the CO molecule. The corresponding optimized structures have been given in Figure 4b,c, respectively. Similar to a perfect surface, when CO reacts with the lattice oxygen (Ot), the CO2 product is generated and a new oxygen vacancy is created, while for the case of the O2 − group, one O atom of the active oxygen species transfers to CO and the CO2 product is physically adsorbed on the surface. It is interesting that after releasing CO2 molecule, the perfect WO3(001) surface is reproduced since one oxygen atom occupies the vacancy site. Contrasting the total energies of these two systems, the latter is about 2.93 eV more stable than the former. Hence, CO tends to react with the active oxygen species O2 − for the O2 pre-adsorbed WO3(001) surface, which is in conformity with  In the case of CO oxidation on the WO3(001) surface which is modified by pre-adsorbed oxygen, both oxygen species on this surface, namely the top oxygen and the oxygens belonging to the O2 − group may react with the CO molecule. The corresponding optimized structures have been given in Figure 4b,c, respectively. Similar to a perfect surface, when CO reacts with the lattice oxygen (Ot), the CO2 product is generated and a new oxygen vacancy is created, while for the case of the O2 − group, one O atom of the active oxygen species transfers to CO and the CO2 product is physically adsorbed on the surface. It is interesting that after releasing CO2 molecule, the perfect WO3(001) surface is reproduced since one oxygen atom occupies the vacancy site. Contrasting the total energies of these two systems, the latter is about 2.93 eV more stable than the former. Hence, CO tends to react with the active oxygen species O2 − for the O2 pre-adsorbed WO3(001) surface, which is in conformity with In the case of CO oxidation on the WO 3 (001) surface which is modified by pre-adsorbed oxygen, both oxygen species on this surface, namely the top oxygen and the oxygens belonging to the O 2 − group may react with the CO molecule. The corresponding optimized structures have been given in Figure 4b,c, respectively. Similar to a perfect surface, when CO reacts with the lattice oxygen (O t ), the CO 2 product is generated and a new oxygen vacancy is created, while for the case of the O 2 − group, one O atom of the active oxygen species transfers to CO and the CO 2 product is physically adsorbed on the surface. It is interesting that after releasing CO 2 molecule, the perfect WO 3 (001) surface is reproduced since one oxygen atom occupies the vacancy site. Contrasting the total energies of these two systems, the latter is about 2.93 eV more stable than the former. Hence, CO tends to react with the active oxygen species O 2 − for the O 2 pre-adsorbed WO 3 (001) surface, which is in conformity with the experimental results reported by Hübner et al. [18]. Accordingly, the CO oxidation process on this modified surface can be described by following reaction: Therefore, after reacting with CO, the CO 2 molecule is yielded and the perfect WO 3 (001) surface is reproduced. In addition, the reaction energy of above reaction is strongly exothermic by 4.25 eV.

Mechanism of CO Oxidation on WO 3 (001) Surfaces
In summary, a possible full oxidation cycle can be proposed for the WO 3 (001) surface as a CO sensor. As can be seen from the schematic representation of the catalytic cycle shown in Figure 6, during the oxidation of CO on the perfect WO 3 (001) surface, the surface terminal oxygen (O t ) is consumed along with the generation of CO 2 . At the same time, the WO 3 (001) surface becomes defective, which causes a decrease of the resistivity. When the defective WO 3 (001) surface is exposed to air, the O 2 molecule prefers to be adsorbed on the vacancy site and then the active O 2 − species is formed on the surface. Due to the electron transfer from the surface to the molecule, the surface resistance is enhanced. Finally, the surface active oxygen species (O 2 − ) reacts with CO, and after releasing of the CO 2 , the original WO 3 (001) surface is regenerated and the electronic signal is recovered.
Sensors 2017, 17, 1898 8 of 12 the experimental results reported by Hübner et al. [18]. Accordingly, the CO oxidation process on this modified surface can be described by following reaction: Therefore, after reacting with CO, the CO2 molecule is yielded and the perfect WO3(001) surface is reproduced. In addition, the reaction energy of above reaction is strongly exothermic by 4.25 eV.

Mechanism of CO Oxidation on WO3(001) Surfaces
In summary, a possible full oxidation cycle can be proposed for the WO3(001) surface as a CO sensor. As can be seen from the schematic representation of the catalytic cycle shown in Figure 6, during the oxidation of CO on the perfect WO3(001) surface, the surface terminal oxygen (Ot) is consumed along with the generation of CO2. At the same time, the WO3(001) surface becomes defective, which causes a decrease of the resistivity. When the defective WO3(001) surface is exposed to air, the O2 molecule prefers to be adsorbed on the vacancy site and then the active O2 − species is formed on the surface. Due to the electron transfer from the surface to the molecule, the surface resistance is enhanced. Finally, the surface active oxygen species (O2 − ) reacts with CO, and after releasing of the CO2, the original WO3(001) surface is regenerated and the electronic signal is recovered. Actually, the total oxidation process can be decomposed into three steps: (1) CO oxidation on the perfect WO3(001) surface and the formation of the defective WO3(001) surface; (2) the creation of the O2 − active species; (3) CO oxidation on the O2-preadsorbed WO3(001) surface and the regeneration of the original WO3(001) surface. All these steps are extensively exothermic and seem to be thermodynamically feasible. However, which is the rate-limiting step? In order to answer this question, we have carried out additional calculations to obtain the minimum energy paths (MEP) of the overall process. The calculated energy profiles for oxidation of CO on the perfect and O2preadsorbed WO3(001) surfaces by using CINEB method are presented in Figure 7.
For the perfect WO3(001) surface (Figure 7a), a transition state (TS1) is identified with an energy barrier of 0.91 eV, and the vibrational frequency calculation shows that there is only one imaginary frequency (273 i·cm −1 ) for this configuration. As for TS1, the CO molecule bonds with Ot atom, and the length of C-Ot bond is 1.561 Å. As a result of the formation of C-Ot bond, the configuration of the WO3(001) surface is changed remarkably, especially the bond between the six-coordinated tungsten atom (W6f) and the terminal oxygen atom (Ot) is elongated to 1.859 Å, which is about 0.14 Å longer Actually, the total oxidation process can be decomposed into three steps: (1) CO oxidation on the perfect WO 3 (001) surface and the formation of the defective WO 3 (001) surface; (2) the creation of the O 2 − active species; (3) CO oxidation on the O 2 -preadsorbed WO 3 (001) surface and the regeneration of the original WO 3 (001) surface. All these steps are extensively exothermic and seem to be thermodynamically feasible. However, which is the rate-limiting step?
In order to answer this question, we have carried out additional calculations to obtain the minimum energy paths (MEP) of the overall process. The calculated energy profiles for oxidation of CO on the perfect and O 2 -preadsorbed WO 3 (001) surfaces by using CINEB method are presented in Figure 7. For the perfect WO 3 (001) surface (Figure 7a), a transition state (TS1) is identified with an energy barrier of 0.91 eV, and the vibrational frequency calculation shows that there is only one imaginary frequency (273 i·cm −1 ) for this configuration. As for TS1, the CO molecule bonds with O t atom, and the length of C-O t bond is 1.561 Å. As a result of the formation of C-O t bond, the configuration of the WO 3 (001) surface is changed remarkably, especially the bond between the six-coordinated tungsten atom (W 6f ) and the terminal oxygen atom (O t ) is elongated to 1.859 Å, which is about 0.14 Å longer than that in the initial state. Because of the considerable variation of the surface geometry, an obvious energy barrier is required to produce CO 2  than that in the initial state. Because of the considerable variation of the surface geometry, an obvious energy barrier is required to produce CO2 on the perfect surface. While concerning on the O2preadsorbed WO3(001) surface, the initial state is corresponding to an intermediate that the C atom of CO is bonded with two O atoms of O2 − , as mentioned in Section 3.2. The CO2 molecule can be generated from this configuration, and meanwhile the perfect WO3(001) surface is reproduced. The transition state (TS2) of this process is shown in Figure 7b, in which one of the W-Om bond tends to be broken and the corresponding bond length is enlarged to 2.383 Å; in the meantime, the length of one C-Om bond decreases from 1.368 Å to 1.242 Å, while the length of another C-Om bond increases to 1.775 Å. The energy barrier is calculated to be 0.65 eV, and the vibrational frequency calculation demonstrates that there is only one imaginary frequency (387 i·cm −1 ) for this transition state. Compared the heights of the energy barrier of those two steps, it seems that the CO oxidation on the perfect WO3(001) surface is the rate-determining step from the kinetics viewpoint.

Conclusions
In this work, the oxidation reactions of CO molecule on the WO 3 (001) surfaces for CO sensing have been systematically investigated by DFT calculations. Owing to the formation of active oxygen species at the surface and the generation of the surface oxygen vacancies, the oxidation of CO on the WO 3 (001) surface results in obvious variations of the electronic properties which are directly related to the change of the resistance of WO 3 sensor. Our results suggest that the adsorption of O 2 molecule on the perfect WO 3 (001) surface is thermodynamically unfavorable and has little effect on the surface resistance, while a strong chemisorption of O 2 occuring on the defective surface is predicted. The O 2 molecule adsorbed at the vacancy site leads to the formation of an important oxygen species (namely O 2 − ) for further CO oxidation reactions, while also enhancing the surface resistivity. We have shown that CO is oxidized to CO 2 by the top oxygen atom for the perfect WO 3 (001) surface, resulting in the formation of a defective surface with oxygen vacancy at surface and the reduction of surface resistivity. However, concerning the CO oxidation on the O 2 -preadsorbed WO 3  The bond lengths (Å) close to the adsorption site are given, and the data in the parenthesis are in relative to the defective WO 3 (001) surface before O 2 adsorption. In addition, the corresponding adsorption energies have also been provided.