Unraveling the Reaction Mechanism of HCHO Catalytic Oxidation on Pristine Co 3 O 4 (110) Surface: A Theoretical Study

: Various reaction mechanisms for the catalytic degradation of formaldehyde (HCHO) remain to be debated. Density functional theory (DFT) was applied to investigate whether the catalytic oxidation of HCHO on pristine Co 3 O 4 (110) surface follows the Mars-van Krevelen (MvK) mechanism or the Langmuir–Hinshelwood (L-H) mechanism. Firstly, HCHO and O 2 co-adsorb on the surface and two H atoms from HCHO are peculiarly prone to transfer to O 2 , forming CO and HOOH. For the MvK mechanism, CO 2 is generated through CO grabbing a lattice oxygen. Meanwhile, the O–O bond of HOOH is broken into two OH groups. One OH ﬁlls the oxygen vacancy and its H atom moves to another OH group for H 2 O formation. For the L-H mechanism, CO directly obtains one OH group to generate COOH. Subsequently, the H atom of COOH transfers to another OH group along with CO 2 and H 2 O generation. Both two mechanisms exhibit a similar maximum activation barrier. The lattice oxygen in the MvK mechanism and the surface-absorbed OH group in the L-H mechanism are the key reactive oxygen species. The small difference in energetic span further suggests that the catalytic cycle through the two mechanisms is feasible. This theoretical study provides new insight into the catalytic reaction path of HCHO oxidation on pristine Co 3 O 4 surface.


Introduction
Formaldehyde (HCHO) is one of the most concerning indoor pollutants leading to hazardous effects on human health [1,2], and significant efforts have been made to settle indoor HCHO emissions. Room-temperature catalytic oxidation represents an attractive technology for complete conversion of HCHO to H 2 O and CO 2 without the formation of harmful by-products or secondary pollutants, thus making it the most promising HCHO removal technique compared with conventional adsorption and photo-catalytic oxidation [3][4][5][6][7]. Supported noble metals (e.g., Pt [8], Pd [9], Au [10], and Ag [11]) are the most effective catalysts for HCHO catalytic oxidation at room temperature. Nevertheless, the high price and scarcity of noble metals may restrain their wide application in the long term. Transition metal oxides, such as MnOx [6], Co 3 O 4 [12], CeO 2 [13], TiO 2 [14], and their composites [15][16][17], exhibit comparable catalytic performance and are cost-effective for low temperature HCHO oxidation. Among these catalysts, Co 3 O 4 -based catalysts have recently been attractive for low-temperature catalytic applications due to their strong oxidative The location of all possible intermediates on the Co3O4 (110) surface should be confirmed. The most stable adsorption configurations of HCHO and O2 have been given in Figure 2. In addition, Figure 3 presents the adsorption configurations of possible intermediates. The corresponding adsorption energies and key structural parameters are listed in Table 1.  The location of all possible intermediates on the Co 3 O 4 (110) surface should be confirmed. The most stable adsorption configurations of HCHO and O 2 have been given in Figure 2. In addition, Figure 3 presents the adsorption configurations of possible intermediates. The corresponding adsorption energies and key structural parameters are listed in Table 1.     To better understand the desorption behavior of the obtained product CO 2 and H 2 O molecules at ambient conditions, the desorption time (τ) is implemented [30], which is expressed in Section 3.1. The calculated desorption time for CO 2 and H 2 O molecules at ambient temperature are 1.14 × 10 −3 and 1.76 s, respectively, indicating that CO 2 and H 2 O molecules are physical adsorbed. Therefore, they can desorb easily from the Co 3 O 4 surface, which facilitates the complete catalytic reaction.

Reactions Starting from HCHO and O 2 Co-Adsorbing on Co 3 O 4 (110) Surface
From the result of the absorption calculation, the adsorption energies of HCHO and O 2 are 1.28 eV and 0.85 eV, respectively, suggesting that HCHO presents stronger adsorption capability than O 2 on Co 3 O 4 (110) surface. While for the co-adsorption configuration (Figure 4) Table 2, all reactions on Co3O4 (110) surface are represented by Rn-m (n = 1~5; m = 1~10). The reactions from R1-1 to R1-4 represent four possible initial steps when HCHO and O2 co-adsorb on Co3O4 (110) surface. Figure 4 presents the potential energy profiles of possible pathways of the four possible initial steps together with transition states (TSs) and final states (FSs) on the Co3O4 (110) surface.  We first considered the E-R mechanism on the Co 3 O 4 (110) surface. The first element reaction is the contact of O 2 with HCHO to form CH 2 O 2 and an O atom. If gaseous O 2 is contacted with HCHO pre-adsorbed on the surface, there will be no conversion into CH 2 O 2 and O due to the lack of a transition state. Whereas, if HCHO in the gaseous phase is contacted with surface pre-adsorbed O 2 , it will convert into CH 2 O 2 and an O atom. However, the activation energy can reach as high as 5.51 eV. Therefore, the E-R mechanism was excluded from consideration. Subsequently, the L-H mechanism and MvK mechanism were investigated in detail. From the co-adsorption of HCHO and O 2 on the Co 3 O 4 (110) surface to the CO 2 and H 2 O production, HCHO would lose two H atoms and gain one O atom for the formation of CO 2 . Meanwhile, O 2 would lose one O atom and gain two H atoms for the formation of H 2 O. Based on these two mechanisms, the corresponding activation barriers and reaction energy of all possible elementary reactions involved in HCHO oxidation have been listed in Table 2.

The Possible First Step of HCHO Oxidation
According to Table 2, all reactions on Co 3 O 4 (110) surface are represented by Rn-m (n = 1~5; m = 1~10). The reactions from R1-1 to R1-4 represent four possible initial steps when HCHO and O 2 co-adsorb on Co 3 O 4 (110) surface. Figure 4 presents the potential energy profiles of possible pathways of the four possible initial steps together with transition states (TSs) and final states (FSs) on the Co 3  In the final state, HCO adsorbs on the hollow site and OOH adsorbs on the Co 3+ site. The activation barrier and reaction energy of this elementary reaction are 0.52 eV and −1.64 eV, respectively. In TS1-4, the C-H distance is elongated to 2.29 Å from 1.11 Å of the adsorbed HCHO. In the final state, HCO adsorbs on the hollow site with the H atom adsorbing on the Co 3+ site. The activation barrier and reaction energy are 1.05 eV and −3.07 eV, respectively.  ), and the configuration is no different with HCHO adsorbing on the pristine surface similar to the final state of R1-1, thus this reaction is not considered. Through comparing the activation barrier and reaction energy, it is found that R1-3 of HCO and OOH formation is the most favorable reaction with the absolutely low activation barrier. Moreover, R1-3 is exothermic, indicating this step is not only thermodynamically but also kinetically favored. It is worth mentioning that although R1-4 is the most exothermic, its activation barrier is much higher than that of R1-3, which is kinetically hindered. Thus, the first step of HCHO reacting with O 2 is in favor of forming HCO and OOH on the Co 3 O 4 (110) surface, and the subsequent pathway of HCHO oxidation is considered starting from HCO and OOH.
In order to investigate why O 2 comfortably accepts one H atom for OOH formation, the PDOS and charge density difference is displayed in Figure 5. The energy levels of Co minority α-spin d orbitals and O 2 π* orbitals are well matched, leading to partial occupation of the formed d-π*orbitals. While the strong spin polarization provides large exchange stabilization energy for the majority β-spin orbitals, resulting in Co β-spin d-orbitals with energy levels about 1.0 eV lower than the π* orbitals of O 2 . Therefore, no conspicuous interaction of β orbitals is observed, indicating that only the α π* orbitals of O 2 are partially occupied, which forces O 2 to be of a radical nature, and active for hydrogenation. When O 2 is hydrogenated to OOH, one electron transfers from the H atom to the β π* orbitals of O 2 , and both α and β DOS of Co 3d orbitals overlap with OOH's π* orbitals, which further weakens the O-O bond. Therefore, the enhanced interaction and larger occupation of the π* orbitals in OOH leads to a lower O-O bond order, which is responsible for the lower dissociation barrier than that for O 2 .  The corresponding elementary reactions are revealed in Table 2, where the reactions related to MvK mechanism are marked R2-n and R3-n. The adsorbed HCO can react with Olatt to generate HCOO and OV, followed by the OOH dissociation into OH and an O atom, and O atom filling OV to restore the surface (R2-1). Subsequently, CO2 is formed by OH oxidation through C-H breaking away from HCOO (R2-2), and H atom migration to OH to produce H2O (R2-3). Another alternative reaction path is described below: HCO first dehydrogenates into CO (R3-1), which can pick up Olatt to form CO2 and OV (R3-2). Then, OOH is dissociated into OH and an O atom, which fills OV to restore Olatt (R3-3). Meanwhile, OH combines with H atom to form H2O (R3-4). In addition, Olatt can also adsorb H atom from HCO dehydrogenation to form COOH (R3-5), which is further oxidized to CO2

MvK Mechanism
The corresponding elementary reactions are revealed in Table 2, where the reactions related to MvK mechanism are marked R2-n and R3-n. The adsorbed HCO can react with O latt to generate HCOO and O V , followed by the OOH dissociation into OH and an O atom, and O atom filling O V to restore the surface (R2-1). Subsequently, CO 2 is formed by OH oxidation through C-H breaking away from HCOO (R2-2), and H atom migration to OH to produce H 2 O (R2-3). Another alternative reaction path is described below: HCO first dehydrogenates into CO (R3-1), which can pick up O latt to form CO 2 and  (R3-9), and the formed O V can be restored by an O atom produced from the HOOH decomposition, accompanied by the formation of H 2 O (R3-10). Therefore, four possible routes account for the MvK mechanism. The potential energy profile and possible reaction paths of TSs and FSs on Co 3 O 4 (110) surface are shown in Figures 6 and 7. The difference in line color indicates different paths. As shown in Figure 6, after HCO and OOH co-adsorption, HCO is more favorable for connecting to O latt to form HCOO than dissociating into CO and H atom, because the dissociation barrier of 4.26 eV is much higher than that of HCOO formation with almost no activation barrier. Even so, the CO path is still considered, because concerning the catalytic cycles, one transition state does not determine the kinetics.  Figure 7, the H atom of HCO first transfers to surface (R3-1) or OOH (R3-8) with the activation barrier of 4.26 eV and 1.62 eV, respectively, indicating that H atom preferentially bonds to OOH rather than surface.  Figure 7, the H atom of HCO first transfers to surface (R3-1) or OOH (R3-8) with the activation barrier of 4.26 eV and 1.62 eV, respectively, indicating that H atom preferentially bonds to OOH rather than surface. Starting from the reaction of CO + H + OOH (R3-2, R3-5), CO binds to Olatt for CO2 formation through TS3-2 and binds to lattice OH for COOH formation through TS3-5 with the activation barrier of 2.02 eV and 5.36 eV, respectively. The two reaction steps are endothermic with reaction energies of 1.59 and 1.84 eV, respectively, suggesting the combination of CO with lattice OH for COOH formation is blocked kinetically and thermodynamically. The following OV filling by OOH dissociation through TS3-3 and TS3-6 exhibits the activation barrier of 1.16 eV and 1.80 eV, respectively, which are different from that of  are 2.24 eV, 4.26 eV, 5.36 eV, and 1.85 eV, respectively, which means that the efficiency of the catalytic cycles of the purple line marked reaction path are satisfactory. In short, irrespective of whether considering single route or catalytic cycles, the specific reaction paths representing the MvK mechanism are described below: firstly, two H atoms of HCHO continuously transfer to O2, forming CO and HOOH. Then, CO grabs Olatt to generate CO2, and HOOH dissociates into two OH groups with one of them occupying OV, and its H atom moves to another OH for H2O formation.  Starting from the reaction of CO + H + OOH (R3-2, R3-5), CO binds to O latt for CO 2 formation through TS3-2 and binds to lattice OH for COOH formation through TS3-5 with the activation barrier of 2.02 eV and 5.36 eV, respectively. The two reaction steps are endothermic with reaction energies of 1.59 and 1.84 eV, respectively, suggesting the combination of CO with lattice OH for COOH formation is blocked kinetically and thermodynamically. The following O V filling by OOH dissociation through TS3-3 and TS3-6 exhibits the activation barrier of 1.16 eV and 1.80 eV, respectively, which are different from that of R2-1, indicating that OOH dissociation is affected by co-adsorbents. As for the reaction of OH combining with H atom (TS3-4) and the reaction of H atom of COOH transferring to OH for H 2 O formation (TS3-7), their activation barriers are 1.40 eV and 1.24 eV, respectively. Starting from the reaction of CO+HOOH, CO reacts with O latt to produce CO 2 , and HOOH dissociates into two OH groups. One OH occupies O V , the other OH reacts with H atom to produce H 2 O. The activation barrier for these three elementary reactions (R3-9, R3-10, R2-3) are 1.85, 1.00, and 1.09 eV, respectively. Through comparing the four reaction paths, the purple line in Figure 7 is the most preferable as the maximum activation barrier of 1.85 eV is much lower than other three paths with the maximum barrier of 4.26 eV.
As for the catalytic cycles, the TDTS for blue, red, green and purple line marked reaction paths are TS2-2, TS3-1, TS3-5, and TS3-9, respectively. Their corresponding TDI are HCOO + OH, HCOO + O V + OOH, CO + H + OOH and CO + HOOH, respectively. As the TDTS comes after the TDI, according to formula (5a), the δE for these four reaction routes are 2.24 eV, 4.26 eV, 5.36 eV, and 1.85 eV, respectively, which means that the efficiency of the catalytic cycles of the purple line marked reaction path are satisfactory. In short, irrespective of whether considering single route or catalytic cycles, the specific reaction paths representing the MvK mechanism are described below: firstly, two H atoms of HCHO continuously transfer to O 2 , forming CO and HOOH. Then, CO grabs O latt to generate CO 2 , and HOOH dissociates into two OH groups with one of them occupying O V , and its H atom moves to another OH for H 2 O formation.

L-H Mechanism
The difference between the L-H mechanism and the MvK mechanism is that the ROS binding to carbon intermediates are derived from surface adsorbed oxygen species, rather than O latt . The specific reactions related to the L-H mechanism are marked R4-n and R5-n in Table 2. Starting from HCO and OOH absorbed on Co 3 O 4 (110) surface, the O-O bond of OOH dissociates into OH and O atom (R4-1), which can bind to HCO for HCOO (R4-2) or HCOOH formation (R4-5). HCOO can be oxidized by OH to produce CO 2 and H 2 O (R4-3 and R4-4); whereas HCOOH combines with O atom to form HCOO and OH (R4-6 and R4-7), which in turn react to produce CO 2 and H 2 O (R4-8). In addition, HCO can be dehydrogenated to form CO (R5-1). The O-O bond of OOH decomposes into O atom and an OH group (R5-2), the former combines with CO to form CO 2 (R5-3) and the latter combines with H atom to form H 2 O (R5-4). Moreover, OH can also combine with CO to form COOH, which is subsequently converted into CO 2 (R5-5 and R5-6). The H atom from HCO dehydrogenation can bind to OOH for HOOH formation (R5-7). It reacts with CO to form COOH and OH (R5-8), which are finally converted to CO 2 and H 2 O (R5-9). Therefore, five possible routes account for the L-H mechanism. The potential energy profile and possible reaction pathways of TSs and FSs on the Co 3 O 4 (110) surface are shown in Figures 8 and 9. As shown in Figure 8, HCO follows the L-H mechanism to grab surface adsorbed oxygen species via two reaction paths. After HCO and OOH co-adsorption, O-O bond of OOH is broken to form an O atom and OH adsorbed on Co 3+ site through TS4-1. The dissociation barrier is 0.68 eV and the reaction energy is 0.21 eV. In TS4-2, an O atom approaches HCO, and the C-O bond length is shortened from 3.36 Å to 1.98 Å; In TS4-5, OH rotates and moves to HCO, and the C-O distance is shortened from 3.13 Å to 2.11 Å. The activation barrier of the two transition states are 4.05 eV and 1.11 eV, respectively, and the reaction energies are −0.65 eV and 0.04 eV, respectively, indicating that the combination of HCO to OH is kinetically feasible. This is against that of the MvK mechanism, in which HCO preferentially combines with O latt , suggesting that the lattice oxygen species and adsorbed oxygen species possess different electronic properties that affect their reaction capability. In addition, for transition states (TS4-6, TS4-7, and TS4-8) through which HCOOH is converted to CO 2 and H 2 O, their energy barriers are lower than those through HCOO paths (TS4-3 and TS4-4), indicating that the route starting from HCO combining with OH is preferable. formula (5a), the δE for these five routes are 4.26 eV, 2.29 eV, 6.57 eV, 5.16 eV, and 1.65 eV, respectively, which means that the efficiency of catalytic cycles of the light blue line marked path is satisfactory. Therefore, the optimal reaction path of the HCHO oxidation process is as follows: two H atoms of HCHO are successively transferred directly to O2 to form HOOH. Subsequently, the O-O bond of HOOH is broken to generate two OH. One OH binds to CO to form COOH, whose H atom further combines with another OH to finally generate CO2 and H2O.  As revealed in Figure 9, another three possible reaction paths start with the dehydrogenation of adsorbed HCO to form CO, which further follows the L-H mechanism to grab surface adsorbed oxygen species. The H atom generated by the dehydrogenation of HCO can be combined with lattice oxygen through TS5-1,whose activation barrier and reaction energy are 4.26 eV and 2.78 eV, respectively. The H atom can also be combined with OOH through TS5-7 to form HOOH, whose activation barrier and reaction energy are 1.62 eV and −1.70 eV, respectively. In this reaction, the C-H distance is elongated to 1.49 Å along with the H-O distance shortened to 1.28 Å. Therefore, it can be inferred that H atom preferentially bonds with OOH rather than other locations on the surface after cleaving away from HCO. Starting from the reaction of CO + H + OOH, the O-O bond of OOH ruptures again through TS5-2, whose activation barrier and reaction energy are 0.98 eV and 0.37 eV, respectively. CO can react with O atom to form CO 2 via TS5-3 or OH to form COOH via TS5-5. Their activation barriers are 6.20 eV and 2.30 eV, respectively, and their reaction energies are −0.55 eV and 0.12 eV, respectively. This suggests that the CO reaction with OH is more preferable than O atom, which is consistent with the HCO reaction with OH or O, further indicating that surface adsorbed OH is an important ROS. The following COOH dehydrogenation by O atom via TS5-6 may be prevented by the high activation barrier of 4.68 eV. Starting from the reaction of CO+HOOH, CO can directly capture OH from HOOH for COOH formation via TS5-8 with the activation barrier as low as 0.52 eV. Meanwhile, the O-O distance is elongated 2.28 Å and C-O distance is shortened to 2.24 Å. This reaction step is also kinetically favored with reaction energy of −1.63 eV. The H atom of COOH can transfer to OH through TS5-9 with the activation barrier and reaction energy of 1.24 and 0.84 eV, respectively. Comparing to R5-6 with dehydrogenation of COOH with the H atom adsorbed on the O atom, H atom prefers to be close to OH, which is similar to the fact that the H atom of HCO preferentially reacts directly with the OOH rather than bond with the surface absorbed O atom. In conclusion, among five reaction paths, the light blue line marked route in Figure 9 is the most favorable, because the maximum energy barrier is much lower than that of other four paths.
Catalysts 2022, 12, x FOR PEER REVIEW 13 of 18 Figure 9. The potential energy profile of HCHO oxidation based on the L-H mechanism through CO grabbing the surface adsorbed oxygen species together with the structures of TSs and FSs on Co3O4 (110) surface.

Comparison of HCHO Catalytic Oxidation through MvK and L-H Mechanism
Starting from HCHO and O2 co-adsorption, the most favorable reaction paths that belong to MvK and L-H mechanism are shown in Figure 10 and Scheme 1. Two H atoms of HCHO transfer to O2 continuously for CO and HOOH formation are the first two favorable steps. For MvK mechanism, CO grabs Olatt to generate CO2 firstly. The maximum activation barrier is 1.85 eV in this reaction path. The subsequent steps are the O-O bond of HOOH breaking and O vacancy filling by O atom of OH. Finally, H atom move to another OH for H2O formation. For L-H mechanism, COOH is formed through CO drawing OH from HOOH, and then H atom of COOH is taken away by another OH for CO2 and H2O formation. The maximum activation barrier of this reaction path is 1.65 eV, cor- In Figures 8 and 9, the TDTS and TDI marked in different colors represent different paths of TDTS and TDI. As the TDTS comes after the TDI for the five routes, according to formula (5a), the δE for these five routes are 4.26 eV, 2.29 eV, 6.57 eV, 5.16 eV, and 1.65 eV, respectively, which means that the efficiency of catalytic cycles of the light blue line marked path is satisfactory. Therefore, the optimal reaction path of the HCHO oxidation process is as follows: two H atoms of HCHO are successively transferred directly to O 2 to form HOOH. Subsequently, the O-O bond of HOOH is broken to generate two OH. One OH binds to CO to form COOH, whose H atom further combines with another OH to finally generate CO 2 and H 2 O.

Comparison of HCHO Catalytic Oxidation through MvK and L-H Mechanism
Starting from HCHO and O 2 co-adsorption, the most favorable reaction paths that belong to MvK and L-H mechanism are shown in Figure 10 and Scheme 1. Two H atoms of HCHO transfer to O 2 continuously for CO and HOOH formation are the first two favorable steps. For MvK mechanism, CO grabs O latt to generate CO 2 firstly. The maximum activation barrier is 1.85 eV in this reaction path. The subsequent steps are the O-O bond of HOOH breaking and O vacancy filling by O atom of OH. Finally, H atom move to another OH for H 2 O formation. For L-H mechanism, COOH is formed through CO drawing OH from HOOH, and then H atom of COOH is taken away by another OH for CO 2 and H 2 O formation. The maximum activation barrier of this reaction path is 1.65 eV, corresponding to the second H atom of HCHO dehydrogenation, which is slightly lower than that of MvK mechanism. Therefore, the highest energy barriers to overcome for the MvK and L-H mechanisms are similar, making both mechanisms feasible. The δE of the two paths correspond exactly to the activation barrier, suggesting that the catalytic cycle through the two mechanisms are equivalent to some extent. It is worth noting that due to the relatively strong exotherm of the reaction, HCHO cannot be oxidized smoothly at room temperature if the energy released in the previous cycles cannot be fully utilized for subsequent cycles. In addition, the maximum δE cannot be affected by the reaction energy according to formula (5b), resulting in TDTS appearing after TDI in all possible paths through MvK and L-H mechanism.
Catalysts 2022, 12, x FOR PEER REVIEW 14 of 18 through the two mechanisms are equivalent to some extent. It is worth noting that due to the relatively strong exotherm of the reaction, HCHO cannot be oxidized smoothly at room temperature if the energy released in the previous cycles cannot be fully utilized for subsequent cycles. In addition, the maximum δE cannot be affected by the reaction energy according to formula (5b), resulting in TDTS appearing after TDI in all possible paths through MvK and L-H mechanism.

Surface Models
Co3O4 has a spinel structure (Fd3m) which contains half-filled octahedral sites with Co 3+ cations and tetrahedral sites with Co 2+ cations. For the Co3O4 (110) surface, it bears two different terminations, usually denoted as the A and B terminations: the (110)-A termination exposes two types of cations (Co 2+ and Co 3+ ) and one type of anion (three-fold coordinated O3c), whereas the (110)-B termination has only one type of cation (Co 3+ ) and two types of anions (two-fold coordinated O2c and three-fold coordinated O3c). Chen et al. [31] have reported the curves of Gibbs surface energy of these two terminations against oxygen chemical potential and found that the terminal B surface possessed a lower Gibbs surface energy in oxygen-rich conditions. Considering the oxygen chemical potential under the common work conditions of HCHO oxidation (PO2/P0 = 0.2; T = 300~330 K), the (110)-B termination was energetically more stable than the (110)-A termination. Therefore, the (110)-B termination was chosen to model the catalyst surface. We simulated symmetric slabs with an odd number of five layers, for which the total dipole moment was zero. This slab was stoichiometric and symmetric along the surface normal plane. The p(2 × √3) supercell slabs were utilized for Co3O4 (110)-B surface, which can be seen in Figure 1. The bottom two Co-O layers are fixed. Whereas the topmost three Co-O layers and the adsorbates are fully relaxed in all calculations.

Computational Details
All the calculations were performed in the framework of the density functional theory (DFT) by using the Cambridge Sequential Total Energy Package (CASTEP) in Material Studio 8.0 of Accelrys. The generalized gradient approximation (GGA) was chosen to represent the exchange-correlation potential in the formulation of the Perdew-Burke-Ern-Scheme 1. Elementary reaction steps of HCHO catalytic oxidation based on MvK and L-H mechanism on Co 3 O 4 (110) surface.

Surface Models
Co 3 O 4 has a spinel structure (Fd3m) which contains half-filled octahedral sites with Co 3+ cations and tetrahedral sites with Co 2+ cations. For the Co 3 O 4 (110) surface, it bears two different terminations, usually denoted as the A and B terminations: the (110)-A termination exposes two types of cations (Co 2+ and Co 3+ ) and one type of anion (three-fold coordinated O 3c ), whereas the (110)-B termination has only one type of cation (Co 3+ ) and two types of anions (two-fold coordinated O 2c and three-fold coordinated O 3c ). Chen et al. [31] have reported the curves of Gibbs surface energy of these two terminations against oxygen chemical potential and found that the terminal B surface possessed a lower Gibbs surface energy in oxygen-rich conditions. Considering the oxygen chemical potential under the common work conditions of HCHO oxidation (P O2 /P 0 = 0.2; T = 300~330 K), the (110)-B termination was energetically more stable than the (110)-A termination. Therefore, the (110)-B termination was chosen to model the catalyst surface. We simulated symmetric slabs with an odd number of five layers, for which the total dipole moment was zero. This slab was stoichiometric and symmetric along the surface normal plane. The p(2 × √ 3) supercell slabs were utilized for Co 3 O 4 (110)-B surface, which can be seen in Figure 1. The bottom two Co-O layers are fixed. Whereas the topmost three Co-O layers and the adsorbates are fully relaxed in all calculations.

Computational Details
All the calculations were performed in the framework of the density functional theory (DFT) by using the Cambridge Sequential Total Energy Package (CASTEP) in Material Studio 8.0 of Accelrys. The generalized gradient approximation (GGA) was chosen to represent the exchange-correlation potential in the formulation of the Perdew-Burke-Ernzerhof (PBE) [32]. Owing to the magnetic properties of Co, all calculations were spin-polarized with an energy cutoff of 380 eV. The Brillouin zone was sampled by a 2 × 2 × 1 k-points grid generated via the Monkhorst-Pack procedure [33]. The geometry optimization was converged when the energy differences between two electronic optimization steps were smaller than 10 −5 eV, and the forces for ions were less than 0.05 eV/Å. For the transition state (TS) search calculations of all elementary reactions in HCHO oxidation process, the complete LST/QST was adopted for search protocol, and the convergence tolerance of RMS convergence resorted to 0.25 eV/Å. In order to further confirm that the transition from reactant to product went through a transition state structure, the obtained transition state from TS search will be further checked via TS confirmation. The output of a TS confirmation calculation is another trajectory document, which follows the Intrinsic Reaction Path (IRP) as discussed in reaction paths.
The adsorption energy of all reactants, intermediates, and product species can be calculated through the following formula: where E species/slab represents the total energy of Co 3 O 4 (110) surface adsorbing certain species, E species represents the energy of sole species, E slab represents the slab energy of Co 3 O 4 (110) surface. Based on the calculation results, all the adsorption energies are negative. Therefore, we take absolute values to compare the adsorption energies of different surface species.
The desorption time (τ) was calculated through the following formula: where A is bond vibration frequency in the range of 1012 Hz, k B is the Boltzmann constant (8.63 × 10 −5 eV/K) and T is the room temperature of 298.15 K. E des is the desorption energy.
For a reaction such as R (reactant) →·P (product) on catalyst surface, the activation barrier (E a ) and reaction energy (∆E) were calculated according to the following formulas: Where E R and E P are the total energies of the adsorbed reactant and product, respectively, and E TS represent the total energies of the transition state.
The energetic span (δE) model was also employed to elucidate the efficiency of the catalytic cycles. According to the literature, there were only two states to determine δE, namely determining transition state (DTS) and determining intermediate state (DIS), the smaller the energy span, the faster the reaction. δE is shown as: δE = T TDTS −I TDI , if TDTS appears after TDI (a) T TDTS −I TDI + ∆E r , if TDTS appears before TDI (b)

Conclusions
DFT calculations have been performed to investigate possible HCHO catalytic oxidation paths on pristine Co 3 O 4 (110) surface for comparisons of different reaction mechanisms. In addition, the maximum δE is calculated to state the catalytic cycle. The following results were obtained. HCHO and O 2 prefer to co-adsorb on the Co 3 O 4 (110) surface. The transfer of the H atom of HCHO to O 2 for HCO and OOH formation represents the first preferable step rather than O 2 dissociation. The electron property of PDOS analysis further suggests that only the α π* orbitals of O 2 are partially occupied, forcing O 2 to be of a radical nature, which is active for hydrogenation. HCO is further prone to transfer its H atom to OOH to generate CO and HOOH. Regarding the MvK mechanism, through CO grabbing O latt , CO 2 is produced and the O vacancy is filled by one OH group originating from HOOH bond breakage. Meanwhile, the H atom approaches in close proximity to OH to form H 2 O. For the L-H mechanism, CO obtains one OH from HOOH, then COOH gives an H atom to another OH for the formation of CO 2 and H 2 O. Comparing the maximum activation barrier and δE, both the MvK and L-H mechanism are found to be feasible. Lattice oxygen in the MvK mechanism and surface OH in the L-H mechanism are both key ROS for oxidation of CO intermediates, and the catalytic cycle is almost equivalent.